# Parsing/RPN calculator algorithm

(Redirected from Reverse polish notation)
Parsing/RPN calculator algorithm
You are encouraged to solve this task according to the task description, using any language you may know.

Create a stack-based evaluator for an expression in   reverse Polish notation (RPN)   that also shows the changes in the stack as each individual token is processed as a table.

• Assume an input of a correct, space separated, string of tokens of an RPN expression
• Test with the RPN expression generated from the   Parsing/Shunting-yard algorithm   task:

3 4 2 * 1 5 - 2 3 ^ ^ / +

• Print or display the output here

Notes
•   ^   means exponentiation in the expression above.
•   /   means division.

## 11l

Translation of: Python
[Float] a
[String = ((Float, Float) -> Float)] b
b[‘+’] = (x, y) -> y + x
b[‘-’] = (x, y) -> y - x
b[‘*’] = (x, y) -> y * x
b[‘/’] = (x, y) -> y / x
b[‘^’] = (x, y) -> y ^ x

L(c) ‘3 4 2 * 1 5 - 2 3 ^ ^ / +’.split(‘ ’)
I c C b
V first  = a.pop()
V second = a.pop()
a.append(b[c](first, second))
E
a.append(Float(c))
print(c‘ ’a)
Output:
3 [3]
4 [3, 4]
2 [3, 4, 2]
* [3, 8]
1 [3, 8, 1]
5 [3, 8, 1, 5]
- [3, 8, -4]
2 [3, 8, -4, 2]
3 [3, 8, -4, 2, 3]
^ [3, 8, -4, 8]
^ [3, 8, 65536]
/ [3, 0.00012207]
+ [3.00012207]

## 360 Assembly

Translation of: FORTRAN

For concision, only integer arithmetic is handled, but input numbers can be of any length. The formal task is not completed, but the spirit of it is.

*        RPN calculator         RC 25/01/2019
REVPOL   CSECT
USING  REVPOL,R13         base register
B      72(R15)            skip savearea
DC     17F'0'             savearea
STM    R14,R12,12(R13)    save previous context
XPRNT  TEXT,L'TEXT        print expression !?
L      R4,0               js=0  offset in stack
LA     R5,0               ns=0  number of stack items
LA     R6,0               jt=0  offset in text
LA     R7,TEXT            r7=@text
MVC    CC,0(R7)           cc first char of token
DO WHILE=(CLI,CC,NE,X'00')  do while cc<>'0'x
MVC    CTOK,=CL5' '         ctok=''
MVC    CTOK(1),CC           ctok=cc
CLI    CC,C' '              if cc=' '
BE     ITERATE              then goto iterate
IF CLI,CC,GE,C'0',AND,CLI,CC,LE,C'9' THEN
XDECI  R2,0(R7)             r2=cint(text); r1=@text
ST     R2,STACK(R4)         stack(js)=cc
SR     R1,R7                lt  length of token
BCTR   R1,0                 lt-1
EX     R1,MVCV              MVC CTOK("R1"),0(R7)
AR     R6,R1                jt+=lt-1
AR     R7,R1                @text+=lt-1
LA     R4,4(R4)             js+=4
LA     R5,1(R5)             ns++
ELSE     ,                    else
MVC    DEED,=C'Exec'        deed='Exec'
LA     R9,STACK-8(R4)       @stack(j-1)
IF CLI,CC,EQ,C'+' THEN        if cc='+' then
L      R1,STACK-8(R4)         stack(j-1)
A      R1,STACK-4(R4)         stack(j-1)+stack(j)
ST     R1,0(R9)               stack(j-1)=stack(j-1)+stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'-' THEN        if cc='-' then
L      R1,STACK-8(R4)         stack(j-1)
S      R1,STACK-4(R4)         stack(j-1)-stack(j)
ST     R1,0(R9)               stack(j-1)=stack(j-1)-stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'*' THEN        if cc='*' then
L      R3,STACK-8(R4)         stack(j-1)
M      R2,STACK-4(R4)         stack(j-1)*stack(j)
ST     R3,0(R9)               stack(j-1)=stack(j-1)*stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'/' THEN        if cc='/' then
L      R2,STACK-8(R4)         stack(j-1)
SRDA   R2,32                  for sign propagation
D      R2,STACK-4(R4)         stack(j-1)/stack(j)
ST     R3,0(R9)               stack(j-1)=stack(j-1)/stack(j)
ENDIF    ,                    endif
IF CLI,CC,EQ,C'^' THEN        if cc='^' then
LA     R3,1                   r3=1
L      R0,STACK-4(R4)         r0=stack(j) [loop count]
EXPONENT M      R2,STACK-8(R4)         r3=r3*stack(j-1)
BCT    R0,EXPONENT            if r0--<>0 then goto exponent
ST     R3,0(R9)               stack(j-1)=stack(j-1)^stack(j)
ENDIF    ,                    endif
S      R4,=F'4'             js-=4
BCTR   R5,0                 ns--
ENDIF    ,                  endif
MVC    PG,=CL80' '          clean buffer
MVC    PG(4),DEED           output deed
MVC    PG+5(5),CTOK         output cc
MVC    PG+11(6),=C'Stack:'  output
LA     R2,1                 i=1
LA     R3,STACK             @stack
LA     R9,PG+18             @buffer
DO WHILE=(CR,R2,LE,R5)        do i=1 to ns
L      R1,0(R3)               stack(i)
XDECO  R1,XDEC                edit stack(i)
MVC    0(5,R9),XDEC+7         output stack(i)
LA     R2,1(R2)               i=i+1
LA     R3,4(R3)               @stack+=4
LA     R9,6(R9)               @buffer+=6
ENDDO    ,                    enddo
XPRNT  PG,L'PG              print
ITERATE  LA     R6,1(R6)             jt++
LA     R7,1(R7)             @text++
MVC    CC,0(R7)             cc next char
ENDDO    ,                  enddo
L      R1,STACK           stack(1)
XDECO  R1,XDEC            edit stack(1)
MVC    XDEC(4),=C'Val='   output
XPRNT  XDEC,L'XDEC        print stack(1)
L      R13,4(0,R13)       restore previous savearea pointer
LM     R14,R12,12(R13)    restore previous context
XR     R15,R15            rc=0
BR     R14                exit
MVCV     MVC    CTOK(0),0(R7)      patern mvc
TEXT     DC     C'3 4 2 * 1 5 - 2 3 ^ ^ / +',X'00'
STACK    DS     16F                stack(16)
DEED     DS     CL4
CC       DS     C
CTOK     DS     CL5
PG       DS     CL80
XDEC     DS     CL12
YREGS
END    REVPOL
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / +
Load 2     Stack:     3     4     2
Exec *     Stack:     3     8
Load 1     Stack:     3     8     1
Load 5     Stack:     3     8     1     5
Exec -     Stack:     3     8    -4
Load 2     Stack:     3     8    -4     2
Load 3     Stack:     3     8    -4     2     3
Exec ^     Stack:     3     8    -4     8
Exec ^     Stack:     3     8 65536
Exec /     Stack:     3     0
Exec +     Stack:     3
Val=       3

## Action!

INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit

DEFINE PTR="CARD"
DEFINE BUFFER_SIZE="60"
DEFINE ENTRY_SIZE="6"
DEFINE MAX_SIZE="10"
BYTE ARRAY stack(BUFFER_SIZE)
BYTE stackSize=[0]

BYTE FUNC IsEmpty()
IF stackSize=0 THEN
RETURN (1)
FI
RETURN (0)

PTR FUNC GetPtr(BYTE i)
RETURN (stack+i*ENTRY_SIZE)

PROC Push(REAL POINTER v)
REAL POINTER p

IF stackSize=MAX_SIZE THEN
PrintE("Error: stack is full!")
Break()
FI
p=GetPtr(stackSize)
RealAssign(v,p)
stackSize==+1
RETURN

PROC Pop(REAL POINTER v)
REAL POINTER p

IF IsEmpty() THEN
PrintE("Error: stack is empty!")
Break()
FI
stackSize==-1
p=GetPtr(stackSize)
RealAssign(p,v)
RETURN

PROC PrintStack()
INT i
REAL POINTER p

FOR i=0 TO stackSize-1
DO
p=GetPtr(i)
PrintR(p) Put(32)
OD
PutE()
RETURN

BYTE FUNC GetToken(CHAR ARRAY s BYTE start CHAR ARRAY t)
BYTE pos

pos=start
WHILE pos<=s(0) AND s(pos)#'
DO
pos==+1
OD
SCopyS(t,s,start,pos-1)
RETURN (pos)

PROC MyPower(REAL POINTER base,exp,res)
INT i,expI
REAL tmp

expI=RealToInt(exp)
IF expI<0 THEN Break() FI

IntToReal(1,res)
FOR i=1 TO expI
DO
RealMult(res,base,tmp)
RealAssign(tmp,res)
OD
RETURN

PROC Process(CHAR ARRAY s)
DEFINE Pop21="Pop(v2) Pop(v1)"
CHAR ARRAY t(100)
BYTE i,j
CHAR c
REAL v1,v2,v3

i=1
WHILE i<=s(0)
DO
WHILE i<=s(0) AND s(i)='
DO i==+1 OD
IF i>s(0) THEN EXIT FI

i=GetToken(s,i,t)
IF SCompare(t,"+")=0 THEN
Print("calc +: ")
ELSEIF SCompare(t,"-")=0 THEN
Pop21 RealSub(v1,v2,v3)
Print("calc -: ")
ELSEIF SCompare(t,"*")=0 THEN
Pop21 RealMult(v1,v2,v3)
Print("calc *: ")
ELSEIF SCompare(t,"/")=0 THEN
Pop21 RealDiv(v1,v2,v3)
Print("calc /: ")
ELSEIF SCompare(t,"^")=0 THEN
Pop21 MyPower(v1,v2,v3)
Print("calc ^: ")
ELSE
ValR(t,v3)
PrintF("push %S: ",t)
FI
Push(v3)
PrintStack()
OD
RETURN

PROC Test(CHAR ARRAY s)
PrintE(s) PutE()
Process(s)
RETURN

PROC Main()
Put(125) PutE() ;clear the screen
Test("3 4 2 * 1 5 - 2 3 ^ ^ / +")
RETURN
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / +

push 3: 3
push 4: 3 4
push 2: 3 4 2
calc *: 3 8
push 1: 3 8 1
push 5: 3 8 1 5
calc -: 3 8 -4
push 2: 3 8 -4 2
push 3: 3 8 -4 2 3
calc ^: 3 8 -4 8
calc ^: 3 8 65536
calc /: 3 1.22070312E-04
calc +: 3.00012207

procedure RPN_Calculator is

(Index_Type => Positive, Element_Type => Float);
Stack: Float_Vec.Vector;

Cursor: Positive := Input'First;
New_Cursor: Positive;

begin
loop
while Cursor <= Input'Last and then Input(Cursor)=' ' loop
Cursor := Cursor + 1;
end loop;

exit when Cursor > Input'Last;

New_Cursor := Cursor;
while New_Cursor <= Input'Last and then Input(New_Cursor) /= ' ' loop
New_Cursor := New_Cursor + 1;
end loop;

-- try to read a number and push it to the stack
declare
Last: Positive;
Value: Float;
X, Y: Float;
begin
IIO.Get(From => Input(Cursor .. New_Cursor - 1),
Item => Value,
Last => Last);
Stack.Append(Value);
Cursor := New_Cursor;

exception -- if reading the number fails, try to read an operator token
when others =>
Y := Stack.Last_Element; Stack.Delete_Last; -- pick two elements
X := Stack.Last_Element; Stack.Delete_Last; -- from the stack
case Input(Cursor) is
when '+' => Stack.Append(X+Y);
when '-' => Stack.Append(X-Y);
when '*' => Stack.Append(X*Y);
when '/' => Stack.Append(X/Y);
when '^' => Stack.Append(X ** Integer(Float'Rounding(Y)));
when others => raise Program_Error with "unecpected token '"
& Input(Cursor) & "' at column" & Integer'Image(Cursor);
end case;
Cursor := New_Cursor;
end;

for I in Stack.First_Index .. Stack.Last_Index loop
IIO.Put(Stack.Element(I), Aft => 5, Exp => 0);
end loop;
end loop;

IIO.Put(Item => Stack.Last_Element, Aft => 5, Exp => 0);

end RPN_Calculator;
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / +
3.00000
3.00000  4.00000
3.00000  4.00000  2.00000
3.00000  8.00000
3.00000  8.00000  1.00000
3.00000  8.00000  1.00000  5.00000
3.00000  8.00000 -4.00000
3.00000  8.00000 -4.00000  2.00000
3.00000  8.00000 -4.00000  2.00000  3.00000
3.00000  8.00000 -4.00000  8.00000
3.00000  8.00000 65536.00000
3.00000  0.00012
3.00012
Result =  3.00012

## ALGOL 68

Works with: ALGOL 68G version Any - tested with release 2.8.win32
# RPN Expression evaluator - handles numbers and + - * / ^    #
#     the right-hand operand for ^ is converted to an integer #

# expression terminator #
CHAR end of expression character = REPR 12;

# evaluates the specified rpn expression #
PROC evaluate = ( STRING rpn expression )VOID:
BEGIN

[ 256 ]REAL   stack;
INT           stack pos := 0;

# pops an element off the stack #
PROC pop = REAL:
BEGIN
stack pos -:= 1;
stack[ stack pos + 1 ]
END; # pop #

INT rpn pos := LWB rpn expression;

# evaluate tokens from the expression until we get the end of expression #
WHILE

# get the next token from the string #

STRING token type;
REAL   value;

# skip spaces #
WHILE rpn expression[ rpn pos ] = " "
DO
rpn pos +:= 1
OD;

# handle the token #
IF rpn expression[ rpn pos ] = end of expression character
THEN
# no more tokens #
FALSE

ELSE
# have a token #

IF  rpn expression[ rpn pos ] >= "0"
AND rpn expression[ rpn pos ] <= "9"
THEN
# have a number #

# find where the nmumber is in the expression #
INT  number start = rpn pos;
WHILE (   rpn expression[ rpn pos ] >= "0"
AND rpn expression[ rpn pos ] <= "9"
)
OR rpn expression[ rpn pos ] = "."
DO
rpn pos +:= 1
OD;

# read the number from the expression #
FILE number f;
associate( number f
, LOC STRING := rpn expression[ number start : rpn pos - 1 ]
);
get( number f, ( value ) );
close( number f );

token type := "number"

ELSE
# must be an operator #
CHAR op      = rpn expression[ rpn pos ];
rpn pos    +:= 1;

REAL arg1   := pop;
REAL arg2   := pop;
token type  := op;

value := IF   op = "+"
THEN
# add the top two stack elements #
arg1 + arg2
ELIF op = "-"
THEN
# subtract the top two stack elements #
arg2 - arg1
ELIF op = "*"
THEN
# multiply the top two stack elements #
arg2 * arg1
ELIF op = "/"
THEN
# divide the top two stack elements #
arg2 / arg1
ELIF op = "^"
THEN
# raise op2 to the power of op1 #
arg2 ^ ENTIER arg1
ELSE
# unknown operator #
print( ( "Unknown operator: """ + op + """", newline ) );
0
FI

FI;

TRUE
FI
DO
# push the new value on the stack and show the new stack #

stack[ stack pos +:= 1 ] := value;

print( ( ( token type + "            " )[ 1 : 8 ] ) );
FOR element FROM LWB stack TO stack pos
DO
print( ( " ", fixed( stack[ element ], 8, 4 ) ) )
OD;
print( ( newline ) )

OD;

print( ( "Result is: ", fixed( stack[ stack pos ], 12, 8 ), newline ) )

END; # evaluate #

main: (

# get the RPN expresson from the user #

STRING rpn expression;

print( ( "Enter expression: " ) );
read( ( rpn expression, newline ) );

# add a space to terminate the final token and an expression terminator #
rpn expression +:= " " + end of expression character;

# execute the expression #
evaluate( rpn expression )

)
Output:
Enter expression: 3 4 2 * 1 5 - 2 3 ^ ^ / +
number    +3.0000
number    +3.0000  +4.0000
number    +3.0000  +4.0000  +2.0000
*         +3.0000  +8.0000
number    +3.0000  +8.0000  +1.0000
number    +3.0000  +8.0000  +1.0000  +5.0000
-         +3.0000  +8.0000  -4.0000
number    +3.0000  +8.0000  -4.0000  +2.0000
number    +3.0000  +8.0000  -4.0000  +2.0000  +3.0000
^         +3.0000  +8.0000  -4.0000  +8.0000
^         +3.0000  +8.0000 +65536.0
/         +3.0000  +0.0001
+         +3.0001
Result is:  +3.00012207

## ANTLR

### Java

grammar rpnC ;
//
//  rpn Calculator
//
//  Nigel Galloway - April 7th., 2012
//
@members {
Stack<Double> s = new Stack<Double>();
}
rpn	:	(WS* (num|op) (WS | WS* NEWLINE {System.out.println(s.pop());}))*;
num	:	'-'? Digit+ ('.' Digit+)? {s.push(Double.parseDouble(\$num.text));};
Digit	:	'0'..'9';
op	:	'-' {double x = s.pop(); s.push(s.pop() - x);}
|	'/' {double x = s.pop(); s.push(s.pop() / x);}
|	'*' {s.push(s.pop() * s.pop());}
|	'^' {double x = s.pop(); s.push(Math.pow(s.pop(), x));}
|	'+' {s.push(s.pop() + s.pop());};
WS	:	(' ' | '\t'){skip()};
NEWLINE	:	'\r'? '\n';

Produces:

>java Test
3 4 2 * 1 5 - 2 3 ^ ^ / +
^Z
3.0001220703125

## AutoHotkey

Works with: AutoHotkey_L

Output is in clipboard.

evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
evalRPN(s){
stack := []
out := "For RPN expression: '" s "'`r`n`r`nTOKEN`t`tACTION`t`t`tSTACK`r`n"
Loop Parse, s
If A_LoopField is number
t .= A_LoopField
else
{
If t
stack.Insert(t)
, out .= t "`tPush num onto top of stack`t" stackShow(stack) "`r`n"
, t := ""
If InStr("+-/*^", l := A_LoopField)
{
a := stack.Remove(), b := stack.Remove()
stack.Insert(	 l = "+" ? b + a
:l = "-" ? b - a
:l = "*" ? b * a
:l = "/" ? b / a
:l = "^" ? b **a
:0	)
out .= l "`tApply op " l " to top of stack`t" stackShow(stack) "`r`n"
}
}
r := stack.Remove()
out .= "`r`n The final output value is: '" r "'"
clipboard := out
return r
}
StackShow(stack){
for each, value in stack
out .= A_Space value
return subStr(out, 2)
}
Output:
For RPN expression: '3 4 2 * 1 5 - 2 3 ^ ^ / +'

TOKEN		ACTION			STACK
3	Push num onto top of stack	3
4	Push num onto top of stack	3 4
2	Push num onto top of stack	3 4 2
*	Apply op * to top of stack	3 8
1	Push num onto top of stack	3 8 1
5	Push num onto top of stack	3 8 1 5
-	Apply op - to top of stack	3 8 -4
2	Push num onto top of stack	3 8 -4 2
3	Push num onto top of stack	3 8 -4 2 3
^	Apply op ^ to top of stack	3 8 -4 8
^	Apply op ^ to top of stack	3 8 65536
/	Apply op / to top of stack	3 0.000122
+	Apply op + to top of stack	3.000122

The final output value is: '3.000122'

## BASIC

### ANSI BASIC

Works with: Decimal BASIC
1000 DECLARE EXTERNAL SUB rpn
1010 PUBLIC NUMERIC R(64)                             ! stack
1020 PUBLIC STRING expn\$                              ! for keyboard input
1030 PUBLIC NUMERIC i, lenn, n, true, false           ! global values
1040 LET true = -1
1050 LET false = 0
1060 DO
1070    PRINT "enter an RPN expression:"
1080    INPUT expn\$
1090    IF LEN( expn\$ ) = 0 THEN EXIT DO
1100    PRINT "expn: ";expn\$
1110    CALL rpn( expn\$ )
1120 LOOP
1130 END
1140 !
1150 ! interpret reverse polish (postfix) expression
1160 EXTERNAL SUB rpn( expn\$ )
1170 DECLARE EXTERNAL FUNCTION is_digit, get_number
1180 DECLARE EXTERNAL SUB print_stack
1190 DECLARE STRING ch\$
1200 LET expn\$ = expn\$ & " "                          ! must terminate line with space
1210 LET lenn = LEN( expn\$ )
1220 LET i = 0
1230 LET n = 1
1240 LET R(n) = 0.0                                   ! push zero for unary operations
1250 DO
1260    IF i >= lenn THEN EXIT DO                     ! at end of line
1270    LET i = i + 1
1280    IF expn\$(i:i) <> " " THEN                     ! skip white spaces
1290       IF is_digit( expn\$(i:i) ) = true THEN      ! push number onto stack
1300          LET n = n + 1
1310          LET R(n) = get_number
1320          CALL print_stack
1330       ELSEIF expn\$(i:i) = "+" then               ! add and pop stack
1340          IF n < 2 THEN
1350             PRINT "stack underflow"
1360          ELSE
1370             LET R(n-1) = R(n-1) + R(n)
1380             LET n = n - 1
1390             CALL print_stack
1400          END IF
1410       ELSEIF expn\$(i:i) = "-" then               ! subtract and pop stack
1420          IF n < 2 THEN
1430             PRINT "stack underflow"
1440          ELSE
1450             LET R(n-1) = R(n-1) - R(n)
1460             LET n = n - 1
1470             CALL print_stack
1480          END IF
1490       ELSEIF expn\$(i:i) = "*" then               ! multiply and pop stack
1500          IF n < 2 THEN
1510             PRINT "stack underflow"
1520          ELSE
1530             LET R(n-1) = R(n-1) * R(n)
1540             LET n = n - 1
1550             CALL print_stack
1560          END IF
1570       ELSEIF expn\$(i:i) = "/" THEN               ! divide and pop stack
1580          IF n < 2 THEN
1590             PRINT "stack underflow"
1600          ELSE
1610             LET R(n-1) = R(n-1) / R(n)
1620             LET n = n - 1
1630             CALL print_stack
1640          END IF
1650       ELSEIF expn\$(i:i) = "^" THEN               ! raise to power and pop stack
1660          IF n < 2 THEN
1670             PRINT "stack underflow"
1680          ELSE
1690             LET R(n-1) = R(n-1) ^ R(n)
1700             LET n = n - 1
1710             CALL print_stack
1720          END IF
1730       ELSE
1740          PRINT REPEAT\$( " ", i+5 ); "^ error"
1750          EXIT DO
1760       END IF
1770    END IF
1780 LOOP
1790 PRINT "result: "; R(n)                           ! end of main program
1800 END SUB
1810 !
1820 ! extract a number from a string
1830 EXTERNAL FUNCTION get_number
1840 DECLARE EXTERNAL FUNCTION is_digit
1850 LET i1 = i                                       ! start of number substring
1860 DO                                               ! get integer part
1870    LET i = i + 1
1880    IF is_digit( expn\$(i:i) ) = false THEN
1890       IF expn\$(i:i) = "." THEN
1900          LET i = i + 1
1910          DO WHILE is_digit( expn\$(i:i) ) = true  ! get fractional part
1920             LET i = i + 1
1930          LOOP
1940       END IF
1950       EXIT DO
1960    END IF
1970 LOOP
1980 LET get_number = VAL( expn\$(i1:i - 1) )
1990 END FUNCTION
2000 !
2010 ! check for digit character
2020 EXTERNAL FUNCTION is_digit( ch\$ )
2030 IF "0" <= ch\$ AND ch\$ <= "9" THEN
2040    LET is_digit = true
2050 ELSE
2060    LET is_digit = false
2070 END IF
2080 END FUNCTION
2090 !
2100 EXTERNAL SUB print_stack
2110 PRINT expn\$(i:i);"    ";
2120 FOR ptr=n TO 2 STEP -1
2130    PRINT USING "-----%.####":R(ptr);
2140 NEXT ptr
2150 PRINT
2160 END SUB
Output:
enter an RPN expression:
? 3 4 2 * 1 5 - 2 3 ^ ^ / +
expn: 3 4 2 * 1 5 - 2 3 ^ ^ / +
3.0000
4.0000     3.0000
2.0000     4.0000     3.0000
*         8.0000     3.0000
1.0000     8.0000     3.0000
5.0000     1.0000     8.0000     3.0000
-        -4.0000     8.0000     3.0000
2.0000    -4.0000     8.0000     3.0000
3.0000     2.0000    -4.0000     8.0000     3.0000
^         8.0000    -4.0000     8.0000     3.0000
^     65536.0000     8.0000     3.0000
/         0.0001     3.0000
+         3.0001
result:  3.0001220703125
enter an RPN expression:
?

