First-class functions/Use numbers analogously: Difference between revisions
Thundergnat (talk | contribs) m (syntax highlighting fixup automation) |
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{{trans|Python}} |
{{trans|Python}} |
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< |
<syntaxhighlight lang="11l">V (x, xi, y, yi) = (2.0, 0.5, 4.0, 0.25) |
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V z = x + y |
V z = x + y |
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V zi = 1.0 / (x + y) |
V zi = 1.0 / (x + y) |
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V numlist = [x, y, z] |
V numlist = [x, y, z] |
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V numlisti = [xi, yi, zi] |
V numlisti = [xi, yi, zi] |
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print(zip(numlist, numlisti).map((n, inversen) -> multiplier(inversen, n)(.5)))</ |
print(zip(numlist, numlisti).map((n, inversen) -> multiplier(inversen, n)(.5)))</syntaxhighlight> |
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{{out}} |
{{out}} |
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=={{header|Ada}}== |
=={{header|Ada}}== |
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< |
<syntaxhighlight lang="ada">with Ada.Text_IO; |
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procedure Firstclass is |
procedure Firstclass is |
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generic |
generic |
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end; |
end; |
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end loop; |
end loop; |
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end Firstclass;</ |
end Firstclass;</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre>5.00000E-01 |
<pre>5.00000E-01 |
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Line 73: | Line 73: | ||
Note: Standard ALGOL 68's scoping rules forbids exporting a '''proc'''[edure] (or '''format''') out of it's scope (closure). Hence this specimen will run on [[ELLA ALGOL 68]], but is non-standard. For a discussion of first-class functions in ALGOL 68 consult [http://www.cs.ru.nl/~kees/home/papers/psi96.pdf "The Making of Algol 68"] - [[wp:Cornelis_H.A._Koster|C.H.A. Koster]] (1993). <!-- Retrieved April 28, 2007 --> |
Note: Standard ALGOL 68's scoping rules forbids exporting a '''proc'''[edure] (or '''format''') out of it's scope (closure). Hence this specimen will run on [[ELLA ALGOL 68]], but is non-standard. For a discussion of first-class functions in ALGOL 68 consult [http://www.cs.ru.nl/~kees/home/papers/psi96.pdf "The Making of Algol 68"] - [[wp:Cornelis_H.A._Koster|C.H.A. Koster]] (1993). <!-- Retrieved April 28, 2007 --> |
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< |
<syntaxhighlight lang="algol68">REAL |
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x := 2, |
x := 2, |
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xi := 0.5, |
xi := 0.5, |
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Line 94: | Line 94: | ||
inv n = inv num list[key]; |
inv n = inv num list[key]; |
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print ((multiplier(inv n, n)(.5), new line)) |
print ((multiplier(inv n, n)(.5), new line)) |
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OD</ |
OD</syntaxhighlight> |
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Output: |
Output: |
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<pre> |
<pre> |
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Line 110: | Line 110: | ||
=={{header|Axiom}}== |
=={{header|Axiom}}== |
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< |
<syntaxhighlight lang="axiom">(x,xi,y,yi) := (2.0,0.5,4.0,0.25) |
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(z,zi) := (x+y,1/(x+y)) |
(z,zi) := (x+y,1/(x+y)) |
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(numbers,invers) := ([x,y,z],[xi,yi,zi]) |
(numbers,invers) := ([x,y,z],[xi,yi,zi]) |
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multiplier(a:Float,b:Float):(Float->Float) == (m +-> a*b*m) |
multiplier(a:Float,b:Float):(Float->Float) == (m +-> a*b*m) |
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[multiplier(number,inver) 0.5 for number in numbers for inver in invers] |
[multiplier(number,inver) 0.5 for number in numbers for inver in invers] |
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</ |
</syntaxhighlight>Output: |
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< |
<syntaxhighlight lang="axiom"> [0.5,0.5,0.5] |
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Type: List(Float)</ |
Type: List(Float)</syntaxhighlight> |
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We can also curry functions, possibly with function composition, with the same output as before: |
We can also curry functions, possibly with function composition, with the same output as before: |
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< |
<syntaxhighlight lang="axiom">mult(n:Float):(Float->Float) == curryLeft(*$Float,n)$MAPPKG3(Float,Float,Float) |
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[mult(number*inver) 0.5 for number in numbers for inver in invers] |
[mult(number*inver) 0.5 for number in numbers for inver in invers] |
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[(mult(number)*mult(inver)) 0.5 for number in numbers for inver in invers]</ |
[(mult(number)*mult(inver)) 0.5 for number in numbers for inver in invers]</syntaxhighlight> |
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Using the Spad code in [[First-class functions#Axiom]], this can be done more economically using: |
Using the Spad code in [[First-class functions#Axiom]], this can be done more economically using: |
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< |
<syntaxhighlight lang="axiom">(map(mult,numbers)*map(mult,invers)) 0.5</syntaxhighlight> |
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For comparison, [[First-class functions#Axiom]] gave: |
For comparison, [[First-class functions#Axiom]] gave: |
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< |
<syntaxhighlight lang="axiom">fns := [sin$Float, cos$Float, (x:Float):Float +-> x^3] |
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inv := [asin$Float, acos$Float, (x:Float):Float +-> x^(1/3)] |
inv := [asin$Float, acos$Float, (x:Float):Float +-> x^(1/3)] |
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[(f*g) 0.5 for f in fns for g in inv] |
[(f*g) 0.5 for f in fns for g in inv] |
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</syntaxhighlight> |
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</lang> |
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- which has the same output. |
- which has the same output. |
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=={{header|BBC BASIC}}== |
=={{header|BBC BASIC}}== |
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{{works with|BBC BASIC for Windows}} |
{{works with|BBC BASIC for Windows}} |
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< |
<syntaxhighlight lang="bbcbasic"> REM Create some numeric variables: |
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x = 2 : xi = 1/2 |
x = 2 : xi = 1/2 |
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y = 4 : yi = 0.25 |
y = 4 : yi = 0.25 |
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Line 160: | Line 160: | ||
DIM p% LEN(f$) + 4 |
DIM p% LEN(f$) + 4 |
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$(p%+4) = f$ : !p% = p%+4 |
$(p%+4) = f$ : !p% = p%+4 |
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= p%</ |
= p%</syntaxhighlight> |
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'''Output:''' |
'''Output:''' |
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<pre> |
<pre> |
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Line 168: | Line 168: | ||
</pre> |
</pre> |
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Compare with the implementation of First-class functions: |
Compare with the implementation of First-class functions: |
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< |
<syntaxhighlight lang="bbcbasic"> REM Create some functions and their inverses: |
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DEF FNsin(a) = SIN(a) |
DEF FNsin(a) = SIN(a) |
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DEF FNasn(a) = ASN(a) |
DEF FNasn(a) = ASN(a) |
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DIM p% LEN(f$) + 4 |
DIM p% LEN(f$) + 4 |
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$(p%+4) = f$ : !p% = p%+4 |
$(p%+4) = f$ : !p% = p%+4 |
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= p%</ |
= p%</syntaxhighlight> |
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=={{header|C sharp|C#}}== |
=={{header|C sharp|C#}}== |
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{{works with|C#|4.0}} |
{{works with|C#|4.0}} |
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The structure here is exactly the same as the C# entry in [[First-class functions]]. The "var" keyword allows us to use the same initialization code for an array of doubles as an array of functions. Note that variable names have been changed to correspond with the new functionality. |
The structure here is exactly the same as the C# entry in [[First-class functions]]. The "var" keyword allows us to use the same initialization code for an array of doubles as an array of functions. Note that variable names have been changed to correspond with the new functionality. |
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< |
<syntaxhighlight lang="csharp">using System; |
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using System.Linq; |
using System.Linq; |
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Line 233: | Line 233: | ||
} |
} |
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} |
} |
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</syntaxhighlight> |
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</lang> |
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=={{header|C++}}== |
=={{header|C++}}== |
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< |
<syntaxhighlight lang="cpp">#include <array> |
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#include <iostream> |
#include <iostream> |
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Line 263: | Line 263: | ||
} |
} |
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} |
} |
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</syntaxhighlight> |
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</lang> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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Line 272: | Line 272: | ||
=={{header|Clojure}}== |
=={{header|Clojure}}== |
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< |
<syntaxhighlight lang="clojure">(def x 2.0) |
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(def xi 0.5) |
(def xi 0.5) |
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(def y 4.0) |
(def y 4.0) |
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Line 287: | Line 287: | ||
> (for [[n i] (zipmap numbers invers)] |
> (for [[n i] (zipmap numbers invers)] |
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((multiplier n i) 0.5)) |
((multiplier n i) 0.5)) |
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(0.5 0.5 0.5)</ |
(0.5 0.5 0.5)</syntaxhighlight> |
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For comparison: |
For comparison: |
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< |
<syntaxhighlight lang="clojure"> |
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(use 'clojure.contrib.math) |
(use 'clojure.contrib.math) |
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(let [fns [#(Math/sin %) #(Math/cos %) (fn [x] (* x x x))] |
(let [fns [#(Math/sin %) #(Math/cos %) (fn [x] (* x x x))] |
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inv [#(Math/asin %) #(Math/acos %) #(expt % 1/3)]] |
inv [#(Math/asin %) #(Math/acos %) #(expt % 1/3)]] |
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(map #(% 0.5) (map #(comp %1 %2) fns inv))) |
(map #(% 0.5) (map #(comp %1 %2) fns inv))) |
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</syntaxhighlight> |
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</lang> |
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Output: |
Output: |
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<pre>(0.5 0.4999999999999999 0.5000000000000001)</pre> |
<pre>(0.5 0.4999999999999999 0.5000000000000001)</pre> |
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Line 300: | Line 300: | ||
=={{header|Common Lisp}}== |
=={{header|Common Lisp}}== |
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< |
<syntaxhighlight lang="lisp">(defun multiplier (f g) |
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#'(lambda (x) (* f g x))) |
#'(lambda (x) (* f g x))) |
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Line 319: | Line 319: | ||
inverse |
inverse |
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value |
value |
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(funcall multiplier value))))</ |
(funcall multiplier value))))</syntaxhighlight> |
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Output: |
Output: |
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Line 329: | Line 329: | ||
The code from [[First-class functions]], for comparison: |
The code from [[First-class functions]], for comparison: |
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< |
<syntaxhighlight lang="lisp">(defun compose (f g) (lambda (x) (funcall f (funcall g x)))) |
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(defun cube (x) (expt x 3)) |
(defun cube (x) (expt x 3)) |
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(defun cube-root (x) (expt x (/ 3))) |
(defun cube-root (x) (expt x (/ 3))) |
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Line 341: | Line 341: | ||
function |
function |
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value |
value |
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(funcall composed value)))</ |
(funcall composed value)))</syntaxhighlight> |
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Output: |
Output: |
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Line 350: | Line 350: | ||
=={{header|D}}== |
=={{header|D}}== |
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< |
<syntaxhighlight lang="d">import std.stdio; |
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auto multiplier(double a, double b) |
auto multiplier(double a, double b) |
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Line 374: | Line 374: | ||
writefln("%f * %f * %f == %f", f[i], r[i], 1.0, mult(1)); |
writefln("%f * %f * %f == %f", f[i], r[i], 1.0, mult(1)); |
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} |
} |
