Truth table
From Rosetta Code
Truth table is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A truth table is a display of the inputs to, and the output of a Boolean equation organised as a table where each row gives one combination of input values and the corresponding value of the equation.
- Task
- Input a Boolean equation from the user as a string then calculate and print a formatted truth table for the given equation.
(One can assume that the user input is correct). - Print and show output for Boolean equations of two and three input variables, but any program should not be limited to that many variables in the equation.
- Either reverse-polish or infix notation expressions are allowed.
- Cf.
- Ref.
- Wolfram mathworld entry on truth tables.
- Some examples from Google.
Contents |
[edit] D
import std.stdio, std.traits, std.range, std.algorithm;
void truthTable(size_t N)
(immutable bool function(in bool[N]) pure nothrow fun,
in string expression, in char[N] vars...)
if (N > 0) {
writefln("\n\n%( %2c %) %s\n", vars, expression);
bool[N] bits;
foreach (immutable i; 0 .. 2 ^^ N) {
N.iota.map!(j => (i & (1 << (N - j - 1))) != 0).copy(bits[]);
writefln("%(%2d %) : %d", bits, fun(bits));
}
}
bool xor(in bool[2] args) pure nothrow {
return args[0] != args[1];
}
bool stu(in bool[3] args) pure nothrow {
return args[0] || (args[1] ^ args[2]);
}
bool abcd(in bool[4] args) pure nothrow {
return args[0] ^ (args[1] ^ (args[2] ^ args[3]));
}
void main() {
truthTable(&xor, "A ^ B", 'A', 'B');
truthTable(&stu, "S | ( T ^ U )", 'S', 'T', 'U');
truthTable(&abcd, "A ^ (B ^ (C ^ D))", 'A', 'B', 'C', 'D');
}
- Output:
A B A ^ B 0 0 : 0 0 1 : 1 1 0 : 1 1 1 : 0 S T U S | ( T ^ U ) 0 0 0 : 0 0 0 1 : 1 0 1 0 : 1 0 1 1 : 0 1 0 0 : 1 1 0 1 : 1 1 1 0 : 1 1 1 1 : 1 A B C D A ^ (B ^ (C ^ D)) 0 0 0 0 : 0 0 0 0 1 : 1 0 0 1 0 : 1 0 0 1 1 : 0 0 1 0 0 : 1 0 1 0 1 : 0 0 1 1 0 : 0 0 1 1 1 : 1 1 0 0 0 : 1 1 0 0 1 : 0 1 0 1 0 : 0 1 0 1 1 : 1 1 1 0 0 : 0 1 1 0 1 : 1 1 1 1 0 : 1 1 1 1 1 : 0
[edit] Go
Variance from statement of task: Runtime evaluation or code generation is not directly supported in Go. The function tt here does however accept functions with any number of arguments and produce the corresponding truth table.
package main
import (
"fmt"
"reflect"
)
func xor(a, b bool) bool {
return a != b
}
func stu(s, t, u bool) bool {
return s || xor(t, u)
}
func abcd(a, b, c, d bool) bool {
return xor(a, xor(b, xor(c, d)))
}
func main() {
tt(xor, "A B A ^ B")
tt(stu, "S T U S | ( T ^ U )")
tt(abcd, "A B C D A ^ (B ^ (C ^ D))")
}
func tt(f interface{}, label string) {
fmt.Println()
fmt.Println(label)
tv := []bool{false, true}
v := reflect.ValueOf(f)
n := reflect.TypeOf(f).NumIn()
a := make([]reflect.Value, n)
lines := 1 << uint(n)
for l := 0; l < lines; l++ {
s := " "
lBits := l
for i := range a {
ba := tv[lBits & 1]
s = fmt.Sprintf("%-5t %s", ba, s)
a[n-1-i] = reflect.ValueOf(ba)
lBits >>= 1
}
fmt.Println(s, v.Call(a)[0].Bool())
}
}
Output:
A B A ^ B false false false false true true true false true true true false S T U S | ( T ^ U ) false false false false false false true true false true false true false true true false true false false true true false true true true true false true true true true true A B C D A ^ (B ^ (C ^ D)) false false false false false false false false true true false false true false true false false true true false false true false false true false true false true false false true true false false false true true true true true false false false true true false false true false true false true false false true false true true true true true false false false true true false true true true true true false true true true true true false
[edit] J
Implementation:
truthTable=:3 :0
assert. -. 1 e. 'data expr names table' e.&;: y
names=. ~. (#~ _1 <: nc) ;:expr=. y
data=. #:i.2^#names
(names)=. |:data
(' ',;:inv names,<expr),(1+#@>names,<expr)":data,.".expr
)
The argument is expected to be a valid boolean J sentence which, among other things, does not use any of the words used within the implementation (but any single-character name is valid).
