Jensen's Device: Difference between revisions
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{{wikipedia}}
{{task|Classic CS problems and programs}}
This task is an exercise in [[
'''Jensen's Device''' is a computer programming technique devised by Danish computer scientist [
The following program was proposed to illustrate the technique. It computes the 100th [
'''begin'''
Line 25:
'''end'''
The above exploits [[wp:Call-by-name#Call_by_name|call by name]] to produce the correct answer (5.187...). It depends on the assumption that an expression passed as an actual parameter to a procedure would be re-evaluated in the caller's context every time the corresponding formal parameter's value was required. If the last parameter to ''sum'' had been passed by value, and assuming the initial value of ''i'' were 1, the result would have been 100 × 1/1 = 100.
Moreover, the ''first'' parameter to ''sum'', representing the "bound" variable of the summation, must also be passed by name (or at least by reference), otherwise changes to it (made within ''sum'') would not be visible in the caller's context when computing each of the values to be added.
(On the other hand, the global variable does not have to use the same identifier, in this case ''i'', as the formal parameter.)
[[wp:Donald_Knuth|Donald Knuth]] later proposed the [[Man or boy test|Man or Boy Test]] as a more rigorous exercise.
<br><br>
=={{header|11l}}==
{{trans|C#}}
<syntaxhighlight lang="11l">F sum(&i, lo, hi, term)
V temp = 0.0
i = lo
L i <= hi
temp += term()
i++
R temp
F main()
Int i
print(sum(&i, 1, 100, () -> 1 / @i))
main()</syntaxhighlight>
{{out}}
<pre>
5.18738
</pre>
=={{header|Ada}}==
<syntaxhighlight lang="ada">with Ada.Text_IO; use Ada.Text_IO;
procedure Jensen_Device is
function Sum
( I : not null access Float;
Lo, Hi : Float;
F : access function return Float
) return Float is
Temp : Float := 0.0;
begin
I.all := Lo;
while I.all <= Hi loop
Temp := Temp + F.all;
I.all := I.all + 1.0;
end loop;
return Temp;
end Sum;
I : aliased Float;
function Inv_I return Float is
begin
return 1.0 / I;
end Inv_I;
begin
Put_Line (Float'Image (Sum (I'Access, 1.0, 100.0, Inv_I'Access)));
end Jensen_Device;</syntaxhighlight>
<pre>
5.18738E+00
</pre>
=={{header|ALGOL 60}}==
Honor given where honor is due. In Algol 60, 'call by name' is the default argument evaluation.
'''begin'''
'''integer''' i;
'''real procedure''' sum (i, lo, hi, term);
'''value''' lo, hi;
'''integer''' i, lo, hi;
'''real''' term;
'''comment''' term is passed by-name, and so is i;
'''begin'''
'''real''' temp;
temp := 0;
'''for''' i := lo '''step''' 1 '''until''' hi '''do'''
temp := temp + term;
sum := temp
'''end''';
'''comment''' note the correspondence between the mathematical notation and the call to sum;
print (sum (i, 1, 100, 1/i))
'''end'''
=={{header|ALGOL 68}}==
{{trans|ALGOL 60}}
<syntaxhighlight lang="algol68">BEGIN
INT i;
PROC sum = (REF INT
COMMENT term is passed by-name, and so is i COMMENT
BEGIN
REAL temp := 0;
WHILE i <= hi DO # ALGOL 68 has a "for" loop but it creates a distinct #
temp +:= term; # variable which would not be shared with the passed "i" #
i +:= 1 # Here the actual passed "i" is incremented. #
OD;
END;
COMMENT note the correspondence between the mathematical notation and the call to sum COMMENT
print (sum (i, 1, 100, REAL: 1/i))
END</
Output: +5.18737751763962e +0
=={{header|ALGOL W}}==
{{Trans|ALGOL 68}}
Algol W retained Algol 60's call by name but also offered additional parameter passing modes.
<br>This version uses call by name for the i parameter but uses a procedure parameter for the summed expression.
<br>The expression supplied in the call is automatically converted to a procedure by the compiler.
<syntaxhighlight lang="algolw">begin
integer i;
real procedure sum ( integer %name% i; integer value lo, hi; real procedure term );
% i is passed by-name, term is passed as a procedure which makes it effectively passed by-name %
begin
real temp;
temp := 0;
i := lo;
while i <= hi do begin % The Algol W "for" loop (as in Algol 68) creates a distinct %
temp := temp + term; % variable which would not be shared with the passed "i" %
i := i + 1 % Here the actual passed "i" is incremented. %
end while_i_le_temp;
temp
end;
% note the correspondence between the mathematical notation and the call to sum %
write( sum( i, 1, 100, 1/i ) )
end.</syntaxhighlight>
{{out}}
<pre>
</pre>
=={{header|AppleScript}}==
<syntaxhighlight lang="applescript">set i to 0
on jsum(i, lo, hi, term)
set {temp, i's contents} to {0, lo}
repeat while i's contents ≤ hi
set {temp, i's contents} to {temp + (term's f(i)), (i's contents) + 1}
end repeat
return temp
end jsum
script term_func
on f(i)
return 1 / i
end f
end script
return jsum(a reference to i, 1, 100, term_func)</syntaxhighlight>
Output: 5.18737751764
=={{header|ARM Assembly}}==
{{works with|as|Raspberry Pi}}
<syntaxhighlight lang="arm assembly">
/* ARM assembly Raspberry PI */
/* program jensen.s */
/* compil as with option -mcpu=<processor> -mfpu=vfpv4 -mfloat-abi=hard */
/* link with gcc */
/* Constantes */
.equ EXIT, 1 @ Linux syscall
/* Initialized data */
.data
szFormat: .asciz "Result = %.8f \n"
.align 4
/* UnInitialized data */
.bss
/* code section */
.text
.global main
main:
mov r0,#1 @ first indice
mov r1,#100 @ last indice
adr r2,funcdiv @ address function
bl funcSum
vcvt.f64.f32 d1, s0 @ conversion double float for print by C
ldr r0,iAdrszFormat @ display format
vmov r2,r3,d1 @ parameter function printf for float double
bl printf @ display float double
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc 0 @ perform system call
iAdrszFormat: .int szFormat
/******************************************************************/
/* function sum */
/******************************************************************/
/* r0 contains begin */
/* r1 contains end */
/* r2 contains address function */
/* r0 return result */
funcSum:
push {r0,r3,lr} @ save registers
mov r3,r0
mov r0,#0 @ init r0
vmov s3,r0 @ and s3
vcvt.f32.s32 s3, s3 @ convert in float single précision (32bits)
1: @ begin loop
mov r0,r3 @ loop indice -> parameter function
blx r2 @ call function address in r2
vadd.f32 s3,s0 @ addition float
add r3,#1 @ increment indice
cmp r3,r1 @ end ?