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}</ |
}</syntaxhighlight> |
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Output: |
Output: |
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<pre>2.000000 * 0.500000 * 1.000000 == 1.000000 |
<pre>2.000000 * 0.500000 * 1.000000 == 1.000000 |
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Line 384: | Line 384: | ||
This is written to have identical structure to [[First-class functions#E]], though the variable names are different. |
This is written to have identical structure to [[First-class functions#E]], though the variable names are different. |
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< |
<syntaxhighlight lang="e">def x := 2.0 |
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def xi := 0.5 |
def xi := 0.5 |
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def y := 4.0 |
def y := 4.0 |
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def b := reverse[i] |
def b := reverse[i] |
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println(`s = $s, a = $a, b = $b, multiplier($a, $b)($s) = ${multiplier(a, b)(s)}`) |
println(`s = $s, a = $a, b = $b, multiplier($a, $b)($s) = ${multiplier(a, b)(s)}`) |
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}</ |
}</syntaxhighlight> |
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Output: |
Output: |
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Line 414: | Line 414: | ||
{{trans|C#}} |
{{trans|C#}} |
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ELENA 5.0 : |
ELENA 5.0 : |
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< |
<syntaxhighlight lang="elena">import system'routines; |
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import extensions; |
import extensions; |
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Line 432: | Line 432: | ||
multiplied.forEach:(multiplier){ console.printLine(multiplier(0.5r)) } |
multiplied.forEach:(multiplier){ console.printLine(multiplier(0.5r)) } |
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}</ |
}</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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Line 441: | Line 441: | ||
=={{header|Erlang}}== |
=={{header|Erlang}}== |
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<syntaxhighlight lang="erlang"> |
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<lang Erlang> |
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-module( first_class_functions_use_numbers ). |
-module( first_class_functions_use_numbers ). |
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multiplier( N1, N2 ) -> fun(M) -> N1 * N2 * M end. |
multiplier( N1, N2 ) -> fun(M) -> N1 * N2 * M end. |
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</syntaxhighlight> |
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</lang> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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Line 465: | Line 465: | ||
=={{header|F_Sharp|F#}}== |
=={{header|F_Sharp|F#}}== |
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< |
<syntaxhighlight lang="fsharp"> |
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let x = 2.0 |
let x = 2.0 |
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let xi = 0.5 |
let xi = 0.5 |
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Line 479: | Line 479: | ||
|> List.map ((|>) 0.5) |
|> List.map ((|>) 0.5) |
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|> printfn "%A" |
|> printfn "%A" |
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</syntaxhighlight> |
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</lang> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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=={{header|Factor}}== |
=={{header|Factor}}== |
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Compared to http://rosettacode.org/wiki/First-class_functions, the call to "compose" is replaced with the call to "mutliplier" |
Compared to http://rosettacode.org/wiki/First-class_functions, the call to "compose" is replaced with the call to "mutliplier" |
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< |
<syntaxhighlight lang="factor">USING: arrays kernel literals math prettyprint sequences ; |
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IN: q |
IN: q |
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: example ( -- ) |
: example ( -- ) |
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0.5 A B create-all |
0.5 A B create-all |
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[ call( x -- y ) ] with map . ;</ |
[ call( x -- y ) ] with map . ;</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre>{ 0.5 0.5 0.5 }</pre> |
<pre>{ 0.5 0.5 0.5 }</pre> |
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Line 510: | Line 510: | ||
=={{header|Fantom}}== |
=={{header|Fantom}}== |
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< |
<syntaxhighlight lang="fantom"> |
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class Main |
class Main |
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{ |
{ |
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Line 531: | Line 531: | ||
} |
} |
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} |
} |
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</syntaxhighlight> |
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</lang> |
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The <code>combine</code> function is very similar to the <code>compose</code> function in 'First-class functions'. In both cases a new function is returned: |
The <code>combine</code> function is very similar to the <code>compose</code> function in 'First-class functions'. In both cases a new function is returned: |
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< |
<syntaxhighlight lang="fantom"> |
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static |Obj -> Obj| compose (|Obj -> Obj| fn1, |Obj -> Obj| fn2) |
static |Obj -> Obj| compose (|Obj -> Obj| fn1, |Obj -> Obj| fn2) |
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{ |
{ |
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return |Obj x -> Obj| { fn2 (fn1 (x)) } |
return |Obj x -> Obj| { fn2 (fn1 (x)) } |
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} |
} |
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</syntaxhighlight> |
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</lang> |
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=={{header|Go}}== |
=={{header|Go}}== |
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At point C, numbers and their inverses have been multiplied and bound to first class functions. The ordered collection arrays could be modified at this point and the function objects would be unaffected. |
At point C, numbers and their inverses have been multiplied and bound to first class functions. The ordered collection arrays could be modified at this point and the function objects would be unaffected. |
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< |
<syntaxhighlight lang="go">package main |
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import "fmt" |
import "fmt" |
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Line 591: | Line 591: | ||
return n1n2 * m |
return n1n2 * m |
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} |
} |
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}</ |
}</syntaxhighlight> |
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Output: |
Output: |
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<pre> |
<pre> |
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Line 614: | Line 614: | ||
[[/Go interface type|This can also be done with an interface type]] rather than the "empty interface" (<code>interface{}</code>) for better type safety and to avoid the <code>eval</code> function and type switch. |
[[/Go interface type|This can also be done with an interface type]] rather than the "empty interface" (<code>interface{}</code>) for better type safety and to avoid the <code>eval</code> function and type switch. |
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< |
<syntaxhighlight lang="go">package main |
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import "fmt" |
import "fmt" |
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Line 661: | Line 661: | ||
panic("unsupported multiplier type") |
panic("unsupported multiplier type") |
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return 0 // never reached |
return 0 // never reached |
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}</ |
}</syntaxhighlight> |
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=={{header|Groovy}}== |
=={{header|Groovy}}== |
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< |
<syntaxhighlight lang="groovy">def multiplier = { n1, n2 -> { m -> n1 * n2 * m } } |
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def ε = 0.00000001 // tolerance(epsilon): acceptable level of "wrongness" to account for rounding error |
def ε = 0.00000001 // tolerance(epsilon): acceptable level of "wrongness" to account for rounding error |
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Line 675: | Line 675: | ||
} |
} |
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println() |
println() |
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}</ |
}</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre>2.000 * 0.500 * 1.000 == 1.000 |
<pre>2.000 * 0.500 * 1.000 == 1.000 |
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Line 697: | Line 697: | ||
=={{header|Haskell}}== |
=={{header|Haskell}}== |
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< |
<syntaxhighlight lang="haskell">module Main |
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where |
where |
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Line 724: | Line 724: | ||
in printf "%f * %f * 0.5 = %f\n" number inverse (new_function 0.5) |
in printf "%f * %f * 0.5 = %f\n" number inverse (new_function 0.5) |
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mapM_ print_pair pairs |
mapM_ print_pair pairs |
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</syntaxhighlight> |
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</lang> |
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This is very close to the first-class functions example, but given as a full Haskell program rather than an interactive session. |
This is very close to the first-class functions example, but given as a full Haskell program rather than an interactive session. |
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Line 735: | Line 735: | ||
[[First-class functions]] task solution. The solution here |
[[First-class functions]] task solution. The solution here |
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is simpler and more direct since it handles a specific function definition. |
is simpler and more direct since it handles a specific function definition. |
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< |
<syntaxhighlight lang="unicon">import Utils |
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procedure main(A) |
procedure main(A) |
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Line 744: | Line 744: | ||
procedure multiplier(n1,n2) |
procedure multiplier(n1,n2) |
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return makeProc { repeat inVal := n1 * n2 * (inVal@&source)[1] } |
return makeProc { repeat inVal := n1 * n2 * (inVal@&source)[1] } |
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end</ |
end</syntaxhighlight> |
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A sample run: |
A sample run: |
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Line 760: | Line 760: | ||
This seems to satisfy the new problem statement: |
This seems to satisfy the new problem statement: |
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< |
<syntaxhighlight lang="j"> x =: 2.0 |
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xi =: 0.5 |
xi =: 0.5 |
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y =: 4.0 |
y =: 4.0 |
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Line 770: | Line 770: | ||
rev =: xi,yi,zi |
rev =: xi,yi,zi |
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multiplier =: 2 : 'm * n * ]'</ |
multiplier =: 2 : 'm * n * ]'</syntaxhighlight> |
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An equivalent but perhaps prettier definition of multiplier would be: |
An equivalent but perhaps prettier definition of multiplier would be: |
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< |
<syntaxhighlight lang="j">multiplier=: {{m*n*]}}</syntaxhighlight> |
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Or, if J's "right bracket is the right identity function" bothers you, you might prefer the slightly more verbose but still equivalent: |
Or, if J's "right bracket is the right identity function" bothers you, you might prefer the slightly more verbose but still equivalent: |
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< |
<syntaxhighlight lang="j">multiplier=: {{m*n*{{y}}}}</syntaxhighlight> |
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Example use: |
Example use: |
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<lang> fwd multiplier rev 0.5 |
<syntaxhighlight lang="text"> fwd multiplier rev 0.5 |
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0.5 0.5 0.5</ |
0.5 0.5 0.5</syntaxhighlight> |
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For contrast, here are the final results from [[First-class functions#J]]: |
For contrast, here are the final results from [[First-class functions#J]]: |
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<lang> BA unqcol 0.5 |
<syntaxhighlight lang="text"> BA unqcol 0.5 |
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0.5 0.5 0.5 0.5</ |
0.5 0.5 0.5 0.5</syntaxhighlight> |
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===Tacit (unorthodox) version=== |
===Tacit (unorthodox) version=== |
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Although the pseudo-code to generate the numbers can certainly be written (see above [http://rosettacode.org/wiki/First-class_functions/Use_numbers_analogously#Explicit_version Explicit version] ) this is not done for this version because it would destroy part of the analogy (J encourages, from the programming perspective, to process all components at once as opposed to one component at a time). In addition, this version is done in terms of boxed lists of numbers instead of plain list of numbers, again, to preserve the analogy. |
Although the pseudo-code to generate the numbers can certainly be written (see above [http://rosettacode.org/wiki/First-class_functions/Use_numbers_analogously#Explicit_version Explicit version] ) this is not done for this version because it would destroy part of the analogy (J encourages, from the programming perspective, to process all components at once as opposed to one component at a time). In addition, this version is done in terms of boxed lists of numbers instead of plain list of numbers, again, to preserve the analogy. |
