Rosetta Code

Catamorphism

Revision as of 19:36, 28 January 2021 by Chunes (talk | contribs) (→‎{{header|Quackery}}: remove nests)

Reduce is a function or method that is used to take the values in an array or a list and apply a function to successive members of the list to produce (or reduce them to), a single value.

Task
Catamorphism
You are encouraged to solve this task according to the task description, using any language you may know.


Task

Show how reduce (or foldl or foldr etc), work (or would be implemented) in your language.


See also



11l

<lang 11l>print((1..3).reduce((x, y) -> x + y)) print((1..3).reduce(3, (x, y) -> x + y)) print([1, 1, 3].reduce((x, y) -> x + y)) print([1, 1, 3].reduce(2, (x, y) -> x + y))</lang>

Output:
6
9
5
7

ABAP

This works in ABAP version 7.40 and above.

<lang ABAP> report z_catamorphism.

data(numbers) = value int4_table( ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ).

write: |numbers = { reduce string( 

 init output = `[`
      index = 1
 for number in numbers
 next output = cond string(
        when index eq lines( numbers )
        then |{ output }, { number } ]|
        when index > 1
        then |{ output }, { number }|
        else |{ output } { number }| )
      index = index + 1 ) }|, /.

write: |sum(numbers) = { reduce int4( 

 init result = 0
 for number in numbers
 next result = result + number ) }|, /.

write: |product(numbers) = { reduce int4( 

 init result = 1
 for number in numbers
 next result = result * number ) }|, /.

data(strings) = value stringtab( ( `reduce` ) ( `in` ) ( `ABAP` ) ).

write: |strings = { reduce string( 

 init output = `[`
      index = 1
 for string in strings
 next output = cond string(
        when index eq lines( strings )
        then |{ output }, { string } ]|
        when index > 1
        then |{ output }, { string }|
        else |{ output } { string }| )
      index = index + 1 ) }|, /.

write: |concatenation(strings) = { reduce string( 

 init text = ``
 for string in strings
 next text = |{ text } { string }| ) }|, /.

</lang>

Output:
numbers = [ 1, 2, 3, 4, 5 ]

sum(numbers) = 15

product(numbers) = 120

strings = [ reduce, in, ABAP ]

concatenation(strings) =  reduce in ABAP

Ada

<lang Ada>with Ada.Text_IO;

procedure Catamorphism is 

  type Fun is access function (Left, Right: Natural) return Natural;
  type Arr is array(Natural range <>) of Natural;
  
  function Fold_Left (F: Fun; A: Arr) return Natural is
     Result: Natural := A(A'First);
  begin
     for I in A'First+1 .. A'Last loop

Result := F(Result, A(I)); 

     end loop;
     return Result;
  end Fold_Left;
  
  function Max (L, R: Natural) return Natural is (if L > R then L else R);
  function Min (L, R: Natural) return Natural is (if L < R then L else R);     
  function Add (Left, Right: Natural) return Natural is (Left + Right);
  function Mul (Left, Right: Natural) return Natural is (Left * Right);
         
  package NIO is new Ada.Text_IO.Integer_IO(Natural);

begin 

  NIO.Put(Fold_Left(Min'Access, (1,2,3,4)), Width => 3);
  NIO.Put(Fold_Left(Max'Access, (1,2,3,4)), Width => 3);
  NIO.Put(Fold_Left(Add'Access, (1,2,3,4)), Width => 3);
  NIO.Put(Fold_Left(Mul'Access, (1,2,3,4)), Width => 3);

end Catamorphism;</lang>

Output:
  1  4 10 24

Aime

<lang aime>integer s;

s = 0; list(1, 2, 3, 4, 5, 6, 7, 8, 9).ucall(add_i, 1, s); o_(s, "\n");</lang>

Output:
45

ALGOL 68

<lang algol68># applies fn to successive elements of the array of values #

  1. the result is 0 if there are no values #

PROC reduce = ( []INT values, PROC( INT, INT )INT fn )INT: 

    IF UPB values < LWB values
    THEN # no elements #
         0
    ELSE # there are some elements #
         INT result := values[ LWB values ];
         FOR pos FROM LWB values + 1 TO UPB values
         DO
             result := fn( result, values[ pos ] )
         OD;
         result
    FI; # reduce #
  1. test the reduce procedure #

BEGIN print( ( reduce( ( 1, 2, 3, 4, 5 ), ( INT a, b )INT: a + b ), newline ) ) # sum # 

   ; print( ( reduce( ( 1, 2, 3, 4, 5 ), ( INT a, b )INT: a * b ), newline ) ) # product #
   ; print( ( reduce( ( 1, 2, 3, 4, 5 ), ( INT a, b )INT: a - b ), newline ) ) # difference #

END</lang>

Output:
        +15
       +120
        -13

AppleScript

Translation of: JavaScript

Iteratively implemented foldl and foldr, using the same argument sequence as in the corresponding JavaScript array methods reduce() and reduceRight().

(Note that to obtain first-class functions from user-defined AppleScript handlers, we have to 'lift' them into script objects).

<lang AppleScript>-- CATAMORPHISMS --------------------------------------------------

-- the arguments available to the called function f(a, x, i, l) are -- a: current accumulator value -- x: current item in list -- i: [ 1-based index in list ] optional -- l: [ a reference to the list itself ] optional

-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs) 

   tell mReturn(f)
       set v to startValue
       set lng to length of xs
       repeat with i from 1 to lng
           set v to |λ|(v, item i of xs, i, xs)
       end repeat
       return v
   end tell

end foldl

-- the arguments available to the called function f(a, x, i, l) are -- a: current accumulator value -- x: current item in list -- i: [ 1-based index in list ] optional -- l: [ a reference to the list itself ] optional

-- foldr :: (a -> b -> a) -> a -> [b] -> a on foldr(f, startValue, xs) 

   tell mReturn(f)
       set v to startValue
       set lng to length of xs
       repeat with i from lng to 1 by -1
           set v to |λ|(v, item i of xs, i, xs)
       end repeat
       return v
   end tell

end foldr


-- OTHER FUNCTIONS DEFINED IN TERMS OF FOLDL AND FOLDR ------------

-- concat :: a -> [a] | [String] -> String on concat(xs) 

   script append
       on |λ|(a, b)
           a & b
       end |λ|
   end script
   
   if length of xs > 0 and class of (item 1 of xs) is string then
       set unit to ""
   else
       set unit to {}
   end if
   foldl(append, unit, xs)

end concat

-- product :: Num a => [a] -> a on product(xs) 

   script
       on |λ|(a, b)
           a * b
       end |λ|
   end script
   
   foldr(result, 1, xs)

end product

-- sum :: Num a => [a] -> a on sum(xs) 

   script
       on |λ|(a, b)
           a + b
       end |λ|
   end script
   
   foldl(result, 0, xs)

end sum


-- TEST ----------------------------------------------------------- on run 

   set xs to {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
   
   {sum(xs), product(xs), concat(xs)}
   
   --> {55, 3628800, "10987654321"}

end run


-- GENERIC FUNCTION -----------------------------------------------

-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f) 

   if class of f is script then
       f
   else
       script
           property |λ| : f
       end script
   end if

end mReturn</lang>

Output:
{55, 3628800, "10987654321"}

BBC BASIC

<lang bbcbasic> 

     DIM a(4)
     a() = 1, 2, 3, 4, 5
     PRINT FNreduce(a(), "+")
     PRINT FNreduce(a(), "-")
     PRINT FNreduce(a(), "*")
     END

     DEF FNreduce(arr(), op$)
     REM!Keep tmp, arr()
     LOCAL I%, tmp
     tmp = arr(0)
     FOR I% = 1 TO DIM(arr(), 1)
       tmp = EVAL("tmp " + op$ + " arr(I%)")
     NEXT
     = tmp

</lang>

Output:
        15
       -13
       120

Bracmat

<lang bracmat>( ( fold 

 =   f xs init first rest
   .   !arg:(?f.?xs.?init)
     & ( !xs:&!init
       |   !xs:%?first ?rest
         & !f$(!first.fold$(!f.!rest.!init))
       )
 )