ble 1b @ no loop
vmov s0,s3 @ return float result in s0
100:
pop {r0,r3,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* compute 1/r0 */
/******************************************************************/
/* r0 contains the value */
/* r0 return result */
funcdiv:
push {r1,lr} @ save registers
vpush {s1} @ save float registers
cmp r0,#0 @ division by zero -> end
beq 100f
ldr r1,fUn @ load float constant 1.0
vmov s0,r1 @ in float register s3
vmov s1,r0 @
vcvt.f32.s32 s1, s1 @conversion in float single précision (32 bits)
vdiv.f32 s0,s0,s1 @ division 1/r0
@ and return result in s0
100:
vpop {s1} @ restaur float registers
pop {r1,lr} @ restaur registers
bx lr @ return
fUn: .float 1
</syntaxhighlight>
=={{header|Arturo}}==
{{trans|Ruby}}
<syntaxhighlight lang="rebol">harmonicSum: function [variable, lo, hi, term][
result: new 0.0
loop lo..hi 'n ->
'result + do ~"|variable|: |n| |term|"
result
]
print ["harmonicSum 1->100:" harmonicSum 'i 1 100 {1.0 / i}]</syntaxhighlight>
{{out}}
<pre>harmonicSum 1->100: 5.187377517639621</pre>
=={{header|Asymptote}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="Asymptote">real temp = 0;
for(int i = 1; i <= 100; ++i) {
temp += 1/i;
}
write(temp);</syntaxhighlight>
{{out}}
<pre>5.18737751763962</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f JENSENS_DEVICE.AWK
# converted from FreeBASIC
BEGIN {
evaluation()
exit(0)
}
function evaluation( hi,i,lo,tmp) {
lo = 1
hi = 100
for (i=lo; i<=hi; i++) {
tmp += (1/i)
}
printf("%.15f\n",tmp)
}
</syntaxhighlight>
{{out}}
<pre>
5.187377517639621
</pre>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
Same code as [[#GW-BASIC|GW-BASIC]]
==={{header|BASIC256}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="basic256">
call Evaluation()
end
subroutine Evaluation()
lo = 1 : hi = 100 : temp = 0
for i = lo to hi
temp += (1/i) ##r(i)
next i
print temp
end subroutine</syntaxhighlight>
{{out}}
<pre>5.18737751764</pre>
==={{header|BBC BASIC}}===
{{works with|BBC BASIC for Windows}}
<syntaxhighlight lang="bbcbasic"> PRINT FNsum(j, 1, 100, FNreciprocal)
END
DEF FNsum(RETURN i, lo, hi, RETURN func)
LOCAL temp
FOR i = lo TO hi
temp += FN(^func)
NEXT
= temp
DEF FNreciprocal = 1/i</syntaxhighlight>
Output:
<pre>5.18737752</pre>
==={{header|Chipmunk Basic}}===
{{trans|QBasic}}
{{works with|Chipmunk Basic|3.6.4}}
<syntaxhighlight lang="vbnet">100 call evaluation
110 end
120 sub evaluation()
130 lo = 1
140 hi = 100
150 temp = 0
160 for i = lo to hi
170 temp = temp+(1/i)
180 next i
190 print temp
200 end sub</syntaxhighlight>
==={{header|Craft Basic}}===
<syntaxhighlight lang="basic">precision 4
define lo = 1, hi = 100, temp = 0
for i = lo to hi
let temp = temp + (1 / i)
wait
next i
print temp</syntaxhighlight>
{{out| Output}}<pre>5.1873</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="vbnet">Sub Evaluation
Dim As Integer i, lo = 1, hi = 100
Dim As Double temp = 0
For i = lo To hi
temp += (1/i) ''r(i)
Next i
Print temp
End Sub
Evaluation
Sleep</syntaxhighlight>
{{out}}
<pre>5.187377517639621</pre>
==={{header|FutureBasic}}===
<syntaxhighlight lang="futurebasic">local fn JensensDevice( lo as long, hi as long ) as double
double i, temp = 0.0
for i = lo to hi
temp = temp + (1/i)
next
end fn = temp
print fn JensensDevice( 1, 100 )
HandleEvents</syntaxhighlight>
{{output}}
<pre>5.187377517639621</pre>
==={{header|Gambas}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">Sub Evaluation()
Dim i As Integer, lo As Integer = 1, hi As Integer = 100
Dim tmp As Float = 0
For i = lo To hi
tmp += (1 / i)
Next
Print tmp
End Sub
Public Sub Main()
Evaluation
End </syntaxhighlight>
==={{header|GW-BASIC}}===
{{works with|PC-BASIC|any}}
{{works with|BASICA}}
{{works with|Applesoft BASIC}}
{{works with|Chipmunk Basic}}
{{works with|QBasic}}
{{works with|QB64}}
{{works with|Quite BASIC}}
{{works with|MSX BASIC}}
<syntaxhighlight lang="qbasic">100 GOSUB 120
110 END
120 REM Evaluation
130 LET A = 1
140 LET B = 100
150 LET T = 0
160 FOR I = A TO B
170 LET T = T + (1/I)
180 NEXT I
190 PRINT T
200 RETURN</syntaxhighlight>
==={{header|Minimal BASIC}}===
<syntaxhighlight lang="qbasic">100 GOSUB 120
110 GOTO 210
120 REM Evaluation
130 LET A = 1
140 LET B = 100
150 LET T = 0
160 FOR I = A TO B
170 LET T = T+(1/I)
180 NEXT I
190 PRINT T
200 RETURN
210 END</syntaxhighlight>
==={{header|MSX Basic}}===
{{works with|MSX BASIC|any}}
Same code as [[#GW-BASIC|GW-BASIC]]
==={{header|PureBasic}}===
{{trans|C}}
<syntaxhighlight lang="purebasic">Prototype.d func()
Global i
Procedure.d Sum(*i.Integer, lo, hi, *term.func)
Protected Temp.d
For i=lo To hi
temp + *term()
Next
ProcedureReturn Temp
EndProcedure
Procedure.d term_func()
ProcedureReturn 1/i
EndProcedure
Answer.d = Sum(@i, 1, 100, @term_func())</syntaxhighlight>
==={{header|QBasic}}===
{{works with|QBasic|1.1}}
{{works with|QuickBasic|4.5}}
{{works with|Run BASIC}}
{{works with|Just BASIC}}
{{works with|Liberty BASIC}}
{{works with|True BASIC}}
<syntaxhighlight lang="qbasic">CALL EVALUATION
END
SUB Evaluation
LET lo = 1
LET hi = 100
LET temp = 0
FOR i = lo TO hi
LET temp = temp + (1 / i)
NEXT i
PRINT temp
END SUB</syntaxhighlight>
==={{header|QB64}}===
Same code as [[#QBasic|QBasic]]
==={{header|Quite BASIC}}===
Same code as [[#GW-BASIC|GW-BASIC]]
==={{header|Run BASIC}}===
Same code as [[#QBasic|QBasic]]
==={{header|True BASIC}}===
Same code as [[#QBasic|QBasic]]
==={{header|uBasic/4tH}}===
Since uBasic/4tH does not support floating point numbers, fixed point has to be used. Of course, precision suffers significantly.
<syntaxhighlight lang="qbasic">' ** NOTE: it requires a 64-bit uBasic; number ranges are limited. **
If Info("wordsize") < 64 Then Print "This program requires a 64-bit uBasic" : End
Dim @i(1)
i = 0 ' fake something that resembles a pointer
Print Using "+?.####";FUNC(_Ftoi(FUNC(_Sum(i, 1, 100, _Term))))
End
_Sum
Param (4)
Local (1)
e@ = 0
For @i(a@) = b@ To c@ : e@ = e@ + FUNC(d@) : Next
Return (e@)
_Term Return (FUNC(_Fdiv(1, @i(i))))
_Fdiv Param (2) : Return ((a@*16384)/b@)
_Ftoi Param (1) : Return ((10000*a@)/16384)</syntaxhighlight>
{{Out}}
<pre>5.1850
0 OK, 0:313 </pre>
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="yabasic">Evaluation()
end
sub Evaluation()
lo = 1 : hi = 100 : temp = 0
for i = lo to hi
temp = temp + (1/i) //r(i)
next i
print temp
end sub</syntaxhighlight>
{{out}}
<pre>5.18738</pre>
==={{header|ZX Spectrum Basic}}===
<syntaxhighlight lang="qbasic">10 DEF FN r(x)=1/x
20 LET f$="FN r(i)"
30 LET lo=1: LET hi=100
40 GO SUB 1000
50 PRINT temp
60 STOP
1000 REM Evaluation
1010 LET temp=0
1020 FOR i=lo TO hi
1030 LET temp=temp+VAL f$
1040 NEXT i
1050 RETURN </syntaxhighlight>
{{out}}
<pre>5.1873775</pre>
=={{header|Bracmat}}==
<syntaxhighlight lang="bracmat">( ( sum
= I lo hi Term temp
. !arg:((=?I),?lo,?hi,(=?Term))
& 0:?temp
& !lo:?!I
& whl
' ( !!I:~>!hi
& !temp+!Term:?temp
& 1+!!I:?!I
)
& !temp
)
& sum$((=i),1,100,(=!i^-1))
);</syntaxhighlight>
Output:
<pre>14466636279520351160221518043104131447711/2788815009188499086581352357412492142272</pre>
=={{header|C}}==
<syntaxhighlight lang="c">#include <stdio.h>
int i;
double sum(int *i, int lo, int hi, double (*term)()) {
double temp = 0;
for (*i = lo; *i <= hi; (*i)++)
temp += term();
return temp;
}
double term_func() { return 1.0 / i; }
int main () {
printf("%f\n", sum(&i, 1, 100, term_func));
return 0;
}</syntaxhighlight>
Output: 5.18738
{{works with|gcc}}
Alternatively, C's macros provide a closer imitation of ALGOL's call-by-name semantics:
<syntaxhighlight lang="c">#include <stdio.h>
int i;
#define sum(i, lo_byname, hi_byname, term) \
({ \
int lo = lo_byname; \
int hi = hi_byname; \
\
double temp = 0; \
for (i = lo; i <= hi; ++i) \
temp += term; \
temp; \
})
int main () {
printf("%f\n", sum(i, 1, 100, 1.0 / i));
return 0;
}</syntaxhighlight>
Output: 5.187378
=={{header|C sharp}}==
Can be simulated via lambda expressions:
<syntaxhighlight lang="csharp">using System;
class JensensDevice
{
public static double Sum(ref int i, int lo, int hi, Func<double> term)
{
double temp = 0.0;
for (i = lo; i <= hi; i++)
{
temp += term();
}
return temp;
}
static void Main()
{
int i = 0;
Console.WriteLine(Sum(ref i, 1, 100, () => 1.0 / i));
}
}</syntaxhighlight>
=={{header|C++}}==
<syntaxhighlight lang="cpp">
#include <iostream>
#define SUM(i,lo,hi,term)\
[&](const int _lo,const int _hi){\
decltype(+(term)) sum{};\
for (i = _lo; i <= _hi; ++i) sum += (term);\
return sum;\
}((lo),(hi))
int i;
double sum(int &i, int lo, int hi, double (*term)()) {
double temp = 0;
for (i = lo; i <= hi; i++)
temp += term();
return temp;
}
double term_func() { return 1.0 / i; }
int main () {
std::cout << sum(i, 1, 100, term_func) << std::endl;
std::cout << SUM(i,1,100,1.0/i) << "\n";
return 0;
}</syntaxhighlight>
Output: 5.18738
5.18738
=={{header|Clipper}}==
With hindsight Algol60 provided this feature in a way that is terrible for program maintenance, because the calling code looks innocuous.