Example use:
truthTable '-.b'
b -.b
0 1
1 0
truthTable 'a*b'
a b a*b
0 0 0
0 1 0
1 0 0
1 1 1
truthTable 'a+.b'
a b a+.b
0 0 0
0 1 1
1 0 1
1 1 1
truthTable 'a<:b'
a b a<:b
0 0 1
0 1 1
1 0 0
1 1 1
truthTable '(a*bc)+.d'
a bc d (a*bc)+.d
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
[edit] Java
This example would require a system of pages that would be moderately complicated to set up and follow (or a really huge page that would also be hard to follow) since there is no eval in Java, so you can find information about it here. There is a link to an executable jar file with the required source files there. The program shows the expression and the truth table in a window. The expression must use prefix notation, single characters for input names (numerals, lowercase letters, and uppercase letters are the easiest to read), and the outputs can be shown as 1/0 or T/F. There is also a "Check" button which will make sure that the operators have enough operands. The window looks something like this:
[edit] Javascript
Actually a HTML document. Save as a .html document and double-click it. You should be fine.
<!DOCTYPE html><html><head><title>Truth table</title><script>
var elem,expr,vars;
function isboolop(chr){return "&|!^".indexOf(chr)!=-1;}
function varsindexof(chr){
var i;
for(i=0;i<vars.length;i++){if(vars[i][0]==chr)return i;}
return -1;
}
function printtruthtable(){
var i,str;
elem=document.createElement("pre");
expr=prompt("Boolean expression:\nAccepts single-character variables (except for \"T\" and \"F\", which specify explicit true or false values), postfix, with \"&|!^\" for and, or, not, xor, respectively; optionally seperated by whitespace.").replace(/\s/g,"");
vars=[];
for(i=0;i<expr.length;i++)if(!isboolop(expr[i])&&expr[i]!="T"&&expr[i]!="F"&&varsindexof(expr[i])==-1)vars.push([expr[i],-1]);
if(vars.length==0)return;
str="";
for(i=0;i<vars.length;i++)str+=vars[i][0]+" ";
elem.innerHTML="<b>"+str+expr+"</b>\n";
vars[0][1]=false;
truthpartfor(1);
vars[0][1]=true;
truthpartfor(1);
vars[0][1]=-1;
document.body.appendChild(elem);
}
function truthpartfor(index){
if(index==vars.length){
var str,i;
str="";
for(i=0;i<index;i++)str+=(vars[i][1]?"<b>T</b>":"F")+" ";
elem.innerHTML+=str+(parsebool()?"<b>T</b>":"F")+"\n";
return;
}
vars[index][1]=false;
truthpartfor(index+1);
vars[index][1]=true;
truthpartfor(index+1);
vars[index][1]=-1;
}
function parsebool(){
var stack,i,idx;
console.log(vars);
stack=[];
for(i=0;i<expr.length;i++){
if(expr[i]=="T")stack.push(true);
else if(expr[i]=="F")stack.push(false);
else if((idx=varsindexof(expr[i]))!=-1)stack.push(vars[idx][1]);
else if(isboolop(expr[i])){
switch(expr[i]){
case "&":stack.push(stack.pop()&stack.pop());break;
case "|":stack.push(stack.pop()|stack.pop());break;
case "!":stack.push(!stack.pop());break;
case "^":stack.push(stack.pop()^stack.pop());break;
}
} else alert("Non-conformant character "+expr[i]+" in expression. Should not be possible.");
console.log(stack);
}
return stack[0];
}
</script></head><body onload="printtruthtable()"></body></html>
[edit] Liberty BASIC
This at first seems trivial, given our lovely 'eval' function. However it is complicated by LB's use of 'non-zero' for 'true', and by the requirements of accepting different numbers and names of variables. My program assumes all space-separated words in the expression$ are either a logic-operator, bracket delimiter, or variable name. Since a truth table for 8 or more variables is of silly length, I regard that as a practical limit.
print " TRUTH TABLES"
print " Input a valid Boolean expression for creating the truth table "
print " Use lowercase 'and', 'or', 'xor', '(', 'not(' and ')'."