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<lang> multiplier=. train@:((;:'&*') ;~ an@: *) |
<syntaxhighlight lang="text"> multiplier=. train@:((;:'&*') ;~ an@: *) |
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]A=. 2 ; 4 ; (2 + 4) NB. Corresponds to ]A=. box (1&o.)`(2&o.)`(^&3) |
]A=. 2 ; 4 ; (2 + 4) NB. Corresponds to ]A=. box (1&o.)`(2&o.)`(^&3) |
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Line 807: | Line 807: | ||
└───┴───┴───┘ |
└───┴───┴───┘ |
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BA of &> 0.5 NB. Corresponds to BA of &> 0.5 (exactly) |
BA of &> 0.5 NB. Corresponds to BA of &> 0.5 (exactly) |
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0.5 0.5 0.5</ |
0.5 0.5 0.5</syntaxhighlight> |
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Please refer to [http://rosettacode.org/wiki/First-class_functions#Tacit_.28unorthodox.29_version First-class functions tacit (unorthodox) version] for the definitions of the functions train, an and of. |
Please refer to [http://rosettacode.org/wiki/First-class_functions#Tacit_.28unorthodox.29_version First-class functions tacit (unorthodox) version] for the definitions of the functions train, an and of. |
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Line 813: | Line 813: | ||
=={{header|jq}}== |
=={{header|jq}}== |
||
It may be helpful to compare the following definition of "multiplier" with its Ruby counterpart [[#Ruby|below]]. Whereas the Ruby definition must name all its positional parameters, the jq equivalent is defined as a filter that obtains them implicitly from its input. |
It may be helpful to compare the following definition of "multiplier" with its Ruby counterpart [[#Ruby|below]]. Whereas the Ruby definition must name all its positional parameters, the jq equivalent is defined as a filter that obtains them implicitly from its input. |
||
< |
<syntaxhighlight lang="jq"># Infrastructure: |
||
# zip this and that |
# zip this and that |
||
def zip(that): |
def zip(that): |
||
Line 833: | Line 833: | ||
def multiplier(j): .[0] * .[1] * j; |
def multiplier(j): .[0] * .[1] * j; |
||
numlist|zip(invlist) | map( multiplier(0.5) )</ |
numlist|zip(invlist) | map( multiplier(0.5) )</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
$ jq -n -c -f First_class_functions_Use_numbers_analogously.jq |
$ jq -n -c -f First_class_functions_Use_numbers_analogously.jq |
||
Line 841: | Line 841: | ||
=={{header|JavaScript}}== |
=={{header|JavaScript}}== |
||
< |
<syntaxhighlight lang="javascript">const x = 2.0; |
||
const xi = 0.5; |
const xi = 0.5; |
||
const y = 4.0; |
const y = 4.0; |
||
Line 860: | Line 860: | ||
} |
} |
||
test().join('\n');</ |
test().join('\n');</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 873: | Line 873: | ||
In Julia, like Python and R, functions can be treated as like as other Types. |
In Julia, like Python and R, functions can be treated as like as other Types. |
||
< |
<syntaxhighlight lang="julia">x, xi = 2.0, 0.5 |
||
y, yi = 4.0, 0.25 |
y, yi = 4.0, 0.25 |
||
z, zi = x + y, 1.0 / ( x + y ) |
z, zi = x + y, 1.0 / ( x + y ) |
||
Line 882: | Line 882: | ||
numlisti = [xi, yi, zi] |
numlisti = [xi, yi, zi] |
||
@show collect(multiplier(n, invn)(0.5) for (n, invn) in zip(numlist, numlisti))</ |
@show collect(multiplier(n, invn)(0.5) for (n, invn) in zip(numlist, numlisti))</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 888: | Line 888: | ||
=={{header|Kotlin}}== |
=={{header|Kotlin}}== |
||
< |
<syntaxhighlight lang="scala">// version 1.1.2 |
||
fun multiplier(n1: Double, n2: Double) = { m: Double -> n1 * n2 * m} |
fun multiplier(n1: Double, n2: Double) = { m: Double -> n1 * n2 * m} |
||
Line 905: | Line 905: | ||
println("${multiplier(a[i], ai[i])(m)} = multiplier(${a[i]}, ${ai[i]})($m)") |
println("${multiplier(a[i], ai[i])(m)} = multiplier(${a[i]}, ${ai[i]})($m)") |
||
} |
} |
||
}</ |
}</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 915: | Line 915: | ||
=={{header|Lua}}== |
=={{header|Lua}}== |
||
<syntaxhighlight lang="lua"> |
|||
<lang Lua> |
|||
-- This function returns another function that |
-- This function returns another function that |
||
-- keeps n1 and n2 in scope, ie. a closure. |
-- keeps n1 and n2 in scope, ie. a closure. |
||
Line 935: | Line 935: | ||
print(v .. " * " .. invs[k] .. " * 0.5 = " .. new_function(0.5)) |
print(v .. " * " .. invs[k] .. " * 0.5 = " .. new_function(0.5)) |
||
end |
end |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 944: | Line 944: | ||
=={{header|M2000 Interpreter}}== |
=={{header|M2000 Interpreter}}== |
||
<syntaxhighlight lang="m2000 interpreter"> |
|||
<lang M2000 Interpreter> |
|||
Module CheckIt { |
Module CheckIt { |
||
\\ by default numbers are double |
\\ by default numbers are double |
||
Line 978: | Line 978: | ||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 990: | Line 990: | ||
This code demonstrates the example using structure similar to function composition, however the composition function is replace with the multiplier function. |
This code demonstrates the example using structure similar to function composition, however the composition function is replace with the multiplier function. |
||
< |
<syntaxhighlight lang="mathematica">multiplier[n1_,n2_]:=n1 n2 #& |
||
num={2,4,2+4}; |
num={2,4,2+4}; |
||
numi=1/num; |
numi=1/num; |
||
multiplierfuncs = multiplier @@@ Transpose[{num, numi}]; |
multiplierfuncs = multiplier @@@ Transpose[{num, numi}]; |
||
</syntaxhighlight> |
|||
</lang> |
|||
The resulting functions are unity multipliers: |
The resulting functions are unity multipliers: |
||
Line 1,002: | Line 1,002: | ||
Note that unlike Composition, the above definition of multiplier only allows for exactly two arguments. The definition can be changed to allow any nonzero number of arguments: |
Note that unlike Composition, the above definition of multiplier only allows for exactly two arguments. The definition can be changed to allow any nonzero number of arguments: |
||
< |
<syntaxhighlight lang="mathematica">multiplier[arg__] := Times[arg, #] & |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Nemerle}}== |
=={{header|Nemerle}}== |
||
{{trans|Python}} |
{{trans|Python}} |
||
< |
<syntaxhighlight lang="nemerle">using System; |
||
using System.Console; |
using System.Console; |
||
using Nemerle.Collections.NCollectionsExtensions; |
using Nemerle.Collections.NCollectionsExtensions; |
||
Line 1,023: | Line 1,023: | ||
WriteLine($[multiplier(n, m) (0.5)|(n, m) in ZipLazy(nums, inums)]); |
WriteLine($[multiplier(n, m) (0.5)|(n, m) in ZipLazy(nums, inums)]); |
||
} |
} |
||
}</ |
}</syntaxhighlight> |
||
=={{header|Never}}== |
=={{header|Never}}== |
||
<syntaxhighlight lang="never"> |
|||
<lang Never> |
|||
func multiplier(a : float, b : float) -> (float) -> float { |
func multiplier(a : float, b : float) -> (float) -> float { |
||
let func(m : float) -> float { a * b * m } |
let func(m : float) -> float { a * b * m } |
||
Line 1,051: | Line 1,051: | ||
0 |
0 |
||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{output}} |
{{output}} |
||
<pre> |
<pre> |
||
Line 1,060: | Line 1,060: | ||
=={{header|Nim}}== |
=={{header|Nim}}== |
||
<syntaxhighlight lang="nim"> |
|||
<lang Nim> |
|||
func multiplier(a, b: float): auto = |
func multiplier(a, b: float): auto = |
||
let ab = a * b |
let ab = a * b |
||
Line 1,080: | Line 1,080: | ||
let f = multiplier(list[i], invlist[i]) |
let f = multiplier(list[i], invlist[i]) |
||
# ... and apply it. |
# ... and apply it. |
||
echo f(0.5)</ |
echo f(0.5)</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 1,089: | Line 1,089: | ||
=={{header|Objeck}}== |
=={{header|Objeck}}== |
||
Similar however this code does not generate a list of functions. |
Similar however this code does not generate a list of functions. |
||
< |
<syntaxhighlight lang="objeck">use Collection.Generic; |
||
class FirstClass { |
class FirstClass { |
||
Line 1,118: | Line 1,118: | ||
} |
} |
||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
{{output}} |
{{output}} |
||
Line 1,129: | Line 1,129: | ||
=={{header|OCaml}}== |
=={{header|OCaml}}== |
||
< |
<syntaxhighlight lang="ocaml"># let x = 2.0;; |
||
# let y = 4.0;; |
# let y = 4.0;; |
||
Line 1,149: | Line 1,149: | ||
(* or just apply the generated function immediately... *) |
(* or just apply the generated function immediately... *) |
||
# List.map2 (fun n inv -> (multiplier n inv) 0.5) coll inv_coll;; |
# List.map2 (fun n inv -> (multiplier n inv) 0.5) coll inv_coll;; |
||
- : float list = [0.5; 0.5; 0.5]</ |
- : float list = [0.5; 0.5; 0.5]</syntaxhighlight> |
||
=={{header|Oforth}}== |
=={{header|Oforth}}== |
||
< |
<syntaxhighlight lang="oforth">: multiplier(n1, n2) #[ n1 n2 * * ] ; |
||
: firstClassNum |
: firstClassNum |
||
Line 1,163: | Line 1,163: | ||
x y + ->z |
x y + ->z |
||
x y + inv ->zi |
x y + inv ->zi |
||
[ x, y, z ] [ xi, yi, zi ] zipWith(#multiplier) map(#[ 0.5 swap perform ] ) . ;</ |
[ x, y, z ] [ xi, yi, zi ] zipWith(#multiplier) map(#[ 0.5 swap perform ] ) . ;</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 1,170: | Line 1,170: | ||
=={{header|Oz}}== |
=={{header|Oz}}== |
||
< |
<syntaxhighlight lang="oz">declare |
||
[X Y Z] = [2.0 4.0 Z=X+Y] |
[X Y Z] = [2.0 4.0 Z=X+Y] |
||
Line 1,188: | Line 1,188: | ||
do |
do |
||
{Show {{Multiplier N I} 0.5}} |
{Show {{Multiplier N I} 0.5}} |
||
end</ |
end</syntaxhighlight> |
||
"Multiplier" is like "Compose", but with multiplication instead of function application. Otherwise the code is identical except for the argument types (numbers instead of functions). |
"Multiplier" is like "Compose", but with multiplication instead of function application. Otherwise the code is identical except for the argument types (numbers instead of functions). |
||
Line 1,194: | Line 1,194: | ||
=={{header|PARI/GP}}== |
=={{header|PARI/GP}}== |
||
{{works with|PARI/GP|2.4.2 and above}} |
{{works with|PARI/GP|2.4.2 and above}} |
||
< |
<syntaxhighlight lang="parigp">multiplier(n1,n2)={ |
||
x -> n1 * n2 * x |
x -> n1 * n2 * x |
||
}; |
}; |
||
Line 1,203: | Line 1,203: | ||
print(multiplier(y,yi)(0.5)); |
print(multiplier(y,yi)(0.5)); |
||
print(multiplier(z,zi)(0.5)); |
print(multiplier(z,zi)(0.5)); |
||
};</ |
};</syntaxhighlight> |
||
The two are very similar, though as requested the test numbers are in 6 variables instead of two vectors. |
The two are very similar, though as requested the test numbers are in 6 variables instead of two vectors. |
||
=={{header|Perl}}== |
=={{header|Perl}}== |
||
< |
<syntaxhighlight lang="perl">sub multiplier { |
||
my ( $n1, $n2 ) = @_; |
my ( $n1, $n2 ) = @_; |
||
sub { |
sub { |
||
Line 1,227: | Line 1,227: | ||
print multiplier( $number, $inverse )->(0.5), "\n"; |
print multiplier( $number, $inverse )->(0.5), "\n"; |
||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
Output: |
Output: |
||
<pre>0.5 |
<pre>0.5 |
||
Line 1,234: | Line 1,234: | ||
</pre> |
</pre> |
||
The entry in first-class functions uses the same technique: |
The entry in first-class functions uses the same technique: |
||
< |
<syntaxhighlight lang="perl">sub compose { |
||
my ($f, $g) = @_; |
my ($f, $g) = @_; |
||
Line 1,243: | Line 1,243: | ||
... |
... |
||
compose($flist1[$_], $flist2[$_]) -> (0.5) |
compose($flist1[$_], $flist2[$_]) -> (0.5) |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Phix}}== |
=={{header|Phix}}== |
||
Just as there is no real support for first class functions, not much that is pertinent to this task for numbers either, but the manual way is just as trivial: |
Just as there is no real support for first class functions, not much that is pertinent to this task for numbers either, but the manual way is just as trivial: |
||
<!--< |
<!--<syntaxhighlight lang="phix">(phixonline)--> |
||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mtable</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mtable</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
||
Line 1,271: | Line 1,271: | ||
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yi</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> |
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">yi</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> |
||
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zi</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> |
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">multiplier</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zi</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> |
||
<!--</ |
<!--</syntaxhighlight>--> |
||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 1,281: | Line 1,281: | ||
Compared to first class functions, there are (as in my view there should be) significant differences in the treatment of numbers and functions, but as mentioned on that page tagging ctable entries should be quite sufficient. |
Compared to first class functions, there are (as in my view there should be) significant differences in the treatment of numbers and functions, but as mentioned on that page tagging ctable entries should be quite sufficient. |
||
<!--< |
<!--<syntaxhighlight lang="phix">(phixonline)--> |
||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ctable</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ctable</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
||
Line 1,308: | Line 1,308: | ||
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_composite</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- displays 1</span> |
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_composite</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- displays 1</span> |
||
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_composite</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- displays 2.5</span> |
<span style="color: #0000FF;">?</span><span style="color: #000000;">call_composite</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- displays 2.5</span> |
||
<!--</ |
<!--</syntaxhighlight>--> |
||
=={{header|PicoLisp}}== |
=={{header|PicoLisp}}== |
||
< |
<syntaxhighlight lang="picolisp">(load "@lib/math.l") |
||
(de multiplier (N1 N2) |
(de multiplier (N1 N2) |
||
Line 1,322: | Line 1,322: | ||
(prinl (format ((multiplier Inv Num) 0.5) *Scl)) ) |
(prinl (format ((multiplier Inv Num) 0.5) *Scl)) ) |
||
(list X Y Z) |
(list X Y Z) |
||
(list Xi Yi Zi) ) )</ |
(list Xi Yi Zi) ) )</syntaxhighlight> |
||
Output: |
Output: |
||
<pre>0.500000 |
<pre>0.500000 |
||
Line 1,330: | Line 1,330: | ||
that the function 'multiplier' above accepts two numbers, while 'compose' |