& out 

 $ ( fold
   $ ( (=a b.!arg:(?a.?b)&!a+!b)
     . 1 2 3 4 5
     . 0
     )
   )

& (product=a b.!arg:(?a.?b)&!a*!b) & out$(fold$(product.1 2 3 4 5.1)) );</lang> Output: 

15
120

C

<lang C>#include <stdio.h>

typedef int (*intFn)(int, int);

int reduce(intFn fn, int size, int *elms) { 

   int i, val = *elms;
   for (i = 1; i < size; ++i)
       val = fn(val, elms[i]);
   return val;

}

int add(int a, int b) { return a + b; } int sub(int a, int b) { return a - b; } int mul(int a, int b) { return a * b; }

int main(void) { 

   int nums[] = {1, 2, 3, 4, 5};
   printf("%d\n", reduce(add, 5, nums));
   printf("%d\n", reduce(sub, 5, nums));
   printf("%d\n", reduce(mul, 5, nums));
   return 0;

}</lang>

Output:
15
-13
120

C#

<lang csharp>var nums = Enumerable.Range(1, 10);

int summation = nums.Aggregate((a, b) => a + b);

int product = nums.Aggregate((a, b) => a * b);

string concatenation = nums.Aggregate(String.Empty, (a, b) => a.ToString() + b.ToString());

Console.WriteLine("{0} {1} {2}", summation, product, concatenation);</lang>

C++

<lang cpp>#include <iostream>

  1. include <numeric>
  2. include <functional>
  3. include <vector>

int main() { std::vector<int> nums = { 1, 2, 3, 4, 5 }; auto nums_added = std::accumulate(std::begin(nums), std::end(nums), 0, std::plus<int>()); auto nums_other = std::accumulate(std::begin(nums), std::end(nums), 0, [](const int& a, const int& b) { return a + 2 * b; }); std::cout << "nums_added: " << nums_added << std::endl; std::cout << "nums_other: " << nums_other << std::endl; }</lang>

Output:
nums_added: 15
nums_other: 30

Clojure

For more detail, check Rich Hickey's blog post on Reducers.

<lang clojure>; Basic usage > (reduce * '(1 2 3 4 5)) 120

Using an initial value

> (reduce + 100 '(1 2 3 4 5)) 115 </lang>

Common Lisp

<lang lisp>; Basic usage > (reduce #'* '(1 2 3 4 5)) 120

Using an initial value

> (reduce #'+ '(1 2 3 4 5) :initial-value 100) 115

Using only a subsequence

> (reduce #'+ '(1 2 3 4 5) :start 1 :end 4) 9

Apply a function to each element first

> (reduce #'+ '((a 1) (b 2) (c 3)) :key #'cadr) 6

Right-associative reduction

> (reduce #'expt '(2 3 4) :from-end T) 2417851639229258349412352

Compare with

> (reduce #'expt '(2 3 4)) 4096</lang>

D

<lang d>void main() { 

   import std.stdio, std.algorithm, std.range, std.meta, std.numeric,
          std.conv, std.typecons;

   auto list = iota(1, 11);
   alias ops = AliasSeq!(q{a + b}, q{a * b}, min, max, gcd);

   foreach (op; ops)
       writeln(op.stringof, ": ", list.reduce!op);

   // std.algorithm.reduce supports multiple functions in parallel:
   reduce!(ops[0], ops[3], text)(tuple(0, 0.0, ""), list).writeln;

}</lang>

Output:
"a + b": 55
"a * b": 3628800
min(T1,T2,T...) if (is(typeof(a < b))): 1
max(T1,T2,T...) if (is(typeof(a < b))): 10
gcd(T): 1
Tuple!(int,double,string)(55, 10, "12345678910")

DCL

<lang DCL>$ list = "1,2,3,4,5" $ call reduce list "+" $ show symbol result $ $ numbers = "5,4,3,2,1" $ call reduce numbers "-" $ show symbol result $ $ call reduce list "*" $ show symbol result $ exit $ $ reduce: subroutine $ local_list = 'p1 $ value = f$integer( f$element( 0, ",", local_list )) $ i = 1 $ loop: $ element = f$element( i, ",", local_list ) $ if element .eqs. "," then $ goto done $ value = value 'p2 f$integer( element ) $ i = i + 1 $ goto loop $ done: $ result == value $ exit $ endsubroutine</lang>

Output:
$ @catamorphism
  RESULT == 15   Hex = 0000000F  Octal = 00000000017
  RESULT == -5   Hex = FFFFFFFB  Octal = 37777777773
  RESULT == 120   Hex = 00000078  Octal = 00000000170

Déjà Vu

This is a foldl: <lang dejavu>reduce f lst init: if lst: f reduce @f lst init pop-from lst else: init

!. reduce @+ [ 1 10 200 ] 4 !. reduce @- [ 1 10 200 ] 4 </lang>

Output:
215
-207

EchoLisp

<lang scheme>

rem
the foldX family always need an initial value
fold left a list

(foldl + 0 (iota 10)) ;; 0 + 1 + .. + 9 

 → 45
fold left a sequence

(lib 'sequences) (foldl * 1 [ 1 .. 10]) 

   → 362880 ;; 10!
folding left and right

(foldl / 1 ' ( 1 2 3 4)) 

   → 8/3

(foldr / 1 '(1 2 3 4)) 

   → 3/8
scanl gives the list (or sequence) of intermediate values

(scanl * 1 '( 1 2 3 4 5)) 

  → (1 1 2 6 24 120)

</lang>

Elena

ELENA 5.0 : <lang elena>import system'collections; import system'routines; import extensions; import extensions'text;

public program() { 

   var numbers := new Range(1,10).summarize(new ArrayList());

   var summary := numbers.accumulate(new Variable(0), (a,b => a + b));

   var product := numbers.accumulate(new Variable(1), (a,b => a * b));

   var concatenation := numbers.accumulate(new StringWriter(), (a,b => a.toPrintable() + b.toPrintable()));

   console.printLine(summary," ",product," ",concatenation)

}</lang>

Output:
55 362880 12345678910

Elixir

<lang elixir>iex(1)> Enum.reduce(1..10, fn i,acc -> i+acc end) 55 iex(2)> Enum.reduce(1..10, fn i,acc -> i*acc end) 3628800 iex(3)> Enum.reduce(10..-10, "", fn i,acc -> acc <> to_string(i) end) "109876543210-1-2-3-4-5-6-7-8-9-10"</lang>

Erlang

Translation of: Haskell

<lang erlang> -module(catamorphism).

-export([test/0]).

test() -> Nums = lists:seq(1,10), Summation = lists:foldl(fun(X, Acc) -> X + Acc end, 0, Nums), Product = lists:foldl(fun(X, Acc) -> X * Acc end, 1, Nums), Concatenation = lists:foldr( fun(X, Acc) -> integer_to_list(X) ++ Acc end, "", Nums), {Summation, Product, Concatenation}. </lang>

Output: 

{55,3628800,"12345678910"}

F#

In the REPL:

> let nums = [1 .. 10];;

val nums : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]

> let summation = List.fold (+) 0 nums;;

val summation : int = 55

> let product = List.fold (*) 1 nums;;

val product : int = 3628800

> let concatenation = List.foldBack (fun x y -> x + y) (List.map (fun i -> i.ToString()) nums) "";;

val concatenation : string = "12345678910"

Factor

<lang factor>{ 1 2 4 6 10 } 0 [ + ] reduce .</lang>

Output:
23

Forth

Forth has three traditions for iterating over the members of a data structure. Under the first, the data structure has words that help you navigate over it and normal Forth looping structures are used. Under the second, the data structure has dedicated looping words and you supply the code that's run for each member. Under the third, the data structure has a loop-over-members word that accepts a function to be run against each member.