<syntaxhighlight lang="clipper">// Jensen's device in Clipper (or Harbour)
// A fairly direct translation of the Algol 60
// John M Skelton 11-Feb-2012
function main()
local i
? transform(sum(@i, 1, 100, {|| 1 / i}), "##.###############")
// @ is the quite rarely used pass by ref, {|| ...} is a
// code block (an anonymous function, here without arguments)
// The @i makes it clear that something unusual is occurring;
// a called function which modifies a parameter is commonly
// poor design!
return 0
function sum(i, lo, hi, bFunc)
local temp := 0
for i = lo to hi
temp += eval(bFunc)
next i
return temp
</syntaxhighlight>
=={{header|Common Lisp}}==
Common Lisp does not have call-by-name for functions; however, it can be directly simulated by a macro wrapping selected parameters in lambdas.
<syntaxhighlight lang="lisp">(declaim (inline %sum))
(defun %sum (lo hi func)
(loop for i from lo to hi sum (funcall func i)))
(defmacro sum (i lo hi term)
`(%sum ,lo ,hi (lambda (,i) ,term)))</syntaxhighlight>
<syntaxhighlight lang="lisp">CL-USER> (sum i 1 100 (/ 1 i))
14466636279520351160221518043104131447711/2788815009188499086581352357412492142272
CL-USER> (float (sum i 1 100 (/ 1 i)))
5.1873775</syntaxhighlight>
=={{header|D}}==
There are better ways to do this in D, but this is closer to the original Algol version:
<syntaxhighlight lang="d">double sum(ref int i, in int lo, in int hi, lazy double term)
pure @safe /*nothrow @nogc*/ {
double result = 0.0;
for (i = lo; i <= hi; i++)
result += term();
return result;
}
void main() {
import std.stdio;
int i;
sum(i, 1, 100, 1.0/i).writeln;
}</syntaxhighlight>
{{out}}
<pre>5.18738</pre>
=={{header|Dart}}==
{{trans|C++}}
<syntaxhighlight lang="dart">double i = 0;
double sum(int lo, int hi, double Function() term) {
double temp = 0;
for (i = lo.toDouble(); i <= hi; i++) temp += term();
return temp;
}
double termFunc() {
return 1.0 / i;
}
void main() {
print(sum(1, 100, termFunc));
}</syntaxhighlight>
{{out}}
<pre>5.187377517639621</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
type TTerm = function(i: integer): real;
function Term(I: integer): double;
begin
Term := 1 / I;
end;
function Sum(var I: integer; Lo, Hi: integer; Term: TTerm): double;
begin
Result := 0;
I := Lo;
while I <= Hi do
begin
Result := Result + Term(I);
Inc(I);
end;
end;
procedure ShowJensenDevice(Memo: TMemo);
var I: LongInt;
begin
Memo.Lines.Add(FloatToStrF(Sum(I, 1, 100, @Term), ffFixed,18,15));
end;
</syntaxhighlight>
{{out}}
<pre>
5.187377517639621
Elapsed Time: 1.037 ms.
</pre>
=={{header|DWScript}}==
Must use a "while" loop, as "for" loop variables are restricted to local variable for code clarity, and this indeed a case where any kind of extra clarity helps.
<syntaxhighlight lang="delphi">function sum(var i : Integer; lo, hi : Integer; lazy term : Float) : Float;
begin
i:=lo;
while i<=hi do begin
Result += term;
Inc(i);
end;
end;
var i : Integer;
PrintLn(sum(i, 1, 100, 1.0/i));</syntaxhighlight>
Output: 5.187...
=={{header|E}}==
In E, the distinct mutable locations behind assignable variables can be reified as [http://wiki.erights.org/wiki/Slot Slot] objects. The E language allows a variable name (''noun'') to be bound to a particular slot, and the slot of an already-bound noun to be extracted, using the <tt>&</tt> operator.
(The definition of the outer <var>i</var> has been moved down to emphasize that it is unrelated to the <var>i</var> inside of <var>sum</var>.)
<syntaxhighlight lang="e">pragma.enable("one-method-object") # "def _.get" is experimental shorthand
def sum(&i, lo, hi, &term) { # bind i and term to passed slots
var temp := 0
i := lo
while (i <= hi) { # E has numeric-range iteration but it creates a distinct
temp += term # variable which would not be shared with the passed i
i += 1
}
return temp
}
{
var i := null
sum(&i, 1, 100, def _.get() { return 1/i })
}</syntaxhighlight>
<tt>1/i</tt> is not a noun, so there is no slot associated with it; so we use <tt>def _.get() { return 1/i }</tt> to define a slot object which does the computation when it is read as a slot.
The value returned by the above program (expression) is 5.187377517639621.
This emulation of the original call-by-name is of course unidiomatic; a natural version of the same computation would be:
<syntaxhighlight lang="e">def sum(lo, hi, f) {
var temp := 0
for i in lo..hi { temp += f(i) }
return temp
}
sum(1, 100, fn i { 1/i })</syntaxhighlight>
=={{header|Elixir}}==
{{trans|Erlang}}
<syntaxhighlight lang="elixir">defmodule JensenDevice do
def task, do: sum( 1, 100, fn i -> 1 / i end )
defp sum( i, high, _term ) when i > high, do: 0
defp sum( i, high, term ) do
temp = term.( i )
temp + sum( i + 1, high, term )
end
end
IO.puts JensenDevice.task</syntaxhighlight>
{{out}}
<pre>
5.1873775176396215
</pre>
=={{header|EMal}}==
<syntaxhighlight lang="emal">
fun sum = real by int lo, int hi, fun term
real temp = 0.0
for int i = lo; i <= hi; ++i do temp += term(i) end
return temp
end
writeLine(sum(1, 100, real by int i do return 1.0/i end))
</syntaxhighlight>
{{out}}
<pre>
5.1873775176396202608051176755
</pre>
=={{header|Erlang}}==
No call by name, no macros, so I use a fun(ction). Actually, the the macro part is a lie. Somebody else, that knows how, could do a parse transform.
<syntaxhighlight lang="erlang">
-module( jensens_device ).
-export( [task/0] ).
task() ->
sum( 1, 100, fun (I) -> 1 / I end ).
sum( I, High, _Term ) when I > High -> 0;
sum( I, High, Term ) ->
Temp = Term( I ),
Temp + sum( I + 1, High, Term ).