that the function 'multiplier' above accepts two numbers, while 'compose' |
||
below accepts two functions: |
below accepts two functions: |
||
< |
<syntaxhighlight lang="picolisp">(load "@lib/math.l") |
||
(de compose (F G) |
(de compose (F G) |
||
Line 1,346: | Line 1,346: | ||
(prinl (format ((compose Inv Fun) 0.5) *Scl)) ) |
(prinl (format ((compose Inv Fun) 0.5) *Scl)) ) |
||
'(sin cos cube) |
'(sin cos cube) |
||
'(asin acos cubeRoot) )</ |
'(asin acos cubeRoot) )</syntaxhighlight> |
||
With a similar output: |
With a similar output: |
||
<pre>0.500001 |
<pre>0.500001 |
||
Line 1,354: | Line 1,354: | ||
=={{header|Python}}== |
=={{header|Python}}== |
||
This new task: |
This new task: |
||
< |
<syntaxhighlight lang="python">IDLE 2.6.1 |
||
>>> # Number literals |
>>> # Number literals |
||
>>> x,xi, y,yi = 2.0,0.5, 4.0,0.25 |
>>> x,xi, y,yi = 2.0,0.5, 4.0,0.25 |
||
Line 1,368: | Line 1,368: | ||
>>> [multiplier(inversen, n)(.5) for n, inversen in zip(numlist, numlisti)] |
>>> [multiplier(inversen, n)(.5) for n, inversen in zip(numlist, numlisti)] |
||
[0.5, 0.5, 0.5] |
[0.5, 0.5, 0.5] |
||
>>></ |
>>></syntaxhighlight> |
||
The Python solution to First-class functions for comparison: |
The Python solution to First-class functions for comparison: |
||
< |
<syntaxhighlight lang="python">>>> # Some built in functions and their inverses |
||
>>> from math import sin, cos, acos, asin |
>>> from math import sin, cos, acos, asin |
||
>>> # Add a user defined function and its inverse |
>>> # Add a user defined function and its inverse |
||
Line 1,385: | Line 1,385: | ||
>>> [compose(inversef, f)(.5) for f, inversef in zip(funclist, funclisti)] |
>>> [compose(inversef, f)(.5) for f, inversef in zip(funclist, funclisti)] |
||
[0.5, 0.4999999999999999, 0.5] |
[0.5, 0.4999999999999999, 0.5] |
||
>>></ |
>>></syntaxhighlight> |
||
As can be see, the treatment of functions is very close to the treatment of numbers. there are no extra wrappers, or function pointer syntax added, for example. |
As can be see, the treatment of functions is very close to the treatment of numbers. there are no extra wrappers, or function pointer syntax added, for example. |
||
=={{header|R}}== |
=={{header|R}}== |
||
< |
<syntaxhighlight lang="r">multiplier <- function(n1,n2) { (function(m){n1*n2*m}) } |
||
x = 2.0 |
x = 2.0 |
||
xi = 0.5 |
xi = 0.5 |
||
Line 1,403: | Line 1,403: | ||
Output |
Output |
||
[1] 0.5 0.5 0.5 |
[1] 0.5 0.5 0.5 |
||
</syntaxhighlight> |
|||
</lang> |
|||
Compared to original first class functions |
Compared to original first class functions |
||
< |
<syntaxhighlight lang="r">sapply(mapply(compose,f1,f2),do.call,list(.5)) |
||
[1] 0.5 0.5 0.5</ |
[1] 0.5 0.5 0.5</syntaxhighlight> |
||
=={{header|Racket}}== |
=={{header|Racket}}== |
||
<syntaxhighlight lang="racket"> |
|||
<lang Racket> |
|||
#lang racket |
#lang racket |
||
Line 1,429: | Line 1,429: | ||
((multiplier n i) 0.5)) |
((multiplier n i) 0.5)) |
||
;; -> '(0.5 0.5 0.5) |
;; -> '(0.5 0.5 0.5) |
||
</syntaxhighlight> |
|||
</lang> |
|||
=={{header|Raku}}== |
=={{header|Raku}}== |
||
(formerly Perl 6) |
(formerly Perl 6) |
||
{{works with|Rakudo|2015-09-10}} |
{{works with|Rakudo|2015-09-10}} |
||
<lang |
<syntaxhighlight lang="raku" line>sub multiplied ($g, $f) { return { $g * $f * $^x } } |
||
my $x = 2.0; |
my $x = 2.0; |
||
Line 1,446: | Line 1,446: | ||
my @inverses = $xi, $yi, $zi; |
my @inverses = $xi, $yi, $zi; |
||
for flat @numbers Z @inverses { say multiplied($^g, $^f)(.5) }</ |
for flat @numbers Z @inverses { say multiplied($^g, $^f)(.5) }</syntaxhighlight> |
||
Output: |
Output: |
||
<pre>0.5 |
<pre>0.5 |
||
Line 1,456: | Line 1,456: | ||
The REXX language doesn't have an easy method to call functions by using a variable name, |
The REXX language doesn't have an easy method to call functions by using a variable name, |
||
<br>but the '''interpret''' instruction can be used to provide that capability. |
<br>but the '''interpret''' instruction can be used to provide that capability. |
||
< |
<syntaxhighlight lang="rexx">/*REXX program to use a first-class function to use numbers analogously. */ |
||
nums= 2.0 4.0 6.0 /*various numbers, can have fractions.*/ |
nums= 2.0 4.0 6.0 /*various numbers, can have fractions.*/ |
||
invs= 1/2.0 1/4.0 1/6.0 /*inverses of the above (real) numbers.*/ |
invs= 1/2.0 1/4.0 1/6.0 /*inverses of the above (real) numbers.*/ |
||
Line 1,468: | Line 1,468: | ||
@: return left( arg(1) / 1, 15) /*format the number, left justified. */ |
@: return left( arg(1) / 1, 15) /*format the number, left justified. */ |
||
multiplier: procedure expose n1n2; parse arg n1,n2; n1n2= n1 * n2; return 'a_new_func' |
multiplier: procedure expose n1n2; parse arg n1,n2; n1n2= n1 * n2; return 'a_new_func' |
||
a_new_func: return n1n2 * arg(1)</ |
a_new_func: return n1n2 * arg(1)</syntaxhighlight> |
||
{{out|output|text= when using the internal default inputs:}} |
{{out|output|text= when using the internal default inputs:}} |
||
<pre> |
<pre> |
||
Line 1,477: | Line 1,477: | ||
=={{header|Ruby}}== |
=={{header|Ruby}}== |
||
< |
<syntaxhighlight lang="ruby">multiplier = proc {|n1, n2| proc {|m| n1 * n2 * m}} |
||
numlist = [x=2, y=4, x+y] |
numlist = [x=2, y=4, x+y] |
||
invlist = [0.5, 0.25, 1.0/(x+y)] |
invlist = [0.5, 0.25, 1.0/(x+y)] |
||
p numlist.zip(invlist).map {|n, invn| multiplier[invn, n][0.5]} |
p numlist.zip(invlist).map {|n, invn| multiplier[invn, n][0.5]} |
||
# => [0.5, 0.5, 0.5]</ |
# => [0.5, 0.5, 0.5]</syntaxhighlight> |
||
This structure is identical to the treatment of Ruby's [[First-class functions#Ruby|first-class functions]] -- create a Proc object that returns a Proc object (a closure). These examples show that 0.5 times number ''n'' (or passed to function ''f'') times inverse of ''n'' (or passed to inverse of ''f'') returns the original number, 0.5. |
This structure is identical to the treatment of Ruby's [[First-class functions#Ruby|first-class functions]] -- create a Proc object that returns a Proc object (a closure). These examples show that 0.5 times number ''n'' (or passed to function ''f'') times inverse of ''n'' (or passed to inverse of ''f'') returns the original number, 0.5. |
||
=={{header|Rust}}== |
=={{header|Rust}}== |
||
< |
<syntaxhighlight lang="rust">#![feature(conservative_impl_trait)] |
||
fn main() { |
fn main() { |
||
let (x, xi) = (2.0, 0.5); |
let (x, xi) = (2.0, 0.5); |
||
Line 1,506: | Line 1,506: | ||
move |m| x*y*m |
move |m| x*y*m |
||
} |
} |
||
</syntaxhighlight> |
|||
</lang> |
|||
This is very similar to the [[First-class functions#Rust|first-class functions]] implementation save that the type inference works a little bit better here (e.g. when declaring <code>numlist</code> and <code>invlist</code>) and <code>multiplier</code>'s declaration is substantially simpler than <code>compose</code>'s. Both of these boil down to the fact that closures and regular functions are actually different types in Rust so we have to be generic over them but here we are only dealing with 64-bit floats. |
This is very similar to the [[First-class functions#Rust|first-class functions]] implementation save that the type inference works a little bit better here (e.g. when declaring <code>numlist</code> and <code>invlist</code>) and <code>multiplier</code>'s declaration is substantially simpler than <code>compose</code>'s. Both of these boil down to the fact that closures and regular functions are actually different types in Rust so we have to be generic over them but here we are only dealing with 64-bit floats. |
||
=={{header|Scala}}== |
=={{header|Scala}}== |
||
< |
<syntaxhighlight lang="scala">scala> val x = 2.0 |
||
x: Double = 2.0 |
x: Double = 2.0 |
||
Line 1,544: | Line 1,544: | ||
0.5 |
0.5 |
||
0.5 |
0.5 |
||
0.5</ |
0.5</syntaxhighlight> |
||
=={{header|Scheme}}== |
=={{header|Scheme}}== |
||
This implementation closely follows the Scheme implementation of the [[First-class functions]] problem. |
This implementation closely follows the Scheme implementation of the [[First-class functions]] problem. |
||
< |
<syntaxhighlight lang="scheme">(define x 2.0) |
||
(define xi 0.5) |
(define xi 0.5) |
||
(define y 4.0) |
(define y 4.0) |
||
Line 1,566: | Line 1,566: | ||
(newline)) |
(newline)) |
||
n1 n2)) |
n1 n2)) |
||
(go number inverse)</ |
(go number inverse)</syntaxhighlight> |
||
Output: |
Output: |
||
0.5 |
0.5 |
||
Line 1,573: | Line 1,573: | ||
=={{header|Sidef}}== |
=={{header|Sidef}}== |
||
< |
<syntaxhighlight lang="ruby">func multiplier(n1, n2) { |
||
func (n3) { |
func (n3) { |
||
n1 * n2 * n3 |
n1 * n2 * n3 |
||
Line 1,591: | Line 1,591: | ||
for f,g (numbers ~Z inverses) { |
for f,g (numbers ~Z inverses) { |
||
say multiplier(f, g)(0.5) |
say multiplier(f, g)(0.5) |
||
}</ |
}</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 1,601: | Line 1,601: | ||
=={{header|Slate}}== |
=={{header|Slate}}== |
||
{{incorrect|Slate|Compare and contrast the resultant program with the corresponding entry in First-class functions.}} |
{{incorrect|Slate|Compare and contrast the resultant program with the corresponding entry in First-class functions.}} |
||
< |
<syntaxhighlight lang="slate">define: #multiplier -> [| :n1 :n2 | [| :m | n1 * n2 * m]]. |
||
define: #x -> 2. |
define: #x -> 2. |
||
define: #y -> 4. |
define: #y -> 4. |
||
Line 1,607: | Line 1,607: | ||
define: #numlisti -> (numlist collect: [| :x | 1.0 / x]). |
define: #numlisti -> (numlist collect: [| :x | 1.0 / x]). |
||
numlist with: numlisti collect: [| :n1 :n2 | (multiplier applyTo: {n1. n2}) applyWith: 0.5].</ |
numlist with: numlisti collect: [| :n1 :n2 | (multiplier applyTo: {n1. n2}) applyWith: 0.5].</syntaxhighlight> |
||
=={{header|Tcl}}== |
=={{header|Tcl}}== |
||
{{works with|Tcl|8.5}} |
{{works with|Tcl|8.5}} |
||
< |
<syntaxhighlight lang="tcl">package require Tcl 8.5 |
||
proc multiplier {a b} { |
proc multiplier {a b} { |
||
list apply {{ab m} {expr {$ab*$m}}} [expr {$a*$b}] |
list apply {{ab m} {expr {$ab*$m}}} [expr {$a*$b}] |
||
}</ |
}</syntaxhighlight> |
||
Note that, as with Tcl's solution for [[First-class functions#Tcl|First-class functions]], the resulting term must be expanded on application. For example, study this interactive session: |
Note that, as with Tcl's solution for [[First-class functions#Tcl|First-class functions]], the resulting term must be expanded on application. For example, study this interactive session: |
||
< |
<syntaxhighlight lang="tcl">% set mult23 [multiplier 2 3] |
||
apply {{ab m} {expr {$ab*$m}}} 6 |
apply {{ab m} {expr {$ab*$m}}} 6 |
||
% {*}$mult23 5 |
% {*}$mult23 5 |
||
30</ |
30</syntaxhighlight> |
||
Formally, for the task: |
Formally, for the task: |
||
< |
<syntaxhighlight lang="tcl">set x 2.0 |
||
set xi 0.5 |
set xi 0.5 |
||
set y 4.0 |
set y 4.0 |
||
Line 1,631: | Line 1,631: | ||
foreach a $numlist b $numlisti { |
foreach a $numlist b $numlisti { |
||
puts [format "%g * %g * 0.5 = %g" $a $b [{*}[multiplier $a $b] 0.5]] |
puts [format "%g * %g * 0.5 = %g" $a $b [{*}[multiplier $a $b] 0.5]] |
||
}</ |
}</syntaxhighlight> |
||
Which produces this output: |
Which produces this output: |
||
<pre>2 * 0.5 * 0.5 = 0.5 |
<pre>2 * 0.5 * 0.5 = 0.5 |
||
Line 1,642: | Line 1,642: | ||
composition operator (+), and is named in compliance |
composition operator (+), and is named in compliance |
||
with the task specification. |
with the task specification. |
||
< |
<syntaxhighlight lang="ursala">#import std |
||
#import flo |
#import flo |
||
Line 1,652: | Line 1,652: | ||
#cast %eL |
#cast %eL |
||
main = (gang multiplier*p\numbers inverses) 0.5</ |
main = (gang multiplier*p\numbers inverses) 0.5</syntaxhighlight> |
||
The multiplier could have been written in pattern |
The multiplier could have been written in pattern |
||
matching form like this. |
matching form like this. |
||
< |
<syntaxhighlight lang="ursala">multiplier("a","b") "c" = times(times("a","b"),"c")</syntaxhighlight> |
||
The main program might also have been written with an |
The main program might also have been written with an |
||
anonymous function like this. |
anonymous function like this. |
||
< |
<syntaxhighlight lang="ursala">main = (gang (//times+ times)*p\numbers inverses) 0.5</syntaxhighlight> |
||
output: |
output: |
||
<pre> |
<pre> |
||
Line 1,666: | Line 1,666: | ||
=={{header|Wren}}== |
=={{header|Wren}}== |
||
{{libheader|Wren-fmt}} |
{{libheader|Wren-fmt}} |
||
< |
<syntaxhighlight lang="ecmascript">import "/fmt" for Fmt |
||
var multiplier = Fn.new { |n1, n2| Fn.new { |m| n1 * n2 * m } } |
var multiplier = Fn.new { |n1, n2| Fn.new { |m| n1 * n2 * m } } |
||
Line 1,686: | Line 1,686: | ||
var m = 0.5 // rather than 1 to compare with first-class functions task |
var m = 0.5 // rather than 1 to compare with first-class functions task |
||
Fmt.print("$0.1g * $g * $0.1g = $0.1g", x, y, m, multiplier.call(x, y).call(m)) |
Fmt.print("$0.1g * $g * $0.1g = $0.1g", x, y, m, multiplier.call(x, y).call(m)) |
||
}</ |
}</syntaxhighlight> |
||
{{out}} |
{{out}} |
||
Line 1,697: | Line 1,697: | ||
=={{header|zkl}}== |
=={{header|zkl}}== |
||
< |
<syntaxhighlight lang="zkl">var x=2.0, y=4.0, z=(x+y), c=T(x,y,z).apply(fcn(n){ T(n,1.0/n) }); |
||
//-->L(L(2,0.5),L(4,0.25),L(6,0.166667))</ |
//-->L(L(2,0.5),L(4,0.25),L(6,0.166667))</syntaxhighlight> |
||
< |
<syntaxhighlight lang="zkl">fcn multiplier(n1,n2){ return('*.fp(n1,n2)) }</syntaxhighlight> |
||
This is actually partial evaluation, multiplier returns n1*n2*X where X isn't known yet. So multiplier(2,3)(4) --> (2*3*)4 --> 24. Even better, multiplier(2,3)(4,5) --> 120, multiplier(2,3)(4,5,6) --> 720, multiplier(2,3)() --> 6. |
This is actually partial evaluation, multiplier returns n1*n2*X where X isn't known yet. So multiplier(2,3)(4) --> (2*3*)4 --> 24. Even better, multiplier(2,3)(4,5) --> 120, multiplier(2,3)(4,5,6) --> 720, multiplier(2,3)() --> 6. |
||
Alternatively, |
Alternatively, |
||
< |
<syntaxhighlight lang="zkl">fcn multiplier(n1,n2){ fcn(n,X){ n*X }.fp(n1*n2) }</syntaxhighlight> |
||
< |
<syntaxhighlight lang="zkl">var ms=c.apply(fcn([(n1,n2)]){ multiplier(n1,n2) }); |
||
//-->L(Deferred,Deferred,Deferred) // lazy eval of n*(1/n)*X |
//-->L(Deferred,Deferred,Deferred) // lazy eval of n*(1/n)*X |
||
ms.run(True,1.0) //-->L(1,1,1) |
ms.run(True,1.0) //-->L(1,1,1) |
||
ms.run(True,5.0) //-->L(5,5,5) |
ms.run(True,5.0) //-->L(5,5,5) |
||
ms.run(True,0.5) //-->L(0.5,0.5,0.5)</ |
ms.run(True,0.5) //-->L(0.5,0.5,0.5)</syntaxhighlight> |
||
List.run(True,X), for each item in the list, does i(X) and collects the results into another list. Sort of an inverted map or fold. |
List.run(True,X), for each item in the list, does i(X) and collects the results into another list. Sort of an inverted map or fold. |
||
Revision as of 13:14, 27 August 2022
You are encouraged to solve this task according to the task description, using any language you may know.