print " Take special care to precede closing bracket with a space."
print " You can use any alphanumeric variable names, but no spaces."
print " You can refer again to a variable used already."
print " Program assumes <8 variables will be used.."
print " eg 'A xor B and not( C or A )'"
print " or 'Too_High xor not( Fuel_Out )'"
[start]
input " "; expression$
if expression$ ="" then [start]
'used$ =""
numVariables =0 ' count of detected variable names
variableNames$ ="" ' filled with detected variable names
i =1 ' index to space-delimited word in the expression$
[parse]
m$ =word$( expression$, i, " ")
if m$ ="" then [analyse]
' is it a reserved word, or a variable name already met?
if m$ <>"and" and m$ <>"or" and m$ <>"not(" and m$ <>")" and m$ <>"xor"_
and not( instr( variableNames$, m$)) then
variableNames$ =variableNames$ +m$ +" ": numVariables =numVariables +1
end if
i =i +1
goto [parse]
[analyse]
for i =1 to numVariables
ex$ =FindReplace$( expression$, word$( variableNames$, i, " "), chr$( 64 +i), 1)
expression$ =ex$
next i
'print " "; numVariables; " variables, simplifying to "; expression$
print ,;
for j =1 to numVariables
print word$( variableNames$, j, " "),
next j
print "Result"
for i =0 to ( 2^numVariables) -1
print ,;
A =i mod 2: print A,
if numVariables >1 then B =int( i /2) mod 2: print B,
if numVariables >2 then C =int( i /4) mod 2: print C,
if numVariables >3 then D =int( i /4) mod 2: print D,
if numVariables >4 then E =int( i /4) mod 2: print E,
if numVariables >5 then F =int( i /4) mod 2: print F,
if numVariables >6 then G =int( i /4) mod 2: print G,
' .......................... etc
'e =eval( expression$)
if eval( expression$) <>0 then e$ ="1" else e$ ="0"
print "==> "; e$
next i
goto [start]
end
function FindReplace$( FindReplace$, find$, replace$, replaceAll)
if ( ( FindReplace$ <>"") and ( find$ <>"")) then
fLen = len( find$)
rLen = len( replace$)
do
fPos = instr( FindReplace$, find$, fPos)
if not( fPos) then exit function
pre$ = left$( FindReplace$, fPos -1)
post$ = mid$( FindReplace$, fPos +fLen)
FindReplace$ = pre$ +replace$ +post$
fPos = fPos +(rLen -fLen) +1
loop while ( replaceAll)
end if
end function
Too_High and Fuel_Out
Too_High Fuel_Out Result
0 0 ==> 0
1 0 ==> 0
0 1 ==> 0
1 1 ==> 1
Fat or Ugly and not( Rich )
Fat Ugly Rich Result
0 0 0 ==> 0
1 0 0 ==> 1
0 1 0 ==> 1
1 1 0 ==> 1
0 0 1 ==> 0
1 0 1 ==> 0
0 1 1 ==> 0
1 1 1 ==> 0
[edit] Mathematica
VariableNames[data_] := Module[ {TokenRemoved},
TokenRemoved = StringSplit[data,{"~And~","~Or~","~Xor~","!","(",")"}];
Union[Select[Map[StringTrim,TokenRemoved] , Not[StringMatchQ[#,""]]&]]
]
TruthTable[BooleanEquation_] := Module[ {TestDataSet},
TestDataSet = MapThread[Rule,{ToExpression@VariableNames[BooleanEquation],#}]&/@
Tuples[{False,True}, Length[VariableNames[BooleanEquation]]];
Join[List[Flatten[{VariableNames[BooleanEquation],BooleanEquation}]],
Flatten[{#/.Rule[x_,y_] -> y,ReplaceAll[ToExpression[BooleanEquation],#]}]&/@TestDataSet]//Grid
]
Example usage:
TruthTable["V ~Xor~ (B ~Xor~ (K ~Xor~ D ) )"] B D K V V ~Xor~ (B ~Xor~ (K ~Xor~ D ) ) False False False False False False False False True True False False True False True False False True True False False True False False True False True False True False False True True False False False True True True True True False False False True True False False True False True False True False False True False True True True True True False False False True True False True True True True True False True True True True True False
[edit] Perl
Note: can't process stuff like "X xor Y"; "xor" would be treated as a variable name here.