There's no need to distinguish between the different kinds of looping ("this one collects function returns into a list; this one threads an accumulator between the function-calls; this one threads two accumulators through the function-calls; this one expects no return values whatsoever from the function-calls") because in Forth all that the looping words have to do is make the data stack available for the function's use. When that's the case, all of these variations, that are so important in other languages, are functionally equivalent.

Although it's possible to have a generic higher-order word that can operate under all kinds of data structures -- this just requires that one settle on an object system and then derive a collections library from it -- this is rarely done. Typically each data structure has its own looping words.

To demonstrate the above points we'll just loop over the bytes of a string.

Some helper words for these examples:

<lang forth>: lowercase? ( c -- f ) 

 [char] a [ char z 1+ ] literal within ;
char-upcase ( c -- C )
 dup lowercase? if bl xor then ;</lang>

Using normal looping words:

<lang forth>: string-at ( c-addr u +n -- c ) 

 nip + c@ ;
string-at! ( c-addr u +n c -- )
 rot drop  -rot  + c! ;
type-lowercase ( c-addr u -- )
 dup 0 ?do
   2dup i string-at  dup lowercase?  if emit else drop then
 loop  2drop ;
upcase ( 'string' -- 'STRING' )
 dup 0 ?do
   2dup 2dup  i string-at  char-upcase  i swap string-at!
 loop ;
count-lowercase ( c-addr u -- n )
 0 -rot dup 0 ?do
   2dup i string-at  lowercase? if rot 1+ -rot then
 loop  2drop ;</lang>

Briefly, a variation:

<lang forth>: next-char ( a +n -- a' n' c -1 ) ( a 0 -- 0 ) 

 dup if 2dup  1 /string  2swap drop c@ true
 else 2drop 0 then ;
type-lowercase ( c-addr u -- )
 begin next-char while
   dup lowercase? if emit else drop then
 repeat ;</lang>

Using dedicated looping words:

<lang forth>: each-char[ ( c-addr u -- ) 

 postpone BOUNDS postpone ?DO
 postpone I postpone C@ ;  immediate

 \ interim code: ( c -- )
]each-char ( -- )
 postpone LOOP ;  immediate
type-lowercase ( c-addr u -- )
 each-char[ dup lowercase? if emit else drop then ]each-char ;
upcase ( 'string' -- 'STRING' )
 2dup each-char[ char-upcase i c! ]each-char ;
count-lowercase ( c-addr u -- n )
 0 -rot each-char[ lowercase? if 1+ then ]each-char ;</lang>

Using higher-order words:

<lang forth>: each-char ( c-addr u xt -- ) 

 {: xt :}  bounds ?do
   i c@ xt execute
 loop ;
type-lowercase ( c-addr u -- )
 [: dup lowercase? if emit else drop then ;]
 each-char ;

\ producing a new string

upcase ( 'string' -- 'STRING' )
 dup cell+ allocate throw -rot
 [: ( new-string-addr c -- new-string-addr )
   upcase over c+! ;] each-char  $@ ;
count-lowercase ( c-addr u -- n )
 0 -rot [: lowercase? if 1+ then ;] each-char ;</lang>

In these examples COUNT-LOWERCASE updates an accumulator, UPCASE (mostly) modifies the string in-place, and TYPE-LOWERCASE performs side-effects and returns nothing to the higher-order word.

Fortran

If Fortran were to offer the ability to pass a parameter "by name", as is used in Jensen's device, then the code might be something like <lang Fortran> SUBROUTINE FOLD(t,F,i,ist,lst) 

      INTEGER t
      BYNAME F
       DO i = ist,lst
         t = F
       END DO
     END SUBROUTINE FOLD      !Result in temp.

     temp = a(1); CALL FOLD(temp,temp*a(i),i,2,N)</lang>

Here, the function manifests as the expression that is the second parameter of subroutine FOLD, and the "by name" protocol for parameter F means that within the subroutine whenever there is a reference to F, its value is evaluated afresh in the caller's environment using the current values of temp and i as modified by the subroutine - they being passed by reference so that changes within the subroutine affect the originals. An evaluation for a different function requires merely another statement with a different expression.

Fortran however does not provide such a facility. Any parameter that is an expression is evaluated once in the caller's environment, the result placed in temporary storage, and the address of that storage location is passed to the subroutine. Repeated references to that parameter will elicit the same value. But there is special provision for passing a function to a routine, involving the special word EXTERNAL. For every different function in mind, one must diligently supply a name, and work through the overhead of declaring each such function. There is an additional word, INTRINSIC, for use when an intrinsic function (such as SIN) is to be passed as such a parameter since it will appear as its name only, and with the absence of the (...) that would be used for the function's parameters when in an arithmetic expression, it would otherwise be taken as being the name of an ordinary variable.

Here is such an arrangement, in the style of F77 though somewhat affected by F90 in that the END statement names the routine being ended. Similarly, to abate petty complaints about the types of the functions being undeclared, explicit types are specified, though unselecting the compiler diagnostic for that would match the habits of earlier compilers. Also in F90 is the MODULE protocol which involves rather more organised checking of types and additional facilities for arrays so that N need not be passed because secret additional parameters do so.

However, only programmer diligence in devising functions with the correct type of result and the correct type and number of parameters will evade mishaps. Note that the EXTERNAL statement does not specify the number or type of parameters. If the function is invoked multiple times within a subroutine, the compiler may check for consistency. This may cause trouble when some parameters are optional so that different invocations do not match.

The function's name is used as a working variable within the function (as well as it holding the function's value on exit) so that the expression F(IFOLD,A(I)) is not a recursive invocation of function IFOLD because there are no (parameters) appended to the function's name. Earlier compilers did not allow such usage so that a separate working variable would be required. <lang Fortran> INTEGER FUNCTION IFOLD(F,A,N) !"Catamorphism"... 

      INTEGER F	!We're working only with integers.
      EXTERNAL F	!This is a function, not an array.
      INTEGER A(*)	!An 1-D array, of unspecified size.
      INTEGER N	!The number of elements.
      INTEGER I	!A stepper.
       IFOLD = 0		!A default value.
       IF (N.LE.0) RETURN	!Dodge silly invocations.
       IFOLD = A(1)		!The function is to have two arguments.
       IF (N.EQ.1) RETURN	!So, if there is only one element, silly.
       DO I = 2,N		!Otherwise, stutter along the array.
         IFOLD = F(IFOLD,A(I))		!Applying the function.
       END DO			!On to the next element.
     END FUNCTION IFOLD!Thus, F(A(1),A(2)), or F(F(A(1),A(2)),A(3)), or F(F(F(A(1),A(2)),A(3)),A(4)), etc.

     INTEGER FUNCTION IADD(I,J)
      INTEGER I,J
       IADD = I + J
     END FUNCTION IADD

     INTEGER FUNCTION IMUL(I,J)
      INTEGER I,J
       IMUL = I*J
     END FUNCTION IMUL

     INTEGER FUNCTION IDIV(I,J)
      INTEGER I,J
       IDIV = I/J
     END FUNCTION IDIV

     INTEGER FUNCTION IVID(I,J)
      INTEGER I,J
       IVID = J/I
     END FUNCTION IVID

     PROGRAM POKE
     INTEGER ENUFF
     PARAMETER (ENUFF = 6)
     INTEGER A(ENUFF)
     PARAMETER (A = (/1,2,3,4,5,6/))
     INTEGER MSG
     EXTERNAL IADD,IMUL,IDIV,IVID	!Warn that these are the names of functions.