In First-class functions, a language is showing how its manipulation of functions is similar to its manipulation of other types.
This tasks aim is to compare and contrast a language's implementation of first class functions, with its normal handling of numbers.
Write a program to create an ordered collection of a mixture of literally typed and expressions producing a real number, together with another ordered collection of their multiplicative inverses. Try and use the following pseudo-code to generate the numbers for the ordered collections:
x = 2.0 xi = 0.5 y = 4.0 yi = 0.25 z = x + y zi = 1.0 / ( x + y )
Create a function multiplier, that given two numbers as arguments returns a function that when called with one argument, returns the result of multiplying the two arguments to the call to multiplier that created it and the argument in the call:
new_function = multiplier(n1,n2) # where new_function(m) returns the result of n1 * n2 * m
Applying the multiplier of a number and its inverse from the two ordered collections of numbers in pairs, show that the result in each case is one.
Compare and contrast the resultant program with the corresponding entry in First-class functions. They should be close.
To paraphrase the task description: Do what was done before, but with numbers rather than functions
11l
V (x, xi, y, yi) = (2.0, 0.5, 4.0, 0.25)
V z = x + y
V zi = 1.0 / (x + y)
V multiplier = (n1, n2) -> (m -> @=n1 * @=n2 * m)
V numlist = [x, y, z]
V numlisti = [xi, yi, zi]
print(zip(numlist, numlisti).map((n, inversen) -> multiplier(inversen, n)(.5)))
- Output:
[0.5, 0.5, 0.5]
Ada
with Ada.Text_IO;
procedure Firstclass is
generic
n1, n2 : Float;
function Multiplier (m : Float) return Float;
function Multiplier (m : Float) return Float is
begin
return n1 * n2 * m;
end Multiplier;
num, inv : array (1 .. 3) of Float;
begin
num := (2.0, 4.0, 6.0);
inv := (1.0/2.0, 1.0/4.0, 1.0/6.0);
for i in num'Range loop
declare
function new_function is new Multiplier (num (i), inv (i));
begin
Ada.Text_IO.Put_Line (Float'Image (new_function (0.5)));
end;
end loop;
end Firstclass;
- Output:
5.00000E-01 5.00000E-01 5.00000E-01
ALGOL 68
Note: Standard ALGOL 68's scoping rules forbids exporting a proc[edure] (or format) out of it's scope (closure). Hence this specimen will run on ELLA ALGOL 68, but is non-standard. For a discussion of first-class functions in ALGOL 68 consult "The Making of Algol 68" - C.H.A. Koster (1993).
REAL
x := 2,
xi := 0.5,
y := 4,
yi := 0.25,
z := x + y,
zi := 1 / ( x + y );
MODE F = PROC(REAL)REAL;
PROC multiplier = (REAL n1, n2)F: ((REAL m)REAL: n1 * n2 * m);
# Numbers as members of collections #
[]REAL num list = (x, y, z),
inv num list = (xi, yi, zi);
# Apply numbers from list #
FOR key TO UPB num list DO
REAL n = num list[key],
inv n = inv num list[key];
print ((multiplier(inv n, n)(.5), new line))
OD
Output:
+.500000000000000e +0 +.500000000000000e +0 +.500000000000000e +0
Comparing and contrasting with the First Class Functions example:
As noted above, in order to do what is required by this task and the First Class Functions task, extensions to Algol 68 must be used.
The First Class Functions example uses C. H. Lindsey's partial parameterization extension to Algol 68 which implemented in Algol 68G but not in algol68toc. This example uses an alternative (technically, invalid Algol 68 as the author notes) accepted by algol68toc but not Algol 68G.
Axiom
(x,xi,y,yi) := (2.0,0.5,4.0,0.25)
(z,zi) := (x+y,1/(x+y))
(numbers,invers) := ([x,y,z],[xi,yi,zi])
multiplier(a:Float,b:Float):(Float->Float) == (m +-> a*b*m)
[multiplier(number,inver) 0.5 for number in numbers for inver in invers]
Output:
[0.5,0.5,0.5]
Type: List(Float)
We can also curry functions, possibly with function composition, with the same output as before:
mult(n:Float):(Float->Float) == curryLeft(*$Float,n)$MAPPKG3(Float,Float,Float)
[mult(number*inver) 0.5 for number in numbers for inver in invers]
[(mult(number)*mult(inver)) 0.5 for number in numbers for inver in invers]
Using the Spad code in First-class functions#Axiom, this can be done more economically using:
(map(mult,numbers)*map(mult,invers)) 0.5
For comparison, First-class functions#Axiom gave:
fns := [sin$Float, cos$Float, (x:Float):Float +-> x^3]
inv := [asin$Float, acos$Float, (x:Float):Float +-> x^(1/3)]
[(f*g) 0.5 for f in fns for g in inv]
- which has the same output.
BBC BASIC
REM Create some numeric variables:
x = 2 : xi = 1/2
y = 4 : yi = 0.25
z = x + y : zi = 1 / (x + y)
REM Create the collections (here structures are used):
DIM c{x, y, z}
DIM ci{x, y, z}
c.x = x : c.y = y : c.z = z
ci.x = xi : ci.y = yi : ci.z = zi
REM Create some multiplier functions:
multx = FNmultiplier(c.x, ci.x)
multy = FNmultiplier(c.y, ci.y)
multz = FNmultiplier(c.z, ci.z)
REM Test applying the compositions:
x = 1.234567 : PRINT x " ", FN(multx)(x)
x = 2.345678 : PRINT x " ", FN(multy)(x)
x = 3.456789 : PRINT x " ", FN(multz)(x)
END
DEF FNmultiplier(n1,n2)
LOCAL f$, p%
f$ = "(m)=" + STR$n1 + "*" + STR$n2 + "*m"
DIM p% LEN(f$) + 4
$(p%+4) = f$ : !p% = p%+4
= p%
Output:
1.234567 1.234567 2.345678 2.345678 3.456789 3.45678901
Compare with the implementation of First-class functions:
REM Create some functions and their inverses:
DEF FNsin(a) = SIN(a)
DEF FNasn(a) = ASN(a)
DEF FNcos(a) = COS(a)
DEF FNacs(a) = ACS(a)
DEF FNcube(a) = a^3
DEF FNroot(a) = a^(1/3)
dummy = FNsin(1)
REM Create the collections (here structures are used):
DIM cA{Sin%, Cos%, Cube%}
DIM cB{Asn%, Acs%, Root%}
cA.Sin% = ^FNsin() : cA.Cos% = ^FNcos() : cA.Cube% = ^FNcube()
cB.Asn% = ^FNasn() : cB.Acs% = ^FNacs() : cB.Root% = ^FNroot()
REM Create some function compositions:
AsnSin% = FNcompose(cB.Asn%, cA.Sin%)
AcsCos% = FNcompose(cB.Acs%, cA.Cos%)
RootCube% = FNcompose(cB.Root%, cA.Cube%)
REM Test applying the compositions:
x = 1.234567 : PRINT x, FN(AsnSin%)(x)
x = 2.345678 : PRINT x, FN(AcsCos%)(x)
x = 3.456789 : PRINT x, FN(RootCube%)(x)
END
DEF FNcompose(f%,g%)
LOCAL f$, p%
f$ = "(x)=" + CHR$&A4 + "(&" + STR$~f% + ")(" + \
\ CHR$&A4 + "(&" + STR$~g% + ")(x))"
DIM p% LEN(f$) + 4
$(p%+4) = f$ : !p% = p%+4
= p%
C#
The structure here is exactly the same as the C# entry in First-class functions. The "var" keyword allows us to use the same initialization code for an array of doubles as an array of functions. Note that variable names have been changed to correspond with the new functionality.
using System;
using System.Linq;
class Program
{
static void Main(string[] args)
{
double x, xi, y, yi, z, zi;
x = 2.0;
xi = 0.5;
y = 4.0;
yi = 0.25;
z = x + y;
zi = 1.0 / (x + y);
var numlist = new[] { x, y, z };
var numlisti = new[] { xi, yi, zi };
var multiplied = numlist.Zip(numlisti, (n1, n2) =>
{
Func<double, double> multiplier = m => n1 * n2 * m;
return multiplier;
});
foreach (var multiplier in multiplied)
Console.WriteLine(multiplier(0.5));
}
}
C++
#include <array>
#include <iostream>
int main()
{
double x = 2.0;
double xi = 0.5;
double y = 4.0;
double yi = 0.25;
double z = x + y;
double zi = 1.0 / ( x + y );
const std::array values{x, y, z};
const std::array inverses{xi, yi, zi};
auto multiplier = [](double a, double b)
{
return [=](double m){return a * b * m;};
};
for(size_t i = 0; i < values.size(); ++i)
{
auto new_function = multiplier(values[i], inverses[i]);
double value = new_function(i + 1.0);
std::cout << value << "\n";
}
}
- Output:
1 2 3
Clojure
(def x 2.0)
(def xi 0.5)
(def y 4.0)
(def yi 0.25)
(def z (+ x y))
(def zi (/ 1.0 (+ x y)))
(def numbers [x y z])
(def invers [xi yi zi])
(defn multiplier [a b]
(fn [m] (* a b m)))
> (for [[n i] (zipmap numbers invers)]
((multiplier n i) 0.5))
(0.5 0.5 0.5)
For comparison:
(use 'clojure.contrib.math)
(let [fns [#(Math/sin %) #(Math/cos %) (fn [x] (* x x x))]
inv [#(Math/asin %) #(Math/acos %) #(expt % 1/3)]]
(map #(% 0.5) (map #(comp %1 %2) fns inv)))
Output:
(0.5 0.4999999999999999 0.5000000000000001)
Common Lisp
(defun multiplier (f g)
#'(lambda (x) (* f g x)))
(let* ((x 2.0)
(xi 0.5)
(y 4.0)
(yi 0.25)
(z (+ x y))
(zi (/ 1.0 (+ x y)))
(numbers (list x y z))
(inverses (list xi yi zi)))
(loop with value = 0.5
for number in numbers
for inverse in inverses
for multiplier = (multiplier number inverse)
do (format t "~&(~A * ~A)(~A) = ~A~%"
number
inverse
value
(funcall multiplier value))))
Output:
(2.0 * 0.5)(0.5) = 0.5 (4.0 * 0.25)(0.5) = 0.5 (6.0 * 0.16666667)(0.5) = 0.5
The code from First-class functions, for comparison:
(defun compose (f g) (lambda (x) (funcall f (funcall g x))))
(defun cube (x) (expt x 3))
(defun cube-root (x) (expt x (/ 3)))
(loop with value = 0.5
for function in (list #'sin #'cos #'cube )
for inverse in (list #'asin #'acos #'cube-root)
for composed = (compose inverse function)
do (format t "~&(~A ∘ ~A)(~A) = ~A~%"
inverse
function
value
(funcall composed value)))
Output:
(#<FUNCTION ASIN> ∘ #<FUNCTION SIN>)(0.5) = 0.5 (#<FUNCTION ACOS> ∘ #<FUNCTION COS>)(0.5) = 0.5 (#<FUNCTION CUBE-ROOT> ∘ #<FUNCTION CUBE>)(0.5) = 0.5
D
import std.stdio;
auto multiplier(double a, double b)
{
return (double c) => a * b * c;
}
void main()
{
double x = 2.0;
double xi = 0.5;
double y = 4.0;
double yi = 0.25;
double z = x + y;
double zi = 1.0 / (z);
double[3] f = [x, y, z];
double[3] r = [xi, yi, zi];
foreach (i; 0..3)
{
auto mult = multiplier(f[i], r[i]);
writefln("%f * %f * %f == %f", f[i], r[i], 1.0, mult(1));
}
}
Output:
2.000000 * 0.500000 * 1.000000 == 1.000000 4.000000 * 0.250000 * 1.000000 == 1.000000 6.000000 * 0.166667 * 1.000000 == 1.000000
E
This is written to have identical structure to First-class functions#E, though the variable names are different.
def x := 2.0
def xi := 0.5
def y := 4.0
def yi := 0.25
def z := x + y
def zi := 1.0 / (x + y)
def forward := [x, y, z ]
def reverse := [xi, yi, zi]
def multiplier(a, b) {
return fn x { a * b * x }
}
def s := 0.5
for i => a in forward {
def b := reverse[i]
println(`s = $s, a = $a, b = $b, multiplier($a, $b)($s) = ${multiplier(a, b)(s)}`)
}
Output:
s = 0.5, a = 2.0, b = 0.5, multiplier(2.0, 0.5)(0.5) = 0.5 s = 0.5, a = 4.0, b = 0.25, multiplier(4.0, 0.25)(0.5) = 0.5 s = 0.5, a = 6.0, b = 0.16666666666666666, multiplier(6.0, 0.16666666666666666)(0.5) = 0.5
Note: def g := reverse[i]
is needed here because E as yet has no defined protocol for iterating over collections in parallel. Page for this issue.