#!/usr/bin/perl
sub truth_table {
my $s = shift;
my (%seen, @vars);
for ($s =~ /([a-zA-Z_]\w*)/g) {
$seen{$_} //= do { push @vars, $_; 1 };
}
print "\n", join("\t", @vars, $s), "\n", '-' x 40, "\n";
@vars = map("\$$_", @vars);
$s =~ s/([a-zA-Z_]\w*)/\$$1/g;
$s = "print(".join(',"\t", ', map("($_?'T':'F')", @vars, $s)).",\"\\n\")";
$s = "for my $_ (0, 1) { $s }" for (reverse @vars);
eval $s;
}
truth_table 'A ^ A_1';
truth_table 'foo & bar | baz';
truth_table 'Jim & (Spock ^ Bones) | Scotty';
- Output:
A A_1 A ^ A_1 ---------------------------------------- F F F F T T T F T T T F
foo bar baz foo & bar | baz ---------------------------------------- F F F F F F T T F T F F F T T T T F F F T F T T T T F T T T T T
Jim Spock Bones Scotty Jim & (Spock ^ Bones) | Scotty ---------------------------------------- F F F F F ...<snip for space -- not like you're gonna verify it anyway>... T T T T T
[edit] Perl 6
sub MAIN ($x) {
my @n = $x.comb(/<ident>/);
my &fun = eval "-> {('\\' «~« @n).join(',')} \{ [{ (@n,"so $x").join(',') }] \}";
say (@n,$x).join("\t");
.join("\t").say for map &fun, map { .fmt("\%0{+@n}b").comb».so }, 0 ..^ 2**@n;
}
- Output:
$ truthtable 'A ^ B' A B A ^ B False False False False True True True False True True True False $ truthtable 'foo & bar | baz' foo bar baz foo & bar | baz False False False False False False True True False True False False False True True True True False False False True False True True True True False True True True True True $ truthtable 'Jim & (Spock ^ Bones) | Scotty' Jim Spock Bones Scotty Jim & (Spock ^ Bones) | Scotty False False False False False False False False True True False False True False False False False True True True False True False False False False True False True True False True True False False False True True True True True False False False False True False False True True True False True False True True False True True True True True False False True True True False True True True True True False False True True True True True
[edit] PicoLisp
(de truthTable (Expr)
(let Vars
(uniq
(make
(setq Expr
(recur (Expr) # Convert infix to prefix notation
(cond
((atom Expr) (link Expr))
((== 'not (car Expr))
(list 'not (recurse (cadr Expr))) )
(T
(list
(cadr Expr)
(recurse (car Expr))
(recurse (caddr Expr)) ) ) ) ) ) ) )
(for V Vars
(prin (align -7 V)) )
(prinl)
(bind (mapcar cons Vars)
(do (** 2 (length Vars))
(for "V" Vars
(space (if (print (val "V")) 6 4)) )
(println (eval Expr))
(find '(("V") (set "V" (not (val "V")))) Vars) ) ) ) )
Test:
: (truthTable (str "A and (B or C)"))
A B C
NIL NIL NIL NIL
T NIL NIL NIL
NIL T NIL NIL
T T NIL T
NIL NIL T NIL
T NIL T T
NIL T T NIL
T T T T
: (truthTable (str "not (Foo and (Bar or Mumble))"))
Foo Bar Mumble
NIL NIL NIL T
T NIL NIL T
NIL T NIL T
T T NIL NIL
NIL NIL T T
T NIL T NIL
NIL T T T
T T T NIL
: (truthTable (str "(A xor B) and (B or C)"))
A B C
NIL NIL NIL NIL
T NIL NIL NIL
NIL T NIL T
T T NIL NIL
NIL NIL T NIL
T NIL T T
NIL T T T
T T T NIL
: (truthTable (str "(A xor B) and ((not B) or C)"))
A B C
NIL NIL NIL NIL
T NIL NIL T
NIL T NIL NIL
T T NIL NIL
NIL NIL T NIL
T NIL T T
NIL T T T
T T T NIL
[edit] Python
This accepts correctly formatted Python boolean expressions.