### BBC BASIC

@% = &60B
RPN\$ = "3 4 2 * 1 5 - 2 3 ^ ^ / +"

DIM Stack(1000)
SP% = 0

FOR i% = 1 TO LEN(RPN\$)
Token\$ = MID\$(RPN\$,i%,1)
IF Token\$ <> " " THEN
PRINT Token\$ " :";
CASE Token\$ OF
WHEN "+": PROCpush(FNpop + FNpop)
WHEN "-": PROCpush(-FNpop + FNpop)
WHEN "*": PROCpush(FNpop * FNpop)
WHEN "/": n = FNpop : PROCpush(FNpop / n)
WHEN "^": n = FNpop : PROCpush(FNpop ^ n)
WHEN "0","1","2","3","4","5","6","7","8","9":
PROCpush(VALMID\$(RPN\$,i%))
WHILE ASCMID\$(RPN\$,i%)>=48 AND ASCMID\$(RPN\$,1)<=57
i% += 1
ENDWHILE
ENDCASE
FOR j% = SP%-1 TO 0 STEP -1 : PRINT Stack(j%); : NEXT
PRINT
ENDIF
NEXT i%
END

DEF PROCpush(n)
IF SP% > DIM(Stack(),1) ERROR 100, "Stack full"
Stack(SP%) = n
SP% += 1
ENDPROC

DEF FNpop
IF SP% = 0 ERROR 100, "Stack empty"
SP% -= 1
= Stack(SP%)
Output:
3 :          3
4 :          4          3
2 :          2          4          3
* :          8          3
1 :          1          8          3
5 :          5          1          8          3
- :         -4          8          3
2 :          2         -4          8          3
3 :          3          2         -4          8          3
^ :          8         -4          8          3
^ :      65536          8          3
/ : 0.00012207          3
+ :    3.00012

### FreeBASIC

#define NULL 0

type node
'implement the stack as a linked list
n as double
p as node ptr
end type

function spctok( byref s as string ) as string
'returns everything in the string up to the first space
'modifies the original string to begin at the fist non-space char after the first space
dim as string r
dim as double i = 1
while mid(s,i,1)<>" " and i<=len(s)
r += mid(s,i,1)
i+=1
wend
do
i+=1
loop until mid(s,i,1)<>" " or i >= len(s)
s = right(s,len(s)-i+1)
return r
end function

sub print_stack( byval S as node ptr )
'display everything on the stack
print "Stack   <---   ";
while S->p <> NULL
S = S->p
print S->n;"   ";
wend
print
end sub

sub push( byval S as node ptr, v as double )
'push a value onto the stack
dim as node ptr x
x = allocate(sizeof(node))
x->n = v
x->p = S->p
S->p = x
end sub

function pop( byval S as node ptr ) as double
'pop a value from the stack
if s->P = NULL then return -99999
dim as double r = S->p->n
dim as node ptr junk = S->p
S->p = S->p->p
deallocate(junk)
return r
end function

dim as string s = "3 4 2 * 1 5 - 2 3 ^ ^ / +", c

while len(s) > 0
c = spctok(s)
print "Token: ";c;"  ";
select case c
case "+"
print "Operation +     ";
case "-"
print "Operation -     ";
case "/"
print "Operation /     ";
case "*"
print "Operation *     ";
case "^"
print "Operation ^     ";
case else
print "Operation push  ";
end select
wend
Output:

Token: 3 Operation push Stack <--- 3 Token: 4 Operation push Stack <--- 4 3 Token: 2 Operation push Stack <--- 2 4 3 Token: * Operation * Stack <--- 8 3 Token: 1 Operation push Stack <--- 1 8 3 Token: 5 Operation push Stack <--- 5 1 8 3 Token: - Operation - Stack <--- -4 8 3 Token: 2 Operation push Stack <--- 2 -4 8 3 Token: 3 Operation push Stack <--- 3 2 -4 8 3 Token: ^ Operation ^ Stack <--- 8 -4 8 3 Token: ^ Operation ^ Stack <--- 65536 8 3 Token: / Operation / Stack <--- 0.0001220703125 3 Token: + Operation + Stack <--- 3.0001220703125

### GW-BASIC

Translation of: QuickBASIC

Supports multi-digit numbers and negative numbers.

Works with: BASICA
10 REM Parsing/RPN calculator algorithm
20 MAX.INDEX% = 63
30 REM Stack
40 REM TOP.INDEX% - top index of the stack
50 DIM ELEMS(MAX.INDEX%)
60 EXPR\$ = "3 4 2 * 1 5 - 2 3 ^ ^ / +": GOSUB 200
70 END
190 REM ** Evaluate the expression in RPN
200 GOSUB 1000
210 PRINT "Input", "Operation", "Stack after"
220 REM SP% - start position of token, DP% - position of delimiter
230 DP% = 0
240 REM Loop: do ... until DP% = 0
250  SP% = DP% + 1
260  DP% = INSTR(DP% + 1, EXPR\$, " ")
270  IF DP% = 0 THEN TOKEN\$ = MID\$(EXPR\$, SP%, LEN(EXPR\$) - SP% + 1) ELSE TE% = DP% - 1: TOKEN\$ = MID\$(EXPR\$, SP%, DP% - SP%)
280  PRINT TOKEN\$,
290  IF TOKEN\$ <> "*" THEN 350
300   PRINT "Operate",
310   GOSUB 1060: SECOND = POP
320   GOSUB 1060: FIRST = POP
330   X = FIRST * SECOND: GOSUB 1160
340   GOTO 610
350  IF TOKEN\$ <> "/" THEN 410
360   PRINT "Operate",
370   GOSUB 1060: SECOND = POP
380   GOSUB 1060: FIRST = POP
390   X = FIRST / SECOND: GOSUB 1160
400   GOTO 610
410  IF TOKEN\$ <> "-" THEN 470
420   PRINT "Operate",
430   GOSUB 1060: SECOND = POP
440   GOSUB 1060: FIRST = POP
450   X = FIRST - SECOND: GOSUB 1160
460   GOTO 610
470  IF TOKEN\$ <> "+" THEN 530
480   PRINT "Operate",
490   GOSUB 1060: SECOND = POP
500   GOSUB 1060: FIRST = POP
510   X = FIRST + SECOND: GOSUB 1160
520   GOTO 610
530  IF TOKEN\$ <> "^" THEN 590
540   PRINT "Operate",
550   GOSUB 1060: SECOND = POP
560   GOSUB 1060: FIRST = POP
570   X = FIRST ^ SECOND: GOSUB 1160
580   GOTO 610
590  PRINT "Push",
600  X = VAL(TOKEN\$): GOSUB 1160
610  GOSUB 1100
620 IF DP% <> 0 THEN 250
630 GOSUB 1060:
640 PRINT "Final answer: "; POP
650 GOSUB 1030
660 IF NOT EMPTY% THEN PRINT "Error, too many operands: "; : GOSUB 1100: STOP
670 RETURN
980 REM ** Operations on the stack
990 REM ** Make the stack empty
1000 TOP.INDEX% = MAX.INDEX% + 1
1010 RETURN
1020 REM ** Is the stack empty?
1030 EMPTY% = TOP.INDEX% > MAX.INDEX%
1040 RETURN
1050 REM ** Pop from the stack
1060 GOSUB 1030
1070 IF NOT EMPTY% THEN POP = ELEMS(TOP.INDEX%): TOP.INDEX% = TOP.INDEX% + 1 ELSE PRINT "The stack is empty.": STOP
1080 RETURN
1090 REM ** Print the stack
1100 FOR PTR% = TOP.INDEX% TO MAX.INDEX%
1110  PRINT USING "######.###"; ELEMS(PTR%);
1120 NEXT PTR%
1130 PRINT
1140 RETURN
1150 REM ** Push to the stack
1160 IF TOP.INDEX% > 0 THEN TOP.INDEX% = TOP.INDEX% - 1: ELEMS(TOP.INDEX%) = X ELSE PRINT "The stack is full.": STOP
1170 RETURN
Output:
Input         Operation     Stack after
3             Push               3.000
4             Push               4.000     3.000
2             Push               2.000     4.000     3.000
*             Operate            8.000     3.000
1             Push               1.000     8.000     3.000
5             Push               5.000     1.000     8.000     3.000
-             Operate           -4.000     8.000     3.000
2             Push               2.000    -4.000     8.000     3.000
3             Push               3.000     2.000    -4.000     8.000     3.000
^             Operate            8.000    -4.000     8.000     3.000
^             Operate        65536.000     8.000     3.000
/             Operate            0.000     3.000
+             Operate            3.000

### Liberty BASIC

Works with: Just BASIC
global stack\$

expr\$ = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
print "Expression:"
print expr\$
print

print "Input","Operation","Stack after"

stack\$=""
token\$ = "#"
i = 1
token\$ = word\$(expr\$, i)
token2\$ = " "+token\$+" "

do
print "Token ";i;": ";token\$,
select case
'operation
case instr("+-*/^",token\$)<>0
print "operate",
op2\$=pop\$()
op1\$=pop\$()
if op1\$=""  then
print "Error: stack empty for ";i;"-th token: ";token\$
end
end if

op1=val(op1\$)
op2=val(op2\$)

select case token\$
case "+"
res = op1+op2
case "-"
res = op1-op2
case "*"
res = op1*op2
case "/"
res = op1/op2
case "^"
res = op1^op2
end select

call push str\$(res)
'default:number
case else
print "push",
call push token\$
end select
print "Stack: ";reverse\$(stack\$)
i = i+1
token\$ = word\$(expr\$, i)
token2\$ = " "+token\$+" "
loop until token\$ =""

res\$=pop\$()
print
print "Result:" ;res\$
extra\$=pop\$()
if extra\$<>"" then
print "Error: extra things on a stack: ";extra\$
end if
end

'---------------------------------------
function reverse\$(s\$)
reverse\$ = ""
token\$="#"
while token\$<>""
i=i+1
token\$=word\$(s\$,i,"|")
reverse\$ = token\$;" ";reverse\$
wend
end function
'---------------------------------------
sub push s\$
stack\$=s\$+"|"+stack\$    'stack
end sub

function pop\$()
'it does return empty on empty stack
pop\$=word\$(stack\$,1,"|")
stack\$=mid\$(stack\$,instr(stack\$,"|")+1)
end function
Output:
Expression:
3 4 2 * 1 5 - 2 3 ^ ^ / +

Input         Operation     Stack after
Token 1: 3    push          Stack:  3
Token 2: 4    push          Stack:  3 4
Token 3: 2    push          Stack:  3 4 2
Token 4: *    operate       Stack:  3 8
Token 5: 1    push          Stack:  3 8 1
Token 6: 5    push          Stack:  3 8 1 5
Token 7: -    operate       Stack:  3 8 -4
Token 8: 2    push          Stack:  3 8 -4 2
Token 9: 3    push          Stack:  3 8 -4 2 3
Token 10: ^   operate       Stack:  3 8 -4 8
Token 11: ^   operate       Stack:  3 8 65536
Token 12: /   operate       Stack:  3 0.12207031e-3
Token 13: +   operate       Stack:  3.00012207

Result:3.00012207

### QuickBASIC

Translation of: Java – In fact, stack and tokenizing had to be implemented. Converting string to numbers is based on the VAL function in BASIC.

Supports multi-digit numbers and negative numbers.

' Parsing/RPN calculator algorithm
DECLARE SUB MakeEmpty (S AS ANY)
DECLARE SUB Push (X AS SINGLE, S AS ANY)
DECLARE SUB PrintStack (S AS ANY)
DECLARE SUB EvalRPN (Expr\$)
DECLARE FUNCTION Empty% (S AS ANY)
DECLARE FUNCTION Pop! (S AS ANY)

CONST MAXINDEX = 63

TYPE TNumStack
TopIndex AS INTEGER
Elems(MAXINDEX) AS SINGLE
END TYPE

EvalRPN ("3 4 2 * 1 5 - 2 3 ^ ^ / +")
END

FUNCTION Empty% (S AS TNumStack)
Empty% = S.TopIndex > MAXINDEX
END FUNCTION

SUB EvalRPN (Expr\$)
DIM S AS TNumStack
MakeEmpty S
PRINT "Input", "Operation", "Stack after"
' SP% - start position of token
' DP% - position of delimiter
DP% = 0
DO
SP% = DP% + 1
DP% = INSTR(DP% + 1, Expr\$, " ")
IF DP% <> 0 THEN
TE% = DP% - 1
Token\$ = MID\$(Expr\$, SP%, DP% - SP%)
ELSE
Token\$ = MID\$(Expr\$, SP%, LEN(Expr\$) - SP% + 1)
END IF
PRINT Token\$,
IF Token\$ = "*" THEN
PRINT "Operate",
Second = Pop(S): First = Pop(S)
Push First * Second, S
ELSEIF Token\$ = "/" THEN
PRINT "Operate",
Second = Pop(S): First = Pop(S)
Push First / Second, S
ELSEIF Token\$ = "-" THEN
PRINT "Operate",
Second = Pop(S): First = Pop(S)
Push First - Second, S
ELSEIF Token\$ = "+" THEN
PRINT "Operate",
Second = Pop(S): First = Pop(S)
Push First + Second, S
ELSEIF Token\$ = "^" THEN
PRINT "Operate",
Second = Pop(S): First = Pop(S)
Push First ^ Second, S
ELSE
PRINT "Push",
Push VAL(Token\$), S
END IF
PrintStack S
LOOP UNTIL DP% = 0
IF NOT Empty(S) THEN
PRINT "Error, too many operands: ";
PrintStack S
STOP
END IF
END SUB

SUB MakeEmpty (S AS TNumStack)
S.TopIndex = MAXINDEX + 1
END SUB

FUNCTION Pop (S AS TNumStack)
IF Empty%(S) THEN
PRINT "The stack is empty."
STOP
ELSE
Pop = S.Elems(S.TopIndex)
S.TopIndex = S.TopIndex + 1
END IF
END FUNCTION

SUB PrintStack (S AS TNumStack)
FOR Ptr% = S.TopIndex% TO MAXINDEX
PRINT USING "######.###"; S.Elems(Ptr%);
NEXT Ptr%
PRINT
END SUB

SUB Push (X AS SINGLE, S AS TNumStack)
IF S.TopIndex = 0 THEN
PRINT "The stack is full."
STOP
ELSE
S.TopIndex = S.TopIndex - 1
S.Elems(S.TopIndex) = X
END IF
END SUB
Output:
Input         Operation     Stack after
3             Push               3.000
4             Push               4.000     3.000
2             Push               2.000     4.000     3.000
*             Operate            8.000     3.000
1             Push               1.000     8.000     3.000
5             Push               5.000     1.000     8.000     3.000
-             Operate           -4.000     8.000     3.000
2             Push               2.000    -4.000     8.000     3.000
3             Push               3.000     2.000    -4.000     8.000     3.000
^             Operate            8.000    -4.000     8.000     3.000
^             Operate        65536.000     8.000     3.000
/             Operate            0.000     3.000
+             Operate            3.000

### Run BASIC

prn\$ = "3 4 2 * 1 5 - 2 3 ^ ^ / + "

j = 0
while word\$(prn\$,i + 1," ") <> ""
i = i + 1
n\$ = word\$(prn\$,i," ")
if n\$ < "0" or n\$ > "9" then
num1   = val(word\$(stack\$,s," "))
num2   = val(word\$(stack\$,s-1," "))
n      = op(n\$,num2,num1)
s      = s - 1
stack\$ = stk\$(stack\$,s -1,str\$(n))
print "Push Opr ";n\$;" to stack:  ";stack\$
else
s = s + 1
stack\$ = stack\$ + n\$ + " "
print "Push Num ";n\$;" to stack:  ";stack\$
end if
wend

function stk\$(stack\$,s,a\$)
for i = 1 to s
stk\$ = stk\$ + word\$(stack\$,i," ") + " "
next i
stk\$ = stk\$ + a\$ + " "
end function

FUNCTION op(op\$,a,b)
if op\$ = "*" then op = a * b
if op\$ = "/" then op = a / b
if op\$ = "^" then op = a ^ b
if op\$ = "+" then op = a + b
if op\$ = "-" then op = a - b
end function
Push Num 3 to stack:  3
Push Num 4 to stack:  3 4
Push Num 2 to stack:  3 4 2
Push Opr * to stack:  3 8
Push Num 1 to stack:  3 8 1
Push Num 5 to stack:  3 8 1 5
Push Opr - to stack:  3 8 -4
Push Num 2 to stack:  3 8 -4 2
Push Num 3 to stack:  3 8 -4 2 3
Push Opr ^ to stack:  3 8 -4 8
Push Opr ^ to stack:  3 8 65536
Push Opr / to stack:  3 1.22070312e-4
Push Opr + to stack:  3.00012207

### Sinclair ZX81 BASIC

If you only have 1k of RAM, this program will correctly evaluate the test expression with fewer than 10 bytes to spare. (I know that because I tried running it with the first line modified to allow a stack depth of 7, i.e. allocating space for two more 40-bit floats, and it crashed with an "out of memory" error code before it could print the result of the final addition.) If we desperately needed a few extra bytes there are ways they could be shaved out of the current program; but this version works, and editing a program that takes up almost all your available RAM isn't very comfortable, and to make it really useful for practical purposes you would still want to have 2k or more anyway.

The ZX81 character set doesn't include ^, so we have to use ** instead. Note that this is not two separate stars, although that's what it looks like: you have to enter it by typing SHIFT+H.

No attempt is made to check for invalid syntax, stack overflow or underflow, etc.

10 DIM S(5)
20 LET P=1
30 INPUT E\$
40 LET I=0
50 LET I=I+1
60 IF E\$(I)=" " THEN GOTO 110
70 IF I<LEN E\$ THEN GOTO 50
80 LET W\$=E\$
90 GOSUB 150
100 STOP
110 LET W\$=E\$( TO I-1)
120 LET E\$=E\$(I+1 TO )
130 GOSUB 150
140 GOTO 40
150 IF W\$="+" OR W\$="-" OR W\$="*" OR W\$="/" OR W\$="**" THEN GOTO 250
160 LET S(P)=VAL W\$
170 LET P=P+1
180 PRINT W\$;
190 PRINT ":";
200 FOR I=P-1 TO 1 STEP -1
210 PRINT " ";S(I);
220 NEXT I
230 PRINT
240 RETURN
250 IF W\$="**" THEN LET S(P-2)=ABS S(P-2)
260 LET S(P-2)=VAL (STR\$ S(P-2)+W\$+STR\$ S(P-1))
270 LET P=P-1
280 GOTO 180
Input:
3 4 2 * 1 5 - 2 3 ** ** / +
Output:
3: 3
4: 4 3
2: 2 4 3
*: 8 3
1: 1 8 3
5: 5 1 8 3
-: -4 8 3
2: 2 -4 8 3
3: 3 2 -4 8 3
**: 8 -4 8 3
**: 65536 8 3
/: .00012207031 3
+: 3.0001221

### VBA

Translation of: Liberty BASIC
Global stack\$

Function RPN(expr\$)
Debug.Print "Expression:"
Debug.Print expr\$
Debug.Print "Input", "Operation", "Stack after"

stack\$ = ""
token\$ = "#"
i = 1
token\$ = Split(expr\$)(i - 1) 'split is base 0
token2\$ = " " + token\$ + " "

Do
Debug.Print "Token "; i; ": "; token\$,
'operation
If InStr("+-*/^", token\$) <> 0 Then
Debug.Print "operate",
op2\$ = pop\$()
op1\$ = pop\$()
If op1\$ = "" Then
Debug.Print "Error: stack empty for "; i; "-th token: "; token\$
End
End If

op1 = Val(op1\$)
op2 = Val(op2\$)

Select Case token\$
Case "+"
res = CDbl(op1) + CDbl(op2)
Case "-"
res = CDbl(op1) - CDbl(op2)
Case "*"
res = CDbl(op1) * CDbl(op2)
Case "/"
res = CDbl(op1) / CDbl(op2)
Case "^"
res = CDbl(op1) ^ CDbl(op2)
End Select

Call push2(str\$(res))
'default:number
Else
Debug.Print "push",
Call push2(token\$)
End If
Debug.Print "Stack: "; reverse\$(stack\$)
i = i + 1
If i > Len(Join(Split(expr, " "), "")) Then
token\$ = ""
Else
token\$ = Split(expr\$)(i - 1) 'base 0
token2\$ = " " + token\$ + " "
End If
Loop Until token\$ = ""

Debug.Print
Debug.Print "Result:"; pop\$()
'extra\$ = pop\$()
If stack <> "" Then
Debug.Print "Error: extra things on a stack: "; stack\$
End If
End
End Function

'---------------------------------------
Function reverse\$(s\$)
reverse\$ = ""
token\$ = "#"
While token\$ <> ""
i = i + 1
token\$ = Split(s\$, "|")(i - 1) 'split is base 0
reverse\$ = token\$ & " " & reverse\$
Wend
End Function
'---------------------------------------
Sub push2(s\$)
stack\$ = s\$ + "|" + stack\$ 'stack
End Sub

Function pop\$()
'it does return empty on empty stack
pop\$ = Split(stack\$, "|")(0)
stack\$ = Mid\$(stack\$, InStr(stack\$, "|") + 1)
End Function
Output:
?RPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
Expression:
3 4 2 * 1 5 - 2 3 ^ ^ / +
Input         Operation     Stack after
Token  1 : 3  push          Stack:  3
Token  2 : 4  push          Stack:  3 4
Token  3 : 2  push          Stack:  3 4 2
Token  4 : *  operate       Stack:  3  8
Token  5 : 1  push          Stack:  3  8 1
Token  6 : 5  push          Stack:  3  8 1 5
Token  7 : -  operate       Stack:  3  8 -4
Token  8 : 2  push          Stack:  3  8 -4 2
Token  9 : 3  push          Stack:  3  8 -4 2 3
Token  10 : ^ operate       Stack:  3  8 -4  8
Token  11 : ^ operate       Stack:  3  8  65536
Token  12 : / operate       Stack:  3  .0001220703125
Token  13 : + operate       Stack:   3.0001220703125

Result: 3.0001220703125

### Xojo

Translation of: VBA

Function RPN(expr As String) As String
Dim tokenArray() As String
Dim stack() As String

Dim Wert1 As Double
Dim Wert2 As Double

'Initialize array (removed later)
ReDim tokenArray(1)
ReDim stack(1)

tokenArray = Split(expr, " ")