Elena
ELENA 5.0 :
import system'routines;
import extensions;
public program()
{
real x := 2.0r;
real xi := 0.5r;
real y := 4.0r;
real yi := 0.25r;
real z := x + y;
real zi := 1.0r / (x + y);
var numlist := new real[]{ x, y, z };
var numlisti := new real[]{ xi, yi, zi };
var multiplied := numlist.zipBy(numlisti, (n1,n2 => (m => n1 * n2 * m) )).toArray();
multiplied.forEach:(multiplier){ console.printLine(multiplier(0.5r)) }
}
- Output:
0.5 0.5 0.5
Erlang
-module( first_class_functions_use_numbers ).
-export( [task/0] ).
task() ->
X = 2.0, Xi = 0.5, Y = 4.0, Yi = 0.25, Z = X + Y, Zi = 1.0 / (X + Y),
As = [X, Y, Z],
Bs = [Xi, Yi, Zi],
[io:fwrite( "Value: 2.5 Result: ~p~n", [(multiplier(A, B))(2.5)]) || {A, B} <- lists:zip(As, Bs)].
multiplier( N1, N2 ) -> fun(M) -> N1 * N2 * M end.
- Output:
20> first_class_functions_use_numbers:task(). Value: 2.5 Result: 2.5 Value: 2.5 Result: 2.5 Value: 2.5 Result: 2.5
F#
let x = 2.0
let xi = 0.5
let y = 4.0
let yi = 0.25
let z = x + y
let zi = 1.0 / ( x + y )
let multiplier (n1,n2) = fun (m:float) -> n1 * n2 * m
[x; y; z]
|> List.zip [xi; yi; zi]
|> List.map multiplier
|> List.map ((|>) 0.5)
|> printfn "%A"
- Output:
[0.5; 0.5; 0.5]
Factor
Compared to http://rosettacode.org/wiki/First-class_functions, the call to "compose" is replaced with the call to "mutliplier"
USING: arrays kernel literals math prettyprint sequences ;
IN: q
CONSTANT: x 2.0
CONSTANT: xi 0.5
CONSTANT: y 4.0
CONSTANT: yi .25
CONSTANT: z $[ $ x $ y + ]
CONSTANT: zi $[ 1 $ x $ y + / ]
CONSTANT: A ${ x y z }
CONSTANT: B ${ xi yi zi }
: multiplier ( n1 n2 -- q ) [ * * ] 2curry ;
: create-all ( seq1 seq2 -- seq ) [ multiplier ] 2map ;
: example ( -- )
0.5 A B create-all
[ call( x -- y ) ] with map . ;
- Output:
{ 0.5 0.5 0.5 }
Fantom
class Main
{
static |Float -> Float| combine (Float n1, Float n2)
{
return |Float m -> Float| { n1 * n2 * m }
}
public static Void main ()
{
Float x := 2f
Float xi := 0.5f
Float y := 4f
Float yi := 0.25f
Float z := x + y
Float zi := 1 / (x + y)
echo (combine(x, xi)(0.5f))
echo (combine(y, yi)(0.5f))
echo (combine(z, zi)(0.5f))
}
}
The combine
function is very similar to the compose
function in 'First-class functions'. In both cases a new function is returned:
static |Obj -> Obj| compose (|Obj -> Obj| fn1, |Obj -> Obj| fn2)
{
return |Obj x -> Obj| { fn2 (fn1 (x)) }
}
Go
"Number means value"
Task interpretation 1: "Number" means a numeric value, not any sort of reference. This is the most natural interpretation in Go.
At point A, the six variables have been assigned values, 64 bit floating point numbers, and not references to anything that is evaluated later. Again, at point B, these values have been copied into the array elements. (The arrays being "ordered collections.") The original six variables could be changed at this point and the array values would stay the same.
Multiplier multiplies pairs of values and binds the result to the returned closure. This might be considered a difference from the First-class functions task. In that task, the functions were composed into a new function but not evaluated at the time of composition. They could have been, but that is not the usual meaning of function composition.
This task however, works with numbers, which are not reference types. Specifically, the closure here could could have closed on n1 an n2 individually and delayed multiplication until closure evaluation, but that might seem inconsistent with the task interpretation of working with numbers as values. Also, one would expect that a function named "multiplier" does actually multiply.
Multiplier of this task and compose of the First-class function task are similar in that they both return first class function objects, which are closed on free variables. The free variables in compose held the two (unevaluated) functions being composed. The free variable in multiplier holds the result of multiplication.
At point C, numbers and their inverses have been multiplied and bound to first class functions. The ordered collection arrays could be modified at this point and the function objects would be unaffected.
package main
import "fmt"
func main() {
x := 2.
xi := .5
y := 4.
yi := .25
z := x + y
zi := 1 / (x + y)
// point A
numbers := []float64{x, y, z}
inverses := []float64{xi, yi, zi}
// point B
mfs := make([]func(float64) float64, len(numbers))
for i := range mfs {
mfs[i] = multiplier(numbers[i], inverses[i])
}
// point C
for _, mf := range mfs {
fmt.Println(mf(1))
}
}
func multiplier(n1, n2 float64) func(float64) float64 {
// compute product of n's, store in a new variable
n1n2 := n1 * n2
// close on variable containing product
return func(m float64) float64 {
return n1n2 * m
}
}
Output:
1 1 1
"Number means reference"
Task interpretation 2: "Number" means something abstract, evaluation of which is delayed as long as possible. This interpretation is suggested by the task wording that this program and and the corresponding First-class functions program "should be close" and "do what was done before...."
To implement this behavior, reference types are used for "numbers" and a polymorphic array is used for the ordered collection, allowing both static and computed objects to stored.
At point A, the variables z and zi are assigned function literals, first class function objects closed on x and y. Changing the values of x or y at this point will cause z and zi to return different results. The x and y in these function literals reference the same storage as the x and y assigned values 2 and 4. This is more like the the First-class functions task in that we now have functions which we can compose.
At point B, we have filled the polymorphic arrays with all reference types. References to numeric typed variables x, xi, y, and yi were created with the & operator. z and zi can already be considered reference types in that they reference x and y. Changes to any of x, xi, y, or yi at this point would still affect later results.
Multiplier, in this interpretation of the task, simply composes multiplication of three reference objects, which may be variables or functions. It does not actually multiply and does not even evaluate the three objects. This is very much like the compose function of the First-class functions task.
Pursuant to the task description, this version of multiplier "returns the result of n1 * n2 * m" in the sense that it sets up evaluation of n1, n2, and m to be done at the same time, even if that time is not quite yet.
At point C, changes to x, xi, y, and yi will still propagate through and affect the results returned by the mfs objects. This can be seen as like the First-class functions task in that nothing (nothing numberic anyway) is evaluated until the final composed objects are evaluated.
This can also be done with an interface type rather than the "empty interface" (interface{}
) for better type safety and to avoid the eval
function and type switch.
package main
import "fmt"
func main() {
x := 2.
xi := .5
y := 4.
yi := .25
z := func() float64 { return x + y }
zi := func() float64 { return 1 / (x + y) }
// point A
numbers := []interface{}{&x, &y, z}
inverses := []interface{}{&xi, &yi, zi}
// point B
mfs := make([]func(n interface{}) float64, len(numbers))
for i := range mfs {
mfs[i] = multiplier(numbers[i], inverses[i])
}
// pointC
for _, mf := range mfs {
fmt.Println(mf(1.))
}
}
func multiplier(n1, n2 interface{}) func(interface{}) float64 {
return func(m interface{}) float64 {
// close on interface objects n1, n2, and m
return eval(n1) * eval(n2) * eval(m)
}
}
// utility function for evaluating multiplier interface objects
func eval(n interface{}) float64 {
switch n.(type) {
case float64:
return n.(float64)
case *float64:
return *n.(*float64)
case func() float64:
return n.(func() float64)()
}
panic("unsupported multiplier type")
return 0 // never reached
}
Groovy
def multiplier = { n1, n2 -> { m -> n1 * n2 * m } }
def ε = 0.00000001 // tolerance(epsilon): acceptable level of "wrongness" to account for rounding error
[(2.0):0.5, (4.0):0.25, (6.0):(1/6.0)].each { num, inv ->
def new_function = multiplier(num, inv)
(1.0..5.0).each { trial ->
assert (new_function(trial) - trial).abs() < ε
printf('%5.3f * %5.3f * %5.3f == %5.3f\n', num, inv, trial, trial)
}
println()
}
- Output:
2.000 * 0.500 * 1.000 == 1.000 2.000 * 0.500 * 2.000 == 2.000 2.000 * 0.500 * 3.000 == 3.000 2.000 * 0.500 * 4.000 == 4.000 2.000 * 0.500 * 5.000 == 5.000 4.000 * 0.250 * 1.000 == 1.000 4.000 * 0.250 * 2.000 == 2.000 4.000 * 0.250 * 3.000 == 3.000 4.000 * 0.250 * 4.000 == 4.000 4.000 * 0.250 * 5.000 == 5.000 6.000 * 0.167 * 1.000 == 1.000 6.000 * 0.167 * 2.000 == 2.000 6.000 * 0.167 * 3.000 == 3.000 6.000 * 0.167 * 4.000 == 4.000 6.000 * 0.167 * 5.000 == 5.000
Haskell
module Main
where
import Text.Printf
-- Pseudo code happens to be valid Haskell
x = 2.0
xi = 0.5
y = 4.0
yi = 0.25
z = x + y
zi = 1.0 / ( x + y )
-- Multiplier function
multiplier :: Double -> Double -> Double -> Double
multiplier a b = \m -> a * b * m
main :: IO ()
main = do
let
numbers = [x, y, z]
inverses = [xi, yi, zi]
pairs = zip numbers inverses
print_pair (number, inverse) =
let new_function = multiplier number inverse
in printf "%f * %f * 0.5 = %f\n" number inverse (new_function 0.5)
mapM_ print_pair pairs
This is very close to the first-class functions example, but given as a full Haskell program rather than an interactive session.
Icon and Unicon
The following is a Unicon solution. It can be recast in Icon, but only at the cost of losing the "function-call" syntax on the created "procedure". The solution uses the same basic foundation that is buried in the "compose" procedure in the First-class functions task solution. The solution here is simpler and more direct since it handles a specific function definition.
import Utils
procedure main(A)
mult := multiplier(get(A),get(A)) # first 2 args define function
every write(mult(!A)) # remaining are passed to new function
end
procedure multiplier(n1,n2)
return makeProc { repeat inVal := n1 * n2 * (inVal@&source)[1] }
end
A sample run:
->mu 2 3 4 5 6 7 24 30 36 42 ->
J
Explicit version
This seems to satisfy the new problem statement:
x =: 2.0
xi =: 0.5
y =: 4.0
yi =: 0.25
z =: x + y
zi =: 1.0 % (x + y) NB. / is spelled % in J
fwd =: x ,y ,z
rev =: xi,yi,zi
multiplier =: 2 : 'm * n * ]'
An equivalent but perhaps prettier definition of multiplier would be:
multiplier=: {{m*n*]}}
Or, if J's "right bracket is the right identity function" bothers you, you might prefer the slightly more verbose but still equivalent:
multiplier=: {{m*n*{{y}}}}
Example use:
fwd multiplier rev 0.5
0.5 0.5 0.5
For contrast, here are the final results from First-class functions#J:
BA unqcol 0.5
0.5 0.5 0.5 0.5
Tacit (unorthodox) version
Although the pseudo-code to generate the numbers can certainly be written (see above Explicit version ) this is not done for this version because it would destroy part of the analogy (J encourages, from the programming perspective, to process all components at once as opposed to one component at a time). In addition, this version is done in terms of boxed lists of numbers instead of plain list of numbers, again, to preserve the analogy.
multiplier=. train@:((;:'&*') ;~ an@: *)
]A=. 2 ; 4 ; (2 + 4) NB. Corresponds to ]A=. box (1&o.)`(2&o.)`(^&3)
┌─┬─┬─┐
│2│4│6│
└─┴─┴─┘
]B=. %&.> A NB. Corresponds to ]B =. inverse&.> A
┌───┬────┬────────┐
│0.5│0.25│0.166667│
└───┴────┴────────┘
]BA=. B multiplier&.> A NB. Corresponds to B compose&.> A
┌───┬───┬───┐
│1&*│1&*│1&*│
└───┴───┴───┘
BA of &> 0.5 NB. Corresponds to BA of &> 0.5 (exactly)
0.5 0.5 0.5
Please refer to First-class functions tacit (unorthodox) version for the definitions of the functions train, an and of.
jq
It may be helpful to compare the following definition of "multiplier" with its Ruby counterpart below. Whereas the Ruby definition must name all its positional parameters, the jq equivalent is defined as a filter that obtains them implicitly from its input.