from itertools import product
while True:
bexp = input('\nBoolean expression: ')
bexp = bexp.strip()
if not bexp:
print("\nThank you")
break
code = compile(bexp, '<string>', 'eval')
names = code.co_names
print('\n' + ' '.join(names), ':', bexp)
for values in product(range(2), repeat=len(names)):
env = dict(zip(names, values))
print(' '.join(str(v) for v in values), ':', eval(code, env))
- Sample output
Boolean expression: A ^ B A B : A ^ B 0 0 : 0 0 1 : 1 1 0 : 1 1 1 : 0 Boolean expression: S | ( T ^ U ) S T U : S | ( T ^ U ) 0 0 0 : 0 0 0 1 : 1 0 1 0 : 1 0 1 1 : 0 1 0 0 : 1 1 0 1 : 1 1 1 0 : 1 1 1 1 : 1 Boolean expression: A ^ (B ^ (C ^ D)) A B C D : A ^ (B ^ (C ^ D)) 0 0 0 0 : 0 0 0 0 1 : 1 0 0 1 0 : 1 0 0 1 1 : 0 0 1 0 0 : 1 0 1 0 1 : 0 0 1 1 0 : 0 0 1 1 1 : 1 1 0 0 0 : 1 1 0 0 1 : 0 1 0 1 0 : 0 1 0 1 1 : 1 1 1 0 0 : 0 1 1 0 1 : 1 1 1 1 0 : 1 1 1 1 1 : 0 Boolean expression: Thank you
[edit] Racket
Since the requirement is to read an expression dynamically, eval is a natural choice. The following isn't trying to protect against bad inputs when doing that.
#lang racket
(define (collect-vars sexpr)
(sort
(remove-duplicates
(let loop ([x sexpr])
(cond [(boolean? x) '()]
[(symbol? x) (list x)]
[(list? x) (append-map loop (cdr x))]
[else (error 'truth-table "Bad expression: ~e" x)])))
string<? #:key symbol->string))
(define ns (make-base-namespace))
(define (truth-table sexpr)
(define vars (collect-vars sexpr))
(printf "~a => ~s\n" (string-join (map symbol->string vars)) sexpr)
(for ([i (expt 2 (length vars))])
(define vals
(map (λ(x) (eq? #\1 x))
(reverse (string->list (~r i #:min-width (length vars)
#:pad-string "0"
#:base 2)))))
(printf "~a => ~a\n" (string-join (map (λ(b) (if b "T" "F")) vals))
(if (eval `(let (,@(map list vars vals)) ,sexpr) ns) "T" "F"))))
(printf "Enter an expression: ")
(truth-table (read))
Sample run:
Enter an expression: (and (or z x) (or y (not z))) x y z => (and (or z x) (or y (not z))) F F F => F T F F => T F T F => F T T F => T F F T => F T F T => F F T T => T T T T => T
[edit] REXX
I had the thought that this program would just transform the boolean expression into what REXX approves of, and just step
through the 26 possible propositional constants (which makes a deeply nested DO construct, if nothing else, it looks pretty).
I later added support for all 16 boolean functions --- REXX natively supports three infix operators:
- & (and)
- | (or)
- && (xor)
and one prefix operator:
- ¬ (not or negation).
Some REXX intepreters also (or instead) support:
- \ (backslash)
- / (forward slash)
- ~ (tidle)
- ^ (carot)
Also included is support for two boolean values: TRUE and FALSE which are part of boolean expressions.
/*REXX program displays a truth table the variables and an expression. */
/*Infix notation is supported with one character propositional constants*/
/*variables (propositional constants) allowed: A──►Z, a──►z except u. */
/*All propositional constants are case insensative (except lowercase v).*/
parse arg expression /*get expression from the C.L. */
if expression\='' then do /*Got one? Then show user's stuff*/
call truthTable expression /*show and tell T.T.*/
exit /*we're all done with truth table*/
end
call truthTable "G ^ H ; XOR" /*txt after ; is shown in output.*/
call truthTable "i | j ; OR"
call truthTable "G nxor H ; NXOR"
call truthTable "k ! t ; NOR"
call truthTable "p & q ; AND"
call truthTable "e ¡ f ; NAND"
call truthTable "S | (T ^ U )"
call truthTable "(p=>q) v (q=>r)"
call truthTable "A ^ (B ^ (C ^ D))"
exit /*quit while we're ahead, by gum.*/
/* ↓↓↓ no way, Jose. ↓↓↓ */ /*shows a 32,768 line truth table*/
call truthTable "A^(B^(C^(D^(E^(F^(G^(H^(I^(J^(L^(N^(N^(O^P)))))))))))))"
exit /*stick a fork in it, we're done.*/
/*─────────────────────────────────────truthTable subroutine────────────*/
truthTable: procedure; parse arg $ ';' comm 1 $o; $o=strip($o)
$=translate(strip($),'|',"v"); $u=$; upper $u
$u=translate($u,'()()()',"[]{}«»"); $$.=0; PCs=; hdrPCs=
@abc='abcdefghijklmnopqrstuvwxyz'; @abcU=@abc; upper @abcU
/* The boxed table below was constructed from an old IBM publication:
"PL/I Language Specifications" ─── March 1968.