     MSG = 6	!Standard output.
     WRITE (MSG,1) ENUFF,A
   1 FORMAT ('To apply a function in the "catamorphic" style ',
    1 "to the ",I0," values ",/,(20I3))

     WRITE (MSG,*) "Iadd",IFOLD(IADD,A,ENUFF)
     WRITE (MSG,*) "Imul",IFOLD(IMUL,A,ENUFF)
     WRITE (MSG,*) "Idiv",IFOLD(IDIV,A,ENUFF)
     WRITE (MSG,*) "Ivid",IFOLD(IVID,A,ENUFF)
     END PROGRAM POKE

</lang> Output: 

To apply a function in the "catamorphic" style to the 6 values
  1  2  3  4  5  6
 Iadd          21
 Imul         720
 Idiv           0
 Ivid           6

FreeBASIC

<lang freebasic>' FB 1.05.0 Win64

Type IntFunc As Function(As Integer, As Integer) As Integer

Function reduce(a() As Integer, f As IntFunc) As Integer 

   if array is empty or function pointer is null, return 0 say
  If UBound(a) = -1 OrElse f = 0 Then Return 0 
  Dim result As Integer = a(LBound(a))
  For i As Integer = LBound(a) + 1 To UBound(a)
    result = f(result, a(i)) 
  Next
  Return result

End Function

Function add(x As Integer, y As Integer) As Integer 

 Return x + y

End Function

Function subtract(x As Integer, y As Integer) As Integer 

 Return x - y

End Function

Function multiply(x As Integer, y As Integer) As Integer 

 Return x * y

End Function

Function max(x As Integer, y As Integer) As Integer 

 Return IIf(x > y, x, y)

End Function

Function min(x As Integer, y As Integer) As Integer 

 Return IIf(x < y, x, y)

End Function

Dim a(4) As Integer = {1, 2, 3, 4, 5} Print "Sum is  :"; reduce(a(), @add) Print "Difference is :"; reduce(a(), @subtract) Print "Product is  :"; reduce(a(), @multiply) Print "Maximum is  :"; reduce(a(), @max) Print "Minimum is  :"; reduce(a(), @min) Print "No op is  :"; reduce(a(), 0) Print Print "Press any key to quit" Sleep </lang>

Output:
Sum is        : 15
Difference is :-13
Product is    : 120
Maximum is    : 5
Minimum is    : 1
No op is      : 0

Go

<lang go>package main

import ( "fmt" )

func main() { n := []int{1, 2, 3, 4, 5}

fmt.Println(reduce(add, n)) fmt.Println(reduce(sub, n)) fmt.Println(reduce(mul, n)) }

func add(a int, b int) int { return a + b } func sub(a int, b int) int { return a - b } func mul(a int, b int) int { return a * b }

func reduce(rf func(int, int) int, m []int) int { r := m[0] for _, v := range m[1:] { r = rf(r, v) } return r }</lang>

Output:
15
-13
120

Groovy

Groovy provides an "inject" method for all aggregate classes that performs a classic tail-recursive reduction, driven by a closure argument. The result of each iteration (closure invocation) is used as the accumulated valued for the next iteration. If a first argument is provided as well as a second closure argument, that first argument is used as a seed accumulator for the first iteration. Otherwise, the first element of the aggregate is used as the seed accumulator, with reduction iteration proceeding across elements 2 through n. <lang groovy>def vector1 = [1,2,3,4,5,6,7] def vector2 = [7,6,5,4,3,2,1] def map1 = [a:1, b:2, c:3, d:4]

println vector1.inject { acc, val -> acc + val } // sum println vector1.inject { acc, val -> acc + val*val } // sum of squares println vector1.inject { acc, val -> acc * val } // product println vector1.inject { acc, val -> acc<val?val:acc } // max println ([vector1,vector2].transpose().inject(0) { acc, val -> acc + val[0]*val[1] }) //dot product (with seed 0)

println (map1.inject { Map.Entry accEntry, Map.Entry entry -> // some sort of weird map-based reduction 

   [(accEntry.key + entry.key):accEntry.value + entry.value ].entrySet().toList().pop()

})</lang>

Output:
28
140
5040
7
84
abcd=10

Haskell

<lang haskell>main :: IO () main = 

 putStrLn . unlines $
 [ show . foldr (+)    0  -- sum
 , show . foldr (*)    1  -- product
 , foldr ((++) . show) "" -- concatenation
 ] <*>
 1 .. 10</lang>
Output:
55
3628800
12345678910

and the generality of folds is such that if we replace all three of these (function, identity) combinations ((+), 0), ((*), 1) ((++), "") with the Monoid operation mappend (<>) and identity mempty, we can still obtain the same results:

<lang haskell>import Data.Monoid

main :: IO () main = 

 let xs = [1 .. 10]
 in (putStrLn . unlines)
      [ (show . getSum     . foldr (<>) mempty) (Sum     <$> xs)
      , (show . getProduct . foldr (<>) mempty) (Product <$> xs)
      , (show .              foldr (<>) mempty) (show    <$> xs) 
      , (show .              foldr (<>) mempty) (words
                    "Love is one damned thing after each other")
      ]</lang>
Output:
55
3628800
"12345678910"
"Loveisonedamnedthingaftereachother"

Also available are foldl1 and foldr1 which implicitly take first element as starting value. However they are not safe as they fail on empty lists.

Prelude folds work only on lists, module Data.Foldable a typeclass for more general fold - interface remains the same.

Icon and Unicon

Works in both languages: <lang unicon>procedure main(A) 

   write(A[1],": ",curry(A[1],A[2:0]))

end

procedure curry(f,A) 

   r := A[1]
   every r := f(r, !A[2:0])
   return r

end</lang>

Sample runs: 

->cata + 3 1 4 1 5 9
+: 23
->cata - 3 1 4 1 5 9
-: -17
->cata \* 3 1 4 1 5 9
*: 540
->cata "||" 3 1 4 1 5 9
||: 314159

J

Solution:<lang j> /</lang> Example:<lang j> +/ 1 2 3 4 5 15 

  */ 1 2 3 4 5

120 

  !/ 1 2 3 4 5  NB.  "n ! k" is "n choose k"

45</lang> Insert * into 1 2 3 4 5 becomes 1 * 2 * 3 * 4 * 5 evaluated right to left<lang j> 1 * 2 * 3 * 20 1 * 2 * 60 1 * 120 120 </lang> What are the implications for -/  ? For %/  ?

Java

Works with: Java version 8

<lang java>import java.util.stream.Stream;

public class ReduceTask { 

   public static void main(String[] args) {
       System.out.println(Stream.of(1, 2, 3, 4, 5).mapToInt(i -> i).sum());
       System.out.println(Stream.of(1, 2, 3, 4, 5).reduce(1, (a, b) -> a * b));
   }

}</lang>

Output:
15
120

JavaScript

ES5

<lang javascript>var nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

function add(a, b) { 

   return a + b;

}

var summation = nums.reduce(add);

function mul(a, b) { 

   return a * b;

}

var product = nums.reduce(mul, 1);

var concatenation = nums.reduce(add, "");

console.log(summation, product, concatenation);</lang>


Note that the JavaScript Array methods include a right fold ( .reduceRight() ) as well as a left fold:

<lang JavaScript>(function (xs) { 

   'use strict';

   // foldl :: (b -> a -> b) -> b -> [a] -> b
   function foldl(f, acc, xs) {
       return xs.reduce(f, acc);
   }

   // foldr :: (b -> a -> b) -> b -> [a] -> b
   function foldr(f, acc, xs) {
       return xs.reduceRight(f, acc);
   }

   // Test folds in both directions
   return [foldl, foldr].map(function (f) {
       return f(function (acc, x) {
           return acc + (x * 2).toString() + ' ';
       }, [], xs);
   });

})([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);</lang>

Output:
["0 2 4 6 8 10 12 14 16 18 ", 
"18 16 14 12 10 8 6 4 2 0 "]

ES6

<lang javascript>var nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

console.log(nums.reduce((a, b) => a + b, 0)); // sum of 1..10 console.log(nums.reduce((a, b) => a * b, 1)); // product of 1..10 console.log(nums.reduce((a, b) => a + b, )); // concatenation of 1..10</lang>

jq

jq has an unusual and unusually powerful "reduce" control structure. A full description is beyond the scope of this short article, but an important point is that "reduce" is stream-oriented. Reduction of arrays is however trivially achieved using the ".[]" filter for converting an array to a stream of its values.

The simplest use of "reduce" can be illustrated by this definition of "factorial": 

def factorial: reduce range(2;.+1) as $i (1; . * $i);

If the input is a non-negative integer, n, this will compute n!.