# Infrastructure:
# zip this and that
def zip(that):
. as $this | reduce range(0;length) as $i ([]; . + [ [$this[$i], that[$i]] ]);
# The task:
def x: 2.0;
def xi: 0.5;
def y: 4.0;
def yi: 0.25;
def z: x + y;
def zi: 1.0 / (x + y);
def numlist: [x,y,z];
def invlist: [xi, yi, zi];
# Input: [x,y]
def multiplier(j): .[0] * .[1] * j;
numlist|zip(invlist) | map( multiplier(0.5) )
- Output:
$ jq -n -c -f First_class_functions_Use_numbers_analogously.jq [0.5,0.5,0.5]
As of this writing, there is no entry for jq at First-class functions.
JavaScript
const x = 2.0;
const xi = 0.5;
const y = 4.0;
const yi = 0.25;
const z = x + y;
const zi = 1.0 / (x + y);
const pairs = [[x, xi], [y, yi], [z, zi]];
const testVal = 0.5;
const multiplier = (a, b) => m => a * b * m;
const test = () => {
return pairs.map(([a, b]) => {
const f = multiplier(a, b);
const result = f(testVal);
return `${a} * ${b} * ${testVal} = ${result}`;
});
}
test().join('\n');
- Output:
2 * 0.5 * 0.5 = 0.5 4 * 0.25 * 0.5 = 0.5 6 * 0.16666666666666666 * 0.5 = 0.5
Julia
In Julia, like Python and R, functions can be treated as like as other Types.
x, xi = 2.0, 0.5
y, yi = 4.0, 0.25
z, zi = x + y, 1.0 / ( x + y )
multiplier = (n1, n2) -> (m) -> n1 * n2 * m
numlist = [x , y, z]
numlisti = [xi, yi, zi]
@show collect(multiplier(n, invn)(0.5) for (n, invn) in zip(numlist, numlisti))
- Output:
collect(((multiplier(n, invn))(0.5) for (n, invn) = zip(numlist, numlisti))) = [0.5, 0.5, 0.5]
Kotlin
// version 1.1.2
fun multiplier(n1: Double, n2: Double) = { m: Double -> n1 * n2 * m}
fun main(args: Array<String>) {
val x = 2.0
val xi = 0.5
val y = 4.0
val yi = 0.25
val z = x + y
val zi = 1.0 / ( x + y)
val a = doubleArrayOf(x, y, z)
val ai = doubleArrayOf(xi, yi, zi)
val m = 0.5
for (i in 0 until a.size) {
println("${multiplier(a[i], ai[i])(m)} = multiplier(${a[i]}, ${ai[i]})($m)")
}
}
- Output:
0.5 = multiplier(2.0, 0.5)(0.5) 0.5 = multiplier(4.0, 0.25)(0.5) 0.5 = multiplier(6.0, 0.16666666666666666)(0.5)
Lua
-- This function returns another function that
-- keeps n1 and n2 in scope, ie. a closure.
function multiplier (n1, n2)
return function (m)
return n1 * n2 * m
end
end
-- Multiple assignment a-go-go
local x, xi, y, yi = 2.0, 0.5, 4.0, 0.25
local z, zi = x + y, 1.0 / ( x + y )
local nums, invs = {x, y, z}, {xi, yi, zi}
-- 'new_function' stores the closure and then has the 0.5 applied to it
-- (this 0.5 isn't in the task description but everyone else used it)
for k, v in pairs(nums) do
new_function = multiplier(v, invs[k])
print(v .. " * " .. invs[k] .. " * 0.5 = " .. new_function(0.5))
end
- Output:
2 * 0.5 * 0.5 = 0.5 4 * 0.25 * 0.5 = 0.5 6 * 0.16666666666667 * 0.5 = 0.5
M2000 Interpreter
Module CheckIt {
\\ by default numbers are double
x = 2
xi = 0.5
y = 4
yi = 0.25
z = x + y
zi = 1 / ( x + y )
Composed=lambda (a, b)-> {
=lambda a,b (n)->{
=a*b*n
}
}
numbers=(x,y,z)
inverses=(xi,yi,zi)
Dim Base 0, combo(3)
combo(0)=Composed(x,xi), Composed(y,yi), Composed(z,zi)
num=each(numbers)
inv=each(inverses)
fun=each(combo())
While num, inv, fun {
Print $("0.00"), Array(num);" * ";Array(inv);" * 0.50 = "; combo(fun^)(0.5),$("")
Print
}
}
Checkit
\\ for functions we have this definition
Composed=lambda (f1, f2) -> {
=lambda f1, f2 (x)->{
=f1(f2(x))
}
}
- Output:
2.00 * 0.50 * 0.50 = 0.50 4.00 * 0.25 * 0.50 = 0.50 6.00 * 0.17 * 0.50 = 0.50
Mathematica / Wolfram Language
This code demonstrates the example using structure similar to function composition, however the composition function is replace with the multiplier function.
multiplier[n1_,n2_]:=n1 n2 #&
num={2,4,2+4};
numi=1/num;
multiplierfuncs = multiplier @@@ Transpose[{num, numi}];
The resulting functions are unity multipliers:
Table[i[0.666], {i, multiplierfuncs}] {0.666, 0.666, 0.666}
Note that unlike Composition, the above definition of multiplier only allows for exactly two arguments. The definition can be changed to allow any nonzero number of arguments:
multiplier[arg__] := Times[arg, #] &
Nemerle
using System;
using System.Console;
using Nemerle.Collections.NCollectionsExtensions;
module FirstClassNums
{
Main() : void
{
def x = 2.0; def xi = 0.5;
def y = 4.0; def yi = 0.25;
def z = x + y; def zi = 1.0 / (x + y);
def multiplier = fun (a, b) {fun (c) {a * b * c}};
def nums = [x, y, z];
def inums = [xi, yi, zi];
WriteLine($[multiplier(n, m) (0.5)|(n, m) in ZipLazy(nums, inums)]);
}
}
Never
func multiplier(a : float, b : float) -> (float) -> float {
let func(m : float) -> float { a * b * m }
}
func main() -> int {
var x = 2.0;
var xi = 0.5;
var y = 4.0;
var yi = 0.25;
var z = x + y;
var zi = 1.0 / z;
var f = [ x, y, z ] : float;
var i = [ xi, yi, zi ] : float;
var c = 0;
var mult = let func(m : float) -> float { 0.0 };
for (c = 0; c < 3; c = c + 1) {
mult = multiplier(f[c], i[c]);
prints(f[c] + " * " + i[c] + " * " + 1.0 + " = " + mult(1) + "\n")
};
0
}
- Output:
2.00 * 0.50 * 1.00 = 1.00 4.00 * 0.25 * 1.00 = 1.00 6.00 * 0.17 * 1.00 = 1.00
Nim
func multiplier(a, b: float): auto =
let ab = a * b
result = func(c: float): float = ab * c
let
x = 2.0
xi = 0.5
y = 4.0
yi = 0.25
z = x + y
zi = 1.0 / ( x + y )
let list = [x, y, z]
let invlist = [xi, yi, zi]
for i in 0..list.high:
# Create a multiplier function...
let f = multiplier(list[i], invlist[i])
# ... and apply it.
echo f(0.5)
- Output:
0.5 0.5 0.5
Objeck
Similar however this code does not generate a list of functions.
use Collection.Generic;
class FirstClass {
function : Main(args : String[]) ~ Nil {
x := 2.0;
xi := 0.5;
y := 4.0;
yi := 0.25;
z := x + y;
zi := 1.0 / (x + y);
numlist := CompareVector->New()<FloatHolder>;
numlist->AddBack(x); numlist->AddBack(y); numlist->AddBack(z);
numlisti := Vector->New()<FloatHolder>;
numlisti->AddBack(xi); numlisti->AddBack(yi); numlisti->AddBack(zi);
each(i : numlist) {
v := numlist->Get(i); vi := numlisti->Get(i);
mult := Multiplier(v, vi);
r := mult(0.5);
"{$v} * {$vi} * 0.5 = {$r}"->PrintLine();
};
}
function : Multiplier(a : FloatHolder, b : FloatHolder) ~ (FloatHolder) ~ FloatHolder {
return \(FloatHolder) ~ FloatHolder : (c) => a * b * c;
}
}
- Output:
2 * 0.5 * 0.5 = 0.5 4 * 0.25 * 0.5 = 0.5 6 * 0.166667 * 0.5 = 0.5
OCaml
# let x = 2.0;;
# let y = 4.0;;
# let z = x +. y;;
# let coll = [ x; y; z];;
# let inv_coll = List.map (fun x -> 1.0 /. x) coll;;
# let multiplier n1 n2 = (fun t -> n1 *. n2 *. t);;
(* create a list of new functions *)
# let func_list = List.map2 (fun n inv -> (multiplier n inv)) coll inv_coll;;
# List.map (fun f -> f 0.5) func_list;;
- : float list = [0.5; 0.5; 0.5]
(* or just apply the generated function immediately... *)
# List.map2 (fun n inv -> (multiplier n inv) 0.5) coll inv_coll;;
- : float list = [0.5; 0.5; 0.5]
Oforth
: multiplier(n1, n2) #[ n1 n2 * * ] ;
: firstClassNum
| x xi y yi z zi |
2.0 ->x
0.5 ->xi
4.0 ->y
0.25 ->yi
x y + ->z
x y + inv ->zi
[ x, y, z ] [ xi, yi, zi ] zipWith(#multiplier) map(#[ 0.5 swap perform ] ) . ;
- Output:
[0.5, 0.5, 0.5]
Oz
declare
[X Y Z] = [2.0 4.0 Z=X+Y]
[XI YI ZI] = [0.5 0.25 1.0/(X+Y)]
fun {Multiplier A B}
fun {$ M}
A * B * M
end
end
in
for
N in [X Y Z]
I in [XI YI ZI]
do
{Show {{Multiplier N I} 0.5}}
end
"Multiplier" is like "Compose", but with multiplication instead of function application. Otherwise the code is identical except for the argument types (numbers instead of functions).
PARI/GP
multiplier(n1,n2)={
x -> n1 * n2 * x
};
test()={
my(x = 2.0, xi = 0.5, y = 4.0, yi = 0.25, z = x + y, zi = 1.0 / ( x + y ));
print(multiplier(x,xi)(0.5));
print(multiplier(y,yi)(0.5));
print(multiplier(z,zi)(0.5));
};
The two are very similar, though as requested the test numbers are in 6 variables instead of two vectors.
Perl
sub multiplier {
my ( $n1, $n2 ) = @_;
sub {
$n1 * $n2 * $_[0];
};
}
my $x = 2.0;
my $xi = 0.5;
my $y = 4.0;
my $yi = 0.25;
my $z = $x + $y;
my $zi = 1.0 / ( $x + $y );
my %zip;
@zip{ $x, $y, $z } = ( $xi, $yi, $zi );
while ( my ( $number, $inverse ) = each %zip ) {
print multiplier( $number, $inverse )->(0.5), "\n";
}
Output:
0.5 0.5 0.5
The entry in first-class functions uses the same technique:
sub compose {
my ($f, $g) = @_;
sub {
$f -> ($g -> (@_));
};
}
...
compose($flist1[$_], $flist2[$_]) -> (0.5)
Phix
Just as there is no real support for first class functions, not much that is pertinent to this task for numbers either, but the manual way is just as trivial:
with javascript_semantics sequence mtable = {} function multiplier(atom n1, atom n2) mtable = append(mtable,{n1,n2}) return length(mtable) end function function call_multiplier(integer f, atom m) atom {n1,n2} = mtable[f] return n1*n2*m end function constant x = 2, xi = 0.5, y = 4, yi = 0.25, z = x + y, zi = 1 / ( x + y ) ?call_multiplier(multiplier(x,xi),0.5) ?call_multiplier(multiplier(y,yi),0.5) ?call_multiplier(multiplier(z,zi),0.5)
- Output:
0.5 0.5 0.5
I should perhaps note that output in Phix automatically rounds to the specified precision (10 d.p. if none) so 4.9999 to two decimal places is shown as 5.00, and you can be pretty sure that sort of thing is happening on the last line.