┌────────────────────────────────────────────────────────────┐
│ bool(bitsA, bitsB, BF) │
├────────────────────────────────────────────────────────────┤
│ performs the boolean function BF ┌──────┬─────────┐ │
│ on the A bitstring │ BF │ common │ │
│ with the B bitstring. │ value│ name │ │
│ ├──────┼─────────┤ │
│ BF must be a one to four bit │ 0000 │boolfalse│ │
│ value (from 0000 ──► 1111), │ 0001 │ and │ │
│ leading zeroes can be omitted. │ 0010 │ NaIMPb │ │
│ │ 0011 │ boolB │ │
│ BF may have multiple values (one │ 0100 │ NbIMPa │ │
│ for each pair of bitstrings): │ 0101 │ boolA │ │
│ │ 0110 │ xor │ │
│ ┌──────┬──────┬───────────────┐ │ 0111 │ or │ │
│ │ Abit │ Bbit │ returns │ │ 1000 │ nor │ │
│ ├──────┼──────┼───────────────┤ │ 1001 │ nxor │ │
│ │ 0 │ 0 │ 1st bit in BF │ │ 1010 │ notB │ │
│ │ 0 │ 1 │ 2nd bit in BF │ │ 1011 │ bIMPa │ │
│ │ 1 │ 0 │ 3rd bit in BF │ │ 1100 │ notA │ │
│ │ 1 │ 1 │ 4th bit in BF │ │ 1101 │ aIMPb │ │
│ └──────┴──────┴───────────────┘ │ 1110 │ nand │ │
│ │ 1111 │booltrue │ │
│ ┌──┴──────┴─────────┤ │
│ │ A 0101 │ │
│ │ B 0011 │ │
│ └───────────────────┘ │
└────────────────────────────────────────────────────────────┘ */
?='ff'x /*─────────infix operators───────*/
op.= /*a single quote (') wasn't */
/* implemented for negation. */
op.0 ='false boolFALSE' /*unconditionally FALSE */
op.1 ='& and *' /* AND, conjunction */
op.2 ='naimpb NaIMPb' /*not A implies B */
op.3 ='boolb boolB' /*B (value of) */
op.4 ='nbimpa NbIMPa' /*not B implies A */
op.5 ='boola boolA' /*A (value of) */
op.6 ='&& xor % ^' /* XOR, exclusive OR */
op.7 ='| or + v' /* OR, disjunction */
op.8 ='nor nor ! ↓' /* NOR, not OR, Pierce operator */
op.9 ='xnor xnor nxor' /*NXOR, not exclusive OR, not XOR*/
op.10='notb notB' /*not B (value of) */
op.11='bimpa bIMPa' /* B implies A */
op.12='nota notA' /*not A (value of) */
op.13='aimpb aIMPb' /* A implies B */
op.14='nand nand ¡ ↑' /*NAND, not AND, Sheffer operator*/
op.15='true boolTRUE' /*unconditionally TRUE */
/*alphabetic names need changing.*/
op.16='\ NOT ~ ─ . ¬' /* NOT, negation */
op.17='> GT' /*conditional */
op.18='>= GE ─> => ──> ==>' "1a"x /*conditional */
op.19='< LT' /*conditional */
op.20='<= LE <─ <= <── <==' /*conditional */
op.21='\= NE ~= ─= .= ¬=' /*conditional */
op.22='= EQ EQUAL EQUALS =' "1b"x /*biconditional */
op.23='0 boolTRUE' /*TRUEness */
op.24='1 boolFALSE' /*FALSEness */
do jj=0 while op.jj\=='' | jj<16 /*change opers──►what REXX likes.*/
new=word(op.jj,1)
do kk=2 to words(op.jj) /*handle each token separately. */
_=word(op.jj,kk); upper _
if wordpos(_,$u)==0 then iterate /*no such animal in this string. */
if datatype(new,'m') then new!=? /*expresion needs transcribing. */
else new!=new
$u=changestr(_,$u,new!) /*transcribe the function (maybe)*/
if new!==? then $u=changeFunc($u,?,new) /*use internal bool name.*/
end /*kk*/
end /*jj*/
$u=translate($u, '()', "{}") /*finish cleaning up transcribing*/
do jj=1 for length(@abcU) /*see what variables are used. */
_=substr(@abcU,jj,1) /*use available upercase alphabet*/
if pos(_,$u)==0 then iterate /*found one? No, keep looking. */
$$.jj=1 /*found: set upper bound for it.*/
PCs=PCs _ /*also, add to propositional cons*/
hdrPCs=hdrPCS center(_,length('false')) /*build a PC header.*/