</syntaxhighlight>
{{out}}
<pre>
4> jensens_device:task().
5.1873775176396215
</pre>
=={{header|Euler}}==
{{Trans|ALGOL 60}}
'''begin'''
'''new''' i; '''new''' sum;
sum <- ` '''formal''' i; '''formal''' lo; '''formal''' hi; '''formal''' term;
'''begin'''
'''new''' temp; '''label''' loop;
temp <- 0;
i <- lo;
loop: '''begin'''
temp <- temp + term;
'''if''' [ i <- i + 1 ] <= hi '''then''' '''goto''' loop '''else''' 0
'''end''';
temp
'''end'''
';
'''out''' sum( @i, 1, 100, `1/i' )
'''end''' $
{{out}}
<pre>
NUMBER 5.1873775176
</pre>
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
printfn "%.14f" (List.fold(fun n g->n+1.0/g) 0.0 [1.0..100.0]);;
</syntaxhighlight>
{{out}}
<pre>
5.18737751763962
</pre>
=={{header|Factor}}==
Similar to the Java and Kotlin examples:
<syntaxhighlight lang="factor">: sum ( lo hi term -- x ) [ [a,b] ] dip map-sum ; inline
1 100 [ recip ] sum .</syntaxhighlight>
This version is a bit closer to the original, as it increments <code>i</code> in the caller's namespace.
<syntaxhighlight lang="factor">SYMBOL: i
: sum ( i lo hi term -- x )
[ [a,b] ] dip pick [ inc ] curry compose map-sum nip ;
inline
i 1 100 [ recip ] sum .</syntaxhighlight>
{{out}}
<pre>
5+522561233577855727314756256041670736351/2788815009188499086581352357412492142272
</pre>
=={{header|Forth}}==
This version passes i on the stack:
<syntaxhighlight lang="forth">: sum 0 s>f 1+ swap ?do i over execute f+ loop drop ;
:noname s>f 1 s>f fswap f/ ; 1 100 sum f.</syntaxhighlight>
Output: 5.18737751763962
The following version passes i and 1/i as execution tokens and is thus closer to the original, but less idiomatic:
<syntaxhighlight lang="forth">: sum ( i-xt lo hi term-xt -- r )
\ stack effects: i-xt ( -- addr ); term-xt ( -- r1 )
0e swap 1+ rot ?do ( r1 xt1 xt2 )
i 2 pick execute ! dup execute f+
loop 2drop ;
variable i1 \ avoid conflict with Forth word I
' i1 1 100 :noname 1e i1 @ s>f f/ ; sum f.</syntaxhighlight>
Inspired by the macro-based versions here's a more idiomatic approach that is closer to the original than the first version above (Forth-2012 code):
<syntaxhighlight lang="forth">: sum< ( run-time: hi+1 lo -- 0e )
0e0 postpone fliteral postpone ?do ; immediate
: >sum ( run-time: r1 r2 -- r3 )
postpone f+ postpone loop ; immediate
: main ( -- )
101 1 sum< 1e0 i s>f f/ >sum f. ;
main</syntaxhighlight>
This splits <code>sum</code> in two macros: <code>sum<</code> and <code>>sum</code>; in <code>main</code> these two words surround the code corresponding to <code>1/i</code> in the Algol 60 version. The loop limits are <code>101 1</code>, passed on the stack to <code>sum<</code> in the order and semantics (upper bound is excluded) idiomatic in Forth.
Concerning the <code>i</code> parameter of the Algol 60 version, that is an artifact of the role of variables for storing data and passing it around in Algol-family languages. Forth's counted loops can access the current loop counter of the innermost loop with <code>i</code> (which is not a variable) without setting a variable, and that is also what one uses inside <code>sum<</code> ... <code>>sum</code>, as shown in <code>main</code>.
=={{header|Fortran}}==
Fortran does not offer call-by-name in the manner of the Algol language. It passes parameters by reference (i.e. by passing the storage address) and alternatively uses copy-in, copy-out to give the same effect, approximately, as by reference. If a parameter is an arithmetic expression, it will be evaluated and its value stored in a temporary storage area, whose address will be passed to the routine. This evaluation is done once only for each call, thus vitiating the repeated re-evaluation required by Jensen's device every time within the routine that the parameter is accessed. So, this will ''not'' work<syntaxhighlight lang="fortran"> FUNCTION SUM(I,LO,HI,TERM)
SUM = 0
DO I = LO,HI
SUM = SUM + TERM
END DO
END FUNCTION SUM
WRITE (6,*) SUM(I,1,100,1.0/I)
END</syntaxhighlight>
Here, type declarations have been omitted to save space because they won't help - until there appears a "BY NAME" or some such phrasing. Although variable <code>I</code> in the calling routine will have its value adjusted as the DO-loop in SUM proceeds (the parameter being passed by reference), this won't affect the evaluation of 1.0/I, which will be performed once using whatever value is in the caller's variable (it is uninitialised, indeed, undeclared also and so by default an integer) then the function is invoked with the address of the location containing that result. The function will make many references to that result, obtaining the same value each time. The fact that the caller's <code>I</code> will be changed each time doesn't matter.
Fortran does offer a facility to pass a function as a parameter using the EXTERNAL declaration, as follows - SUM is a F90 library function, so a name change to SUMJ: <syntaxhighlight lang="fortran"> FUNCTION SUMJ(I,LO,HI,TERM) !Attempt to follow Jensen's Device...
INTEGER I !Being by reference is workable.
INTEGER LO,HI !Just as any other parameters.
EXTERNAL TERM !Thus, not a variable, but a function.
SUMJ = 0
DO I = LO,HI !The specified span.
SUMJ = SUMJ + TERM(I) !Number and type of parameters now apparent.
END DO !TERM will be evaluated afresh, each time.
END FUNCTION SUMJ !So, almost there.
FUNCTION THIS(I) !A function of an integer.
INTEGER I
THIS = 1.0/I !Convert to floating-point.
END !Since 1/i will mostly give zero.
PROGRAM JENSEN !Aspiration.
EXTERNAL THIS !Thus, not a variable, but a function.
INTEGER I !But this is a variable, not a function.
WRITE (6,*) SUMJ(I,1,100,THIS) !No statement as to the parameters of THIS.
END</syntaxhighlight>
The result of this is 5.187378, however it does not follow the formalism of Jensen's Device. The invocation statement SUMJ(I,1,100,THIS) does not contain the form of the function but only its name, and the function itself is defined separately. This means that the convenience of different functions via the likes of SUM(I,1,100,1.0/I**2) is unavailable, a separately-defined function with its own name must be defined for each such function. Further, the SUM routine must invoke TERM(I) itself, explicitly supplying the appropriate parameter. And the fact that variable <code>I</code> is a parameter to SUM is an irrelevance, and might as well be omitted from SUMJ.
Incidentally, a subroutine such as TEST(A,B) invoked as TEST(X,X) enables the discovery of copy-in, copy-out parameter passing. Within the routine, modify the value of A and look to see if B suddenly has a new value also.
=={{header|Go}}==
<syntaxhighlight lang="go">package main
import "fmt"
var i int
func sum(i *int, lo, hi int, term func() float64) float64 {
temp := 0.0
for *i = lo; *i <= hi; (*i)++ {
temp += term()
}
return temp
}
func main() {
fmt.Printf("%f\n", sum(&i, 1, 100, func() float64 { return 1.0 / float64(i) }))
}</syntaxhighlight>
{{out}}
<pre>
5.187378
</pre>
=={{header|Groovy}}==
{{trans|JavaScript}}
Solution:
<syntaxhighlight lang="groovy">def sum = { i, lo, hi, term ->
(lo..hi).sum { i.value = it; term() }
}
def obj = [:]
println (sum(obj, 1, 100, { 1 / obj.value }))</syntaxhighlight>
Output:
<pre>5.1873775176</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import Control.Monad.ST
import Data.STRef
sum_ :: STRef s Double -> Double -> Double
-> ST s Double -> ST s Double
sum_ ref lo hi term =
do
vs <- forM [lo .. hi]
(\k -> do { writeSTRef ref k
; term } )
return $ sum vs
foo :: Double
foo =
runST $
do ref <- newSTRef undefined
-- initial value doesn't matter
sum_ ref 1 100 $
do
k <- readSTRef ref
return $ recip k
main :: IO ()
main = print foo</syntaxhighlight>
{{Out}}
<pre>5.187377517639621</pre>
=={{header|Huginn}}==
<syntaxhighlight lang="huginn">harmonic_sum( i, lo, hi, term ) {
temp = 0.0;
i *= 0.0;
i += lo;
while ( i <= hi ) {
temp += term();
i += 1.0;
}
return ( temp );
}
main() {
i = 0.0;
print( "{}\n".format( harmonic_sum( i, 1.0, 100.0, @[i](){ 1.0 / i; } ) ) );
}</syntaxhighlight>
{{Output}}<pre>5.18737751764</pre>
=={{header|Icon}} and {{header|Unicon}}==
Traditional call by name and reference are not features of Icon/Unicon. Procedures parameters are passed by value (immutable types) and reference (mutable types). However, a similar effect may be accomplished by means of co-expressions. The example below was selected for cleanliness of calling.