Dim i As integer
i = 0

While i <= tokenArray.Ubound
If  tokenArray(i) = "+" Then
Wert2 = Val(stack.pop)
Wert1 = Val(stack.pop)
stack.Append(Str(Wert1+Wert2))
ElseIf tokenArray(i) = "-" Then
Wert2 = Val(stack.pop)
Wert1 = Val(stack.pop)
stack.Append(Str(Wert1-Wert2))
ElseIf tokenArray(i) = "*" Then
Wert2 = Val(stack.pop)
Wert1 = Val(stack.pop)
stack.Append(Str(Wert1*Wert2))
ElseIf tokenArray(i) = "/" Then
Wert2 = Val(stack.pop)
Wert1 = Val(stack.pop)
stack.Append(Str(Wert1/Wert2))
ElseIf tokenArray(i) = "^" Then
Wert2 = Val(stack.pop)
Wert1 = Val(stack.pop)
stack.Append(Str(pow(Wert1,Wert2)))
Else
stack.Append(tokenArray(i))
End If
i = i +1
Wend

Return stack(2)

End Function

Output:
?RPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
Expression:
3 4 2 * 1 5 - 2 3 ^ ^ / +

Input         Operation     Stack after
Token  1 : 3  push          Stack:  3
Token  2 : 4  push          Stack:  3 4
Token  3 : 2  push          Stack:  3 4 2
Token  4 : *  operate       Stack:  3  8
Token  5 : 1  push          Stack:  3  8 1
Token  6 : 5  push          Stack:  3  8 1 5
Token  7 : -  operate       Stack:  3  8 -4
Token  8 : 2  push          Stack:  3  8 -4 2
Token  9 : 3  push          Stack:  3  8 -4 2 3
Token  10 : ^ operate       Stack:  3  8 -4  8
Token  11 : ^ operate       Stack:  3  8  65536
Token  12 : / operate       Stack:  3  .000122
Token  13 : + operate       Stack:   3.000122

Result: 3.000122

## Bracmat

(  ( show
=   line a
.   \n:?line
&   whl
' (!arg:%?a ?arg&!a " " !line:?line)
& put\$(str\$!line)
)
& :?stack
&   map
\$ ( (
=   a b
.   show\$(!arg !stack)
&     (     !arg
: ( "+"
| "-"
| "*"
| "/"
| "^"
)
& !stack:%?a %?b ?stack
& ( !arg:"+"&!a+!b
| !arg:"-"&-1*!a+!b
| !arg:"*"&!a*!b
| !arg:"/"&!a*!b^-1
| !a^!b
)
| !arg
)
!stack
: ?stack
)
. vap\$((=.!arg).get'(,STR)." ")
)
& out\$!stack
)

Input from keyboard:

3 4 2 * 1 5 - 2 3 ^ ^ / +

Output:

3
3 4
3 4 2
3 4 2 *
3 8 1
3 8 1 5
3 8 1 5 -
3 8 -4 2
3 8 -4 2 3
3 8 -4 2 3 ^
3 8 -4 9 ^
3 8 1/6561 /
3 1/52488 +
157465/52488
{!} 157465/52488

## C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

void die(const char *msg)
{
fprintf(stderr, "%s", msg);
abort();
}

#define MAX_D 256
double stack[MAX_D];
int depth;

void push(double v)
{
if (depth >= MAX_D) die("stack overflow\n");
stack[depth++] = v;
}

double pop()
{
if (!depth) die("stack underflow\n");
return stack[--depth];
}

double rpn(char *s)
{
double a, b;
int i;
char *e, *w = " \t\n\r\f";

for (s = strtok(s, w); s; s = strtok(0, w)) {
a = strtod(s, &e);
if (e > s)		printf(" :"), push(a);
#define binop(x) printf("%c:", *s), b = pop(), a = pop(), push(x)
else if (*s == '+')	binop(a + b);
else if (*s == '-')	binop(a - b);
else if (*s == '*')	binop(a * b);
else if (*s == '/')	binop(a / b);
else if (*s == '^')	binop(pow(a, b));
#undef binop
else {
fprintf(stderr, "'%c': ", *s);
die("unknown oeprator\n");
}
for (i = depth; i-- || 0 * putchar('\n'); )
printf(" %g", stack[i]);
}

if (depth != 1) die("stack leftover\n");

return pop();
}

int main(void)
{
char s[] = " 3 4 2 * 1 5 - 2 3 ^ ^ / + ";
printf("%g\n", rpn(s));
return 0;
}

It's also possible to parse RPN string backwards and recursively; good luck printing out your token stack as a table: there isn't one.

#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <string.h>
#include <math.h>

#define die(msg) fprintf(stderr, msg"\n"), abort();
double get(const char *s, const char *e, char **new_e)
{
const char *t;
double a, b;

for (e--; e >= s && isspace(*e); e--);
for (t = e; t > s && !isspace(t[-1]); t--);

if (t < s) die("underflow");

#define get2(expr) b = get(s, t, (char **)&t), a = get(s, t, (char **)&t), a = expr
a = strtod(t, (char **)&e);
if (e <= t) {
if	(t[0] == '+') get2(a + b);
else if (t[0] == '-') get2(a - b);
else if (t[0] == '*') get2(a * b);
else if (t[0] == '/') get2(a / b);
else if (t[0] == '^') get2(pow(a, b));
else {
fprintf(stderr, "'%c': ", t[0]);
die("unknown token");
}
}
#undef get2

*(const char **)new_e = t;
return a;
}

double rpn(const char *s)
{
const char *e = s + strlen(s);
double v = get(s, e, (char**)&e);

while (e > s && isspace(e[-1])) e--;
if (e == s) return v;

fprintf(stderr, "\"%.*s\": ", e - s, s);
die("front garbage");
}

int main(void)
{
printf("%g\n", rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +"));
return 0;
}

## C#

using System;
using System.Collections.Generic;
using System.Linq;
using System.Globalization;

namespace RPNEvaluator
{
class RPNEvaluator
{
static void Main(string[] args)
{

string rpn = "3 4 2 * 1 5 - 2 3 ^ ^ / +";
Console.WriteLine("{0}\n", rpn);

decimal result = CalculateRPN(rpn);
Console.WriteLine("\nResult is {0}", result);
}

static decimal CalculateRPN(string rpn)
{
string[] rpnTokens = rpn.Split(' ');
Stack<decimal> stack = new Stack<decimal>();
decimal number = decimal.Zero;

foreach (string token in rpnTokens)
{
if (decimal.TryParse(token, out number))
{
stack.Push(number);
}
else
{
switch (token)
{
case "^":
case "pow":
{
number = stack.Pop();
stack.Push((decimal)Math.Pow((double)stack.Pop(), (double)number));
break;
}
case "ln":
{
stack.Push((decimal)Math.Log((double)stack.Pop(), Math.E));
break;
}
case "sqrt":
{
stack.Push((decimal)Math.Sqrt((double)stack.Pop()));
break;
}
case "*":
{
stack.Push(stack.Pop() * stack.Pop());
break;
}
case "/":
{
number = stack.Pop();
stack.Push(stack.Pop() / number);
break;
}
case "+":
{
stack.Push(stack.Pop() + stack.Pop());
break;
}
case "-":
{
number = stack.Pop();
stack.Push(stack.Pop() - number);
break;
}
default:
Console.WriteLine("Error in CalculateRPN(string) Method!");
break;
}
}
PrintState(stack);
}

return stack.Pop();
}

static void PrintState(Stack<decimal> stack)
{
decimal[] arr = stack.ToArray();

for (int i = arr.Length - 1; i >= 0; i--)
{
Console.Write("{0,-8:F3}", arr[i]);
}

Console.WriteLine();
}
}
}
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / +

3.000
3.000   4.000
3.000   4.000   2.000
3.000   8.000
3.000   8.000   1.000
3.000   8.000   1.000   5.000
3.000   8.000   -4.000
3.000   8.000   -4.000  2.000
3.000   8.000   -4.000  2.000   3.000
3.000   8.000   -4.000  8.000
3.000   8.000   65536.000
3.000   0.000
3.000

Result is 3.0001220703125

## C++

#include <vector>
#include <string>
#include <sstream>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <iterator>
#include <cstdlib>

double rpn(const std::string &expr){
std::istringstream iss(expr);
std::vector<double> stack;
std::cout << "Input\tOperation\tStack after" << std::endl;
std::string token;
while (iss >> token) {
std::cout << token << "\t";
double tokenNum;
if (std::istringstream(token) >> tokenNum) {
std::cout << "Push\t\t";
stack.push_back(tokenNum);
} else {
std::cout << "Operate\t\t";
double secondOperand = stack.back();
stack.pop_back();
double firstOperand = stack.back();
stack.pop_back();
if (token == "*")
stack.push_back(firstOperand * secondOperand);
else if (token == "/")
stack.push_back(firstOperand / secondOperand);
else if (token == "-")
stack.push_back(firstOperand - secondOperand);
else if (token == "+")
stack.push_back(firstOperand + secondOperand);
else if (token == "^")
stack.push_back(std::pow(firstOperand, secondOperand));
else { //just in case
std::cerr << "Error" << std::endl;
std::exit(1);
}
}
std::copy(stack.begin(), stack.end(), std::ostream_iterator<double>(std::cout, " "));
std::cout << std::endl;
}
return stack.back();
}

int main() {
std::string s = " 3 4 2 * 1 5 - 2 3 ^ ^ / + ";
std::cout << "Final answer: " << rpn(s) << std::endl;

return 0;
}
Output:
Input	Operation	Stack after
3	Push		3
4	Push		3 4
2	Push		3 4 2
*	Operate		3 8
1	Push		3 8 1
5	Push		3 8 1 5
-	Operate		3 8 -4
2	Push		3 8 -4 2
3	Push		3 8 -4 2 3
^	Operate		3 8 -4 8
^	Operate		3 8 65536
/	Operate		3 0.00012207
+	Operate		3.00012

## Ceylon

import ceylon.collection {

ArrayList
}

shared void run() {

value ops = map {
"+" -> plus<Float>,
"*" -> times<Float>,
"-" -> ((Float a, Float b) => a - b),
"/" -> ((Float a, Float b) => a / b),
"^" -> ((Float a, Float b) => a ^ b)
};

void printTableRow(String|Float token, String description, {Float*} stack) {
}

function calculate(String input) {

value stack = ArrayList<Float>();
value tokens = input.split().map((String element)
=> if(ops.keys.contains(element)) then element else parseFloat(element));

print("Token   Operation                     Stack");

for(token in tokens.coalesced) {
if(is Float token) {
stack.push(token);
printTableRow(token, "push", stack);
} else if(exists op = ops[token], exists first = stack.pop(), exists second = stack.pop()) {
value result = op(second, first);
stack.push(result);
printTableRow(token, "perform ``token`` on ``formatFloat(second, 1, 1)`` and ``formatFloat(first, 1, 1)``", stack);
} else {
}
}
return stack.pop();
}

print(calculate("3 4 2 * 1 5 - 2 3 ^ ^ / +"));
}
Output:
Token   Operation                     Stack
3.0     push                          { 3.0 }
4.0     push                          { 3.0, 4.0 }
2.0     push                          { 3.0, 4.0, 2.0 }
*       perform * on 4.0 and 2.0      { 3.0, 8.0 }
1.0     push                          { 3.0, 8.0, 1.0 }
5.0     push                          { 3.0, 8.0, 1.0, 5.0 }
-       perform - on 1.0 and 5.0      { 3.0, 8.0, -4.0 }
2.0     push                          { 3.0, 8.0, -4.0, 2.0 }
3.0     push                          { 3.0, 8.0, -4.0, 2.0, 3.0 }
^       perform ^ on 2.0 and 3.0      { 3.0, 8.0, -4.0, 8.0 }
^       perform ^ on -4.0 and 8.0     { 3.0, 8.0, 65536.0 }
/       perform / on 8.0 and 65536.0  { 3.0, 1.220703125E-4 }
+       perform + on 3.0 and 0.0      { 3.0001220703125 }
3.0001220703125

## Clojure

This would be a lot simpler and generic if we were allowed to use something other than ^ for exponentiation. ^ isn't a legal clojure symbol.

(ns rosettacode.parsing-rpn-calculator-algorithm
(:require clojure.math.numeric-tower
clojure.string
clojure.pprint))

(def operators
"the only allowable operators for our calculator"
{"+" +
"-" -
"*" *
"/" /
"^" clojure.math.numeric-tower/expt})

(defn rpn
"takes a string and returns a lazy-seq of all the stacks"
[string]
(letfn [(rpn-reducer [stack item] ; this takes a stack and one item and makes a new stack
(if (contains? operators item)
(let [operand-1 (peek stack) ; if we used lists instead of vectors, we could use destructuring, but stacks would look backwards
stack-1 (pop stack)]   ;we're assuming that all the operators are binary
(conj (pop stack-1)
((operators item) (peek stack-1) operand-1)))
(conj stack (Long. item))))] ; if it wasn't an operator, we'll assume it's a long. Could choose bigint, or even read-line
(reductions rpn-reducer [] (clojure.string/split string #"\s+")))) ;reductions is like reduce only shows all the intermediate steps

(let [stacks (rpn "3 4 2 * 1 5 - 2 3 ^ ^ / +")] ;bind it so we can output the answer separately.
(println "stacks: ")
(clojure.pprint/pprint stacks)
(print "answer:" (->> stacks last first)))
Output:

stacks: ([]

[3]
[3 4]
[3 4 2]
[3 8]
[3 8 1]
[3 8 1 5]
[3 8 -4]
[3 8 -4 2]
[3 8 -4 2 3]
[3 8 -4 8]
[3 8 65536]
[3 1/8192]
[24577/8192])

## CLU

% Split string by whitespace
split = iter (expr: string) yields (string)
own whitespace: string := " \r\n\t"
cur: array[char] := array[char]\$[]
for c: char in string\$chars(expr) do
if string\$indexc(c, whitespace) = 0 then
else
if array[char]\$empty(cur) then continue end
yield(string\$ac2s(cur))
cur := array[char]\$[]
end
end
if ~array[char]\$empty(cur) then
yield(string\$ac2s(cur))
end
end split

% Tokenize a RPN expression
token = oneof[number: real, op: char]
tokens = iter (expr: string) yields (token) signals (parse_error(string))
own operators: string := "+-*/^"
for t: string in split(expr) do
if string\$size(t) = 1 cand string\$indexc(t[1], operators)~=0 then
yield(token\$make_op(t[1]))
else
yield(token\$make_number(real\$parse(t)))
signal parse_error(t)
end
end
end
end tokens

% Print the stack
print_stack = proc (stack: array[real])
po: stream := stream\$primary_output()
for num: real in array[real]\$elements(stack) do
stream\$puts(po, f_form(num, 5, 5) || " ")
end
stream\$putl(po, "")
end print_stack

% Evaluate an expression, printing the stack at each point
evaluate_rpn = proc (expr: string) returns (real) signals (parse_error(string), bounds)
stack: array[real] := array[real]\$[]
for t: token in tokens(expr) do
tagcase t
tag number (n: real): array[real]\$addh(stack, n)
tag op (f: char):
r: real := array[real]\$remh(stack)
l: real := array[real]\$remh(stack)
n: real
if     f='+' then n := l+r
elseif f='-' then n := l-r
elseif f='*' then n := l*r
elseif f='/' then n := l/r
elseif f='^' then n := l**r
end
end
print_stack(stack)
end resignal parse_error
return(array[real]\$reml(stack))
end evaluate_rpn

start_up = proc ()
po: stream := stream\$primary_output()
expr: string := "3 4 2 * 1 5 - 2 3 ^ ^ / +"

stream\$putl(po, "Expression: " || expr)
stream\$putl(po, "Result: " || f_form(evaluate_rpn(expr), 5, 5))
end start_up
Output:
Expression: 3 4 2 * 1 5 - 2 3 ^ ^ / +
3.00000
3.00000 4.00000
3.00000 4.00000 2.00000
3.00000 8.00000
3.00000 8.00000 1.00000
3.00000 8.00000 1.00000 5.00000
3.00000 8.00000 -4.00000
3.00000 8.00000 -4.00000 2.00000
3.00000 8.00000 -4.00000 2.00000 3.00000
3.00000 8.00000 -4.00000 8.00000
3.00000 8.00000 65535.99240
3.00000 0.00012
3.00012
Result: 3.00012

## COBOL

IDENTIFICATION DIVISION.
PROGRAM-ID. RPN.
AUTHOR.  Bill Gunshannon.
INSTALLATION.
DATE-WRITTEN.  9 Feb 2020.
************************************************************
** Program Abstract:
**   Create a stack-based evaluator for an expression in
**   reverse Polish notation (RPN)   that also shows the
**   changes in the stack as each individual token is
**   processed as a table.
************************************************************

DATA DIVISION.

WORKING-STORAGE SECTION.

01  LineIn               PIC X(25).
01  IP                   PIC 99
VALUE 1.
01  CInNum               PIC XXXX.

01  Stack                PIC S999999V9999999
OCCURS  50 times.
01  SP                   PIC 99
VALUE 1.
01  Operator             PIC X.
01  Value1               PIC S999999V9999999.
01  Value2               PIC S999999V9999999.
01  Result               PIC S999999V9999999.
01  Idx                  PIC 99.
01  FormatNum            PIC ZZZZZZ9.9999999.
01  Zip                  PIC X.

PROCEDURE DIVISION.

Main-Program.
DISPLAY "Enter the RPN Equation: "
ACCEPT LineIn.

PERFORM UNTIL IP GREATER THAN
FUNCTION STORED-CHAR-LENGTH(LineIn)

UNSTRING LineIn DELIMITED BY SPACE INTO CInNum
WITH POINTER IP

MOVE CInNum TO Operator

PERFORM Do-Operation

PERFORM Show-Stack

END-PERFORM.

DISPLAY "End Result: " FormatNum

STOP RUN.

Do-Operation.

EVALUATE Operator
WHEN "+"
PERFORM Pop
Compute Result = Value2 + Value1
PERFORM Push

WHEN "-"
PERFORM Pop
Compute Result = Value2 - Value1
PERFORM Push

WHEN "*"
PERFORM Pop
Compute Result = Value2 * Value1
PERFORM Push

WHEN "/"
PERFORM Pop
Compute Result = Value2 / Value1
PERFORM Push

WHEN "^"
PERFORM Pop
Compute Result = Value2 ** Value1
PERFORM Push

WHEN NUMERIC
MOVE Operator TO Result
PERFORM Push
END-EVALUATE.

Show-Stack.

DISPLAY "STACK: " WITH NO ADVANCING.
MOVE 1 TO Idx.
PERFORM UNTIL (Idx = SP)
MOVE Stack(Idx) TO FormatNum
IF Stack(Idx) IS NEGATIVE
THEN
DISPLAY "    -" FUNCTION TRIM(FormatNum)
ELSE
END-IF
END-PERFORM.
DISPLAY " ".

Push.

MOVE Result TO Stack(SP)

Pop.

SUBTRACT 1 FROM SP
MOVE Stack(SP) TO Value1
SUBTRACT 1 FROM SP
MOVE Stack(SP) TO Value2.

END-PROGRAM.
Output:

Enter the RPN Equation: 3 4 2 * 1 5 - 2 3 ^ ^ / +
STACK:       3.0000000
STACK:       3.0000000      4.0000000
STACK:       3.0000000      4.0000000      2.0000000
STACK:       3.0000000      8.0000000
STACK:       3.0000000      8.0000000      1.0000000
STACK:       3.0000000      8.0000000      1.0000000      5.0000000
STACK:       3.0000000      8.0000000    -4.0000000
STACK:       3.0000000      8.0000000    -4.0000000      2.0000000
STACK:       3.0000000      8.0000000    -4.0000000      2.0000000      3.0000000
STACK:       3.0000000      8.0000000    -4.0000000      8.0000000
STACK:       3.0000000      8.0000000  65536.0000000
STACK:       3.0000000      0.0001220
STACK:       3.0001220
End Result:       3.0001220

## Common Lisp

(setf (symbol-function '^) #'expt)  ; Make ^ an alias for EXPT

(defun print-stack (token stack)
(format T "~a: ~{~a ~}~%" token (reverse stack)))

(defun rpn (tokens &key stack verbose )
(cond
((and (not tokens) (not stack)) 0)
((not tokens) (car stack))
(T
(let* ((current (car tokens))
(next-stack (if (numberp current)
(cons current stack)
(let* ((arg2 (car stack))
(fun (car tokens)))
(cons (funcall fun arg1 arg2) (cddr stack))))))
(when verbose
(print-stack current next-stack))
(rpn (cdr tokens) :stack next-stack :verbose verbose)))))
Output:
>(defparameter *tokens* '(3 4 2 * 1 5 - 2 3 ^ ^ / +))

*TOKENS*
> (rpn *tokens*)

24577/8192
> (rpn *tokens* :verbose T)
3: 3
4: 3 4
2: 3 4 2
*: 3 8
1: 3 8 1
5: 3 8 1 5
-: 3 8 -4
2: 3 8 -4 2
3: 3 8 -4 2 3
^: 3 8 -4 8
^: 3 8 65536
/: 3 1/8192
+: 24577/8192
24577/8192

## D

Translation of: Go
import std.stdio, std.string, std.conv, std.typetuple;

void main() {
auto input = "3 4 2 * 1 5 - 2 3 ^ ^ / +";
writeln("For postfix expression: ", input);
writeln("\nToken            Action            Stack");
real[] stack;
foreach (tok; input.split()) {
auto action = "Apply op to top of stack";
switch (tok) {
foreach (o; TypeTuple!("+", "-", "*", "/", "^")) {
case o:
mixin("stack[\$ - 2]" ~
(o == "^" ? "^^" : o) ~ "=stack[\$ - 1];");
stack.length--;
break;
}
break;
default:
action = "Push num onto top of stack";
stack ~= to!real(tok);
}
writefln("%3s    %-26s  %s", tok, action, stack);
}
writeln("\nThe final value is ", stack[0]);
}
Output:
For postfix expression: 3 4 2 * 1 5 - 2 3 ^ ^ / +

Token            Action            Stack
3    Push num onto top of stack  [3]
4    Push num onto top of stack  [3, 4]
2    Push num onto top of stack  [3, 4, 2]
*    Apply op to top of stack    [3, 8]
1    Push num onto top of stack  [3, 8, 1]
5    Push num onto top of stack  [3, 8, 1, 5]
-    Apply op to top of stack    [3, 8, -4]
2    Push num onto top of stack  [3, 8, -4, 2]
3    Push num onto top of stack  [3, 8, -4, 2, 3]
^    Apply op to top of stack    [3, 8, -4, 8]
^    Apply op to top of stack    [3, 8, 65536]
/    Apply op to top of stack    [3, 0.00012207]
+    Apply op to top of stack    [3.00012]

The final value is 3.00012

## Delphi

Works with: Delphi version 6.0

This is a good example of creating s simple object to create a stakc for use in parsing the data.