end /*jj*/
$u=PCs '('$u")" /*separate PCs from expression. */
ptr='_────►_' /*a pointer for the truth table. */
hdrPCs=substr(hdrPCs,2) /*create a header for the PCs. */
say hdrPCs left('',length(ptr)-1) $o /*display PC header + expression.*/
say copies('───── ',words(PCs)) left('',length(ptr)-2) copies('─',length($o))
/*Note: "true"s: right─justified*/
do a=0 to $$.1
do b=0 to $$.2
do c=0 to $$.3
do d=0 to $$.4
do e=0 to $$.5
do f=0 to $$.6
do g=0 to $$.7
do h=0 to $$.8
do i=0 to $$.9
do j=0 to $$.10
do k=0 to $$.11
do l=0 to $$.12
do m=0 to $$.13
do n=0 to $$.14
do o=0 to $$.15
do p=0 to $$.16
do q=0 to $$.17
do r=0 to $$.18
do s=0 to $$.19
do t=0 to $$.20
do u=0 to $$.21
do !=0 to $$.22
do w=0 to $$.23
do x=0 to $$.24
do y=0 to $$.25
do z=0 to $$.26
interpret '_=' $u /*evaluate truth T.*/
_=changestr(1,_,'_true') /*convert 1──►_true*/
_=changestr(0,_,'false') /*convert 0──►false*/
_=insert(ptr,_,wordindex(_,words(_))-1) /*──►*/
say translate(_,,'_') /*display truth tab*/
end /*z*/
end /*y*/
end /*x*/
end /*w*/
end /*v*/
end /*u*/
end /*t*/
end /*s*/
end /*r*/
end /*q*/
end /*p*/
end /*o*/
end /*n*/
end /*m*/
end /*l*/
end /*k*/
end /*j*/
end /*i*/
end /*h*/
end /*g*/
end /*f*/
end /*e*/
end /*d*/
end /*c*/
end /*b*/
end /*a*/
say; return
/*─────────────────────────────────────SCAN subroutine──────────────────*/
scan: procedure; parse arg x,at; L=length(x); t=L; lp=0; apost=0; quote=0
if at<0 then do; t=1; x=translate(x,'()',")("); end
do j=abs(at) to t by sign(at); _=substr(x,j,1); __=substr(x,j,2)
if quote then do; if _\=='"' then iterate
if __=='""' then do; j=j+1; iterate; end
quote=0; iterate
end
if apost then do; if _\=="'" then iterate
if __=="''" then do; j=j+1; iterate; end
apost=0; iterate
end
if _=='"' then do; quote=1; iterate; end
if _=="'" then do; apost=1; iterate; end
if _==' ' then iterate
if _=='(' then do; lp=lp+1; iterate; end
if lp\==0 then do; if _==')' then lp=lp-1; iterate; end
if datatype(_,'U') then return j-(at<0)
if at<0 then return j+1
end /*j*/
return min(j,L)
/*─────────────────────────────────────changeFunc subroutine────────────*/
changeFunc: procedure; parse arg z,fC,newF; funcPos=0
do forever
funcPos=pos(fC,z,funcPos+1); if funcPos==0 then return z
origPos=funcPos
z=changestr(fC,z,",'"newF"',")
funcPos=funcPos+length(newF)+4
where=scan(z, funcPos) ; z=insert( '}', z, where)
where=scan(z, 1-origPos) ; z=insert('bool{', z, where)
end /*forever*/
/*─────────────────────────────────────BOOL subroutine──────────────────*/
bool: procedure; arg a,$,b
select
/*0*/ when $=='FALSE' then return 0
/*1*/ when $=='AND' then return a & b
/*2*/ when $=='NAIMPB' then return \ (\a & \b)
/*3*/ when $=='BOOLB' then return b
/*4*/ when $=='NBIMPA' then return \ (\b & \a)
/*5*/ when $=='BOOLA' then return a
/*6*/ when $=='XOR' then return a && b
/*7*/ when $=='OR' then return a | b
/*8*/ when $=='NOR' then return \ (a | b)
/*9*/ when $=='XNOR' then return \ (a && b)
/*a*/ when $=='NOTB' then return \ b
/*c*/ when $=='NOTA' then return \ a
/*d*/ when $=='AIMPB' then return \ (a & \b)
/*e*/ when $=='NAND' then return \ (a & b)
/*f*/ when $=='TRUE' then return 1
otherwise return -13 /*error.*/
end /*select*/
Some older REXXes don't have a changestr BIF, so one is included here ──► CHANGESTR.REX.