<syntaxhighlight lang="icon">record mutable(value) # record wrapper to provide mutable access to immutable types
procedure main()
A := mutable()
write( sum(A, 1, 100, create 1.0/A.value) )
end
procedure sum(A, lo, hi, term)
temp := 0
every A.value := lo to hi do
temp +:= @^term
return temp
end</syntaxhighlight>
Refreshing the co-expression above is more expensive to process but to avoid it requires unary alternation in the call.
<syntaxhighlight lang="icon"> write( sum(A, 1, 100, create |1.0/A.value) )
...
temp +:= @term</syntaxhighlight>
Alternately, we can use a programmer defined control operator (PDCO) approach that passes every argument as a co-expression. Again the refresh co-expression/unary iteration trade-off can be made. The call is cleaner looking but the procedure code is less clear. Additionally all the parameters are passed as individual co-expressions.
<syntaxhighlight lang="icon"> write( sum{A.value, 1, 100, 1.0/A.value} )
...
procedure sum(X)
...
every @X[1] := @X[2] to @X[3] do
temp +:= @^X[4]</syntaxhighlight>
=={{header|J}}==
'''Solution:'''
<syntaxhighlight lang="j">jensen=: monad define
'name lo hi expression'=. y
temp=. 0
for_n. lo+i.1+hi-lo do.
(name)=. n
temp=. temp + ".expression
end.
)</syntaxhighlight>
'''Example:'''
<syntaxhighlight lang="j"> jensen 'i';1;100;'1%i'
5.18738</syntaxhighlight>
Note, however, that in J it is reasonably likely that the expression (or an obvious variation on the expression) can deal with the looping itself. And in typical use this often simplifies to entering the expression and data directly on the command line.
And another obvious variation here would be turning the expression into a named entity (if it has some lasting usefulness).
=={{header|Java}}==
This is Java 8.
<syntaxhighlight lang="java">import java.util.function.*;
import java.util.stream.*;
public class Jensen {
static double sum(int lo, int hi, IntToDoubleFunction f) {
return IntStream.rangeClosed(lo, hi).mapToDouble(f).sum();
}
public static void main(String args[]) {
System.out.println(sum(1, 100, (i -> 1.0/i)));
}
}
</syntaxhighlight>
The program prints '5.187377517639621'.
Java 7 is more verbose, but under the hood does essentially the same thing:
<syntaxhighlight lang="java">public class Jensen2 {
interface IntToDoubleFunction {
double apply(int n);
}
static double sum(int lo, int hi, IntToDoubleFunction f) {
double res = 0;
for (int i = lo; i <= hi; i++)
res += f.apply(i);
return res;
}
public static void main(String args[]) {
System.out.println(
sum(1, 100,
new IntToDoubleFunction() {
public double apply(int i) { return 1.0/i;}
}));
}
}
</syntaxhighlight>
=={{header|JavaScript}}==
{{trans|C}}
Uses an object ''o'' instead of integer pointer ''i'', as the C example does.
<syntaxhighlight lang="javascript">var obj;
function sum(o, lo, hi, term) {
var tmp = 0;
for (o.val = lo; o.val <= hi; o.val++)
tmp += term();
return tmp;
}
obj = {val: 0};
alert(sum(obj, 1, 100, function() {return 1 / obj.val}));</syntaxhighlight>
The alert shows us '5.187377517639621'.
=={{header|Joy}}==
<syntaxhighlight lang="joy">100 [0] [[1.0 swap /] dip +] primrec.</syntaxhighlight>
Joy does not have named parameters.
Neither i nor 1/i are visible in the program.
=={{header|jq}}==
The technique used in the Javascript example can also be used in jq, but in jq it is more idiomatic to use "." to refer to the current term. For example, using sum/3 defined below, we can write: sum(1; 100; 1/.) to perform the task.
<syntaxhighlight lang="jq">def sum(lo; hi; term):
reduce range(lo; hi+1) as $i (0; . + ($i|term));
# The task:
sum(1;100;1/.)</syntaxhighlight>
{{Out}}
$ jq -n -f jensen.jq
5.187377517639621
=={{header|Julia}}==
{{works with|Julia|0.6}}
{{trans|C}}
<syntaxhighlight lang="julia">macro sum(i, loname, hiname, term)
return quote
lo = $loname
hi = $hiname
tmp = 0.0
for i in lo:hi
tmp += $term
end
return tmp
end
end
i = 0
@sum(i, 1, 100, 1.0 / i)</syntaxhighlight>
=={{header|Kotlin}}==
<syntaxhighlight lang="scala">fun sum(lo: Int, hi: Int, f: (Int) -> Double) = (lo..hi).sumByDouble(f)
fun main(args: Array<String>) = println(sum(1, 100, { 1.0 / it }))</syntaxhighlight>
=={{header|Lambdatalk}}==
<syntaxhighlight lang="scheme">
{def jensen
{lambda {:n}
{+ {S.map {lambda {:i} {/ 1 :i}}
{S.serie 1 :n}} }}}
-> jensen
{jensen 100}
-> 5.187377517639621
</syntaxhighlight>
I probably didn't understand this task, what's going on ...
=={{header|Lua}}==
<syntaxhighlight lang="lua">
function sum(var, a, b, str)
local ret = 0
for i = a, b do
ret = ret + setfenv(loadstring("return "..str), {[var] = i})()
end
return ret
end
print(sum("i", 1, 100, "1/i"))
</syntaxhighlight>
=={{header|M2000 Interpreter}}==
The definition of the lazy function has two statements. First statement is a Module with one argument, the actual name of Jensen`s_Device, which make the function to get the same scope as module Jensen`s_Device, and the second statement is =1/i which return the expression.
<syntaxhighlight lang="m2000 interpreter">
Module Jensen`s_Device {
Def double i
Report Lazy$(1/i) ' display the definition of the lazy function
Function Sum (&i, lo, hi, &f()) {
def double temp
For i= lo to hi {
temp+=f()
}
=temp
}
Print Sum(&i, 1, 100, Lazy$(1/i))==5.1873775176392 ' true
Print i=101 ' true
}
Jensen`s_Device
</syntaxhighlight>
Using Decimal for better accuracy. change &i to &any to show that: when any change, change i, so f() use this i.
<syntaxhighlight lang="m2000 interpreter">
Module Jensen`s_Device {
Def decimal i
Function Sum (&any, lo, hi, &f()) {
def decimal temp
For any= lo to hi {
temp+=f()
}
=temp
}
Print Sum(&i, 1, 100, Lazy$(1/i))=5.1873775176396202608051176755@ ' true
Print i=101 ' true
}
Jensen`s_Device
</syntaxhighlight>
Many other examples use single float. So this is one for single.