{This code normally exists in a library, but is presented here for clarity}

function ExtractToken(S: string; Sep: char; var P: integer): string;
{Extract token from S, starting at P up to but not including Sep}
{Terminates with P pointing past Sep or past end of string}
var C: char;
begin
Result:='';
while P<=Length(S) do
begin
C:=S[P]; Inc(P);
if C=Sep then break
else Result:=Result+C;
end;
end;

{Create stack object to handle parsing}

type TRealStack = class(TObject)
private
Data: array of double;
protected
public
function GetStackStr: string;
procedure Push(D: double);
function Pop: double;
end;

procedure TRealStack.Push(D: double);
{Push double on stack}
begin
SetLength(Data,Length(Data)+1);
Data[High(Data)]:=D;
end;

function TRealStack.Pop: double;
{Pop double off stack, raises exception if stack empty}
begin
if Length(Data)<1 then raise exception.Create('Stack Empty');
Result:=Data[High(Data)];
SetLength(Data,Length(Data)-1);
end;

function TRealStack.GetStackStr: string;
{Get string representation of stack data}
var I: integer;
begin
Result:='';
for I:=0 to High(Data) do
begin
if I<>0 then Result:=Result+', ';
Result:=Result+FloatToStrF(Data[I],ffGeneral,18,4);
end;
end;

procedure RPNParser(Memo: TMemo; S: string);
{Parse RPN string and display all operations}
var I: integer;
var Stack: TRealStack;
var Token: string;
var D: double;

function HandleOperator(S: string): boolean;
{Handle numerical operator command}
var Arg1,Arg2: double;
begin
Result:=False;
{Empty comand string? }
if Length(S)>1 then exit;
{Invalid command? }
if not (S[1] in ['+','-','*','/','^']) then exit;
{Get arguments off stack}
Arg1:=Stack.Pop; Arg2:=Stack.Pop;
Result:=True;
{Decode command}
case S[1] of
'+': Stack.Push(Arg2 + Arg1);
'-': Stack.Push(Arg2 - Arg1);
'*': Stack.Push(Arg2 * Arg1);
'/': Stack.Push(Arg2 / Arg1);
'^': Stack.Push(Power(Arg2,Arg1));
else Result:=False;
end;
end;

begin
Stack:=TRealStack.Create;
try
I:=1;
while true do
begin
{Extract one token from string}
Token:=ExtractToken(S,' ',I);
{Exit if no more data}
if Token='' then break;
{If token is a number convert it to a double otherwise, process an operator}
if Token[1] in ['0'..'9'] then Stack.Push(StrToFloat(Token))
else if not HandleOperator(Token) then raise Exception.Create('Illegal Token: '+Token);
end;
finally Stack.Free; end;
end;

procedure ShowRPNParser(Memo: TMemo);
var S: string;
begin
S:='3 4 2 * 1 5 - 2 3 ^ ^ / + ';
RPNParser(Memo,S);
end;
Output:
3 [3]
4 [3, 4]
2 [3, 4, 2]
* [3, 8]
1 [3, 8, 1]
5 [3, 8, 1, 5]
- [3, 8, -4]
2 [3, 8, -4, 2]
3 [3, 8, -4, 2, 3]
^ [3, 8, -4, 8]
^ [3, 8, 65536]
/ [3, 0.0001220703125]
+ [3.0001220703125]
Elapsed Time: 16.409 ms.

## EchoLisp

;; RPN (postfix) evaluator

(lib 'hash)

(define OPS (make-hash))
(hash-set OPS "^" expt)
(hash-set OPS "*" *)
(hash-set OPS "/" //) ;; float divide
(hash-set OPS "+" +)
(hash-set OPS "-" -)

(define (op? op) (hash-ref OPS op))

;; algorithm : https://en.wikipedia.org/wiki/Reverse_Polish_notation#Postfix_algorithm

(define (calculator rpn S)
(for ((token rpn))
(if (op? token)
(let [(op2 (pop S)) (op1 (pop S))]
(unless (and op1 op2) (error "cannot calculate expression at:" token))
(push S ((op? token) op1 op2))
(writeln op1 token op2 "→" (stack-top S)))
(push S (string->number token))))
(pop S))

(define S (stack 'S))
(calculator (text-parse rpn) S ))
Output:
(task "3 4 2 * 1 5 - 2 3 ^ ^ / +")

4      *     2     →     8
1      -     5     →     -4
2      ^     3     →     8
-4     ^     8     →     65536
8     /     65536     →     0.0001220703125
3     +     0.0001220703125     →     3.0001220703125

→ 3.0001220703125

;; RATIONAL CALCULATOR
(hash-set OPS "/" /) ;; rational divide
(task "3 4 2 * 1 5 - 2 3 ^ ^ / +")

4      *     2     →     8
1      -     5     →     -4
2      ^     3     →     8
-4     ^     8     →     65536
8     /     65536     →     1/8192
3     +     1/8192     →     24577/8192

→ 24577/8192

## Ela

type OpType = Push | Operate
deriving Show

type Op = Op (OpType typ) input stack
deriving Show

parse str = split " " str

eval stack []      = []
eval stack (x::xs) = op :: eval nst xs
where (op, nst)  = conv x stack
conv "+"@x = operate x (+)
conv "-"@x = operate x (-)
conv "*"@x = operate x (*)
conv "/"@x = operate x (/)
conv "^"@x = operate x (**)
conv x     = \stack ->
let n = gread x::stack in
(Op Push x n, n)
operate input fn (x::y::ys) =
let n = (y `fn` x) :: ys in
(Op Operate input n, n)

print_line (Op typ input stack) = do
putStr input
putStr "\t"
put typ
putStr "\t\t"
putLn stack

print ((Op typ input stack)@x::xs) lv = print_line x `seq` print xs (head stack)
print [] lv = lv

print_result xs = do
putStrLn "Input\tOperation\tStack after"
res <- return \$ print xs 0
putStrLn ("Result: " ++ show res)

res = parse "3 4 2 * 1 5 - 2 3 ^ ^ / +" |> eval []
print_result res ::: IO
Output:
Input	Operation	Stack after
3	Push		[3]
4	Push		[4,3]
2	Push		[2,4,3]
*	Operate		[8,3]
1	Push		[1,8,3]
5	Push		[5,1,8,3]
-	Operate		[-4,8,3]
2	Push		[2,-4,8,3]
3	Push		[3,2,-4,8,3]
^	Operate		[8,-4,8,3]
^	Operate		[65536,8,3]
/	Operate		[0.0001220703f,3]
+	Operate		[3.000122f]
Result: 3.000122f

## Erlang

-module(rpn).
-export([eval/1]).

parse(Expression) ->
parse(string:tokens(Expression," "),[]).

parse([],Expression) ->
lists:reverse(Expression);
parse(["+"|Xs],Expression) ->
parse(Xs,[fun erlang:'+'/2|Expression]);
parse(["-"|Xs],Expression) ->
parse(Xs,[fun erlang:'-'/2|Expression]);
parse(["*"|Xs],Expression) ->
parse(Xs,[fun erlang:'*'/2|Expression]);
parse(["/"|Xs],Expression) ->
parse(Xs,[fun erlang:'/'/2|Expression]);
parse(["^"|Xs],Expression) ->
parse(Xs,[fun math:pow/2|Expression]);
parse([X|Xs],Expression) ->
{N,_} = string:to_integer(X),
parse(Xs,[N|Expression]).

%% The expression should be entered as a string of numbers and
%% operators separated by spaces. No error handling is included if
%% another string format is used.
eval(Expression) ->
eval(parse(Expression),[]).

eval([],[N]) ->
N;
eval([N|Exp],Stack) when is_number(N) ->
NewStack = [N|Stack],
print(NewStack),
eval(Exp,NewStack);
eval([F|Exp],[X,Y|Stack]) ->
NewStack = [F(Y,X)|Stack],
print(NewStack),
eval(Exp,NewStack).

print(Stack) ->
lists:map(fun (X) when is_integer(X) -> io:format("~12.12b ",[X]);
(X) when is_float(X) -> io:format("~12f ",[X]) end, Stack),
io:format("~n").
Output:
145> rpn:eval("3 4 2 * 1 5 - 2 3 ^ ^ / +").
3
4            3
2            4            3
8            3
1            8            3
5            1            8            3
-4            8            3
2           -4            8            3
3            2           -4            8            3
8.000000           -4            8            3
65536.000000            8            3
0.000122            3
3.000122
3.0001220703125

## F#

Translation of: OCaml

As interactive script

let reduce op = function
| b::a::r -> (op a b)::r
| _ -> failwith "invalid expression"

let interprete s = function
| "+" -> "add",    reduce ( + ) s
| "-" -> "subtr",  reduce ( - ) s
| "*" -> "mult",   reduce ( * ) s
| "/" -> "divide", reduce ( / ) s
| "^" -> "exp",    reduce ( ** ) s
| str -> "push", (System.Double.Parse str) :: s

let interp_and_show s inp =
let op,s'' = interprete s inp
printf "%5s%8s " inp op
List.iter (printf " %-6.3F") (List.rev s'')
printf "\n";
s''

let eval str =
printfn "Token  Action  Stack";
let ss = str.ToString().Split() |> Array.toList
List.fold interp_and_show [] ss
Output:
> eval "3 4 2 * 1 5 - 2 3 ^ ^ / +";;
Token  Action  Stack
3    push  3.000
4    push  3.000  4.000
2    push  3.000  4.000  2.000
*    mult  3.000  8.000
1    push  3.000  8.000  1.000
5    push  3.000  8.000  1.000  5.000
-   subtr  3.000  8.000  -4.000
2    push  3.000  8.000  -4.000 2.000
3    push  3.000  8.000  -4.000 2.000  3.000
^     exp  3.000  8.000  -4.000 8.000
^     exp  3.000  8.000  65536.000
/  divide  3.000  0.000
val it : float list = [3.00012207]

## Factor

Factor is a stack-based evaluator for an expression in reverse Polish notation. In the listener:

IN: scratchpad 3 4 2 * 1 5 - 2 3 ^ ^ / +

--- Data stack:
3+1/8192

To show intermediate steps:

{ 3 4 2 * 1 5 - 2 3 ^ ^ / + }
[ dup pprint bl 1quotation call get-datastack . ] each
Output:
3 { 3 }
4 { 3 4 }
2 { 3 4 2 }
* { 3 8 }
1 { 3 8 1 }
5 { 3 8 1 5 }
- { 3 8 -4 }
2 { 3 8 -4 2 }
3 { 3 8 -4 2 3 }
^ { 3 8 -4 8 }
^ { 3 8 65536 }
/ { 3 1/8192 }
+ { 3+1/8192 }

## Forth

Works with: gforth version 0.7.3

Forth is stack-based, so evaluation is direct:

: ^ over swap 1 ?do over * loop nip ;
s" 3 4 2 * 1 5 - 2 3 ^ ^ / +" evaluate .

To show intermediate steps:

: ^ over swap 1 ?do over * loop nip ;
: detail
begin
cr ." stack: " .s
bl word count dup
0<> while
." , read: " 2dup type evaluate
repeat
2drop
;
detail 3 4 2 * 1 5 - 2 3 ^ ^ / +
Output:
stack: <1> 3 , read: 4
stack: <2> 3 4 , read: 2
stack: <3> 3 4 2 , read: *
stack: <2> 3 8 , read: 1
stack: <3> 3 8 1 , read: 5
stack: <4> 3 8 1 5 , read: -
stack: <3> 3 8 -4 , read: 2
stack: <4> 3 8 -4 2 , read: 3
stack: <5> 3 8 -4 2 3 , read: ^
stack: <4> 3 8 -4 8 , read: ^
stack: <3> 3 8 65536 , read: /
stack: <2> 3 0 , read: +
stack: <1> 3  ok

## Fortran

Since the project is to demonstrate the workings of the scheme to evaluate a RPN text sequence, and the test example contains only single-digit numbers and single-character operators, there is no need to escalate to reading full integers or floating-point numbers, the code for which would swamp the details of the RPN evaluator. As a result, it is easy to scan the text via a DO-loop that works one character at a time since there is no backstepping, probing ahead, nor multi-symbol items that must be combined into a single "token" with states that must be remembered from one character to the next. With multi-character tokens, the scan would be changed to invocations of NEXTTOKEN that would lurch ahead accordingly.

The method is simple (the whole point of RPN) and the function prints a schedule of actions at each step. Possibly this semi-tabular output is what is meant by "as a table". Conveniently, all the operators take two operands and return one, so the SP accountancy can be shared. Unlike ! for example.

The source style is essentially F77 except for the trivial use of the PARAMETER statement, and CYCLE to GO TO the end of the loop when a space is encountered. With the introduction of unfixed-format source style came also the possible use of semicolons to cram more than one statement part on a line so that the CASE and its action statement can be spread across the page rather than use two lines in alternation: for this case a tabular layout results that is easier to read and check. Because the F90 MODULE protocol is not used, the function's type should be declared in the calling routine but the default type suffices.
REAL FUNCTION EVALRP(TEXT)	!Evaluates a Reverse Polish string.
Caution: deals with single digits only.
CHARACTER*(*) TEXT	!The RPN string.
INTEGER SP,STACKLIMIT		!Needed for the evaluation.
PARAMETER (STACKLIMIT = 6)	!This should do.
REAL*8 STACK(STACKLIMIT)		!Though with ^ there's no upper limit.
INTEGER L,D		!Assistants for the scan.
CHARACTER*4 DEED		!A scratchpad for the annotation.
CHARACTER*1 C		!The character of the moment.
WRITE (6,1) TEXT	!A function that writes messages... Improper.
1   FORMAT ("Evaluation of the Reverse Polish string ",A,//	!Still, it's good to see stuff.
1   "Char Token Action  SP:Stack...")	!Such as a heading for the trace.
SP = 0			!Commence with the stack empty.
STACK = -666		!This value should cause trouble.
DO L = 1,LEN(TEXT)	!Step through the text.
C = TEXT(L:L)			!Grab a character.
IF (C.LE." ") CYCLE		!Boring.
D = ICHAR(C) - ICHAR("0")	!Uncouth test to check for a digit.
IF (D.GE.0 .AND. D.LE.9) THEN	!Is it one?
SP = SP + 1				!By going up one.
IF (SP.GT.STACKLIMIT) STOP "Stack overflow!"	!Or, maybe not.
STACK(SP) = D			!And stashing the value.
ELSE				!Otherwise, it must be an operator.
IF (SP.LT.2) STOP "Stack underflow!"	!They all require two operands.
DEED = "XEQ"		!So, I'm about to do so.
SELECT CASE(C)		!Which one this time?
CASE("+"); STACK(SP - 1) = STACK(SP - 1) + STACK(SP)	!A + B = B + A, so it is easy.
CASE("-"); STACK(SP - 1) = STACK(SP - 1) - STACK(SP)	!A is in STACK(SP - 1), B in STACK(SP)
CASE("*"); STACK(SP - 1) = STACK(SP - 1)*STACK(SP)		!Again, order doesn't count.
CASE("/"); STACK(SP - 1) = STACK(SP - 1)/STACK(SP)		!But for division, A/B becomes A B /
CASE("^"); STACK(SP - 1) = STACK(SP - 1)**STACK(SP)	!So, this way around.
CASE DEFAULT		!This should never happen!
STOP "Unknown operator!"	!If the RPN script is indeed correct.
END SELECT			!So much for that operator.
SP = SP - 1		!All of them take two operands and make one.
END IF		!So much for that item.
WRITE (6,2) L,C,DEED,SP,STACK(1:SP)	!Reveal the state now.
2     FORMAT (I4,A6,A7,I4,":",66F14.6)	!Aligned with the heading of FORMAT 1.
END DO			!On to the next symbol.
EVALRP = STACK(1)	!The RPN string being correct, this is the result.
END	!Simple enough!

PROGRAM HSILOP
REAL V
V = EVALRP("3 4 2 * 1 5 - 2 3 ^ ^ / +")	!The specified example.
WRITE (6,*) "Result is...",V
END

Output...

Evaluation of the Reverse Polish string 3 4 2 * 1 5 - 2 3 ^ ^ / +

Char Token Action  SP:Stack...
3     4   Load   2:      3.000000      4.000000
5     2   Load   3:      3.000000      4.000000      2.000000
7     *   XEQ    2:      3.000000      8.000000
9     1   Load   3:      3.000000      8.000000      1.000000
11     5   Load   4:      3.000000      8.000000      1.000000      5.000000
13     -   XEQ    3:      3.000000      8.000000     -4.000000
15     2   Load   4:      3.000000      8.000000     -4.000000      2.000000
17     3   Load   5:      3.000000      8.000000     -4.000000      2.000000      3.000000
19     ^   XEQ    4:      3.000000      8.000000     -4.000000      8.000000
21     ^   XEQ    3:      3.000000      8.000000  65536.000000
23     /   XEQ    2:      3.000000      0.000122
25     +   XEQ    1:      3.000122
Result is...   3.000122

## FunL

def evaluate( expr ) =
stack = []

for token <- expr.split( '''\s+''' )
case number( token )
Some( n ) ->
stack = n : stack
println( "push \$token: \${stack.reversed()}" )
None ->
case {'+': (+), '-': (-), '*': (*), '/': (/), '^': (^)}.>get( token )
Some( op ) ->
println( "perform \$token: \${stack.reversed()}" )
None -> error( "unrecognized operator '\$token'" )

res = evaluate( '3 4 2 * 1 5 - 2 3 ^ ^ / +' )
println( res + (if res is Integer then '' else " or \${float(res)}") )
Output:
push 3: [3]
push 4: [3, 4]
push 2: [3, 4, 2]
perform *: [3, 8]
push 1: [3, 8, 1]
push 5: [3, 8, 1, 5]
perform -: [3, 8, -4]
push 2: [3, 8, -4, 2]
push 3: [3, 8, -4, 2, 3]
perform ^: [3, 8, -4, 8]
perform ^: [3, 8, 65536]
perform /: [3, 1/8192]
perform +: [24577/8192]
24577/8192 or 3.0001220703125

## Go

No error checking.

package main

import (
"fmt"
"math"
"strconv"
"strings"
)

var input = "3 4 2 * 1 5 - 2 3 ^ ^ / +"

func main() {
fmt.Printf("For postfix %q\n", input)
fmt.Println("\nToken            Action            Stack")
var stack []float64
for _, tok := range strings.Fields(input) {
action := "Apply op to top of stack"
switch tok {
case "+":
stack[len(stack)-2] += stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "-":
stack[len(stack)-2] -= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "*":
stack[len(stack)-2] *= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "/":
stack[len(stack)-2] /= stack[len(stack)-1]
stack = stack[:len(stack)-1]
case "^":
stack[len(stack)-2] =
math.Pow(stack[len(stack)-2], stack[len(stack)-1])
stack = stack[:len(stack)-1]
default:
action = "Push num onto top of stack"
f, _ := strconv.ParseFloat(tok, 64)
stack = append(stack, f)
}
fmt.Printf("%3s    %-26s  %v\n", tok, action, stack)
}
fmt.Println("\nThe final value is", stack[0])
}
Output:
For postfix "3 4 2 * 1 5 - 2 3 ^ ^ / +"

Token            Action            Stack
3    Push num onto top of stack  [3]
4    Push num onto top of stack  [3 4]
2    Push num onto top of stack  [3 4 2]
*    Apply op to top of stack    [3 8]
1    Push num onto top of stack  [3 8 1]
5    Push num onto top of stack  [3 8 1 5]
-    Apply op to top of stack    [3 8 -4]
2    Push num onto top of stack  [3 8 -4 2]
3    Push num onto top of stack  [3 8 -4 2 3]
^    Apply op to top of stack    [3 8 -4 8]
^    Apply op to top of stack    [3 8 65536]
/    Apply op to top of stack    [3 0.0001220703125]
+    Apply op to top of stack    [3.0001220703125]

The final value is 3.0001220703125

## Groovy

def evaluateRPN(expression) {
def stack = [] as Stack
def binaryOp = { action -> return { action.call(stack.pop(), stack.pop()) } }
def actions = [
'+': binaryOp { a, b -> b + a },
'-': binaryOp { a, b -> b - a },
'*': binaryOp { a, b -> b * a },
'/': binaryOp { a, b -> b / a },
'^': binaryOp { a, b -> b ** a }
]
expression.split(' ').each { item ->
def action = actions[item] ?: { item as BigDecimal }
stack.push(action.call())

println "\$item: \$stack"
}
assert stack.size() == 1 : "Unbalanced Expression: \$expression (\$stack)"
stack.pop()
}

Test

println evaluateRPN('3 4 2 * 1 5 - 2 3 ^ ^ / +')
Output:
3: [3]
4: [3, 4]
2: [3, 4, 2]
*: [3, 8]
1: [3, 8, 1]
5: [3, 8, 1, 5]
-: [3, 8, -4]
2: [3, 8, -4, 2]
3: [3, 8, -4, 2, 3]
^: [3, 8, -4, 8]
^: [3, 8, 65536]
/: [3, 0.0001220703125]
+: [3.0001220703125]
3.0001220703125

Pure RPN calculator

calcRPN :: String -> [Double]
calcRPN = foldl interprete [] . words

interprete s x
| x `elem` ["+","-","*","/","^"] = operate x s
where
operate op (x:y:s) = case op of
"+" -> x + y:s
"-" -> y - x:s
"*" -> x * y:s
"/" -> y / x:s
"^" -> y ** x:s
λ> calcRPN "3 4 +"
[7.0]

λ> calcRPN "3 4 2 * 1 5 - 2 3 ^ ^ / +"
[3.0001220703125]

Calculation logging

Pure logging. Log as well as a result could be used as a data.

calcRPNLog :: String -> ([Double],[(String, [Double])])
where result = scanl interprete [] commands
commands = words input
mkLog [] = ([], [])
mkLog res = (snd \$ last res, res)
λ> calcRPNLog "3 4 +"
([7.0],[("3",[3.0]),("4",[4.0,3.0]),("+",[7.0])])

λ> mapM_ print \$ snd \$ calcRPNLog "3 4 2 * 1 5 - 2 3 ^ ^ / +"
("3",[3.0])
("4",[4.0,3.0])
("2",[2.0,4.0,3.0])
("*",[8.0,3.0])
("1",[1.0,8.0,3.0])
("5",[5.0,1.0,8.0,3.0])
("-",[-4.0,8.0,3.0])
("2",[2.0,-4.0,8.0,3.0])
("3",[3.0,2.0,-4.0,8.0,3.0])
("^",[8.0,-4.0,8.0,3.0])
("^",[65536.0,8.0,3.0])
("/",[1.220703125e-4,3.0])
("+",[3.0001220703125])

Logging as a side effect. Calculator returns result in IO context:

calcRPNIO :: String -> IO [Double]
calcRPNIO = foldM (verbose interprete) [] . words

verbose f s x = write (x ++ "\t" ++ show res ++ "\n") >> return res
where res = f s x
λ> calcRPNIO "3 4 +"
3	[3.0]
4	[4.0,3.0]
+	[7.0]
[7.0]

λ> calcRPNIO "3 4 2 * 1 5 - 2 3 ^ ^ / +"
3	[3.0]
4	[4.0,3.0]
2	[2.0,4.0,3.0]
*	[8.0,3.0]
1	[1.0,8.0,3.0]
5	[5.0,1.0,8.0,3.0]
-	[-4.0,8.0,3.0]
2	[2.0,-4.0,8.0,3.0]
3	[3.0,2.0,-4.0,8.0,3.0]
^	[8.0,-4.0,8.0,3.0]
^	[65536.0,8.0,3.0]
/	[1.220703125e-4,3.0]
+	[3.0001220703125]
[3.0001220703125]

Or even more general (requires FlexibleInstances and TypeFamilies extensions).