output when using the default input
G H G ^ H ; XOR ───── ───── ─────────── false false ────► false false true ────► true true false ────► true true true ────► false I J i | j ; OR ───── ───── ────────── false false ────► false false true ────► true true false ────► true true true ────► true G H G nxor H ; NXOR ───── ───── ─────────────── false false ────► true false true ────► false true false ────► false true true ────► true K T k ! t ; NOR ───── ───── ─────────── false false ────► true false true ────► false true false ────► false true true ────► false P Q p & q ; AND ───── ───── ─────────── false false ────► false false true ────► false true false ────► false true true ────► true E F e ¡ f ; NAND ───── ───── ──────────── false false ────► true false true ────► true true false ────► true true true ────► false S T U S | (T ^ U ) ───── ───── ───── ──────────── false false false ────► false false false true ────► true false true false ────► true false true true ────► false true false false ────► true true false true ────► true true true false ────► true true true true ────► true P Q R (p=>q) v (q=>r) ───── ───── ───── ─────────────── false false false ────► true false false true ────► true false true false ────► true false true true ────► true true false false ────► true true false true ────► true true true false ────► true true true true ────► true A B C D A ^ (B ^ (C ^ D)) ───── ───── ───── ───── ───────────────── false false false false ────► false false false false true ────► true false false true false ────► true false false true true ────► false false true false false ────► true false true false true ────► false false true true false ────► false false true true true ────► true true false false false ────► true true false false true ────► false true false true false ────► false true false true true ────► true true true false false ────► false true true false true ────► true true true true false ────► true true true true true ────► false
[edit] Ruby
Uses eval, so blindly trusts the user's input. The core true and false objects understand the methods & (and), | (or), ! (not) and ^ (xor) -- [1]
loop do
print "\ninput a boolean expression (e.g. 'a & b'): "
expr = gets.strip.downcase
break if expr.empty?
vars = expr.scan(/\p{Alpha}+/)
if vars.empty?
puts "no variables detected in your boolean expression"
next
end
vars.each {|v| print "#{v}\t"}
puts "| #{expr}"
prefix = []
suffix = []
vars.each do |v|
prefix << "[false, true].each do |#{v}|"
suffix << "end"
end
body = vars.inject("puts ") {|str, v| str + "#{v}.to_s + '\t' + "}
body += '"| " + eval(expr).to_s'
eval (prefix + [body] + suffix).join("\n")
end
Example
input a boolean expression (e.g. 'a & b'): !a a | !a false | true true | false input a boolean expression (e.g. 'a & b'): a|!b a b | a|!b false false | true false true | false true false | true true true | true input a boolean expression (e.g. 'a & b'): ((a^b)^c)^d a b c d | ((a^b)^c)^d false false false false | false false false false true | true false false true false | true false false true true | false false true false false | true false true false true | false false true true false | false false true true true | true true false false false | true true false false true | false true false true false | false true false true true | true true true false false | false true true false true | true true true true false | true true true true true | false
[edit] Tcl
package require Tcl 8.5
puts -nonewline "Enter a boolean expression: "
flush stdout
set exp [gets stdin]
# Generate the nested loops as the body of a lambda term.
set vars [lsort -unique [regexp -inline -all {\$\w+} $exp]]
set cmd [list format [string repeat "%s\t" [llength $vars]]%s]
append cmd " {*}\[[list subst $vars]\] \[[list expr $exp]\]"
set cmd "puts \[$cmd\]"
foreach v [lreverse $vars] {
set cmd [list foreach [string range $v 1 end] {0 1} $cmd]
}
puts [join $vars \t]\tResult
apply [list {} $cmd]
Sample run:
Enter a boolean expression: ($a&&$b)||$c $a $b $c Result 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1