Compared to first class functions, there are (as in my view there should be) significant differences in the treatment of numbers and functions, but as mentioned on that page tagging ctable entries should be quite sufficient.
with javascript_semantics sequence ctable = {} function compose(integer f, g) ctable = append(ctable,{f,g}) integer cdx = length(ctable) return cdx end function function call_composite(integer cdx, atom x) integer {f,g} = ctable[cdx] return f(g(x)) end function function plus1(atom x) return x+1 end function function halve(atom x) return x/2 end function constant m = compose(halve,plus1) ?call_composite(m,1) -- displays 1 ?call_composite(m,4) -- displays 2.5
PicoLisp
(load "@lib/math.l")
(de multiplier (N1 N2)
(curry (N1 N2) (X)
(*/ N1 N2 X `(* 1.0 1.0)) ) )
(let (X 2.0 Xi 0.5 Y 4.0 Yi 0.25 Z (+ X Y) Zi (*/ 1.0 1.0 Z))
(mapc
'((Num Inv)
(prinl (format ((multiplier Inv Num) 0.5) *Scl)) )
(list X Y Z)
(list Xi Yi Zi) ) )
Output:
0.500000 0.500000 0.500001
This follows the same structure as First-class functions#PicoLisp, just that the function 'multiplier' above accepts two numbers, while 'compose' below accepts two functions:
(load "@lib/math.l")
(de compose (F G)
(curry (F G) (X)
(F (G X)) ) )
(de cube (X)
(pow X 3.0) )
(de cubeRoot (X)
(pow X 0.3333333) )
(mapc
'((Fun Inv)
(prinl (format ((compose Inv Fun) 0.5) *Scl)) )
'(sin cos cube)
'(asin acos cubeRoot) )
With a similar output:
0.500001 0.499999 0.500000
Python
This new task:
IDLE 2.6.1
>>> # Number literals
>>> x,xi, y,yi = 2.0,0.5, 4.0,0.25
>>> # Numbers from calculation
>>> z = x + y
>>> zi = 1.0 / (x + y)
>>> # The multiplier function is similar to 'compose' but with numbers
>>> multiplier = lambda n1, n2: (lambda m: n1 * n2 * m)
>>> # Numbers as members of collections
>>> numlist = [x, y, z]
>>> numlisti = [xi, yi, zi]
>>> # Apply numbers from list
>>> [multiplier(inversen, n)(.5) for n, inversen in zip(numlist, numlisti)]
[0.5, 0.5, 0.5]
>>>
The Python solution to First-class functions for comparison:
>>> # Some built in functions and their inverses
>>> from math import sin, cos, acos, asin
>>> # Add a user defined function and its inverse
>>> cube = lambda x: x * x * x
>>> croot = lambda x: x ** (1/3.0)
>>> # First class functions allow run-time creation of functions from functions
>>> # return function compose(f,g)(x) == f(g(x))
>>> compose = lambda f1, f2: ( lambda x: f1(f2(x)) )
>>> # first class functions should be able to be members of collection types
>>> funclist = [sin, cos, cube]
>>> funclisti = [asin, acos, croot]
>>> # Apply functions from lists as easily as integers
>>> [compose(inversef, f)(.5) for f, inversef in zip(funclist, funclisti)]
[0.5, 0.4999999999999999, 0.5]
>>>
As can be see, the treatment of functions is very close to the treatment of numbers. there are no extra wrappers, or function pointer syntax added, for example.
R
multiplier <- function(n1,n2) { (function(m){n1*n2*m}) }
x = 2.0
xi = 0.5
y = 4.0
yi = 0.25
z = x + y
zi = 1.0 / ( x + y )
num = c(x,y,z)
inv = c(xi,yi,zi)
multiplier(num,inv)(0.5)
Output
[1] 0.5 0.5 0.5
Compared to original first class functions
sapply(mapply(compose,f1,f2),do.call,list(.5))
[1] 0.5 0.5 0.5
Racket
#lang racket
(define x 2.0)
(define xi 0.5)
(define y 4.0)
(define yi 0.25)
(define z (+ x y))
(define zi (/ 1.0 (+ x y)))
(define ((multiplier x y) z) (* x y z))
(define numbers (list x y z))
(define inverses (list xi yi zi))
(for/list ([n numbers] [i inverses])
((multiplier n i) 0.5))
;; -> '(0.5 0.5 0.5)
Raku
(formerly Perl 6)
sub multiplied ($g, $f) { return { $g * $f * $^x } }
my $x = 2.0;
my $xi = 0.5;
my $y = 4.0;
my $yi = 0.25;
my $z = $x + $y;
my $zi = 1.0 / ( $x + $y );
my @numbers = $x, $y, $z;
my @inverses = $xi, $yi, $zi;
for flat @numbers Z @inverses { say multiplied($^g, $^f)(.5) }
Output:
0.5 0.5 0.5
The structure of this is identical to first-class function task.
REXX
The REXX language doesn't have an easy method to call functions by using a variable name,
but the interpret instruction can be used to provide that capability.
/*REXX program to use a first-class function to use numbers analogously. */
nums= 2.0 4.0 6.0 /*various numbers, can have fractions.*/
invs= 1/2.0 1/4.0 1/6.0 /*inverses of the above (real) numbers.*/
m= 0.5 /*multiplier when invoking new function*/
do j=1 for words(nums); num= word(nums, j); inv= word(invs, j)
nf= multiplier(num, inv); interpret call nf m /*sets the var RESULT.*/
say 'number=' @(num) 'inverse=' @(inv) 'm=' @(m) 'result=' @(result)
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
@: return left( arg(1) / 1, 15) /*format the number, left justified. */
multiplier: procedure expose n1n2; parse arg n1,n2; n1n2= n1 * n2; return 'a_new_func'
a_new_func: return n1n2 * arg(1)
- output when using the internal default inputs:
number= 2 inverse= 0.5 m= 0.5 result= 0.5 number= 4 inverse= 0.25 m= 0.5 result= 0.5 number= 6 inverse= 0.166666667 m= 0.5 result= 0.5
Ruby
multiplier = proc {|n1, n2| proc {|m| n1 * n2 * m}}
numlist = [x=2, y=4, x+y]
invlist = [0.5, 0.25, 1.0/(x+y)]
p numlist.zip(invlist).map {|n, invn| multiplier[invn, n][0.5]}
# => [0.5, 0.5, 0.5]
This structure is identical to the treatment of Ruby's first-class functions -- create a Proc object that returns a Proc object (a closure). These examples show that 0.5 times number n (or passed to function f) times inverse of n (or passed to inverse of f) returns the original number, 0.5.
Rust
#![feature(conservative_impl_trait)]
fn main() {
let (x, xi) = (2.0, 0.5);
let (y, yi) = (4.0, 0.25);
let z = x + y;
let zi = 1.0/z;
let numlist = [x,y,z];
let invlist = [xi,yi,zi];
let result = numlist.iter()
.zip(&invlist)
.map(|(x,y)| multiplier(*x,*y)(0.5))
.collect::<Vec<_>>();
println!("{:?}", result);
}
fn multiplier(x: f64, y: f64) -> impl Fn(f64) -> f64 {
move |m| x*y*m
}
This is very similar to the first-class functions implementation save that the type inference works a little bit better here (e.g. when declaring numlist
and invlist
) and multiplier
's declaration is substantially simpler than compose
's. Both of these boil down to the fact that closures and regular functions are actually different types in Rust so we have to be generic over them but here we are only dealing with 64-bit floats.
Scala
scala> val x = 2.0
x: Double = 2.0
scala> val xi = 0.5
xi: Double = 0.5
scala> val y = 4.0
y: Double = 4.0
scala> val yi = 0.25
yi: Double = 0.25
scala> val z = x + y
z: Double = 6.0
scala> val zi = 1.0 / ( x + y )
zi: Double = 0.16666666666666666
scala> val numbers = List(x, y, z)
numbers: List[Double] = List(2.0, 4.0, 6.0)
scala> val inverses = List(xi, yi, zi)
inverses: List[Double] = List(0.5, 0.25, 0.16666666666666666)
scala> def multiplier = (n1: Double, n2: Double) => (m: Double) => n1 * n2 * m
multiplier: (Double, Double) => (Double) => Double
scala> def comp = numbers zip inverses map multiplier.tupled
comp: List[(Double) => Double]
scala> comp.foreach(f=>println(f(0.5)))
0.5
0.5
0.5
Scheme
This implementation closely follows the Scheme implementation of the First-class functions problem.
(define x 2.0)
(define xi 0.5)
(define y 4.0)
(define yi 0.25)
(define z (+ x y))
(define zi (/ (+ x y)))
(define number (list x y z))
(define inverse (list xi yi zi))
(define (multiplier n1 n2) (lambda (m) (* n1 n2 m)))
(define m 0.5)
(define (go n1 n2)
(for-each (lambda (n1 n2)
(display ((multiplier n1 n2) m))
(newline))
n1 n2))
(go number inverse)
Output:
0.5 0.5 0.5
Sidef
func multiplier(n1, n2) {
func (n3) {
n1 * n2 * n3
}
}
var x = 2.0
var xi = 0.5
var y = 4.0
var yi = 0.25
var z = (x + y)
var zi = (1 / (x + y))
var numbers = [x, y, z]
var inverses = [xi, yi, zi]
for f,g (numbers ~Z inverses) {
say multiplier(f, g)(0.5)
}
- Output:
0.5 0.5 0.5
Slate
define: #multiplier -> [| :n1 :n2 | [| :m | n1 * n2 * m]].
define: #x -> 2.
define: #y -> 4.
define: #numlist -> {x. y. x + y}.
define: #numlisti -> (numlist collect: [| :x | 1.0 / x]).
numlist with: numlisti collect: [| :n1 :n2 | (multiplier applyTo: {n1. n2}) applyWith: 0.5].
Tcl
package require Tcl 8.5
proc multiplier {a b} {
list apply {{ab m} {expr {$ab*$m}}} [expr {$a*$b}]
}
Note that, as with Tcl's solution for First-class functions, the resulting term must be expanded on application. For example, study this interactive session:
% set mult23 [multiplier 2 3]
apply {{ab m} {expr {$ab*$m}}} 6
% {*}$mult23 5
30
Formally, for the task:
set x 2.0
set xi 0.5
set y 4.0
set yi 0.25
set z [expr {$x + $y}]
set zi [expr {1.0 / ( $x + $y )}]
set numlist [list $x $y $z]
set numlisti [list $xi $yi $zi]
foreach a $numlist b $numlisti {
puts [format "%g * %g * 0.5 = %g" $a $b [{*}[multiplier $a $b] 0.5]]
}
Which produces this output:
2 * 0.5 * 0.5 = 0.5 4 * 0.25 * 0.5 = 0.5 6 * 0.166667 * 0.5 = 0.5
Ursala
The form is very similar to the first class functions task solution in Ursala, except that the multiplier function takes the place of the composition operator (+), and is named in compliance with the task specification.
#import std
#import flo
numbers = <2.,4.,plus(2.,4.)>
inverses = <0.5,0.25,div(1.,plus(2.,4.))>
multiplier = //times+ times
#cast %eL
main = (gang multiplier*p\numbers inverses) 0.5
The multiplier could have been written in pattern matching form like this.
multiplier("a","b") "c" = times(times("a","b"),"c")
The main program might also have been written with an anonymous function like this.
main = (gang (//times+ times)*p\numbers inverses) 0.5
output:
<5.000000e-01,5.000000e-01,5.000000e-01>
Wren
import "/fmt" for Fmt
var multiplier = Fn.new { |n1, n2| Fn.new { |m| n1 * n2 * m } }
var orderedCollection = Fn.new {
var x = 2.0
var xi = 0.5
var y = 4.0
var yi = 0.25
var z = x + y
var zi = 1.0 / ( x + y )
return [[x, y, z], [xi, yi, zi]]
}
var oc = orderedCollection.call()
for (i in 0..2) {
var x = oc[0][i]
var y = oc[1][i]
var m = 0.5 // rather than 1 to compare with first-class functions task
Fmt.print("$0.1g * $g * $0.1g = $0.1g", x, y, m, multiplier.call(x, y).call(m))
}
- Output:
Agreeing with results of first-class functions task:
2.0 * 0.5 * 0.5 = 0.5 4.0 * 0.25 * 0.5 = 0.5 6.0 * 0.166667 * 0.5 = 0.5
zkl
var x=2.0, y=4.0, z=(x+y), c=T(x,y,z).apply(fcn(n){ T(n,1.0/n) });
//-->L(L(2,0.5),L(4,0.25),L(6,0.166667))
fcn multiplier(n1,n2){ return('*.fp(n1,n2)) }
This is actually partial evaluation, multiplier returns n1*n2*X where X isn't known yet. So multiplier(2,3)(4) --> (2*3*)4 --> 24. Even better, multiplier(2,3)(4,5) --> 120, multiplier(2,3)(4,5,6) --> 720, multiplier(2,3)() --> 6.
Alternatively,
fcn multiplier(n1,n2){ fcn(n,X){ n*X }.fp(n1*n2) }
var ms=c.apply(fcn([(n1,n2)]){ multiplier(n1,n2) });
//-->L(Deferred,Deferred,Deferred) // lazy eval of n*(1/n)*X
ms.run(True,1.0) //-->L(1,1,1)
ms.run(True,5.0) //-->L(5,5,5)
ms.run(True,0.5) //-->L(0.5,0.5,0.5)
List.run(True,X), for each item in the list, does i(X) and collects the results into another list. Sort of an inverted map or fold.
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