Some universal definitions:

class Monad m => Logger m where
write :: String -> m ()

instance Logger IO where write = putStr
instance a ~ String => Logger (Writer a) where write = tell

verbose2 f x y = write (show x ++ " " ++
show y ++ " ==> " ++
show res ++ "\n") >> return res
where res = f x y

The use case:

calcRPNM :: Logger m => String -> m [Double]
calcRPNM = foldM (verbose interprete) [] . words
Output:
in REPL
λ> calcRPNM "3 4 2 * 1 5 - 2 3 ^ ^ / +"
[] "3" ==> [3.0]
[3.0] "4" ==> [4.0,3.0]
[4.0,3.0] "2" ==> [2.0,4.0,3.0]
[2.0,4.0,3.0] "*" ==> [8.0,3.0]
[8.0,3.0] "1" ==> [1.0,8.0,3.0]
[1.0,8.0,3.0] "5" ==> [5.0,1.0,8.0,3.0]
[5.0,1.0,8.0,3.0] "-" ==> [-4.0,8.0,3.0]
[-4.0,8.0,3.0] "2" ==> [2.0,-4.0,8.0,3.0]
[2.0,-4.0,8.0,3.0] "3" ==> [3.0,2.0,-4.0,8.0,3.0]
[3.0,2.0,-4.0,8.0,3.0] "^" ==> [8.0,-4.0,8.0,3.0]
[8.0,-4.0,8.0,3.0] "^" ==> [65536.0,8.0,3.0]
[65536.0,8.0,3.0] "/" ==> [1.220703125e-4,3.0]
[1.220703125e-4,3.0] "+" ==> [3.0001220703125]
[3.0001220703125]

λ> runWriter \$ calcRPNM "3 4 +"
([7.0],"[] \"3\" ==> [3.0]\n[3.0] \"4\" ==> [4.0,3.0]\n[4.0,3.0] \"+\" ==> [7.0]\n")

## Icon and Unicon

procedure main()
EvalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
end

invocable all

procedure EvalRPN(expr)          #: evaluate (and trace stack) an RPN string

stack := []
expr ? until pos(0) do {
tab(many(' '))                         # consume previous seperator
token := tab(upto(' ')|0)              # get token
if token := numeric(token) then {      # ... numeric
push(stack,token)
printf("pushed numeric   %i : %s\n",token,list2string(stack))
}
else {                                 # ... operator
every b|a := pop(stack)             # pop & reverse operands
case token of {
"+"|"-"|"*"|"^"   : push(stack,token(a,b))
"/"               : push(stack,token(real(a),b))
default           : runerr(205,token)
}
printf("applied operator %s : %s\n",token,list2string(stack))
}
}
end

procedure list2string(L)         #: format list as a string
every (s := "[ ") ||:= !L || " "
return s || "]"
end
Output:
pushed numeric   3 : [ 3 ]
pushed numeric   4 : [ 4 3 ]
pushed numeric   2 : [ 2 4 3 ]
applied operator * : [ 8 3 ]
pushed numeric   1 : [ 1 8 3 ]
pushed numeric   5 : [ 5 1 8 3 ]
applied operator - : [ -4 8 3 ]
pushed numeric   2 : [ 2 -4 8 3 ]
pushed numeric   3 : [ 3 2 -4 8 3 ]
applied operator ^ : [ 8 -4 8 3 ]
applied operator ^ : [ 65536 8 3 ]
applied operator / : [ 0.0001220703125 3 ]
applied operator + : [ 3.0001220703125 ]

## J

This task's operations are all dyadic - having two arguments. So on each step we may either "shift" a number to the stack or "reduce" two topmost stack items to one.

Our implementation will be a monadic verb: it will take a single argument, which contains both the accumulated stack and the tokens to be processed. First, create initial state of the input:

a: , <;._1 ' ' , '3 4 2 * 1 5 - 2 3 ^ ^ / +'
┌┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┬─┐
││342*15-23^^/+
└┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┘

As an example, let's also add monadic operation _ which inverses the sign of the stack top element.

We're going to read tokens from input one by one. Each time we read a token, we're checking if it's a number - in this case we put the number to the stack - or an operation - in this case we apply the operation to the stack. The monad which returns 1 (true) for a token representing an operation and 0 (false) otherwise is "isOp". The dyad, which moves an input token to the stack, is "doShift". Applying the operation to the stack is "doApply".

There are 6 operations - one monadic "_" and five dyadic "+", "-", "*", "/", "^". For operation, we need to translate input token into operation and apply it to the stack. The dyad which converts the input token to the operation is "dispatch". It uses two miscellaneous adverbs, one for monadic operations - "mo" - and another for dyadic - "dy".

The RPN driver is the monad "consume", which handles one token. The output is the state of the program after the token was consumed - stack in the 0th box, and remaining input afterwards. As a side effect, "consume" is going to print the resulting stack, so running "consume" once for each token will produce intermediate states of the stack.

isOp=: '_+-*/^' e.~ {.@>@{.
mo=: 1 :'(}: , u@{:) @ ['
dy=: 1 :'(_2&}. , u/@(_2&{.)) @ ['
dispatch=: (-mo)`(+dy)`(-dy)`(*dy)`(%dy)`(^dy)@.('_+-*/^' i. {.@>@])
doShift=: (<@, ".@>@{.) , }.@]
doApply=: }.@] ,~ [ <@dispatch {.@]
consume=: [: ([ smoutput@>@{.) >@{. doShift`doApply@.(isOp@]) }.
consume ^: (<:@#) a: , <;._1 ' ' , '3 4 2 * 1 5 - 2 3 ^ ^ / +'
3
3 4
3 4 2
3 8
3 8 1
3 8 1 5
3 8 _4
3 8 _4 2
3 8 _4 2 3
3 8 _4 8
3 8 65536
3 0.00012207
3.00012
┌───────┐
3.00012
└───────┘
consume ^: (<:@#) a: , <;._1 ' ' , '3 _ 4 +'
3
_3
_3 4
1
┌─┐
1
└─┘

### Alternate Implementation

rpn=: 3 :0
queue=. |.3 :'|.3 :y 0'::]each;: y
op=. 1 :'2 (u~/@:{.,}.)S:0 ,@]'
ops=. +op`(-op)`(*op)`(%op)`(^op)`(,&;)
choose=. ((;:'+-*/^')&i.@[)
,ops@.choose/queue
)

Example use:

rpn '3 4 2 * 1 5 - 2 3 ^ ^ / +'
3.00012

To see intermediate result stacks, use this variant (the only difference is the definition of 'op'):

rpnD=: 3 :0
queue=. |.3 :'|.3 :y 0'::]each;: y
op=. 1 :'2 (u~/@:{.,}.)S:0 ,@([smoutput)@]'
ops=. +op`(-op)`(*op)`(%op)`(^op)`(,&;)
choose=. ((;:'+-*/^')&i.@[)
,ops@.choose/queue
)

In other words:

rpnD '3 4 2 * 1 5 - 2 3 ^ ^ / +'
┌─────┐
2 4 3
└─────┘
5 1 8 3
3 2 _4 8 3
8 _4 8 3
65536 8 3
0.00012207 3
3.00012

Note that the seed stack is boxed while computed stacks are not. Note that top of stack here is on the left. Note also that adjacent constants are bundled in the parsing phase. Finally, note that the result of rpn (and of rpnD - lines previous to the last line in the rpnD example here are output and not a part of the result) is the final state of the stack - in the general case it may not contain exactly one value.

## Java

Works with: Java version 1.5+

Supports multi-digit numbers and negative numbers.

public class RPN{
public static void main(String[] args) {
evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +");
}

private static void evalRPN(String expr){
System.out.println("Input\tOperation\tStack after");
for (String token : expr.split("\\s")){
System.out.print(token + "\t");
if (token.equals("*")) {
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand * secondOperand);
} else if (token.equals("/")) {
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand / secondOperand);
} else if (token.equals("-")) {
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand - secondOperand);
} else if (token.equals("+")) {
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(firstOperand + secondOperand);
} else if (token.equals("^")) {
System.out.print("Operate\t\t");
double secondOperand = stack.pop();
double firstOperand = stack.pop();
stack.push(Math.pow(firstOperand, secondOperand));
} else {
System.out.print("Push\t\t");
try {
stack.push(Double.parseDouble(token+""));
} catch (NumberFormatException e) {
System.out.println("\nError: invalid token " + token);
return;
}
}
System.out.println(stack);
}
if (stack.size() > 1) {
System.out.println("Error, too many operands: " + stack);
return;
}
}
}
Output:
Input	Operation	Stack after
3	Push		[3.0]
4	Push		[4.0, 3.0]
2	Push		[2.0, 4.0, 3.0]
*	Operate		[8.0, 3.0]
1	Push		[1.0, 8.0, 3.0]
5	Push		[5.0, 1.0, 8.0, 3.0]
-	Operate		[-4.0, 8.0, 3.0]
2	Push		[2.0, -4.0, 8.0, 3.0]
3	Push		[3.0, 2.0, -4.0, 8.0, 3.0]
^	Operate		[8.0, -4.0, 8.0, 3.0]
^	Operate		[65536.0, 8.0, 3.0]
/	Operate		[1.220703125E-4, 3.0]
+	Operate		[3.0001220703125]

## JavaScript

const e = '3 4 2 * 1 5 - 2 3 ^ ^ / +';
const s = [], tokens = e.split(' ');
for (const t of tokens) {
const n = Number(t);
if (!isNaN(n)) {
s.push(n);
} else {
if (s.length < 2) {
throw new Error(`\${t}: \${s}: insufficient operands.`);
}
const o2 = s.pop(), o1 = s.pop();
switch (t) {
case '+': s.push(o1 + o2); break;
case '-': s.push(o1 - o2); break;
case '*': s.push(o1 * o2); break;
case '/': s.push(o1 / o2); break;
case '^': s.push(Math.pow(o1, o2)); break;
default: throw new Error(`Unrecognized operator: [\${t}]`);
}
}
console.log(`\${t}: \${s}`);
}

if (s.length > 1) {
throw new Error(`\${s}: insufficient operators.`);
}
Output:
3: 3
4: 3,4
2: 3,4,2
*: 3,8
1: 3,8,1
5: 3,8,1,5
-: 3,8,-4
2: 3,8,-4,2
3: 3,8,-4,2,3
^: 3,8,-4,8
^: 3,8,65536
/: 3,0.0001220703125
+: 3.0001220703125

## jq

Works with: jq

Also works with gojq, the Go implementation of jq, and with jackson-jq and fq.

# Input: an array representing a stack, with .[-1] being its top.
# Output: the updated array after applying `op`
def rpn(op):
def two: .[-2:];
def update(\$x): (.[:-2] + [\$x]);
if length<=1 then .
elif op == "+" then update(two | add)
elif op == "*" then update(two | (.[0] * .[1]))
elif op == "/" then update(two | (.[0] / .[1]))
elif op == "-" then update(two | (.[0] - .[1]))
elif op == "^" then update(two | (pow(.[0]; .[1])))
else ("ignoring unrecognized op \(op)" | debug) as \$debug | .
end;

def eval:
foreach .[] as \$item ([];
if (\$item | type) == "number" then . + [\$item]
else rpn(\$item)
end;
"\(\$item) => \(.)" ) ;

"3 4 2 * 1 5 - 2 3 ^ ^ / +"
| split(" ") | map( (try tonumber) // .)
| eval

Invocation: jq -nr -f rpn.jq

Output:
3 => [3]
4 => [3,4]
2 => [3,4,2]
* => [3,8]
1 => [3,8,1]
5 => [3,8,1,5]
- => [3,8,-4]
2 => [3,8,-4,2]
3 => [3,8,-4,2,3]
^ => [3,8,-4,8]
^ => [3,8,65536]
/ => [3,0.0001220703125]
+ => [3.0001220703125]

## Julia

(This code takes advantage of the fact that all of the operands and functions in the specified RPN syntax are valid Julia expressions, so we can use the built-in parse and eval functions to turn them into numbers and the corresponding Julia functions.)

function rpn(s)
stack = Any[]
for op in map(eval, map(parse, split(s)))
if isa(op, Function)
arg2 = pop!(stack)
arg1 = pop!(stack)
push!(stack, op(arg1, arg2))
else
push!(stack, op)
end
println("\$op: ", join(stack, ", "))
end
length(stack) != 1 && error("invalid RPN expression \$s")
return stack[1]
end
rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +")
Output:
3: 3
4: 3, 4
2: 3, 4, 2
*: 3, 8
1: 3, 8, 1
5: 3, 8, 1, 5
-: 3, 8, -4
2: 3, 8, -4, 2
3: 3, 8, -4, 2, 3
^: 3, 8, -4, 8
^: 3, 8, 65536
/: 3, 0.0001220703125
+: 3.0001220703125

(The return value is also 3.0001220703125.)

## Kotlin

// version 1.1.2

fun rpnCalculate(expr: String) {
if (expr.isEmpty()) throw IllegalArgumentException("Expresssion cannot be empty")
println("For expression = \$expr\n")
println("Token           Action             Stack")
val tokens = expr.split(' ').filter { it != "" }
val stack = mutableListOf<Double>()
for (token in tokens) {
val d = token.toDoubleOrNull()
if (d != null) {
println(" \$d   Push num onto top of stack  \$stack")
}
else if ((token.length > 1) || (token !in "+-*/^")) {
throw IllegalArgumentException("\$token is not a valid token")
}
else if (stack.size < 2) {
throw IllegalArgumentException("Stack contains too few operands")
}
else {
val d1 = stack.removeAt(stack.lastIndex)
val d2 = stack.removeAt(stack.lastIndex)
"+"  -> d2 + d1
"-"  -> d2 - d1
"*"  -> d2 * d1
"/"  -> d2 / d1
else -> Math.pow(d2, d1)
})
println(" \$token     Apply op to top of stack    \$stack")
}
}
println("\nThe final value is \${stack[0]}")
}

fun main(args: Array<String>) {
val expr = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
rpnCalculate(expr)
}
Output:
For expression = 3 4 2 * 1 5 - 2 3 ^ ^ / +

Token           Action             Stack
3.0   Push num onto top of stack  [3.0]
4.0   Push num onto top of stack  [3.0, 4.0]
2.0   Push num onto top of stack  [3.0, 4.0, 2.0]
*     Apply op to top of stack    [3.0, 8.0]
1.0   Push num onto top of stack  [3.0, 8.0, 1.0]
5.0   Push num onto top of stack  [3.0, 8.0, 1.0, 5.0]
-     Apply op to top of stack    [3.0, 8.0, -4.0]
2.0   Push num onto top of stack  [3.0, 8.0, -4.0, 2.0]
3.0   Push num onto top of stack  [3.0, 8.0, -4.0, 2.0, 3.0]
^     Apply op to top of stack    [3.0, 8.0, -4.0, 8.0]
^     Apply op to top of stack    [3.0, 8.0, 65536.0]
/     Apply op to top of stack    [3.0, 1.220703125E-4]
+     Apply op to top of stack    [3.0001220703125]

The final value is 3.0001220703125

## Lambdatalk

{calc 3 4 2 * 1 5 - 2 3 pow pow / +}
->
3:
4: 3
2: 4 3
*: 2 4 3
1: 8 3
5: 1 8 3
-: 5 1 8 3
2: -4 8 3
3: 2 -4 8 3
pow: 3 2 -4 8 3
pow: 8 -4 8 3
/: 65536 8 3
+: 0.0001220703125 3
-> 3.0001220703125

where

{def calc
{def calc.r
{lambda {:x :s}
{if {empty? :x}
then -> {car :s}
else {car :x}: {disp :s}{br}
{calc.r {cdr :x}
{if {unop? {car :x}}
then {cons {{car :x} {car :s}} {cdr :s}}
else {if {binop? {car :x}}
then {cons {{car :x} {car {cdr :s}} {car :s}} {cdr {cdr :s}}}
else {cons {car :x} :s}} }}}}}
{lambda {:s}
{calc.r {list :s} nil}}}

using the unop? & binop? functions to test unary and binary operators

{def unop?
{lambda {:op}
{or {W.equal? :op sqrt}       // n sqrt  sqrt(n)
{W.equal? :op exp}        // n exp   exp(n)
{W.equal? :op log}        // n log   log(n)
{W.equal? :op cos}        // n cos   cos(n)
... and so                // ...
}}}

{def binop?
{lambda {:op}
{or {W.equal? :op +}          // m n +     m+n
{W.equal? :op -}          // m n -     m-n
{W.equal? :op *}          // m n *     m*n
{W.equal? :op /}          // m n /     m/n
{W.equal? :op %}          // m n %     m%n
{W.equal? :op pow}        // m n pow   m^n
... and so on             // ...
}}}

and  the list, empty? and disp functions to create
a list from a string, test its emptynes and display it.

{def list
{lambda {:s}
{if {W.empty? {S.rest :s}}
then {cons {S.first :s} nil}
else {cons {S.first :s} {list {S.rest :s}}}}}}

{def empty?
{lambda {:x}
{W.equal? :x nil}}}

{def disp
{lambda {:l}
{if {empty? :l}
then
else {car :l} {disp {cdr :l}}}}}

Note that everything is exclusively built on 5 lambdatalk primitives:
- "cons, car, cdr", to create lists,
- "W.equal?" which test the equality between two words,
- and the "or" boolean function.

## Lua

local stack = {}
function push( a ) table.insert( stack, 1, a ) end
function pop()
if #stack == 0 then return nil end
return table.remove( stack, 1 )
end
function writeStack()
for i = #stack, 1, -1 do
io.write( stack[i], " " )
end
print()
end
function operate( a )
local s
if a == "+" then
push( pop() + pop() )
io.write( a .. "\tadd\t" ); writeStack()
elseif a == "-" then
s = pop(); push( pop() - s )
io.write( a .. "\tsub\t" ); writeStack()
elseif a == "*" then
push( pop() * pop() )
io.write( a .. "\tmul\t" ); writeStack()
elseif a == "/" then
s = pop(); push( pop() / s )
io.write( a .. "\tdiv\t" ); writeStack()
elseif a == "^" then
s = pop(); push( pop() ^ s )
io.write( a .. "\tpow\t" ); writeStack()
elseif a == "%" then
s = pop(); push( pop() % s )
io.write( a .. "\tmod\t" ); writeStack()
else
push( tonumber( a ) )
io.write( a .. "\tpush\t" ); writeStack()
end
end
function calc( s )
local t, a = "", ""
print( "\nINPUT", "OP", "STACK" )
for i = 1, #s do
a = s:sub( i, i )
if a == " " then operate( t ); t = ""
else t = t .. a
end
end
if a ~= "" then operate( a ) end
print( string.format( "\nresult: %.13f", pop() ) )
end
--[[ entry point ]]--
calc( "3 4 2 * 1 5 - 2 3 ^ ^ / +" )
calc( "22 11 *" )
Output:
INPUT   OP      STACK
3       push    3
4       push    3 4
2       push    3 4 2
*       mul     3 8
1       push    3 8 1
5       push    3 8 1 5
-       sub     3 8 -4
2       push    3 8 -4 2
3       push    3 8 -4 2 3
^       pow     3 8 -4 8
^       pow     3 8 65536
/       div     3 0.0001220703125

result: 3.0001220703125

INPUT   OP      STACK
22      push    22
11      push    22 11
*       mul     242

result: 242.0000000000000

## M2000 Interpreter

Module Rpn_Calc {
Rem Form 80,60
function rpn_calc(a\$) {
def m=0
dim token\$()
token\$()=piece\$(a\$," ")
l=len(token\$())
dim type(l)=0, reg(l)
where=-1
for i=0 to  l-1
c=val(token\$(i),"",m)
if m>-1 then
where++
reg(where)=c
else
reg(where-1)=eval(str\$(reg(where-1))+token\$(i)+str\$(reg(where)))
where--
end if
inf=each(reg(),1, where+1)
while inf
export\$<=token\$(i)+" ["+str\$(inf^,"")+"] "+ str\$(array(inf))+{
}
token\$(i)=" "
end while
next i
=reg(0)
}
Global export\$
document export\$
example1=rpn_calc("3 4 2 * 1 5 - 2 3 ^ ^ / +")
example2=rpn_calc("1 2 + 3 4 + ^ 5 6 + ^")
Print example1, example2
Rem Print #-2, Export\$
ClipBoard Export\$
}
Rpn_Calc
Output:
3 [0]  3
4 [0]  3
[1]  4
2 [0]  3
[1]  4
[2]  2
* [0]  3
[1]  8
1 [0]  3
[1]  8
[2]  1
5 [0]  3
[1]  8
[2]  1
[3]  5
- [0]  3
[1]  8
[2] -4
2 [0]  3
[1]  8
[2] -4
[3]  2
3 [0]  3
[1]  8
[2] -4
[3]  2
[4]  3
^ [0]  3
[1]  8
[2] -4
[3]  8
^ [0]  3
[1]  8
[2]  65536
/ [0]  3
[1]  .0001220703125
+ [0]  3.0001220703125
1 [0]  1
2 [0]  1
[1]  2
+ [0]  3
3 [0]  3
[1]  3
4 [0]  3
[1]  3
[2]  4
+ [0]  3
[1]  7
^ [0]  2187
5 [0]  2187
[1]  5
6 [0]  2187
[1]  5
[2]  6
+ [0]  2187
[1]  11
^ [0]  5.47440108942022E+36

## Mathematica/Wolfram Language

(This code takes advantage of the fact that all of the operands and functions in the specified RPN syntax can be used to form valid Mathematica expressions, so we can use the built-in ToExpression function to turn them into numbers and the corresponding Mathematica functions. Note that we need to add braces around arguments, otherwise "-4^8" would be parsed as "-(4^8)" instead of "(-4)^8".)

calc[rpn_] :=
Module[{tokens = StringSplit[rpn], s = "(" <> ToString@InputForm@# <> ")" &, op, steps},
op[o_, x_, y_] := ToExpression[s@x <> o <> s@y];
steps = FoldList[Switch[#2, _?DigitQ, Append[#, FromDigits[#2]],
_, Append[#[[;; -3]], op[#2, #[[-2]], #[[-1]]]]
] &, {}, tokens][[2 ;;]];
Grid[Transpose[{# <> ":" & /@ tokens,
StringRiffle[ToString[#, InputForm] & /@ #] & /@ steps}]]];
Print[calc["3 4 2 * 1 5 - 2 3 ^ ^ / +"]];
Output:
3:   3

4:   3 4

2:   3 4 2

*:   3 8

1:   3 8 1

5:   3 8 1 5

-:   3 8 -4

2:   3 8 -4 2

3:   3 8 -4 2 3

^:   3 8 -4 8

^:   3 8 65536

/:   3 1/8192

+:   24577/8192

## Maxima

rmod(i, j) := mod(j, i)\$
rpow(x, y) := y^x\$

rpn(sexpr) := (
operands: [],
expr: charlist(sexpr),

for token in expr do (
if token = "+" then (
push(pop(operands) + pop(operands), operands)
)
elseif token = "-" then (
push(-1 * (pop(operands) - pop(operands)), operands)
)
elseif token = "*" then (
push(pop(operands) * pop(operands), operands)
)
elseif token = "/" then (
push(1 / (pop(operands) / pop(operands)), operands)
)
elseif token = "%" then (
push(rmod(pop(operands), pop(operands)), operands)
)
elseif token = "^" then (
push(rpow(pop(operands), pop(operands)), operands)
)
elseif token # " " then (
push(parse_string(token), operands)
),

if token # " " then (
print(token, " : ", operands)
)
),

pop(operands)
)\$

rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +"), numer;

### Output

(%i5) ev(rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +"),numer)
3  :  [3]
4  :  [4, 3]
2  :  [2, 4, 3]
*  :  [8, 3]
1  :  [1, 8, 3]
5  :  [5, 1, 8, 3]
-  :  [- 4, 8, 3]
2  :  [2, - 4, 8, 3]
3  :  [3, 2, - 4, 8, 3]
^  :  [8, - 4, 8, 3]
^  :  [65536, 8, 3]
/  :  [1.220703125e-4, 3]
+  :  [3.0001220703125]
(%o5)                           3.0001220703125

## MiniScript

RPN = function(inputText)
tokens = inputText.split
stack = []
while tokens
tok = tokens.pull
if "+-*/^".indexOf(tok) != null then
b = stack.pop
a = stack.pop
if tok == "+" then stack.push a + b
if tok == "-" then stack.push a - b
if tok == "*" then stack.push a * b
if tok == "/" then stack.push a / b
if tok == "^" then stack.push a ^ b
else
stack.push val(tok)
end if
print tok + " --> " + stack
end while
return stack[0]
end function

print RPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
Output:
3 --> [3]
4 --> [3, 4]
2 --> [3, 4, 2]
* --> [3, 8]
1 --> [3, 8, 1]
5 --> [3, 8, 1, 5]
- --> [3, 8, -4]
2 --> [3, 8, -4, 2]
3 --> [3, 8, -4, 2, 3]
^ --> [3, 8, -4, 8]
^ --> [3, 8, 65536]
/ --> [3, 0.000122]
+ --> [3.000122]
3.000122

## N/t/roff

### Classically-oriented version

This implementation does not take advantage of GNU TROFF's ability to handle numerical registers of more than 2 characters.