To understand how this works, consider "3|factorial". The computation starts by setting the implicit state variable to 1; range(2;4) will generate the sequence of values (2,3). The variable $i is set to each value in the stream in turn so that the state variable is multiplied by 2 (". * $i") and then by 3. Notice that since range/2 produces a stream, no array is ever constructed.

For a more complex illustration, see Strand sort.

The "reduce" operator is typically used within a map/reduce framework, but the implicit state variable can be any JSON entity, and so "reduce" is also a general-purpose iterative control structure, the only limitation being that it does not have the equivalent of "break". For that, the "foreach" control structure in recent versions of jq can be used.

Julia

Works with: Julia 1.2

<lang Julia>println([reduce(op, 1:5) for op in [+, -, *]]) println([foldl(op, 1:5) for op in [+, -, *]]) println([foldr(op, 1:5) for op in [+, -, *]])</lang>

Output:
[15, -13, 120]
[15, -13, 120]
[15, 3, 120]

Kotlin

<lang scala>fun main(args: Array<String>) { 

   val a = intArrayOf(1, 2, 3, 4, 5)
   println("Array       : ${a.joinToString(", ")}")
   println("Sum         : ${a.reduce { x, y -> x + y }}")
   println("Difference  : ${a.reduce { x, y -> x - y }}")
   println("Product     : ${a.reduce { x, y -> x * y }}")
   println("Minimum     : ${a.reduce { x, y -> if (x < y) x else y }}")
   println("Maximum     : ${a.reduce { x, y -> if (x > y) x else y }}")

}</lang>

Output:
Array       : 1, 2, 3, 4, 5
Sum         : 15
Difference  : -13
Product     : 120
Minimum     : 1
Maximum     : 5

Logtalk

The Logtalk standard library provides implementations of common meta-predicates such as fold left. The example that follow uses Logtalk's native support for lambda expressions to avoid the need for auxiliary predicates. <lang logtalk>

- object(folding_examples).
   :- public(show/0).
   show :-
       integer::sequence(1, 10, List),
       write('List: '), write(List), nl,
       meta::fold_left([Acc,N,Sum0]>>(Sum0 is Acc+N), 0, List, Sum),
       write('Sum of all elements: '), write(Sum), nl,
       meta::fold_left([Acc,N,Product0]>>(Product0 is Acc*N), 1, List, Product),
       write('Product of all elements: '), write(Product), nl,
       meta::fold_left([Acc,N,Concat0]>>(number_codes(N,NC), atom_codes(NA,NC), atom_concat(Acc,NA,Concat0)), , List, Concat),
       write('Concatenation of all elements: '), write(Concat), nl.
- end_object.

</lang>

Output:
| ?- folding_examples::show.
List: [1,2,3,4,5,6,7,8,9,10]
Sum of all elements: 55
Product of all elements: 3628800
Concatenation of all elements: 12345678910
yes

LOLCODE

Translation of: C

<lang LOLCODE>HAI 1.3

HOW IZ I reducin YR array AN YR size AN YR fn 

   I HAS A val ITZ array'Z SRS 0
   IM IN YR loop UPPIN YR i TIL BOTH SAEM i AN DIFF OF size AN 1
       val R I IZ fn YR val AN YR array'Z SRS SUM OF i AN 1 MKAY
   IM OUTTA YR loop
   FOUND YR val

IF U SAY SO

O HAI IM array 

   I HAS A SRS 0 ITZ 1
   I HAS A SRS 1 ITZ 2
   I HAS A SRS 2 ITZ 3
   I HAS A SRS 3 ITZ 4
   I HAS A SRS 4 ITZ 5

KTHX

HOW IZ I add YR a AN YR b, FOUND YR SUM OF a AN b, IF U SAY SO HOW IZ I sub YR a AN YR b, FOUND YR DIFF OF a AN b, IF U SAY SO HOW IZ I mul YR a AN YR b, FOUND YR PRODUKT OF a AN b, IF U SAY SO

VISIBLE I IZ reducin YR array AN YR 5 AN YR add MKAY VISIBLE I IZ reducin YR array AN YR 5 AN YR sub MKAY VISIBLE I IZ reducin YR array AN YR 5 AN YR mul MKAY

KTHXBYE</lang>

Output:
15
-13
120

Lua

<lang Lua> table.unpack = table.unpack or unpack -- 5.1 compatibility local nums = {1,2,3,4,5,6,7,8,9}

function add(a,b) 

  return a+b

end

function mult(a,b) 

  return a*b

end

function cat(a,b) 

  return tostring(a)..tostring(b)

end

local function reduce(fun,a,b,...) 

  if ... then
     return reduce(fun,fun(a,b),...)
  else
     return fun(a,b)
  end

end

local arithmetic_sum = function (...) return reduce(add,...) end local factorial5 = reduce(mult,5,4,3,2,1)

print("Σ(1..9)  : ",arithmetic_sum(table.unpack(nums))) print("5!  : ",factorial5) print("cat {1..9}: ",reduce(cat,table.unpack(nums)))

</lang>

Output:
Σ(1..9)   : 	45
5!        : 	120
cat {1..9}: 	123456789

M2000 Interpreter

<lang M2000 Interpreter> Module CheckIt { 

     Function Reduce (a, f) {
           if len(a)=0 then Error "Nothing to reduce"
           if len(a)=1 then  =Array(a) : Exit
           k=each(a, 2, -1)
           m=Array(a)
           While k {
                 m=f(m, array(k))
           }
           =m
     }
     a=(1, 2, 3, 4, 5)
     Print "Array", a
     Print "Sum", Reduce(a, lambda (x,y)->x+y)
     Print "Difference", Reduce(a, lambda (x,y)->x-y)
     Print "Product", Reduce(a, lambda (x,y)->x*y)
     Print "Minimum", Reduce(a, lambda (x,y)->if(x<y->x, y))
     Print "Maximum", Reduce(a, lambda (x,y)->if(x>y->x, y))

} CheckIt </lang>

Output:
Array               1         2         3         4          5
Sum                15
Difference        -13
Product           120
Minimum             1
Maximum             5

Maple

The left fold operator in Maple is foldl, and foldr is the right fold operator. <lang Maple>> nums := seq( 1 .. 10 ); 

                         nums := 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

> foldl( `+`, 0, nums ); # compute sum using foldl 

                         55

> foldr( `*`, 1, nums ); # compute product using foldr 

                         3628800</lang>

Compute the horner form of a (sorted) polynomial: <lang Maple>> foldl( (a,b) ->a*T+b, op(map2(op,1,[op( 72*T^5+37*T^4-23*T^3+87*T^2+44*T+29 )]))); 

                   ((((72 T + 37) T - 23) T + 87) T + 44) T + 29</lang>

Mathematica / Wolfram Language

<lang mathematica>Fold[f, x, {a, b, c, d}]</lang>

Output:
f[f[f[f[x, a], b], c], d]

Maxima

<lang maxima>lreduce(f, [a, b, c, d], x0); /* (%o1) f(f(f(f(x0, a), b), c), d) */</lang>

<lang maxima>lreduce("+", [1, 2, 3, 4], 100); /* (%o1) 110 */</lang>

min

Works with: min version 0.19.3

<lang min>(1 2 3 4) 0 '+ reduce puts! ; sum (1 2 3 4) 1 '* reduce puts! ; product</lang>

Output:
10
24

Nemerle

The Nemerle.Collections namespace defines FoldLeft, FoldRight and Fold (an alias for FoldLeft) on any sequence that implements the IEnumerable[T] interface. <lang Nemerle>def seq = [1, 4, 6, 3, 7]; def sum = seq.Fold(0, _ + _); // Fold takes an initial value and a function, here the + operator</lang>