<syntaxhighlight lang="m2000 interpreter">
Module Jensen`s_Device {
Def single i
Function Sum (&any, lo, hi, &f()) {
def single temp
For any= lo to hi {
temp+=f()
}
=temp
}
Print Sum(&i, 1, 100, Lazy$(1/i))=5.187378~ ' true
Print i=101 ' true
}
Jensen`s_Device
</syntaxhighlight>
=={{header|M4}}==
<syntaxhighlight lang="m4">define(`for',
`ifelse($#,0,``$0'',
`ifelse(eval($2<=$3),1,
`pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')
define(`sum',
`pushdef(`temp',0)`'for(`$1',$2,$3,
`define(`temp',eval(temp+$4))')`'temp`'popdef(`temp')')
sum(`i',1,100,`1000/i')</syntaxhighlight>
Output:
<pre>
5142
</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">sum[term_, i_, lo_, hi_] := Block[{temp = 0},
Do[temp = temp + term, {i, lo, hi}];
temp];
SetAttributes[sum, HoldFirst];</syntaxhighlight>
Output:
<pre>In[2]:= sum[1/i, i, 1, 100]
Out[2]= 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272
In[3]:=N[sum[1/i, i, 1, 100]]
Out[3]:=5.18738
</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">mysum(e, v, lo, hi) := block([s: 0], for i from lo thru hi do s: s + subst(v=i, e), s)$
mysum(1/n, n, 1, 10);
7381/2520
/* compare with builtin sum */
sum(1/n, n, 1, 10);
7381/2520
/* what if n is assigned a value ? */
n: 200$
/* still works */
mysum(1/n, n, 1, 10);
7381/2520</syntaxhighlight>
=={{header|NetRexx}}==
<syntaxhighlight lang="netrexx">
import COM.ibm.netrexx.process.
class JensensDevice
properties static
interpreter=NetRexxA
exp=Rexx ""
termMethod=Method
method main(x=String[]) static
say sum('i',1,100,'1/i')
method sum(i,lo,hi,term) static SIGNALS IOException,NoSuchMethodException,IllegalAccessException,InvocationTargetException
sum=0
loop iv=lo to hi
sum=sum+termeval(i,iv,term)
end
return sum
method termeval(i,iv,e) static returns Rexx SIGNALS IOException,NoSuchMethodException,IllegalAccessException,InvocationTargetException
if e\=exp then interpreter=null
exp=e
if interpreter=null then do
termpgm='method term('i'=Rexx) static returns rexx;return' e
fw=FileWriter("termpgm.nrx")
fw.write(termpgm,0,termpgm.length)
fw.close
interpreter=NetRexxA()
interpreter.parse([String 'termpgm.nrx'],[String 'nocrossref'])
termClass=interpreter.getClassObject(null,'termpgm')
classes=[interpreter.getClassObject('netrexx.lang', 'Rexx', 0)]
termMethod=termClass.getMethod('term', classes)
end
return Rexx termMethod.invoke(null,[iv])
</syntaxhighlight>
=={{header|Nim}}==
<syntaxhighlight lang="nim">var i: int
proc harmonicSum(i: var int; lo, hi: int; term: proc: float): float =
i = lo
while i <= hi:
result += term()
inc i
echo harmonicSum(i, 1, 100, proc: float = 1 / i)</syntaxhighlight>
{{out}}
<pre>5.5.187377517639621</pre>
=={{header|Objeck}}==
<syntaxhighlight lang="objeck">
bundle Default {
class Jensens {
i : static : Int;
function : Sum(lo : Int, hi : Int, term : () ~ Float) ~ Float {
temp := 0.0;
for(i := lo; i <= hi; i += 1;) {
temp += term();
};
return temp;
}
function : term() ~ Float {
return 1.0 / i;
}
function : Main(args : String[]) ~ Nil {
Sum(1, 100, term() ~ Float)->PrintLine();
}
}
}
</syntaxhighlight>
Output: 5.18738
=={{header|OCaml}}==
<syntaxhighlight lang="ocaml">let i = ref 42 (* initial value doesn't matter *)
let sum' i lo hi term =
let result = ref 0. in
i := lo;
while !i <= hi do
result := !result +. term ();
incr i
done;
!result
let () =
Printf.printf "%f\n" (sum' i 1 100 (fun () -> 1. /. float !i))</syntaxhighlight>
Output: 5.187378
=={{header|Oforth}}==
<syntaxhighlight lang="oforth">: mysum(lo, hi, term) | i | 0 lo hi for: i [ i term perform + ] ;</syntaxhighlight>
{{out}}
<pre>
mysum(1, 100, #inv) println
5.18737751763962
mysum(1, 100, #[ sq inv ]) println
1.63498390018489
</pre>
=={{header|Oz}}==
Translation using mutable references and an anonymous function:
<syntaxhighlight lang="oz">declare
fun {Sum I Lo Hi Term}
Temp = {NewCell 0.0}
in
I := Lo
for while:@I =< Hi do
Temp := @Temp + {Term}
I := @I + 1
end
@Temp
end
I = {NewCell unit}
in
{Show {Sum I 1 100 fun {$} 1.0 / {Int.toFloat @I} end}}</syntaxhighlight>
Idiomatic code:
<syntaxhighlight lang="oz">declare
fun {Sum Lo Hi F}
{FoldL {Map {List.number Lo Hi 1} F} Number.'+' 0.0}
end
in
{Show {Sum 1 100 fun {$ I} 1.0/{Int.toFloat I} end}}</syntaxhighlight>
=={{header|PARI/GP}}==
GP does not have pass-by-reference semantics for user-generated functions, though some predefined functions do. PARI programming allows this, though such a solution would essentially be identical to the [[#C|C]] solution above.
=={{header|Pascal}}==
<syntaxhighlight lang="pascal">program Jensens_Device;
{$IFDEF FPC}
{$MODE objFPC}
{$ENDIF}
type
tTerm = function(i: integer): real;
function term(i: integer): real;
begin
term := 1 / i;
end;
function sum(var i: LongInt; lo, hi: integer; term: tTerm): real;
begin
result := 0;
i := lo;
while i <= hi do
begin
result := result + term(i);
inc(i);
end;
end;
var
i: LongInt;
begin
writeln(sum(i, 1, 100, @term));
{$IFNDEF UNIX} readln; {$ENDIF}
end.</syntaxhighlight>
Out
<pre> 5.1873775176396206E+000</pre>
=={{header|Perl}}==
<syntaxhighlight lang="perl">my $i;
sub sum {
my ($i, $lo, $hi, $term) = @_;
my $temp = 0;
for ($$i = $lo; $$i <= $hi; $$i++) {
$temp += $term->();
}
return $temp;
}
print sum(\$i, 1, 100, sub { 1 / $i }), "\n";</syntaxhighlight>
Output: 5.18737751763962
Or you can take advantage of the fact that elements of the @_ are aliases of the original:
<syntaxhighlight lang="perl">my $i;
sub sum {
my (undef, $lo, $hi, $term) = @_;
my $temp = 0;
for ($_[0] = $lo; $_[0] <= $hi; $_[0]++) {
$temp += $term->();
}
return $temp;
}
print sum($i, 1, 100, sub { 1 / $i }), "\n";</syntaxhighlight>
Output: 5.18737751763962
=={{header|Phix}}==
Not really as asked for (implicit assumption replaced with explicit parameter) but this gives the required result. <br>
I could also have done what C and PHP are doing, though in Phix I'd have to explicitly assign the static var within the loop.<br>
I wholeheartedly agree with the comment on the Clipper example.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">sumr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">lo</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">hi</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rid</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">lo</span> <span style="color: #008080;">to</span> <span style="color: #000000;">hi</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">rid</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">reciprocal</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">i</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">sumr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">reciprocal</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
5.187377518
</pre>
=={{header|PHP}}==
<syntaxhighlight lang="php">$i;
function sum (&$i, $lo, $hi, $term) {
$temp = 0;
for ($i = $lo; $i <= $hi; $i++) {
$temp += $term();
}
return $temp;
}
echo sum($i, 1, 100, create_function('', 'global $i; return 1 / $i;')), "\n";
//Output: 5.18737751764 (5.1873775176396)
function sum ($lo,$hi)
{
$temp = 0;
for ($i = $lo; $i <= $hi; $i++)
{
$temp += (1 / $i);
}
return $temp;
}
echo sum(1,100);
//Output: 5.1873775176396
</syntaxhighlight>
=={{header|PicoLisp}}==
<syntaxhighlight lang="picolisp">(scl 6)
(de jensen (I Lo Hi Term)
(let Temp 0
(set I Lo)
(while (>= Hi (val I))
(inc 'Temp (Term))
(inc I) )
Temp ) )
(let I (box) # Create indirect reference
(format
(jensen I 1 100 '(() (*/ 1.0 (val I))))
*Scl ) )</syntaxhighlight>
Output:
<pre>-> "5.187383"</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">class Ref(object):
def __init__(self, value=None):
self.value = value
def harmonic_sum(i, lo, hi, term):
# term is passed by-name, and so is i
temp = 0
i.value = lo
while i.value <= hi: # Python "for" loop creates a distinct which
temp += term() # would not be shared with the passed "i"
i.value += 1 # Here the actual passed "i" is incremented.