Works with: GNU TROFF version 1.22.2
.ig
RPN parser implementation in TROFF

..
.\" \(*A stack implementation
.nr Ac 0
.af Ac 1
.de APUSH
.if (\\n(Ac>=0)&(\\n(Ac<27) \{ \
.	nr Ac +1
.	af Ac A
.	nr A\\n(Ac \\\$1
.	af Ac 1
\}
..
.de APOP
.if (\\n(Ac>0)&(\\n(Ac<27) \{ \
.	af Ac A
.	rr A\\n(Ac \\\$1
.	af Ac 1
.	nr Ac -1
..
.\" Facility to print entire stack
.de L2
.af Ac 1
.if \\n(Li<=\\n(Ac \{ \
.	af Li A
\\n(A\\n(Li
.	af Li 1
.	nr Li +1
.	L2
\}
..
.de APRINT
.nr Li 1
.L2
.br
..
.\" Integer exponentiation algorithm
.de L1
.if \\n(Li<\\\$2 \{ \
.	nr Rs \\n(Rs*\\\$1
.	nr Li +1
.	L1 \\\$1 \\\$2
\}
..
.de EXP
.nr Li 0
.nr Rs 1
.L1 \\\$1 \\\$2
..
.\" RPN Parser
.de REAP
.af Ac A
.nr O2 \\n(A\\n(Ac
.af Ac 1
.nr Ai \\n(Ac-1
.af Ai A
.nr O1 \\n(A\\n(Ai
.APOP
.APOP
..
.de RPNPUSH
.ie '\\\$1'+' \{ \
.	REAP
.	nr Rs \\n(O1+\\n(O2
\}
.el \{ \
.	ie '\\\$1'-' \{ \
.		REAP
.		nr Rs \\n(O1-\\n(O2
\}
.	el \{ \
.		ie '\\\$1'*' \{ \
.			REAP
.			nr Rs \\n(O1*\\n(O2
\}
.		el \{ \
.			ie '\\\$1'/' \{ \
.				REAP
.				nr Rs \\n(O1/\\n(O2
\}
.			el \{ \
.				ie '\\\$1'%' \{ \
.					REAP
.					nr Rs \\n(O1%\\n(O2
\}
.				el \{ \
.					ie '\\\$1'^' \{ \
.						REAP
.						EXP \\n(O1 \\n(O2
\}
.					el .nr Rs \\\$1
\}
\}
\}
\}
\}
.APUSH \\n(Rs
.APRINT
..
.de RPNPRINT
.if \\n(Ac>1 .tm ERROR (rpn.roff): Malformed input expression. Evaluation stack size: \\n(Ac > 1 .
\\n(AA
..
.de RPNPARSE
.RPNPUSH \\\$1
.ie \\n(.\$>1 \{ \
.	shift
.	RPNPARSE \\\$@
\}
.el .RPNPRINT
..
.RPNPARSE 3 4 2 * 1 5 - 2 3 ^ ^ / + \" Our input expression

3
3 4
3 4 2
3 8
3 8 1
3 8 1 5
3 8 ‐4
3 8 ‐4 2
3 8 ‐4 2 3
3 8 ‐4 8
3 8 16
3 0
3
3

### Modern version

This version sees great improvement on syntax, stacks can now be as big as they want, and modern GNU Troff constructs are used.

Works with: GNU Troff version 1.22.2
.ig
===========================
Array implementation
===========================
..
.de end
..
.de array
.	nr \\\$1.c 0 1
.	de \\\$1.push end
.		nr \\\$1..\\\\n+[\\\$1.c] \\\\\$1
.	end
.	de \\\$1.pop end
.		if \\\\n[\\\$1.c]>0 \{ \
.			rr \\\$1..\\\\n[\\\$1.c]
.			nr \\\$1.c -1\
.		\}
.	end
.	de \\\$1.dump end
.		nr i 0 1
.		rm ou
.		while \\\\n+i<=\\\\n[\\\$1.c] \{ \
.			as ou "\\\\n[\\\$1..\\\\ni]
.		\}
.		tm \\\\*(ou
.		rr i
.	end
..
.ig
==========================
End array implementation
==========================
..
.array stack
.de hyper3
.	nr rs 1
.	nr i 0 1
.	while \\n+i<=\\\$2 .nr rs \\n(rs*\\\$1
.	rr i
..
.de pop2
.	nr O2 \\n[\\\$1..\\n[\\\$1.c]]
.	\\\$1.pop
.	nr O1 \\n[\\\$1..\\n[\\\$1.c]]
.	\\\$1.pop
..
.de rpn
.	ie '\\\$1'+' \{ \
.		pop2 stack
.		nr rs \\n(O1+\\n(O2
.	\}
.	el \{ \
.	ie '\\\$1'-' \{ \
.		pop2 stack
.		nr rs \\n(O1-\\n(O2
.	\}
.	el \{ \
.	ie '\\\$1'*' \{ \
.		pop2 stack
.		nr rs \\n(O1*\\n(O2
.	\}
.	el \{ \
.	ie '\\\$1'/' \{ \
.		pop2 stack
.		nr rs \\n(O1/\\n(O2
.	\}
.	el \{ \
.	ie '\\\$1'%' \{ \
.		pop2 stack
.		nr rs \\n(O1%\\n(O2
.	\}
.	el \{ \
.	ie '\\\$1'^' \{ \
.		pop2 stack
.		hyper3 \\n(O1 \\n(O2
.	\}
.	el .nr rs \\\$1
.	\}\}\}\}\}
.
.	stack.push \\n(rs
.	stack.dump
.
.	if \\n(.\$>1 \{ \
.		shift
.		rpn \\\$@
.	\}
..
.rpn 3 4 2 * 1 5 - 2 3 ^ ^ / +
.stack.dump

3
3 4
3 4 2
3 8
3 8 1
3 8 1 5
3 8 -4
3 8 -4 2
3 8 -4 2 3
3 8 -4 8
3 8 16
3 0
3
3

## NetRexx

Translation of: Java
/* NetRexx */
options replace format comments java crossref symbols nobinary

numeric digits 20

rpnDefaultExpression = '3 4 2 * 1 5 - 2 3 ^ ^ / +'

parse arg rpnString

if rpnString = '.' then rpnString = rpnDefaultExpression
if rpnString = '' then do
say 'Enter numbers or operators [to stop enter' EODAD']:'
loop label rpnloop forever
if rpnval == EODAD then leave rpnloop
rpnString = rpnString rpnval
end rpnloop
end

rpnString = rpnString.space(1)
say rpnString':' evaluateRPN(rpnString)

return

-- -----------------------------------------------------------------------------
method evaluateRPN(rpnString) public static returns Rexx

op = 0
L = 'L'
R = 'R'
rpnString = rpnString.strip('b')
say 'Input\tOperation\tStack after'
loop label rpn while rpnString.length > 0
parse rpnString token rest
rpnString = rest.strip('b')
say token || '\t\-'
select label tox case token
when '*' then do
say 'Operate\t\t\-'
op[R] = Rexx stack.pop()
op[L] = Rexx stack.pop()
stack.push(op[L] * op[R])
end
when '/' then do
say 'Operate\t\t\-'
op[R] = Rexx stack.pop()
op[L] = Rexx stack.pop()
stack.push(op[L] / op[R])
end
when '+' then do
say 'Operate\t\t\-'
op[R] = Rexx stack.pop()
op[L] = Rexx stack.pop()
stack.push(op[L] + op[R])
end
when '-' then do
say 'Operate\t\t\-'
op[R] = Rexx stack.pop()
op[L] = Rexx stack.pop()
stack.push(op[L] - op[R])
end
when '^' then do
say 'Operate\t\t\-'
op[R] = Rexx stack.pop()
op[L] = Rexx stack.pop()
-- If exponent is a whole number use Rexx built-in exponentiation operation, otherwise use Math.pow()
op[R] = op[R] + 0
if op[R].datatype('w') then stack.push(op[L] ** op[R])
else stack.push(Rexx Math.pow(op[L], op[R]))
end
otherwise do
if token.datatype('n') then do
say 'Push\t\t\-'
stack.push(token)
end
else do
say 'Error\t\t\-'
end
end
end tox
calc = Rexx
say stack.toString
end rpn
say
calc = stack.toString
return calc
Output:
Input	Operation	Stack after
3	Push		[3]
4	Push		[4, 3]
2	Push		[2, 4, 3]
*	Operate		[8, 3]
1	Push		[1, 8, 3]
5	Push		[5, 1, 8, 3]
-	Operate		[-4, 8, 3]
2	Push		[2, -4, 8, 3]
3	Push		[3, 2, -4, 8, 3]
^	Operate		[8, -4, 8, 3]
^	Operate		[65536, 8, 3]
/	Operate		[0.0001220703125, 3]
+	Operate		[3.0001220703125]

3 4 2 * 1 5 - 2 3 ^ ^ / +: [3.0001220703125]

## Nim

Translation of: Python
import math, rdstdin, strutils, tables

type Stack = seq[float]

proc opPow(s: var Stack) =
let b = s.pop
let a = s.pop

proc opMul(s: var Stack) =
let b = s.pop
let a = s.pop

proc opDiv(s: var Stack) =
let b = s.pop
let a = s.pop

let b = s.pop
let a = s.pop

proc opSub(s: var Stack) =
let b = s.pop
let a = s.pop

proc opNum(s: var Stack; num: float) =

let ops = toTable({"^": opPow,
"*": opMul,
"/": opDiv,
"-": opSub})

proc getInput(inp = ""): seq[string] =
var inp = inp
if inp.len == 0:
result = inp.strip.split

proc rpnCalc(tokens: seq[string]): seq[seq[string]] =
var s: Stack
result = @[@["TOKEN","ACTION","STACK"]]
for token in tokens:
var action = ""
action = "Apply op to top of stack"
ops[token](s)
else:
action = "Push num onto top of stack"
s.opNum token.parseFloat

let rpn = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
echo "For RPN expression: ", rpn
let rp = rpnCalc rpn.getInput

var maxColWidths = newSeq[int](rp[0].len)
for i in 0 .. rp[0].high:
for x in rp:
maxColWidths[i] = max(maxColWidths[i], x[i].len + 3)

for x in rp:
for i, y in x:
stdout.write y.alignLeft(maxColWidths[i])
echo ""
Output:
For RPN expression: 3 4 2 * 1 5 - 2 3 ^ ^ / +
TOKEN   ACTION                       STACK
3       Push num onto top of stack   3.0
4       Push num onto top of stack   3.0 4.0
2       Push num onto top of stack   3.0 4.0 2.0
*       Apply op to top of stack     3.0 8.0
1       Push num onto top of stack   3.0 8.0 1.0
5       Push num onto top of stack   3.0 8.0 1.0 5.0
-       Apply op to top of stack     3.0 8.0 -4.0
2       Push num onto top of stack   3.0 8.0 -4.0 2.0
3       Push num onto top of stack   3.0 8.0 -4.0 2.0 3.0
^       Apply op to top of stack     3.0 8.0 -4.0 8.0
^       Apply op to top of stack     3.0 8.0 65536.0
/       Apply op to top of stack     3.0 0.0001220703125
+       Apply op to top of stack     3.0001220703125

## Objeck

use IO;
use Struct;

bundle Default {
class RpnCalc {
function : Main(args : String[]) ~ Nil {
Caculate("3 4 2 * 1 5 - 2 3 ^ ^ / +");
}

function : native : Caculate(rpn : String) ~ Nil {
rpn->PrintLine();

tokens := rpn->Split(" ");
stack := FloatVector->New();
each(i : tokens) {
token := tokens[i]->Trim();
if(token->Size() > 0) {
if(token->Get(0)->IsDigit()) {
}
else {
right := stack->Get(stack->Size() - 1); stack->RemoveBack();
left := stack->Get(stack->Size() - 1); stack->RemoveBack();
select(token->Get(0)) {
label '+': {
}

label '-': {
}

label '*': {
}

label '/': {
}

label '^': {
}
};
};
PrintStack(stack);
};
};
Console->Print("result: ")->PrintLine(stack->Get(0));
}

function : PrintStack(stack : FloatVector) ~ Nil {
"  ["->Print();
each(i : stack) {
stack->Get(i)->Print();
if(i + 1< stack->Size()) {
", "->Print();
};
};
']'->PrintLine();
}
}
}
Output:
3 4 2 * 1 5 - 2 3 ^ ^ / +
[3]
[3, 4]
[3, 4, 2]
[3, 8]
[3, 8, 1]
[3, 8, 1, 5]
[3, 8, -4]
[3, 8, -4, 2]
[3, 8, -4, 2, 3]
[3, 8, -4, 8]
[3, 8, 65536]
[3, 0.00012207]
[3.00012]
result: 3.00012

## OCaml

(* binop : ('a -> 'a -> 'a) -> 'a list -> 'a list *)
let binop op = function
| b::a::r -> (op a b)::r
| _ -> failwith "invalid expression"

(* interp : float list -> string -> string * float list *)
let interp s = function
| "+" -> "add",    binop ( +. ) s
| "-" -> "subtr",  binop ( -. ) s
| "*" -> "mult",   binop ( *. ) s
| "/" -> "divide", binop ( /. ) s
| "^" -> "exp",    binop ( ** ) s
| str -> "push", (float_of_string str) :: s

(* interp_and_show : float list -> string -> float list *)
let interp_and_show s inp =
let op,s' = interp s inp in
Printf.printf "%s\t%s\t" inp op;
List.(iter (Printf.printf "%F ") (rev s'));
print_newline ();
s'

(* rpn_eval : string -> float list *)
let rpn_eval str =
Printf.printf "Token\tAction\tStack\n";
let ss = Str.(split (regexp_string " ") str) in
List.fold_left interp_and_show [] ss

Evaluation of the test expression:

# rpn_eval "3 4 2 * 1 5 - 2 3 ^ ^ / +";;
Token	Action	Stack
3	push	3.
4	push	3. 4.
2	push	3. 4. 2.
*	mult	3. 8.
1	push	3. 8. 1.
5	push	3. 8. 1. 5.
-	subtr	3. 8. -4.
2	push	3. 8. -4. 2.
3	push	3. 8. -4. 2. 3.
^	exp	3. 8. -4. 8.
^	exp	3. 8. 65536.
/	divide	3. 0.0001220703125
- : float list = [3.0001220703125]

## Oforth

Oforth uses RPN and natively parse RPN.

"3 4 2 * 1 5 - 2 3 ^ ^ / +" eval println
Output:
3

To show the changes in the stack, we can use .l after evaluating each word :

: rpn(s) { s words apply(#[ eval .l ]) }

rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +")
Output:
3 |
3 | 4 |
3 | 4 | 2 |
3 | 8 |
3 | 8 | 1 |
3 | 8 | 1 | 5 |
3 | 8 | -4 |
3 | 8 | -4 | 2 |
3 | 8 | -4 | 2 | 3 |
3 | 8 | -4 | 8 |
3 | 8 | 65536 |
3 | 0 |
3 |

## ooRexx

/* ooRexx *************************************************************
* 10.11.2012 Walter Pachl  translated from PL/I via REXX
**********************************************************************/
fid='rpl.txt'
ex=linein(fid)
Say 'Input:' ex
/* ex=' 3 4 2 * 1 5 - 2 3 ^ ^ / +' */
Numeric Digits 15
expr=''
st=.circularqueue~new(100)
Say 'Stack contents:'
do While ex<>''
Parse Var ex ch +1 ex
expr=expr||ch;
if ch<>' ' then do
If pos(ch,'0123456789')>0 Then     /* a digit goes onto stack    */
st~push(ch)
Else Do                            /* an operator                */
op=st~pull                       /* get top element            */
select                           /* and modify the (now) top el*/
when ch='+' Then st~push(st~pull +  op)
when ch='-' Then st~push(st~pull -  op)
when ch='*' Then st~push(st~pull *  op)
when ch='/' Then st~push(st~pull /  op)
when ch='^' Then st~push(st~pull ** op)
end;
Say st~string(' ','L')           /* show stack in LIFO order   */
end
end
end
Say 'The reverse polish expression = 'expr
Say 'The evaluated expression = 'st~pull
Output:
Input: 3 4 2 * 1 5 - 2 3 ^ ^ / +
Stack contents:
3 8
3 8 -4
3 8 -4 8
3 8 65536
3 0.0001220703125
3.0001220703125
The reverse polish expression = 3 4 2 * 1 5 - 2 3 ^ ^ / +
The evaluated expression = 3.0001220703125

## PARI/GP

Due to the nature of the language, it is not trivial to process an expression as a simple space-separated string. Though, this could be done if one calls an external shell program such as sed and pipes the result back hither.

estack = [];

epush(x) = {
estack = vector(#estack + 1, i, if(i <= #estack, estack[i], x));
return(#estack);
};

epop() = {
local(val = estack[#estack]);
estack = vector(#estack - 1, i, estack[i]);
return(val);
};

registerRPNToken(t) = {
local(o1, o2);

if(type(t) == "t_STR",
if(t == "+", o2 = epop(); o1 = epop(); epush(o1 + o2),
if(t == "-", o2 = epop(); o1 = epop(); epush(o1 - o2),
if(t == "*", o2 = epop(); o1 = epop(); epush(o1 * o2),
if(t == "/", o2 = epop(); o1 = epop(); epush(o1 / o2),
if(t == "%", o2 = epop(); o1 = epop(); epush(o1 % o2),
if(t == "^", o2 = epop(); o1 = epop(); epush(o1 ^ o2)
)))))),
if(type(t) == "t_INT" || type(t) == "t_REAL" || type(t) == "t_FRAC",
epush(t))
);
print(estack);
};

parseRPN(s) = {
estack = [];
for(i = 1, #s, registerRPNToken(s[i]));

if(#estack > 1, error("Malformed postfix expression."));
return(estack[1]);
};

parseRPN([3, 4, 2, "*", 1, 5, "-", 2, 3, "^", "^", "/", "+"]); \\ Our input expression

### Output

[3]
[3, 4]
[3, 4, 2]
[3, 8]
[3, 8, 1]
[3, 8, 1, 5]
[3, 8, -4]
[3, 8, -4, 2]
[3, 8, -4, 2, 3]
[3, 8, -4, 8]
[3, 8, 65536]
[3, 1/8192]
[24577/8192]

Whenever possible, PARI/GP tries to manipulate and return results in the simplest form it can. In this case, it deems fractions the most suitable form of output. Nonetheless, converting the fraction 24577/8192 yields 3.0001220703125 as expected.

## Perl

use strict;
use warnings;
use feature 'say';

my \$number   = '[+-]?(?:\.\d+|\d+(?:\.\d*)?)';
my \$operator = '[-+*/^]';

my @tests = ('3 4 2 * 1 5 - 2 3 ^ ^ / +');

for (@tests) {
while (
s/ \s* ((?<left>\$number))     # 1st operand
\s+ ((?<right>\$number))    # 2nd operand
\s+ ((?<op>\$operator))     # operator
(?:\s+|\$)                  # more to parse, or done?
/
' '.evaluate().' '         # substitute results of evaluation
/ex
) {}
say;
}

sub evaluate {
(my \$a = "(\$+{left})\$+{op}(\$+{right})") =~ s/\^/**/;
say \$a;
eval \$a;
}
Output:
(4)*(2)
(1)-(5)
(2)**(3)
(-4)**(8)
(8)/(65536)
(3)+(0.0001220703125)
3.0001220703125

## Phix

with javascript_semantics
procedure evalRPN(string s)
sequence stack = {},
ops = split(s)
for i=1 to length(ops) do
string op = ops[i]
switch op
case "+": stack[-2] = stack[-2]+stack[-1]; stack = stack[1..-2]
case "-": stack[-2] = stack[-2]-stack[-1]; stack = stack[1..-2]
case "*": stack[-2] = stack[-2]*stack[-1]; stack = stack[1..-2]
case "/": stack[-2] = stack[-2]/stack[-1]; stack = stack[1..-2]
case "^": stack[-2] = power(stack[-2],stack[-1]); stack = stack[1..-2]
default : stack = append(stack,scanf(op,"%d")[1][1])
end switch
?{op,stack}
end for
end procedure
evalRPN("3 4 2 * 1 5 - 2 3 ^ ^ / +")
Output:
{"3",{3}}
{"4",{3,4}}
{"2",{3,4,2}}
{"*",{3,8}}
{"1",{3,8,1}}
{"5",{3,8,1,5}}
{"-",{3,8,-4}}
{"2",{3,8,-4,2}}
{"3",{3,8,-4,2,3}}
{"^",{3,8,-4,8}}
{"^",{3,8,65536}}
{"/",{3,0.0001220703}}
{"+",{3.00012207}}

## PHP

<?php
function rpn(\$postFix){
\$stack = Array();
echo "Input\tOperation\tStack\tafter\n" ;
\$token = explode(" ", trim(\$postFix));
\$count = count(\$token);

for(\$i = 0 ; \$i<\$count;\$i++)
{
echo \$token[\$i] ." \t";
\$tokenNum = "";

if (is_numeric(\$token[\$i])) {
echo  "Push";
array_push(\$stack,\$token[\$i]);
}
else
{
echo "Operate";
\$secondOperand = end(\$stack);
array_pop(\$stack);
\$firstOperand = end(\$stack);
array_pop(\$stack);

if (\$token[\$i] == "*")
array_push(\$stack,\$firstOperand * \$secondOperand);
else if (\$token[\$i] == "/")
array_push(\$stack,\$firstOperand / \$secondOperand);
else if (\$token[\$i] == "-")
array_push(\$stack,\$firstOperand - \$secondOperand);
else if (\$token[\$i] == "+")
array_push(\$stack,\$firstOperand + \$secondOperand);
else if (\$token[\$i] == "^")
array_push(\$stack,pow(\$firstOperand,\$secondOperand));
else {
die("Error");
}
}
echo "\t\t" . implode(" ", \$stack) .  "\n";
}
return end(\$stack);
}

echo "Compute Value: " . rpn("3 4 2 * 1 5 - 2 3 ^ ^ / + ");
?>
Output:
Input	Operation	Stack	after
3 	Push		3
4 	Push		3 4
2 	Push		3 4 2
* 	Operate		3 8
1 	Push		3 8 1
5 	Push		3 8 1 5
- 	Operate		3 8 -4
2 	Push		3 8 -4 2
3 	Push		3 8 -4 2 3
^ 	Operate		3 8 -4 8
^ 	Operate		3 8 65536
/ 	Operate		3 0.0001220703125
+ 	Operate		3.0001220703125
Compute Value: 3.0001220703125

## PicoLisp

This is an integer-only calculator:

(de rpnCalculator (Str)
(let (^ **  Stack)  # Define '^' from the built-in '**'
(prinl "Token  Stack")
(for Token (str Str "*+-/\^")
(if (num? Token)
(push 'Stack @)
(set (cdr Stack)
((intern Token) (cadr Stack) (pop 'Stack)) ) )
(prin Token)
(space 6)
(println Stack) )
(println (car Stack)) ) )

Test (note that the top-of-stack is in the left-most position):