Nim

<lang nim>import sequtils

block: 

 let
   numbers = @[5, 9, 11]
   addition = foldl(numbers, a + b)
   substraction = foldl(numbers, a - b)
   multiplication = foldl(numbers, a * b)
   words = @["nim", "is", "cool"]
   concatenation = foldl(words, a & b)

block: 

 let
   numbers = @[5, 9, 11]
   addition = foldr(numbers, a + b)
   substraction = foldr(numbers, a - b)
   multiplication = foldr(numbers, a * b)
   words = @["nim", "is", "cool"]
   concatenation = foldr(words, a & b)</lang>

Oberon-2

Works with: oo2c Version 2

<lang oberon2> MODULE Catamorphism; IMPORT 

 Object,
 NPCT:Tools,
 NPCT:Args,
 IntStr,
 Out;

TYPE 

 BinaryFunc= PROCEDURE (x,y: LONGINT): LONGINT;

VAR 

 data: POINTER TO ARRAY OF LONGINT;
 i: LONGINT;

 PROCEDURE Sum(x,y: LONGINT): LONGINT;
 BEGIN
   RETURN x + y
 END Sum;
 
 PROCEDURE Sub(x,y: LONGINT): LONGINT;
 BEGIN
   RETURN x - y;
 END Sub;
 
 PROCEDURE Mul(x,y: LONGINT): LONGINT;
 BEGIN
   RETURN x * y;
 END Mul;
 
 PROCEDURE Reduce(x: ARRAY OF LONGINT; f: BinaryFunc): LONGINT;
 VAR
   i,res: LONGINT;
 BEGIN
   res := x[0];i := 1;
   WHILE (i < LEN(x)) DO;
     res := f(res,x[i]);
     INC(i)
   END;
   RETURN res
 END Reduce;
 
 PROCEDURE InitData(VAR x: ARRAY OF LONGINT);
 VAR
   i, j: LONGINT;
   res: IntStr.ConvResults;
   aux: Object.CharsLatin1;
 BEGIN
   i := 0;j := 1;
   WHILE (j <= LEN(x)) DO
     aux := Tools.AsString(Args.Get(j));
     IntStr.StrToInt(aux^,x[i],res);
     IF res # IntStr.strAllRight THEN
       Out.String("Incorrect format for data at index ");Out.LongInt(j,0);Out.Ln;
       HALT(1);
     END;
     INC(j);INC(i)
   END
 END InitData;

BEGIN 

 IF Args.Number() = 1 THEN
   Out.String("Invalid number of arguments. ");Out.Ln;
   HALT(0)
 ELSE
   NEW(data,Args.Number() - 1);
   InitData(data^);
   Out.LongInt(Reduce(data^,Sum),0);Out.Ln;
   Out.LongInt(Reduce(data^,Sub),0);Out.Ln;
   Out.LongInt(Reduce(data^,Mul),0);Out.Ln
 END

END Catamorphism. </lang>

Output:
1
-11
-14400

Objeck

<lang objeck> use Collection;

class Reducer { 

 function : Main(args : String[]) ~ Nil {
   values := IntVector->New([1, 2, 3, 4, 5]);
   values->Reduce(Add(Int, Int) ~ Int)->PrintLine();
   values->Reduce(Mul(Int, Int) ~ Int)->PrintLine();
 }

 function : Add(a : Int, b : Int) ~ Int {
   return a + b;
 }
 
 function : Mul(a : Int, b : Int) ~ Int {
   return a * b;
 }

}</lang> Output 

15
120

OCaml

<lang ocaml># let nums = [1;2;3;4;5;6;7;8;9;10];; val nums : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]

  1. let sum = List.fold_left (+) 0 nums;;

val sum : int = 55

  1. let product = List.fold_left ( * ) 1 nums;;

val product : int = 3628800</lang>

Oforth

reduce is already defined into Collection class :

<lang Oforth>[ 1, 2, 3, 4, 5 ] reduce(#max) [ "abc", "def", "gfi" ] reduce(#+)</lang>

PARI/GP

<lang parigp>reduce(f, v)={ 

 my(t=v[1]);
 for(i=2,#v,t=f(t,v[i]));
 t

}; reduce((a,b)->a+b, [1,2,3,4,5,6,7,8,9,10])</lang>

Works with: PARI/GP version 2.8.1+

<lang parigp>fold((a,b)->a+b, [1..10])</lang>

Pascal

Works with: Free Pascal

Should work with many pascal dialects <lang pascal>program reduce;

type // tmyArray = array of LongInt; 

 tmyArray = array[-5..5] of LongInt;
 tmyFunc = function (a,b:LongInt):LongInt;

function add(x,y:LongInt):LongInt; begin 

 add := x+y;

end;

function sub(k,l:LongInt):LongInt; begin 

 sub := k-l;

end;

function mul(r,t:LongInt):LongInt; begin 

 mul := r*t;

end;

function reduce(myFunc:tmyFunc;a:tmyArray):LongInt; var 

 i,res : LongInt;

begin 

 res := a[low(a)];
 For i := low(a)+1 to high(a) do
   res := myFunc(res,a[i]);
 reduce := res;

end;

procedure InitMyArray(var a:tmyArray); var 

 i: LongInt;

begin 

 For i := low(a) to high(a) do
 begin
   //no a[i] = 0
   a[i] := i + ord(i=0);
   write(a[i],',');
 end;
 writeln(#8#32);

end;

var 

 ma : tmyArray;

BEGIN 

 InitMyArray(ma);
 writeln(reduce(@add,ma));
 writeln(reduce(@sub,ma));
 writeln(reduce(@mul,ma));

END.</lang> output 

-5,-4,-3,-2,-1,1,1,2,3,4,5 
1
-11
-1440

Perl

Perl's reduce function is in a standard package. <lang perl>use List::Util 'reduce';

  1. note the use of the odd $a and $b globals

print +(reduce {$a + $b} 1 .. 10), "\n";

  1. first argument is really an anon function; you could also do this:

sub func { $b & 1 ? "$a $b" : "$b $a" } print +(reduce \&func, 1 .. 10), "\n"</lang>

Phix

Translation of: C

<lang Phix>function add(integer a, integer b) 

   return a + b

end function

function sub(integer a, integer b) 

   return a - b

end function

function mul(integer a, integer b) 

   return a * b

end function

function reduce(integer rid, sequence s) object res = s[1] 

   for i=2 to length(s) do
       res = call_func(rid,{res,s[i]})
   end for
   return res

end function

?reduce(routine_id("add"),tagset(5)) ?reduce(routine_id("sub"),tagset(5)) ?reduce(routine_id("mul"),tagset(5))</lang>

Output:
15
-13
120

Phixmonti

<lang Phixmonti>include ..\Utilitys.pmt

def add + enddef def sub - enddef def mul * enddef

def reduce >ps 

   1 get
   swap len 2 swap 2 tolist for
       get rot swap tps exec swap
   endfor
   ps> drop
   swap

enddef


( 1 2 3 4 5 ) getid add reduce ? getid sub reduce ? getid mul reduce ?</lang>


PicoLisp

<lang PicoLisp>(de reduce ("Fun" "Lst") 

  (let "A" (car "Lst")
     (for "N" (cdr "Lst")
        (setq "A" ("Fun" "A" "N")) )
     "A" ) )

(println 

  (reduce + (1 2 3 4 5))
  (reduce * (1 2 3 4 5)) )

(bye)</lang>

PowerShell

'Filter' is a more common sequence function in PowerShell than 'reduce' or 'map', but here is one way to accomplish 'reduce': <lang PowerShell> 1..5 | ForEach-Object -Begin {$result = 0} -Process {$result += $_} -End {$result} </lang>

Output:
15

Prolog

Using foldl from library(apply) and Lambda-Expressions from library(lambda)

  • SWI-Prolog's library(apply) provides a `foldl/4` (the source code of which can be seen here).
  • Ulrich Neumerkel wrote `library(lambda)` which can be found here. (However, SWI-Prolog's Lambda Expressions are by default based on Paulo Moura's library(yall))

<lang Prolog>:- use_module(library(lambda)).

catamorphism :- numlist(1,10,L), foldl(\XS^YS^ZS^(ZS is XS+YS), L, 0, Sum), format('Sum of ~w is ~w~n', [L, Sum]), foldl(\XP^YP^ZP^(ZP is XP*YP), L, 1, Prod), format('Prod of ~w is ~w~n', [L, Prod]), string_to_list(LV, ""), foldl(\XC^YC^ZC^(string_to_atom(XS, XC),string_concat(YC,XS,ZC)), L, LV, Concat), format('Concat of ~w is ~w~n', [L, Concat]).</lang>

Output:
 ?- catamorphism.
Sum of [1,2,3,4,5,6,7,8,9,10] is 55
Prod of [1,2,3,4,5,6,7,8,9,10] is 3628800
Concat of [1,2,3,4,5,6,7,8,9,10] is 12345678910
true.