return temp
i = Ref()
# note the correspondence between the mathematical notation and the
# call to sum it's almost as good as sum(1/i for i in range(1,101))
print harmonic_sum(i, 1, 100, lambda: 1.0/i.value)</syntaxhighlight>
or
<syntaxhighlight lang="python">
def harmonic_sum(i, lo, hi, term):
return sum(term() for i[0] in range(lo, hi + 1))
i = [0]
print(harmonic_sum(i, 1, 100, lambda: 1.0 / i[0]))
</syntaxhighlight>
or
<syntaxhighlight lang="python">
def harmonic_sum(i, lo, hi, term):
return sum(eval(term) for i[0] in range(lo, hi + 1))
i = [0]
print(harmonic_sum(i, 1, 100, "1.0 / i[0]"))
</syntaxhighlight>
Output: 5.18737751764
=={{header|R}}==
R uses a [[wp:Evaluation_strategy#Call_by_need|call by need]] evaluation strategy where function inputs
are evaluated on demand and then cached; functions can bypass the normal argument evaluation by using functions <tt>substitute</tt> and <tt>match.call</tt> to access the parse tree of the as-yet-unevaluated arguments, and using <tt>parent.frame</tt> to access the scope of the caller. There are some proposed
[http://developer.r-project.org/nonstandard-eval.pdf conventions] to do this in a way that is less confusing to the user
of a function; however, ignoring conventions we can come disturbingly close to the ALGOL call-by-name semantics.
<syntaxhighlight lang="r">sum <- function(var, lo, hi, term)
eval(substitute({
.temp <- 0;
for (var in lo:hi) {
.temp <- .temp + term
}
.temp
}, as.list(match.call()[-1])),
enclos=parent.frame())
sum(i, 1, 100, 1/i) #prints 5.187378
##and because of enclos=parent.frame(), the term can involve variables in the caller's scope:
x <- -1
sum(i, 1, 100, i^x) #5.187378</syntaxhighlight>
=={{header|Racket}}==
Racket happens to have an Algol 60-language, so Jensen's Device can
be written just as Jørn Jensen did at Regnecentralen.
<syntaxhighlight lang="racket">
#lang algol60
begin
integer i;
real procedure sum (i, lo, hi, term);
value lo, hi;
integer i, lo, hi;
real term;
comment term is passed by-name, and so is i;
begin
real temp;
temp := 0;
for i := lo step 1 until hi do
temp := temp + term;
sum := temp
end;
comment note the correspondence between the mathematical notation and the call to sum;
printnln (sum (i, 1, 100, 1/i))
end
</syntaxhighlight>
But of course you can also use the more boring popular alternative of first class functions:
<syntaxhighlight lang="racket">
#lang racket/base
(define (sum lo hi f)
(for/sum ([i (in-range lo (add1 hi))]) (f i)))
(sum 1 100 (λ(i) (/ 1.0 i)))
</syntaxhighlight>
=={{header|Raku}}==
(formerly Perl 6)
Rather than playing tricks like Perl 5 does, the declarations of the formal parameters are quite straightforward in Raku:
<syntaxhighlight lang="raku" line>sub sum($i is rw, $lo, $hi, &term) {
my $temp = 0;
loop ($i = $lo; $i <= $hi; $i++) {
$temp += term;
}
return $temp;
}
my $i;
say sum $i, 1, 100, { 1 / $i };</syntaxhighlight>
Note that the C-style "for" loop is pronounced "loop" in Raku, and is the only loop statement that actually requires parens.
=={{header|Rascal}}==
<syntaxhighlight lang="rascal">public num Jenssen(int lo, int hi, num (int i) term){
temp = 0;
while (lo <= hi){
temp += term(lo);
lo += 1;}
return temp;
}</syntaxhighlight>
With as output:
<syntaxhighlight lang="rascal">rascal>Jenssen(1, 100, num(int i){return 1.0/i;})
num: 5.18737751763962026080511767565825315790897212670845165317653395662</syntaxhighlight>
=={{header|REXX}}==
<syntaxhighlight lang="rexx">/*REXX program demonstrates Jensen's device (via call subroutine, and args by name). */
parse arg d . /*obtain optional argument from the CL.*/
if d=='' | d=="," then d= 100 /*Not specified? Then use the default.*/
numeric digits d /*use D decimal digits (9 is default)*/
say 'using ' d " decimal digits:" /*display what's being used for digits.*/
say
say sum( i, 1, 100, "1/i" ) /*invoke SUM (100th harmonic number).*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
sum: procedure; parse arg j,start,finish,exp; $= 0
interpret 'do' j "=" start 'to' finish "; $=$+" exp '; end'
/*comment ──── ═ ─── ═════ ──── ══════ ────────── ═══ ───────── */
/*comment lit var lit var lit var literal var literal */
return $</syntaxhighlight>
{{out|output|text= when using the default input:}}
<pre>
using 100 decimal digits:
5.187377517639620260805117675658253157908972126708451653176533956587219557532550496605687768923120415
</pre>
{{out|output|text= when using the input: <tt> 1000 </tt>}}
<br>(Shown at three-quarter size and with 200 characters per line.)
<pre style="font-size:75%">
using 1000 decimal digits:
5.187377517639620260805117675658253157908972126708451653176533956587219557532550496605687768923120413552951372900080959485764334902003859251284547479399606488677719356437701034351417501628003612133813
93634033610397170258150385609229760925775852490242015786454123413833660918987060275907253504512582948807527866739590394714709377905509971663909084580816222756304901297019081913723833776150679344482592
19985786828216280140988475651174867766685160764730429716983310052063466701008405663630740646670436720827975050329078640945579952223172461998152578702106818073281191723171032278163615245743308956980821
10786794204451169328900410057940565163334352244388766863157323818250401277131246550164879348955299573048040410736739783727083287179928615106959660501145265658411572959372901925824344377263363761945330
17905075097606740175205276891748232922334187250177881689092871712673549165589217457070884105311065936887252732260150280756519586504475363590572034459636088593436136141078274322996362525543164325745468
2
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
# Project : Jensen's Device
decimals(14)
i = 100
see sum(i,1,100,"1/n") + nl
func sum(i,lo,hi,term)
temp = 0
for n = lo to hi step 1
eval("num = " + term)
temp = temp + num
next
return temp
</syntaxhighlight>
Output:
<pre>
5.18737751763962
</pre>
=={{header|RPL}}==
{{works with|Halcyon Calc|4.2.7}}
≪ → idx lo hi term
≪ lo idx STO 0
DO
term EVAL +
1 idx STO+
UNTIL idx EVAL hi > END
idx PURGE
≫
≫
‘SUM’ STO
'K' 1 100 '1/K' SUM
'N' 0 100 '1/FACT(N)' SUM
{{out}}
<pre>
2: 5.18737751764
1: 2.71828182846
</pre>
=={{header|Ruby}}==
Here, setting the variable and evaluating the term are truly executed in the "outer" context:
<syntaxhighlight lang="ruby">def sum(var, lo, hi, term, context)
sum = 0.0
lo.upto(hi) do |n|
sum += eval "#{var} = #{n}; #{term}", context
end
sum
end
p sum "i", 1, 100, "1.0 / i", binding # => 5.18737751763962</syntaxhighlight>
But here is the Ruby way to do it:
<syntaxhighlight lang="ruby">def sum2(lo, hi)
lo.upto(hi).inject(0.0) {|sum, n| sum += yield n}
end
p sum2(1, 100) {|i| 1.0/i} # => 5.18737751763962</syntaxhighlight>
Even more concise: (requires ruby >= 2.4)
<syntaxhighlight lang="ruby">
def sum lo, hi, &term
(lo..hi).sum(&term)
end
p sum(1,100){|i| 1.0/i} # => 5.187377517639621
# or using Rational:
p sum(1,100){|i| Rational(1,i)} # => 14466636279520351160221518043104131447711 / 2788815009188499086581352357412492142272
</syntaxhighlight>
=={{header|Rust}}==
<syntaxhighlight lang="rust">
use std::f32;
fn harmonic_sum<F>(lo: usize, hi: usize, term: F) -> f32
where
F: Fn(f32) -> f32,
{
(lo..hi + 1).fold(0.0, |acc, item| acc + term(item as f32))
}
fn main() {
println!("{}", harmonic_sum(1, 100, |i| 1.0 / i));
}
</syntaxhighlight>
{{out}}
<pre>
5.187378
</pre>
=={{header|Scala}}==
Actually, the <code>i</code> parameter needs to be passed by reference, as done in so many
examples here, so that changes made to it reflect on the parameter that was passed. Scala
supports passing parameters by name, but not by reference, which means it can't change the
value of any parameter passed. The code below gets around that by creating a mutable integer
class, which is effectively the same as passing by reference.