: (rpnCalculator "3 4 2 * 1 5 - 2 3 \^ \^ / +")
Token  Stack
3      (3)
4      (4 3)
2      (2 4 3)
*      (8 3)
1      (1 8 3)
5      (5 1 8 3)
-      (-4 8 3)
2      (2 -4 8 3)
3      (3 2 -4 8 3)
^      (8 -4 8 3)
^      (65536 8 3)
/      (0 3)
+      (3)
3
-> 3

## PL/I

Calculator: procedure options (main);            /* 14 Sept. 2012 */
declare expression character (100) varying initial ('');
declare ch character (1);
declare (stack controlled, operand) float (18);
declare in file input;

open file (in) title ('/CALCULAT.DAT,type(text),recsize(100)');
on endfile (in) go to done;

put ('Stack contents:');
main_loop:
do forever;
get file (in) edit (ch) (a(1));
expression = expression || ch;
if ch = ' ' then iterate;
select (ch);
when ('0', '1', '2', '3', '4', '5', '6', '7', '8', '9')
do; allocate stack; stack = ch; iterate main_loop; end;
when ('+') do; operand = stack; free stack; stack = stack +  operand; end;
when ('-') do; operand = stack; free stack; stack = stack -  operand; end;
when ('*') do; operand = stack; free stack; stack = stack *  operand; end;
when ('/') do; operand = stack; free stack; stack = stack /  operand; end;
when ('^') do; operand = stack; free stack; stack = stack ** operand; end;
end;
call show_stack;
end;

done:
put skip list ('The reverse polish expression = ' || expression);
put skip list ('The evaluated expression = ' || stack);

end Calculator;
Stack contents:
3.0000000000      8.0000000000
3.0000000000      8.0000000000     -4.0000000000
3.0000000000      8.0000000000     -4.0000000000      8.0000000000
3.0000000000      8.0000000000  65536.0000000000
3.0000000000      0.0001220703
3.0001220703
The reverse polish expression = 3 4 2 * 1 5 - 2 3 ^ ^ / +
The evaluated expression =  3.00012207031250000E+0000

The procedure to display the stack:

/* As the stack is push-down pop-up, need to pop it to see what's inside. */
show_stack: procedure;
declare ts float (18) controlled;

do while (allocation(stack) > 0);
allocate ts; ts = stack; free stack;
end;
put skip;
do while (allocation(ts) > 0);
allocate stack; stack = ts; free ts; put edit (stack) (f(18,10));
end;
end show_stack;

## PL/SQL

create or replace function rpn_calc(str varchar2) return number as
type  num_aa    is table of number index by pls_integer;
type  num_stack is record (a num_aa, top pls_integer default 0);
ns    num_stack;
pos1  integer := 1;
pos2  integer;
token varchar2(100);
op2   number;
procedure push(s in out nocopy num_stack, x number) is
begin
s.top := s.top + 1;
s.a(s.top) := x;
end;
function pop(s in out nocopy num_stack) return number is
x number;
begin
x := s.a(s.top);
s.top := s.top - 1;
return x;
end;
procedure print_stack(s num_stack) is  -- for debugging only; remove from final version
ps varchar2(4000);
begin
for i in 1 .. s.top loop
ps := ps || s.a(i) || ' ';
end loop;
dbms_output.put_line('Stack: ' || rtrim(ps));
end;
begin
while pos1 <= length(str) loop
pos2  := instr(str || ' ', ' ', pos1);
token := substr(str, pos1, pos2 - pos1);
pos1  := pos2 + 1;
case token
when '+' then push(ns, pop(ns) + pop(ns));
when '-' then op2 := pop(ns); push(ns, pop(ns) - op2);
when '*' then push(ns, pop(ns) * pop(ns));
when '/' then op2 := pop(ns); push(ns, pop(ns) / op2);
when '^' then op2 := pop(ns); push(ns, power(pop(ns), op2));
else push(ns, to_number(token));
end case;
print_stack(ns);    -- for debugging purposes only
end loop;
return pop(ns);
end rpn_calc;
/

Testing:

begin
dbms_output.put_line(chr(10) || 'Result: ' || rpn_calc('3 4 2 * 1 5 - 2 3 ^ ^ / +'));
end;
/

Output:

Stack: 3
Stack: 3 4
Stack: 3 4 2
Stack: 3 8
Stack: 3 8 1
Stack: 3 8 1 5
Stack: 3 8 -4
Stack: 3 8 -4 2
Stack: 3 8 -4 2 3
Stack: 3 8 -4 8
Stack: 3 8 65536
Stack: 3 .0001220703125
Stack: 3.0001220703125

Result: 3.0001220703125

PL/SQL procedure successfully completed.

## PowerShell

function Invoke-Rpn
{
<#
.SYNOPSIS
A stack-based evaluator for an expression in reverse Polish notation.
.DESCRIPTION
A stack-based evaluator for an expression in reverse Polish notation.

All methods in the Math and Decimal classes are available.
.PARAMETER Expression
A space separated, string of tokens.
.PARAMETER DisplayState
This switch shows the changes in the stack as each individual token is processed as a table.
.EXAMPLE
Invoke-Rpn -Expression "3 4 Max"
.EXAMPLE
Invoke-Rpn -Expression "3 4 Log2"
.EXAMPLE
Invoke-Rpn -Expression "3 4 2 * 1 5 - 2 3 ^ ^ / +"
.EXAMPLE
Invoke-Rpn -Expression "3 4 2 * 1 5 - 2 3 ^ ^ / +" -DisplayState
#>
[CmdletBinding()]
Param
(
[Parameter(Mandatory=\$true)]
[AllowEmptyString()]
[string]
\$Expression,

[Parameter(Mandatory=\$false)]
[switch]
\$DisplayState
)
Begin
{
function Out-State ([System.Collections.Stack]\$Stack)
{
\$array = \$Stack.ToArray()
[Array]::Reverse(\$array)
\$array | ForEach-Object -Process { Write-Host ("{0,-8:F3}" -f \$_) -NoNewline } -End { Write-Host }
}

function New-RpnEvaluation
{
\$stack = New-Object -Type System.Collections.Stack

\$shortcuts = @{
"+" = "Add"; "-" = "Subtract"; "/" = "Divide"; "*" = "Multiply"; "%" = "Remainder"; "^" = "Pow"
}

:ARGUMENT_LOOP foreach (\$argument in \$args)
{
if (\$DisplayState -and \$stack.Count)
{
Out-State \$stack
}

if (\$shortcuts[\$argument])
{
\$argument = \$shortcuts[\$argument]
}

try
{
\$stack.Push([decimal]\$argument)
continue
}
catch
{
}

\$argCountList = \$argument -replace "(\D+)(\d*)",\$2
\$operation = \$argument.Substring(0, \$argument.Length  \$argCountList.Length)

foreach(\$type in [Decimal],[Math])
{
if (\$definition = \$type::\$operation)
{
if (-not \$argCountList)
{
Foreach-Object { (\$_ -split ", ").Count } |
Sort-Object -Unique
}

foreach (\$argCount in \$argCountList)
{
try
{
\$methodArguments = \$stack.ToArray()[(\$argCount1)..0]
\$result = \$type::\$operation.Invoke(\$methodArguments)

\$null = 1..\$argCount | Foreach-Object { \$stack.Pop() }

\$stack.Push(\$result)

continue ARGUMENT_LOOP
}
catch
{
## If error, try with the next number of arguments
}
}
}
}
}

if (\$DisplayState -and \$stack.Count)
{
Out-State \$stack
if (\$stack.Count)
{
Write-Host "`nResult = \$(\$stack.Peek())"
}
}
else
{
\$stack
}
}
}
Process
{
Invoke-Expression -Command "New-RpnEvaluation \$Expression"
}
End
{
}
}

Invoke-Rpn -Expression "3 4 2 * 1 5 - 2 3 ^ ^ / +" -DisplayState
Output:
3.000
3.000   4.000
3.000   4.000   2.000
3.000   8.000
3.000   8.000   1.000
3.000   8.000   1.000   5.000
3.000   8.000   -4.000
3.000   8.000   -4.000  2.000
3.000   8.000   -4.000  2.000   3.000
3.000   8.000   -4.000  8.000
3.000   8.000   65536.000
3.000   0.000
3.000

Result = 3.0001220703125

## Prolog

Works with SWI-Prolog.

rpn(L) :-
writeln('Token  Action                             Stack'),
parse(L, [],[X] ,[]),
format('~nThe final output value is ~w~n', [X]).

% skip spaces
parse([X|L], St) -->
{char_type(X, white)},
parse(L, St).

% detect operators
parse([Op|L], [Y, X | St]) -->
{ is_op(Op, X, Y, V),
writef('    %s', [[Op]]),
with_output_to(atom(Str2), writef('Apply %s on top of stack', [[Op]])),
writef('  %35l', [Str2]),
writef('%w\n', [[V | St]])},
parse(L, [V | St]).

% detect number
parse([N|L], St) -->
{char_type(N, digit)},
parse_number(L, [N], St).

% string is finished
parse([], St) --> St.

% compute numbers
parse_number([N|L], NC, St) -->
{char_type(N, digit)},
parse_number(L, [N|NC], St).

parse_number(S, NC, St) -->
{ reverse(NC, RNC),
number_chars(V, RNC),
writef('%5r', [V]),
with_output_to(atom(Str2), writef('Push num %w on top of stack', [V])),
writef('  %35l', [Str2]),
writef('%w\n', [[V | St]])},
parse(S, [V|St]).

% defining operations
is_op(42, X, Y, V) :-	V is X*Y.
is_op(43, X, Y, V) :-	V is X+Y.
is_op(45, X, Y, V) :-	V is X-Y.
is_op(47, X, Y, V) :-	V is X/Y.
is_op(94, X, Y, V) :-	V is X**Y.
Output:
5 ?- rpn("3 4 2 * 1 5 - 2 3 ^ ^ / +").
Token  Action                             Stack
3  'Push num 3 on top of stack'       [3]
4  'Push num 4 on top of stack'       [4,3]
2  'Push num 2 on top of stack'       [2,4,3]
*  'Apply * on top of stack'          [8,3]
1  'Push num 1 on top of stack'       [1,8,3]
5  'Push num 5 on top of stack'       [5,1,8,3]
-  'Apply - on top of stack'          [-4,8,3]
2  'Push num 2 on top of stack'       [2,-4,8,3]
3  'Push num 3 on top of stack'       [3,2,-4,8,3]
^  'Apply ^ on top of stack'          [8,-4,8,3]
^  'Apply ^ on top of stack'          [65536,8,3]
/  'Apply / on top of stack'          [0.0001220703125,3]
+  'Apply + on top of stack'          [3.0001220703125]

The final output value is 3.0001220703125
true .

## Python

### Version 1

def op_pow(stack):
b = stack.pop(); a = stack.pop()
stack.append( a ** b )
def op_mul(stack):
b = stack.pop(); a = stack.pop()
stack.append( a * b )
def op_div(stack):
b = stack.pop(); a = stack.pop()
stack.append( a / b )
b = stack.pop(); a = stack.pop()
stack.append( a + b )
def op_sub(stack):
b = stack.pop(); a = stack.pop()
stack.append( a - b )
def op_num(stack, num):
stack.append( num )

ops = {
'^': op_pow,
'*': op_mul,
'/': op_div,
'-': op_sub,
}

def get_input(inp = None):
'Inputs an expression and returns list of tokens'

if inp is None:
inp = input('expression: ')
tokens = inp.strip().split()

def rpn_calc(tokens):
stack = []
table = ['TOKEN,ACTION,STACK'.split(',')]
for token in tokens:
if token in ops:
action = 'Apply op to top of stack'
ops[token](stack)
table.append( (token, action, ' '.join(str(s) for s in stack)) )
else:
action = 'Push num onto top of stack'
op_num(stack, eval(token))
table.append( (token, action, ' '.join(str(s) for s in stack)) )
return table

if __name__ == '__main__':
rpn = '3 4 2 * 1 5 - 2 3 ^ ^ / +'
print( 'For RPN expression: %r\n' % rpn )
rp = rpn_calc(get_input(rpn))
maxcolwidths = [max(len(y) for y in x) for x in zip(*rp)]
row = rp[0]
print( ' '.join('{cell:^{width}}'.format(width=width, cell=cell) for (width, cell) in zip(maxcolwidths, row)))
for row in rp[1:]:
print( ' '.join('{cell:<{width}}'.format(width=width, cell=cell) for (width, cell) in zip(maxcolwidths, row)))

print('\n The final output value is: %r' % rp[-1][2])
Output:
For RPN expression: '3 4 2 * 1 5 - 2 3 ^ ^ / +'

TOKEN           ACTION                 STACK
3     Push num onto top of stack 3
4     Push num onto top of stack 3 4
2     Push num onto top of stack 3 4 2
*     Apply op to top of stack   3 8
1     Push num onto top of stack 3 8 1
5     Push num onto top of stack 3 8 1 5
-     Apply op to top of stack   3 8 -4
2     Push num onto top of stack 3 8 -4 2
3     Push num onto top of stack 3 8 -4 2 3
^     Apply op to top of stack   3 8 -4 8
^     Apply op to top of stack   3 8 65536
/     Apply op to top of stack   3 0.0001220703125
+     Apply op to top of stack   3.0001220703125

The final output value is: '3.0001220703125'

### Version 2

a=[]
b={'+': lambda x,y: y+x, '-': lambda x,y: y-x, '*': lambda x,y: y*x,'/': lambda x,y:y/x,'^': lambda x,y:y**x}
for c in '3 4 2 * 1 5 - 2 3 ^ ^ / +'.split():
if c in b: a.append(b[c](a.pop(),a.pop()))
else: a.append(float(c))
print c, a
Output:
3 [3.0]
4 [3.0, 4.0]
2 [3.0, 4.0, 2.0]
* [3.0, 8.0]
1 [3.0, 8.0, 1.0]
5 [3.0, 8.0, 1.0, 5.0]
- [3.0, 8.0, -4.0]
2 [3.0, 8.0, -4.0, 2.0]
3 [3.0, 8.0, -4.0, 2.0, 3.0]
^ [3.0, 8.0, -4.0, 8.0]
^ [3.0, 8.0, 65536.0]
/ [3.0, 0.0001220703125]
+ [3.0001220703125]

## Quackery

On an historical note, the first step in developing the language Quackery, as is the case with many stack based/reverse Polish/concatenative languages, was coding an RP calculator much like this one. With the minor difference that the exponentiation operator in Quackery is ** rather than ^ (which is bitwise xor) the test string "3 4 2 * 1 5 - 2 3 ^ ^ / +" is Quackery code, and could be compiled and evaluated (in the Quackery vernacular, "built and done") by passing it to the Quackery word quackery, which is defined in Quackery as

[ build do ] is quackery ( \$ --> [ ), which neatly sums up the language.

Here we interpret rather than compile the code, using a switch statement (not actually defined in Quackery, so the code to define it is included), and using the provided ancillary stack temp to make the stack activity explicit.

(If the gentle gatekeepers will permit a moment of shameless self-promotion… If you are interested in stack processors or concatenative languages, you may wish to consider that Quackery was designed with the intent of being an entry level language suitable for educational and hobbyist use, accessible at the code level by virtue of being coded in (mostly) non-idiomatic Python (24k source) and Quackery (another 24k of course) with the Python code emphasising a straightforward approach and the use of simple algorithms for the sake of legibility in preference to efficiency.)

[ stack ]                                 is switch.arg (     --> [ )

[ switch.arg put ]                        is switch     (   x -->   )

[ switch.arg release ]                    is otherwise  (     -->   )

[ switch.arg share
!= iff ]else[ done
otherwise
]'[ do ]done[ ]                         is case       (   x -->   )

[ say "Applying: "
swap echo\$ sp
temp take
temp take
swap rot do
temp put ]                              is apply      ( \$ x -->   )

[ say "Pushing:  " dup echo\$ sp
\$->n drop temp put ]                    is isnumber   (   \$ -->   )

[ temp copy echo cr ]                     is display    (     -->   )

[ nest\$ witheach
[ dup switch
[ \$ '+' case [ ' +  apply ]
\$ '-' case [ ' -  apply ]
\$ '*' case [ ' *  apply ]
\$ '/' case [ ' /  apply ]
\$ '^' case [ ' ** apply ]
otherwise  [ isnumber ] ]
display ]
temp take ]                             is rpncalc    (   \$ --> n )

\$ "3 4 2 * 1 5 - 2 3 ^ ^ / +" rpncalc
say "Result: " echo
Output:
Pushing:  3 [ stack 3 ]
Pushing:  4 [ stack 3 4 ]
Pushing:  2 [ stack 3 4 2 ]
Applying: * [ stack 3 8 ]
Pushing:  1 [ stack 3 8 1 ]
Pushing:  5 [ stack 3 8 1 5 ]
Applying: - [ stack 3 8 -4 ]
Pushing:  2 [ stack 3 8 -4 2 ]
Pushing:  3 [ stack 3 8 -4 2 3 ]
Applying: ^ [ stack 3 8 -4 8 ]
Applying: ^ [ stack 3 8 65536 ]
Applying: / [ stack 3 0 ]
Applying: + [ stack 3 ]
Result: 3

## Racket

#lang racket

(define (calculate-RPN expr)
(for/fold ([stack '()]) ([token expr])
(printf "~a\t -> ~a~N" token stack)
(match* (token stack)
[((? number? n) s) (cons n s)]
[('+ (list x y s ___)) (cons (+ x y) s)]
[('- (list x y s ___)) (cons (- y x) s)]
[('* (list x y s ___)) (cons (* x y) s)]
[('/ (list x y s ___)) (cons (/ y x) s)]
[('^ (list x y s ___)) (cons (expt y x) s)]
[(x s) (error "calculate-RPN: Cannot calculate the expression:"
(reverse (cons x s)))])))

Test case

-> (calculate-RPN '(3.0 4 2 * 1 5 - 2 3 ^ ^ / +))
3.0	 -> ()
4	 -> (3.0)
2	 -> (4 3.0)
*	 -> (2 4 3.0)
1	 -> (8 3.0)
5	 -> (1 8 3.0)
-	 -> (5 1 8 3.0)
2	 -> (-4 8 3.0)
3	 -> (2 -4 8 3.0)
^	 -> (3 2 -4 8 3.0)
^	 -> (8 -4 8 3.0)
/	 -> (65536 8 3.0)
+	 -> (1/8192 3.0)
3.0001220703125

(calculate-RPN (in-port read (open-input-string "3.0 4 2 * 1 5 - 2 3 ^ ^ / +")))

## Raku

(formerly Perl 6)

Works with: rakudo version 2015-09-25
my \$proggie = '3 4 2 * 1 5 - 2 3 ^ ^ / +';

class RPN is Array {

method binop(&op) { self.push: self.pop R[&op] self.pop }

method run(\$p) {
for \$p.words {
say "\$_ ({self})";
when /\d/ { self.push: \$_ }
when '+'  { self.binop: &[+] }
when '-'  { self.binop: &[-] }
when '*'  { self.binop: &[*] }
when '/'  { self.binop: &[/] }
when '^'  { self.binop: &[**] }
default   { die "\$_ is bogus" }
}
say self;
}
}

RPN.new.run(\$proggie);
Output:
3 ()
4 (3)
2 (3 4)
* (3 4 2)
1 (3 8)
5 (3 8 1)
- (3 8 1 5)
2 (3 8 -4)
3 (3 8 -4 2)
^ (3 8 -4 2 3)
^ (3 8 -4 8)
/ (3 8 65536)
+ (3 0.0001220703125)
3.0001220703125

## REXX

### version 1

/* REXX ***************************************************************
* 09.11.2012 Walter Pachl  translates from PL/I
**********************************************************************/
fid='rpl.txt'
ex=linein(fid)
Say 'Input:' ex
/* ex=' 3 4 2 * 1 5 - 2 3 ^ ^ / +' */
Numeric Digits 15
expr=''
st.=0
Say 'Stack contents:'
do While ex<>''
Parse Var ex ch +1 ex
expr=expr||ch;
if ch<>' ' then do
select
When pos(ch,'0123456789')>0 Then Do
Call stack ch
Iterate
End
when ch='+' Then do; operand=getstack(); st.sti = st.sti +  operand; end;
when ch='-' Then do; operand=getstack(); st.sti = st.sti -  operand; end;
when ch='*' Then do; operand=getstack(); st.sti = st.sti *  operand; end;
when ch='/' Then do; operand=getstack(); st.sti = st.sti /  operand; end;
when ch='^' Then do; operand=getstack(); st.sti = st.sti ** operand; end;
end;
call show_stack
end
end
Say 'The reverse polish expression = 'expr
Say 'The evaluated expression = 'st.1
Exit
stack: Procedure Expose st.
/* put the argument on top of the stack */
z=st.0+1
st.z=arg(1)
st.0=z
Return
getstack: Procedure Expose st. sti
/* remove and return the stack's top element */
z=st.0
stk=st.z
st.0=st.0-1
sti=st.0
Return stk
show_stack: procedure Expose st.
/* show the stack's contents */
ol=''
do i=1 To st.0
ol=ol format(st.i,5,10)
End
Say ol
Return
Output:
Input: 3 4 2 * 1 5 - 2 3 ^ ^ / +
Stack contents:
3.0000000000     8.0000000000
3.0000000000     8.0000000000    -4.0000000000
3.0000000000     8.0000000000    -4.0000000000     8.0000000000
3.0000000000     8.0000000000 65536.0000000000
3.0000000000     0.0001220703
3.0001220703
The reverse polish expression = 3 4 2 * 1 5 - 2 3 ^ ^ / +
The evaluated expression = 3.0001220703125

### version 2

This REXX version handles tokens (not characters)   so that the RPN could be   (for instance):

3.0   .4e1   2e0   *   +1.   5   -   2   3   **   **   /   +

which is the essentially the same as the default used by the REXX program.