Bare Prolog

This is based on SWI Prolog 8 and has the following specificities:

  • The consbox functor is [|] instead of .
  • The list is terminated by the special atomic thing [] (the empty list)

<lang Prolog> % List to be folded: % % +---+---+---+---[] <-- list backbone/spine, composed of nodes, terminating in the empty list % | | | | % a b c d <-- list items/entries/elements/members % </lang>

linear foldl

<lang Prolog> % Computes "Out" as: % % starter value -->--f-->--f-->--f-->--f-->-- Out % | | | | % a b c d


foldl(Foldy,[Item|Items],Acc,Result) :-  % case of nonempty list 

  !,                                      % GREEN CUT for determinism
  call(Foldy,Item,Acc,AccNext),           % call Foldy(Item,Acc,AccNext)
  foldl(Foldy,Items,AccNext,Result).      % then recurse (open to tail call optimization)

foldl(_,[],Acc,Result) :-  % case of empty list 

  Acc=Result.                             % unification not in head for clarity

</lang>

linear foldr

<lang Prolog> % Computes "Out" as: % % Out --<--f--<--f--<--f--<--f--<-- starter value % | | | | % a b c d

foldr(Foldy,[Item|Items],Starter,AccUp) :-  % case of nonempty list 

  !,                                         % GREEN CUT for determinism
  foldr(Foldy,Items,Starter,AccUpPrev),      % recurse (NOT open to tail-call optimization)
  call(Foldy,Item,AccUpPrev,AccUp).          % call Foldy(Item,AccupPrev,AccUp) as last action

foldr(_,[],Starter,AccUp) :-  % empty list: bounce Starter "upwards" into AccUp 

  AccUp=Starter.                             % unification not in head for clarity

</lang>

Unit tests

This is written using SWI-Prolog's unit testing framework.

Functions (in predicate form) of interest for our test cases:

<lang Prolog>

- use_module(library(clpfd)). % We are using #= instead of the raw "is".

foldy_len(_Item,ThreadIn,ThreadOut) :- 

  succ(ThreadIn,ThreadOut).

foldy_add(Item,ThreadIn,ThreadOut) :- 

  ThreadOut #= Item+ThreadIn.

foldy_mult(Item,ThreadIn,ThreadOut) :- 

  ThreadOut #= Item*ThreadIn.

foldy_squadd(Item,ThreadIn,ThreadOut) :- 

  ThreadOut #= Item+(ThreadIn^2).

% '[|]' is SWI-Prolog specific, replace by '.' as consbox constructor in other Prologs

foldy_build(Item,ThreadIn,ThreadOut) :- 

  ThreadOut = '[|]'(Item,ThreadIn).

foldy_join(Item,ThreadIn,ThreadOut) :- 

  (ThreadIn \= "")
  -> with_output_to(string(ThreadOut),format("~w,~w",[Item,ThreadIn]))
  ;  with_output_to(string(ThreadOut),format("~w",[Item])).

% '=..' ("univ") constructs a term from a list of functor and arguments

foldy_expr(Functor,Item,ThreadIn,ThreadOut) :- 

  ThreadOut =.. [Functor,Item,ThreadIn].

</lang>

<lang Prolog>

- begin_tests(foldr).

in([1,2,3,4,5]).

ffr(Foldy,List,Starter,AccUp) :- foldr(Foldy,List,Starter,AccUp).

test(foo_foldr_len)  :- in(L),ffr(foldy_len , L , 0 , R), R=5. test(foo_foldr_add)  :- in(L),ffr(foldy_add , L , 0 , R), R=15. test(foo_foldr_mult)  :- in(L),ffr(foldy_mult , L , 1 , R), R=120. test(foo_foldr_build)  :- in(L),ffr(foldy_build , L , [] , R), R=[1,2,3,4,5]. test(foo_foldr_squadd) :- in(L),ffr(foldy_squadd , L , 0 , R), R=507425426245. test(foo_foldr_join)  :- in(L),ffr(foldy_join , L , "" , R), R="1,2,3,4,5". test(foo_foldr_expr)  :- in(L),ffr(foldy_expr(*) , L , 1 , R), R=1*(2*(3*(4*(5*1)))).

test(foo_foldr_len_empty)  :- ffr(foldy_len , [], 0 , R), R=0. test(foo_foldr_add_empty)  :- ffr(foldy_add , [], 0 , R), R=0. test(foo_foldr_mult_empty)  :- ffr(foldy_mult , [], 1 , R), R=1. test(foo_foldr_build_empty)  :- ffr(foldy_build , [], [] , R), R=[]. test(foo_foldr_squadd_empty) :- ffr(foldy_squadd , [], 0 , R), R=0. test(foo_foldr_join_empty)  :- ffr(foldy_join , [], "" , R), R="". test(foo_foldr_expr_empty)  :- ffr(foldy_expr(*) , [], 1 , R), R=1.

% library(apply) has no "foldr" so no comparison tests!

- end_tests(foldr).


- begin_tests(foldl).

in([1,2,3,4,5]).

ffl(Foldy,List,Starter,Result) :- foldl(Foldy,List,Starter,Result).

test(foo_foldl_len)  :- in(L),ffl(foldy_len , L , 0 , R), R=5. test(foo_foldl_add)  :- in(L),ffl(foldy_add , L, 0 , R), R=15. test(foo_foldl_mult)  :- in(L),ffl(foldy_mult , L, 1 , R), R=120. test(foo_foldl_build)  :- in(L),ffl(foldy_build , L, [] , R), R=[5,4,3,2,1]. test(foo_foldl_squadd) :- in(L),ffl(foldy_squadd , L, 0 , R), R=21909. test(foo_foldl_join)  :- in(L),ffl(foldy_join , L, "" , R), R="5,4,3,2,1". test(foo_foldl_expr)  :- in(L),ffl(foldy_expr(*) , L, 1 , R), R=5*(4*(3*(2*(1*1)))).

test(foo_foldl_len_empty)  :- ffl(foldy_len , [], 0 , R), R=0. test(foo_foldl_add_empty)  :- ffl(foldy_add , [], 0 , R), R=0. test(foo_foldl_mult_empty)  :- ffl(foldy_mult , [], 1 , R), R=1. test(foo_foldl_build_empty)  :- ffl(foldy_build , [], [] , R), R=[]. test(foo_foldl_squadd_empty) :- ffl(foldy_squadd , [], 0 , R), R=0. test(foo_foldl_join_empty)  :- ffl(foldy_join , [], "" , R), R="". test(foo_foldl_expr_empty)  :- ffl(foldy_expr(*) , [], 1 , R), R=1.

- end_tests(foldl).

rt :- run_tests(foldr),run_tests(foldl). </lang>

Python

<lang python>>>> # Python 2.X >>> from operator import add >>> listoflists = [['the', 'cat'], ['sat', 'on'], ['the', 'mat']] >>> help(reduce) Help on built-in function reduce in module __builtin__:

reduce(...) 

   reduce(function, sequence[, initial]) -> value
   
   Apply a function of two arguments cumulatively to the items of a sequence,
   from left to right, so as to reduce the sequence to a single value.
   For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates
   ((((1+2)+3)+4)+5).  If initial is present, it is placed before the items
   of the sequence in the calculation, and serves as a default when the
   sequence is empty.