<syntaxhighlight lang="scala">class MyInt { var i: Int = _ }
val i = new MyInt
def sum(i: MyInt, lo: Int, hi: Int, term: => Double) = {
var temp = 0.0
i.i = lo
while(i.i <= hi) {
temp = temp + term
i.i += 1
}
temp
}
sum(i, 1, 100, 1.0 / i.i)</syntaxhighlight>
Result:
<pre>
res2: Double = 5.187377517639621
</pre>
=={{header|Scheme}}==
Scheme procedures do not support call-by-name. Scheme macros, however, do:
<syntaxhighlight lang="scheme">
(define-syntax sum
(syntax-rules ()
((sum var low high . body)
(let loop ((var low)
(result 0))
(if (> var high)
result
(loop (+ var 1)
(+ result . body)))))))
</syntaxhighlight>
<pre>
(exact->inexact (sum i 1 100 (/ 1 i)))
5.18737751763962
</pre>
=={{header|Seed7}}==
Seed7 supports call-by-name with function parameters:
<syntaxhighlight lang="seed7">
$ include "seed7_05.s7i";
include "float.s7i";
var integer: i is 0;
const func float: sum (inout integer: i, in integer: lo, in integer: hi,
ref func float: term) is func
result
var float: sum is 0.0
begin
for i range lo to hi do
sum +:= term;
end for;
end func;
const proc: main is func
begin
writeln(sum(i, 1, 100, 1.0/flt(i)) digits 6);
end func;
</syntaxhighlight>
Output:
<pre>
5.187378
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">var i
func sum (i, lo, hi, term) {
var temp = 0
for (*i = lo; *i <= hi; (*i)++) {
temp += term.run
}
return temp
}
say sum(\i, 1, 100, { 1 / i })</syntaxhighlight>
{{out}}
<pre>5.18737751763962026080511767565825315790897212671</pre>
=={{header|Simula}}==
{{trans|algol60}}
{{works with|SIMULA-67}}
Compare with Algol 60, in Simula 67 'call by name' is specified with '''name'''. It is a true 'call by name' evaluation not a 'procedure parameter' emulation.<syntaxhighlight lang="simula">comment Jensen's Device;
begin
integer i;
real procedure sum (i, lo, hi, term);
name i, term;
value lo, hi;
integer i, lo, hi;
real term;
comment term is passed by-name, and so is i;
begin
integer j;
real temp;
temp := 0;
for j := lo step 1 until hi do
begin
i := j;
temp := temp + term
end;
sum := temp
end;
comment note the correspondence between the mathematical notation and the call to sum;
outreal (sum (i, 1, 100, 1/i), 7, 14)
end</syntaxhighlight>
{{out}}
<pre>
5.187378&+000
</pre>
=={{header|Standard ML}}==
<syntaxhighlight lang="sml">val i = ref 42 (* initial value doesn't matter *)
fun sum' (i, lo, hi, term) = let
val result = ref 0.0
in
i := lo;
while !i <= hi do (
result := !result + term ();
i := !i + 1
);
!result
end
val () =
print (Real.toString (sum' (i, 1, 100, fn () => 1.0 / real (!i))) ^ "\n")</syntaxhighlight>
Output: 5.18737751764
=={{header|Swift}}==
<syntaxhighlight lang="swift">var i = 42 // initial value doesn't matter
func sum(inout i: Int, lo: Int, hi: Int, @autoclosure term: () -> Double) -> Double {
var result = 0.0
for i = lo; i <= hi; i++ {
result += term()
}
return result
}
println(sum(&i, 1, 100, 1 / Double(i)))</syntaxhighlight>
(Prior to Swift 1.2, replace <code>@autoclosure term: () -> Double</code> with <code>term: @autoclosure () -> Double</code>.)
{{out}}
<pre>5.187378</pre>
=={{header|Tcl}}==
Here, we set the value of the passed variable in the caller's frame. We then evaluate the passed term there too.
<syntaxhighlight lang="tcl">proc sum {var lo hi term} {
upvar 1 $var x
set sum 0.0
for {set x $lo} {$x < $hi} {incr x} {
set sum [expr {$sum + [uplevel 1 [list expr $term]]}]
}
return $sum
}
puts [sum i 1 100 {1.0/$i}] ;# 5.177377517639621</syntaxhighlight>
However, the solution is expressed more simply like this
<syntaxhighlight lang="tcl">proc sum2 {lo hi lambda} {
set sum 0.0
for {set n $lo} {$n < $hi} {incr n} {
set sum [expr {$sum + [apply $lambda $n]}]
}
return $sum
}
puts [sum2 1 100 {i {expr {1.0/$i}}}] ;# 5.177377517639621</syntaxhighlight>
=={{header|VBA}}==
<syntaxhighlight lang="vb">
Private Function sum(i As String, ByVal lo As Integer, ByVal hi As Integer, term As String) As Double
Dim temp As Double
For k = lo To hi
temp = temp + Evaluate(Replace(term, i, k))
Next k
sum = temp
End Function
Sub Jensen_Device()
Debug.Print sum("i", 1, 100, "1/i")
Debug.Print sum("i", 1, 100, "i*i")
Debug.Print sum("j", 1, 100, "sin(j)")
End Sub
</syntaxhighlight>
{{out}}
<pre>
5,18737751763962
338350
-0,12717101366042
</pre>
=={{header|Wren}}==
As Wren doesn't support call by name, call by reference nor pointers we need to 'box' the global numeric variable 'i' and use a function for 'term' to simulate Jensen's device. This works because all user defined types are reference types and functions can capture external variables.
<syntaxhighlight lang="wren">class Box {
construct new(v) { _v = v }
v { _v }
v=(value) { _v = value }
}
var i = Box.new(0) // any initial value will do here
var sum = Fn.new { |i, lo, hi, term|
var temp = 0
i.v = lo
while (i.v <= hi) {
temp = temp + term.call()
i.v = i.v + 1
}
return temp
}
var s = sum.call(i, 1, 100, Fn.new { 1/i.v })
System.print(s)</syntaxhighlight>
{{out}}
<pre>
5.1873775176396
</pre>
=={{header|zkl}}==
zkl doesn't support call by name/address but does have reference objects. Using an explicit call to term:
<syntaxhighlight lang="zkl">fcn sum(ri, lo,hi, term){
temp:=0.0; ri.set(lo);
do{ temp+=term(ri); } while(ri.inc()<hi); // inc return previous value
return(temp);
}
sum(Ref(0), 1,100, fcn(ri){ 1.0/ri.value }).println();</syntaxhighlight>
Using function application/deferred(lazy) objects, we can make the function call implicit (addition forces evaluation of the LHS):
<syntaxhighlight lang="zkl">fcn sum2(ri, lo,hi, term){
temp:=0.0; ri.set(lo);
do{ temp=term + temp; } while(ri.inc()<hi); // inc return previous value
return(temp);
}
ri:=Ref(0);
sum2(ri, 1,100, 'wrap(){ 1.0/ri.value }).println();</syntaxhighlight>
In this case, we can call sum or sum2 and it does the same thing (the ri parameter will be ignored).
Of course, as others have pointed out, this can be expressed very simply:
<syntaxhighlight lang="zkl">fcn sum3(lo,hi, term){ [lo..hi].reduce('wrap(sum,i){ sum + term(i) },0.0) }
sum3(1,100, fcn(i){ 1.0/i }).println();</syntaxhighlight>
{{out}}
<pre>
5.187378
5.187378
5.187378
</pre>
{{omit from|GUISS}}
{{omit from|gnuplot}}
| |||