/*REXX program  evaluates  a   ═════ Reverse Polish notation  (RPN) ═════   expression. */
parse arg x                                      /*obtain optional arguments from the CL*/
if x=''  then x= "3 4 2 * 1 5 - 2 3 ^ ^ / +"     /*Not specified?  Then use the default.*/
tokens=words(x)                                  /*save the  number  of  tokens   "  ". */
showSteps=1                                      /*set to 0 if working steps not wanted.*/
ox=x                                             /*save the  original  value of  X.     */
do i=1  for tokens;   @.i=word(x,i)  /*assign the input tokens to an array. */
end   /*i*/
x=space(x)                                       /*remove any superfluous blanks in  X. */
L=max(20, length(x))                             /*use 20 for the minimum display width.*/
numeric digits L                                 /*ensure enough decimal digits for ans.*/
say center('operand', L, "─")        center('stack', L+L, "─")           /*display title*/
\$=                                               /*nullify the stack (completely empty).*/
do k=1  for tokens;   ?=@.k;   ??=?       /*process each token from the  @. list.*/
#=words(\$)                                /*stack the count (the number entries).*/
if datatype(?,'N')  then do;  \$=\$ ?;   call show  "add to───►stack";  iterate;  end
if ?=='^'           then ??= "**"         /*REXXify    ^ ───► **    (make legal).*/
interpret 'y='word(\$,#-1)  ??  word(\$,#)  /*compute via the famous REXX INTERPRET*/
if datatype(y,'N')  then y=y/1            /*normalize the number with ÷ by unity.*/
\$=subword(\$, 1, #-2)     y                /*rebuild the stack with the answer.   */
call show ?                               /*display steps (tracing into),  maybe.*/
end   /*k*/
say                                              /*display a blank line, better perusing*/
say ' RPN input:'  ox;   say "  answer──►"\$      /*display original input;  display ans.*/
parse source upper . y .                         /*invoked via  C.L.  or via a REXX pgm?*/
if y=='COMMAND' | \datatype(\$,"W")  then exit    /*stick a fork in it,  we're all done. */
else exit \$  /*return the answer  ───►  the invoker.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: if showSteps  then say center(arg(1), L)            left(space(\$), L);        return

output   when using the default input:

─────────operand───────── ──────────────────────stack───────────────────────
*             3 8
add to───►stack      3 8 1 5
-             3 8 -4
add to───►stack      3 8 -4 2
add to───►stack      3 8 -4 2 3
^             3 8 -4 8
^             3 8 65536
/             3 0.0001220703125
+             3.0001220703125

RPN input: 3 4 2 * 1 5 - 2 3 ^ ^ / +

### version 3 (error checking)

This REXX version is the same as above, but also checks for various errors and allows more operators:

•   checks for illegal operator
•   checks for illegal number
•   checks for illegal bit (logical) values
•   checks for malformed RPN expression
•   checks for division by zero
•   allows alternative exponentiation symbol   **
•   allows logical operations   &   &&   |
•   allows alternative division symbol   ÷
•   allows integer division   %
•   allows remainder division   //
•   allows concatenation   ||
/*REXX program  evaluates  a   ═════ Reverse Polish notation  (RPN) ═════   expression. */
parse arg x                                      /*obtain optional arguments from the CL*/
if x=''  then x= "3 4 2 * 1 5 - 2 3 ^ ^ / +"     /*Not specified?  Then use the default.*/
tokens=words(x)                                  /*save the  number  of  tokens   "  ". */
showSteps=1                                      /*set to 0 if working steps not wanted.*/
ox=x                                             /*save the  original  value of  X.     */
do i=1  for tokens;   @.i=word(x,i)  /*assign the input tokens to an array. */
end   /*i*/
x=space(x)                                       /*remove any superfluous blanks in  X. */
L=max(20, length(x))                             /*use 20 for the minimum display width.*/
numeric digits L                                 /*ensure enough decimal digits for ans.*/
say center('operand', L, "─")        center('stack', L+L, "─")           /*display title*/
Dop= '/ // % ÷';             Bop='& | &&'        /*division operators;  binary operands.*/
Aop= '- + * ^ **'  Dop Bop;  Lop=Aop "||"        /*arithmetic operators; legal operands.*/
\$=                                               /*nullify the stack (completely empty).*/
do k=1  for tokens;   ?=@.k;   ??=?       /*process each token from the  @. list.*/
#=words(\$);  b=word(\$, max(1, #) )        /*the stack count;  the last entry.    */
a=word(\$, max(1, #-1) )      /*stack's  "first"  operand.           */
division  =wordpos(?, Dop)\==0            /*flag:  doing a some kind of division.*/
arith     =wordpos(?, Aop)\==0            /*flag:  doing arithmetic.             */
bitOp     =wordpos(?, Bop)\==0            /*flag:  doing some kind of binary oper*/
if datatype(?, 'N')   then do; \$=\$ ?;  call show  "add to───►stack";  iterate;  end
if wordpos(?, Lop)==0 then do; \$=e 'illegal operator:' ?;      leave; end
if w<2                then do; \$=e 'illegal RPN expression.';  leave; end
if ?=='^'             then ??= "**"       /*REXXify  ^ ──► **   (make it legal). */
if ?=='÷'             then ??= "/"        /*REXXify  ÷ ──► /    (make it legal). */
if division  &  b=0   then do; \$=e 'division by zero.'      ;  leave; end
if bitOp & \isBit(a)  then do; \$=e "token isn't logical: " a;  leave; end
if bitOp & \isBit(b)  then do; \$=e "token isn't logical: " b;  leave; end
interpret 'y='   a   ??   b               /*compute with two stack operands*/
if datatype(y, 'W')   then y=y/1          /*normalize the number with ÷ by unity.*/
_=subword(\$, 1, #-2);      \$=_ y          /*rebuild the stack with the answer.   */
call show ?                               /*display (possibly)  a working step.  */
end   /*k*/
say                                              /*display a blank line, better perusing*/
if word(\$,1)==e  then \$=                         /*handle the special case of errors.   */
say ' RPN input:'  ox;   say " answer───►"\$      /*display original input;  display ans.*/
parse source upper . y .                         /*invoked via  C.L.  or via a REXX pgm?*/
if y=='COMMAND' | \datatype(\$,"W")  then exit    /*stick a fork in it,  we're all done. */
else exit \$  /*return the answer  ───►  the invoker.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
isBit: return arg(1)==0 | arg(1)==1              /*returns   1   if arg1 is a binary bit*/
show:  if showSteps  then say center(arg(1), L)           left(space(\$), L);        return

output   is identical to the 2nd REXX version.

## Ruby

rpn = RPNExpression("3 4 2 * 1 5 - 2 3 ^ ^ / +")
value = rpn.eval
Output:
for RPN expression: 3 4 2 * 1 5 - 2 3 ^ ^ / +
Term	Action	Stack
3	PUSH	[3]
4	PUSH	[3, 4]
2	PUSH	[3, 4, 2]
*	MUL	[3, 8]
1	PUSH	[3, 8, 1]
5	PUSH	[3, 8, 1, 5]
-	SUB	[3, 8, -4]
2	PUSH	[3, 8, -4, 2]
3	PUSH	[3, 8, -4, 2, 3]
^	EXP	[3, 8, -4, 8]
^	EXP	[3, 8, 65536]
/	DIV	[3, 0.0001220703125]
Value = 3.0001220703125

## Rust

fn rpn(text: &str) -> f64 {
let tokens = text.split_whitespace();
let mut stack: Vec<f64> = vec![];
println!("input operation stack");

for token in tokens {
print!("{:^5} ", token);
match token.parse() {
Ok(num) => {
stack.push(num);
println!("push      {:?}", stack);
}
Err(_) => {
match token {
"+" => {
let b = stack.pop().expect("missing first operand");
let a = stack.pop().expect("missing second operand");
stack.push(a + b);
}
"-" => {
let b = stack.pop().expect("missing first operand");
let a = stack.pop().expect("missing second operand");
stack.push(a - b);
}
"*" => {
let b = stack.pop().expect("missing first operand");
let a = stack.pop().expect("missing second operand");
stack.push(a * b);
}
"/" => {
let b = stack.pop().expect("missing first operand");
let a = stack.pop().expect("missing second operand");
stack.push(a / b);
}
"^" => {
let b = stack.pop().expect("missing first operand");
let a = stack.pop().expect("missing second operand");
stack.push(a.powf(b));
}
_ => panic!("unknown operator {}", token),
}
println!("calculate {:?}", stack);
}
}
}

stack.pop().unwrap_or(0.0)
}

fn main() {
let text = "3 4 2 * 1 5 - 2 3 ^ ^ / +";

println!("\nresult: {}", rpn(text));
}
Output:
input operation stack
3   push      [3.0]
4   push      [3.0, 4.0]
2   push      [3.0, 4.0, 2.0]
*   calculate [3.0, 8.0]
1   push      [3.0, 8.0, 1.0]
5   push      [3.0, 8.0, 1.0, 5.0]
-   calculate [3.0, 8.0, -4.0]
2   push      [3.0, 8.0, -4.0, 2.0]
3   push      [3.0, 8.0, -4.0, 2.0, 3.0]
^   calculate [3.0, 8.0, -4.0, 8.0]
^   calculate [3.0, 8.0, 65536.0]
/   calculate [3.0, 0.0001220703125]
+   calculate [3.0001220703125]

result: 3.0001220703125

## Scala

object RPN {
val PRINT_STACK_CONTENTS: Boolean = true

def main(args: Array[String]): Unit = {
val result = evaluate("3 4 2 * 1 5 - 2 3 ^ ^ / +".split(" ").toList)
}

def evaluate(tokens: List[String]): Double = {
import scala.collection.mutable.Stack
val stack: Stack[Double] = new Stack[Double]
for (token <- tokens) {
if (isOperator(token)) token match {
case "+" => stack.push(stack.pop + stack.pop)
case "-" => val x = stack.pop; stack.push(stack.pop - x)
case "*" => stack.push(stack.pop * stack.pop)
case "/" => val x = stack.pop; stack.push(stack.pop / x)
case "^" => val x = stack.pop; stack.push(math.pow(stack.pop, x))
case _ => throw new RuntimeException( s""""\$token" is not an operator""")
}
else stack.push(token.toDouble)

if (PRINT_STACK_CONTENTS) {
print("Input: " + token)
print(" Stack: ")
for (element <- stack.seq.reverse) print(element + " ");
println("")
}
}

stack.pop
}

def isOperator(token: String): Boolean = {
token match {
case "+" => true; case "-" => true; case "*" => true; case "/" => true; case "^" => true
case _ => false
}
}
}
Output:
Input: 3 Stack: 3.0
Input: 4 Stack: 3.0 4.0
Input: 2 Stack: 3.0 4.0 2.0
Input: * Stack: 3.0 8.0
Input: 1 Stack: 3.0 8.0 1.0
Input: 5 Stack: 3.0 8.0 1.0 5.0
Input: - Stack: 3.0 8.0 -4.0
Input: 2 Stack: 3.0 8.0 -4.0 2.0
Input: 3 Stack: 3.0 8.0 -4.0 2.0 3.0
Input: ^ Stack: 3.0 8.0 -4.0 8.0
Input: ^ Stack: 3.0 8.0 65536.0
Input: / Stack: 3.0 1.220703125E-4
Input: + Stack: 3.0001220703125

## Sidef

Translation of: Raku
var proggie = '3 4 2 * 1 5 - 2 3 ^ ^ / +'

class RPN(arr=[]) {

method binop(op) {
var x = arr.pop
var y = arr.pop
arr << y.(op)(x)
}

method run(p) {
p.each_word { |w|
say "#{w} (#{arr})"
given (w) {
when (/\d/) {
arr << Num(w)
}
when (<+ - * />) {
self.binop(w)
}
when ('^') {
self.binop('**')
}
default {
die "#{w} is bogus"
}
}
}
say arr[0]
}
}

RPN.new.run(proggie)
Output:
3 ()
4 (3)
2 (3 4)
* (3 4 2)
1 (3 8)
5 (3 8 1)
- (3 8 1 5)
2 (3 8 -4)
3 (3 8 -4 2)
^ (3 8 -4 2 3)
^ (3 8 -4 8)
/ (3 8 65536)
+ (3 0.0001220703125)
3.0001220703125

## Swift

Translation of: Go
let opa = [
"^": (prec: 4, rAssoc: true),
"*": (prec: 3, rAssoc: false),
"/": (prec: 3, rAssoc: false),
"+": (prec: 2, rAssoc: false),
"-": (prec: 2, rAssoc: false),
]

func rpn(tokens: [String]) -> [String] {
var rpn : [String] = []
var stack : [String] = [] // holds operators and left parenthesis

for tok in tokens {
switch tok {
case "(":
stack += [tok] // push "(" to stack
case ")":
while !stack.isEmpty {
let op = stack.removeLast() // pop item from stack
if op == "(" {
} else {
rpn += [op] // add operator to result
}
}
default:
if let o1 = opa[tok] { // token is an operator?
for op in stack.reverse() {
if let o2 = opa[op] {
if !(o1.prec > o2.prec || (o1.prec == o2.prec && o1.rAssoc)) {
// top item is an operator that needs to come off
rpn += [stack.removeLast()] // pop and add it to the result
continue
}
}
break
}

stack += [tok] // push operator (the new one) to stack
} else { // token is not an operator
rpn += [tok] // add operand to result
}
}
}

return rpn + stack.reverse()
}

func parseInfix(e: String) -> String {
let tokens = e.characters.split{ \$0 == " " }.map(String.init)
return rpn(tokens).joinWithSeparator(" ")
}

var input : String

input = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"
"infix: \(input)"
"postfix: \(parseInfix(input))"
Output:
"postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / +"

## Tcl

# Helper
proc pop stk {
upvar 1 \$stk s
set val [lindex \$s end]
set s [lreplace \$s end end]
return \$val
}

proc evaluate rpn {
set stack {}
foreach token \$rpn {
set act "apply"
switch \$token {
"^" {
# Non-commutative operation
set a [pop stack]
lappend stack [expr {[pop stack] ** \$a}]
}
"/" {
# Non-commutative, special float handling
set a [pop stack]
set b [expr {[pop stack] / double(\$a)}]
if {\$b == round(\$b)} {set b [expr {round(\$b)}]}
lappend stack \$b
}
"*" {
# Commutative operation
lappend stack [expr {[pop stack] * [pop stack]}]
}
"-" {
# Non-commutative operation
set a [pop stack]
lappend stack [expr {[pop stack] - \$a}]
}
"+" {
# Commutative operation
lappend stack [expr {[pop stack] + [pop stack]}]
}
default {
set act "push"
lappend stack \$token
}
}
puts "\$token\t\$act\t\$stack"
}
return [lindex \$stack end]
}

puts [evaluate {3 4 2 * 1 5 - 2 3 ^ ^ / +}]
Output:
3	push	3
4	push	3 4
2	push	3 4 2
*	apply	3 8
1	push	3 8 1
5	push	3 8 1 5
-	apply	3 8 -4
2	push	3 8 -4 2
3	push	3 8 -4 2 3
^	apply	3 8 -4 8
^	apply	3 8 65536
/	apply	3 0.0001220703125
+	apply	3.0001220703125
3.0001220703125

## UNIX Shell

Please note that the asterisk * within the argument string needs to be escaped or quoted, otherwise the shell will interpret and expand it.

Technically, this implementation uses a string to represent a stack and lines to delimit each item of the stack, not spaces as you might expect. However, the input is parsed pretty much as a space-separated argument string, but only with the asterisk quoted.

#!/bin/sh

exp() {
R=1
local i=1

while [ \$i -le \$2 ]; do
R=\$((\$R * \$1))
i=\$((\$i + 1))
done
}

rpn() {
local O1 O2 stack

while [ \$# -ge 1 ]; do
grep -iE '^-?[0-9]+\$' <<< "\$1" > /dev/null 2>&1
if [ "\$?" -eq 0 ]; then
stack=`sed -e '\$a'"\$1" -e '/^\$/d' <<< "\$stack"`
else
grep -iE '^[-\+\*\/\%\^]\$' <<< "\$1" > /dev/null 2>&1
if [ "\$?" -eq 0 ]; then
O2=`sed -n '\$p' <<< "\$stack"`
stack=`sed '\$d' <<< "\$stack"`
O1=`sed -n '\$p' <<< "\$stack"`

case "\$1" in
'+')
stack=`sed -e '\$a'"\$((\$O1 + \$O2))" -e '/^\$/d' -e '\$d' \
<<< "\$stack"`;;
'-')
stack=`sed -e '\$a'"\$((\$O1 - \$O2))" -e '/^\$/d' -e '\$d' \
<<< "\$stack"`;;
'*')
stack=`sed -e '\$a'"\$((\$O1 * \$O2))" -e '/^\$/d' -e '\$d' \
<<< "\$stack"`;;
'/')
stack=`sed -e '\$a'"\$((\$O1 / \$O2))" -e '/^\$/d' -e '\$d' \
<<< "\$stack"`;;
'%')
stack=`sed -e '\$a'"\$((\$O1 % \$O2))" -e '/^\$/d' -e '\$d' \
<<< "\$stack"`;;
'^')
exp \$O1 \$O2
stack=`sed -e '\$a'"\$((\$R))" -e '/^\$/d' -e '\$d' <<< \
"\$stack"`;;
esac
else
echo "Unknown RPN token \`\`\$1''"
fi
fi
echo "\$1" ":" \$stack
shift
done

sed -n '1p' <<< "\$stack"
if [ "`wc -l <<< "\$stack"`" -gt 1 ]; then
echo "Malformed input expression" > /dev/stderr
return 1
else
return 0
fi
}

rpn 3 4 2 '*' 1 5 '-' 2 3 '^' '^' '/' '+'

3 : 3
4 : 3 4
2 : 3 4 2
* : 3 8
1 : 3 8 1
5 : 3 8 1 5
- : 3 8 -4
2 : 3 8 -4 2
3 : 3 8 -4 2 3
^ : 3 8 -4 8
^ : 3 8 65536
/ : 3 0
+ : 3
3

## V (Vlang)

Translation of: C

Updated to V (Vlang) version 0.2.2

import math

const (
supported_operations = ['+', '-', '*', '/', '^']
max_depth = 256
)

struct Stack {
mut:
data  []f32 = [f32(0)].repeat(max_depth)
depth int
}

fn (mut stack Stack) push(value f32) {
if stack.depth >= max_depth {
println('Stack Overflow!!')
return
}
stack.data[stack.depth] = value
stack.depth++
}

fn (mut stack Stack) pop() ?f32 {
if stack.depth > 0 {
stack.depth--
result := stack.data[stack.depth]
return result
}
return error('Stack Underflow!!')
}

fn (stack Stack) peek() ?f32 {
if stack.depth > 0 {
result := stack.data[0]
return result
}
return error('Out of Bounds...')
}

fn (mut stack Stack) rpn(input string) ?f32 {
println('Input: \$input')
tokens := input.split(' ')
mut a := f32(0)
mut b := f32(0)
println('Token     Stack')
for token in tokens {
if token.str.is_digit() {
stack.push(token.f32())
} else if token in supported_operations {
b = stack.pop() or { f32(0) }
a = stack.pop() or { f32(0) }
match token {
'+' {
stack.push(a + b)
}
'-' {
stack.push(a - b)
}
'*' {
stack.push(a * b)
}
'/' {
stack.push(a / b)
}
'^' {
stack.push(f32(math.pow(a, b)))
}
else {
println('Oofffff')
}
}
}
print('\${token:5s}     ')
for i := 0; i < stack.depth; i++ {
if i == stack.depth - 1 {
println('\${stack.data[i]:0.6f} |>')
} else {
print('\${stack.data[i]:0.6f}, ')
}
}
}
return stack.peek()
}

fn main() {
mut calc := Stack{}
result := calc.rpn('3 4 2 * 1 5 - 2 3 ^ ^ / +') or { return }
println('\nResult:   \$result')
}
Output:
Input: 3 4 2 * 1 5 - 2 3 ^ ^ / +
Token     Stack
3     3.000000 |>
4     3.000000, 4.000000 |>
2     3.000000, 4.000000, 2.000000 |>
*     3.000000, 8.000000 |>
1     3.000000, 8.000000, 1.000000 |>
5     3.000000, 8.000000, 1.000000, 5.000000 |>
-     3.000000, 8.000000, -4.000000 |>
2     3.000000, 8.000000, -4.000000, 2.000000 |>
3     3.000000, 8.000000, -4.000000, 2.000000, 3.000000 |>
^     3.000000, 8.000000, -4.000000, 8.000000 |>
^     3.000000, 8.000000, 65536.000000 |>
/     3.000000, 0.000122 |>
+     3.000122 |>

Result:   3.000122

## Wren

Translation of: Kotlin
Library: Wren-seq
import "/seq" for Stack

var rpnCalculate = Fn.new { |expr|
if (expr == "") Fiber.abort("Expression cannot be empty.")
System.print("For expression = %(expr)\n")
System.print("Token           Action             Stack")
var tokens = expr.split(" ").where { |t| t != "" }
var stack = Stack.new()
for (token in tokens) {
var d = Num.fromString(token)
if (d) {
stack.push(d)
System.print(" %(d)     Push num onto top of stack  %(stack)")
} else if ((token.count > 1) || !"+-*/^".contains(token)) {
Fiber.abort("%(token) is not a valid token.")
} else if (stack.count < 2) {
Fiber.abort("Stack contains too few operands.")
} else {
var d1 = stack.pop()
var d2 = stack.pop()
stack.push(token == "+" ? d2 + d1 :
token == "-" ? d2 - d1 :
token == "*" ? d2 * d1 :
token == "/" ? d2 / d1 : d2.pow(d1))
System.print(" %(token)     Apply op to top of stack    %(stack)")
}
}
System.print("\nThe final value is %(stack.pop())")
}

var expr = "3 4 2 * 1 5 - 2 3 ^ ^ / +"
rpnCalculate.call(expr)
Output:
For expression = 3 4 2 * 1 5 - 2 3 ^ ^ / +

Token           Action             Stack
3     Push num onto top of stack  [3]
4     Push num onto top of stack  [3, 4]
2     Push num onto top of stack  [3, 4, 2]
*     Apply op to top of stack    [3, 8]
1     Push num onto top of stack  [3, 8, 1]
5     Push num onto top of stack  [3, 8, 1, 5]
-     Apply op to top of stack    [3, 8, -4]
2     Push num onto top of stack  [3, 8, -4, 2]
3     Push num onto top of stack  [3, 8, -4, 2, 3]
^     Apply op to top of stack    [3, 8, -4, 8]
^     Apply op to top of stack    [3, 8, 65536]
/     Apply op to top of stack    [3, 0.0001220703125]
+     Apply op to top of stack    [3.0001220703125]

The final value is 3.0001220703125

## XPL0

real Stack(10);
int  SP;

proc Push(X);
real X;
[Stack(SP):= X;  SP:= SP+1];

func real Pop;
[SP:= SP-1;  return Stack(SP)];

char Str;  real Top;  int Token, I;
[Str:= "3 4 2 * 1 5 - 2 3 ^^ ^^ / + ";
SP:= 0;
Format(6, 8);
loop    [repeat Token:= Str(0);  Str:= Str+1;
until   Token # ^ ;             \skip space characters
case Token of
^+:   [Top:= Pop;  Push(Pop+Top)];
^-:   [Top:= Pop;  Push(Pop-Top)];
^*:   [Top:= Pop;  Push(Pop*Top)];
^/:   [Top:= Pop;  Push(Pop/Top)];
^^:   [Top:= Pop;  Push(Pow(Pop, Top))];
\$A0:  quit                    \space with MSB set
other [Push(float(Token-^0))];  \single digit number
ChOut(0, Token);
for I:= 0 to SP-1 do            \show stack
RlOut(0, Stack(I));
CrLf(0);
];
]
Output:
3     3.00000000
4     3.00000000     4.00000000
2     3.00000000     4.00000000     2.00000000
*     3.00000000     8.00000000
1     3.00000000     8.00000000     1.00000000
5     3.00000000     8.00000000     1.00000000     5.00000000
-     3.00000000     8.00000000    -4.00000000
2     3.00000000     8.00000000    -4.00000000     2.00000000
3     3.00000000     8.00000000    -4.00000000     2.00000000     3.00000000
^     3.00000000     8.00000000    -4.00000000     8.00000000
^     3.00000000     8.00000000 65536.00000000
/     3.00000000     0.00012207
+     3.00012207

## zkl

var ops=D("^",True,  "*",'*,  "/",'/,  "+",'+,  "-",'-);

fcn parseRPN(e){
println("\npostfix: ", e);
stack:=L();
foreach tok in (e.split()){
op:=ops.find(tok);
if(op){
y := stack.pop(); x := stack.pop();
if(True==op) x=x.pow(y);
else	      x=op(x,y);
stack.append(x);
}
else stack.append(tok.toFloat());
println(tok," --> ",stack);
}
println("result: ", stack[0])
}
tests:=T("3 4 2 * 1 5 - 2 3 ^ ^ / +");
foreach t in (tests) { parseRPN(t) }
Output:
postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / +
3 --> L(3)
4 --> L(3,4)
2 --> L(3,4,2)
* --> L(3,8)
1 --> L(3,8,1)
5 --> L(3,8,1,5)
- --> L(3,8,-4)
2 --> L(3,8,-4,2)
3 --> L(3,8,-4,2,3)
^ --> L(3,8,-4,8)
^ --> L(3,8,65536)
/ --> L(3,0.00012207)
+ --> L(3.00012)
result: 3.00012