>>> reduce(add, listoflists, []) ['the', 'cat', 'sat', 'on', 'the', 'mat'] >>> </lang>

Additional example

<lang python># Python 3.X

from functools import reduce from operator import add, mul

nums = range(1,11)

summation = reduce(add, nums)

product = reduce(mul, nums)

concatenation = reduce(lambda a, b: str(a) + str(b), nums)

print(summation, product, concatenation)</lang>

Quackery

Among its many other uses, witheach can act like reduce. In the Quackery shell (REPL): <lang quackery>/O> 0 ' [ 1 2 3 4 5 ] witheach + ... 1 ' [ 1 2 3 4 5 ] witheach * ...

Stack: 15 120</lang>

R

Sum the numbers in a vector:

<lang R> Reduce('+', c(2,30,400,5000)) 5432 </lang>

Put a 0 between each pair of numbers:

<lang R> Reduce(function(a,b){c(a,0,b)}, c(2,3,4,5)) 2 0 3 0 4 0 5 </lang>

Generate all prefixes of a string:

<lang R> Reduce(paste0, unlist(strsplit("freedom", NULL)), accum=T) "f" "fr" "fre" "free" "freed" "freedo" "freedom" </lang>

Filter and map:

<lang R> Reduce(function(x,acc){if (0==x%%3) c(x*x,acc) else acc}, 0:22, 

      init=c(), right=T)
  0   9  36  81 144 225 324 441

</lang>

Racket

<lang racket>

  1. lang racket

(define (fold f xs init) 

 (if (empty? xs)
     init
     (f (first xs)
        (fold f (rest xs) init))))

(fold + '(1 2 3) 0)  ; the result is 6 </lang>

Raku

(formerly Perl 6)

Works with: Rakudo version 2018.03

Any associative infix operator, either built-in or user-defined, may be turned into a reduce operator by putting it into square brackets (known as "the reduce metaoperator") and using it as a list operator. The operations will work left-to-right or right-to-left automatically depending on the natural associativity of the base operator. <lang perl6>my @list = 1..10; say [+] @list; say [*] @list; say [~] @list; say min @list; say max @list; say [lcm] @list;</lang>

Output:
55
3628800
12345678910
1
10
2520

In addition to the reduce metaoperator, a general higher-order function, reduce, can apply any appropriate function. Reproducing the above in this form, using the function names of those operators, we have: <lang perl6>my @list = 1..10; say reduce &infix:<+>, @list; say reduce &infix:<*>, @list; say reduce &infix:<~>, @list; say reduce &infix:<min>, @list; say reduce &infix:<max>, @list; say reduce &infix:<lcm>, @list;</lang>

REXX

This REXX example is modeled after the Raku example   (it is NOT a translation).

Also, a   list   and   show   function were added, although they aren't a catamorphism, as they don't produce or reduce the values to a   single   value, but are included here to help display the values in the list. <lang rexx>/*REXX program demonstrates a method for catamorphism for some simple functions. */ @list= 1 2 3 4 5 6 7 8 9 10 

                               say 'list:'     fold(@list,  "list")
                               say ' sum:'     fold(@list,  "+"   )
                               say 'prod:'     fold(@list,  "*"   )
                               say ' cat:'     fold(@list,  "||"  )
                               say ' min:'     fold(@list,  "min" )
                               say ' max:'     fold(@list,  "max" )
                               say ' avg:'     fold(@list,  "avg" )
                               say ' GCD:'     fold(@list,  "GCD" )
                               say ' LCM:'     fold(@list,  "LCM" )

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ fold: procedure; parse arg z; arg ,f; z = space(z); BIFs= 'MIN MAX LCM GCD' 

     za= translate(z, f, ' ');                 zf= f"("translate(z, ',' , " ")')'
     if f== '+' | f=="*"       then interpret  "return"  za
     if f== '||'               then return  space(z, 0)
     if f== 'AVG'              then interpret  "return"  fold(z, '+')    "/"    words(z)
     if wordpos(f, BIFs)\==0   then interpret  "return"  zf
     if f=='LIST' | f=="SHOW"  then return z
     return 'illegal function:'     arg(2)

/*──────────────────────────────────────────────────────────────────────────────────────*/ GCD: procedure; $=; do j=1 for arg(); $= $ arg(j) 

                                              end   /*j*/
     parse var $ x z .;    if x=0  then x= z                  /* [↑] build an arg list.*/
     x= abs(x)
                        do k=2  to words($);  y= abs( word($, k));   if y=0  then iterate
                          do until _=0;       _= x // y;      x= y;     y= _
                          end   /*until*/
                        end   /*k*/
     return x

/*──────────────────────────────────────────────────────────────────────────────────────*/ LCM: procedure; $=; do j=1 for arg(); $= $ arg(j) 

                        end   /*j*/
     x= abs(word($, 1))                                       /* [↑] build an arg list.*/
                        do k=2  to words($);   != abs(word($, k));  if !=0  then return 0
                        x= x*!  /  GCD(x, !)                  /*GCD does the heavy work*/
                        end   /*k*/
     return x</lang>
output:
list: 1 2 3 4 5 6 7 8 9 10
 sum: 55
prod: 3628800
 cat: 12345678910
 min: 1
 max: 10
 avg: 5.5
 GCD: 1
 LCM: 2520

Ring

<lang ring> n = list(10) for i = 1 to 10 

   n[i] = i

next

see " +: " + cat(10,"+") + nl+ 

   "  -: " + cat(10,"-") + nl +
   "  *: " + cat(10,"*") + nl +
   "  /: " + cat(10,"/") + nl+
   "  ^: " + cat(10,"^") + nl +
   "min: " + cat(10,"min") + nl+
   "max: " + cat(10,"max") + nl+
   "avg: " + cat(10,"avg") + nl +
   "cat: " + cat(10,"cat") + nl

func cat count,op 

    cat = n[1]
    cat2 = ""
    for i = 2 to count 
        switch op 
               on "+" cat +=  n[i] 
               on "-"  cat -=  n[i]
               on "*" cat *=  n[i]
               on "/" cat /=  n[i]
               on "^" cat ^=  n[i]
               on "max" cat = max(cat,n[i])
               on "min" cat = min(cat,n[i])
               on "avg" cat +=  n[i]
               on "cat" cat2 += string(n[i])
         off
    next

if op = "avg" cat = cat / count ok if op = "cat" decimals(0) cat = string(n[1])+cat2 ok return cat </lang>

Ruby

The method inject (and it's alias reduce) can be used in several ways; the simplest is to give a methodname as argument: <lang ruby># sum: p (1..10).inject(:+)

  1. smallest number divisible by all numbers from 1 to 20:

p (1..20).inject(:lcm) #lcm: lowest common multiple </lang>The most versatile way uses a accumulator object (memo) and a block. In this example Pascal's triangle is generated by using an array [1,1] and inserting the sum of each consecutive pair of numbers from the previous row. <lang ruby>p row = [1] 10.times{p row = row.each_cons(2).inject([1,1]){|ar,(a,b)| ar.insert(-2, a+b)} }

  1. [1]
  2. [1, 1]
  3. [1, 2, 1]
  4. [1, 3, 3, 1]
  5. [1, 4, 6, 4, 1]
  6. [1, 5, 10, 10, 5, 1]
  7. [1, 6, 15, 20, 15, 6, 1]
  8. etc

</lang>

Run BASIC

<lang runbasic>for i = 1 to 10 :n(i) = i:next i

print " +: ";" ";cat(10,"+") print " -: ";" ";cat(10,"-") print " *: ";" ";cat(10,"*") print " /: ";" ";cat(10,"/") print " ^: ";" ";cat(10,"^") print "min: ";" ";cat(10,"min") print "max: ";" ";cat(10,"max") print "avg: ";" ";cat(10,"avg") print "cat: ";" ";cat(10,"cat")

function cat(count,op$) cat = n(1) for i = 2 to count 

if op$ = "+" 	then cat = cat + n(i)
if op$ = "-" 	then cat = cat - n(i)
if op$ = "*" 	then cat = cat * n(i) 
if op$ = "/" 	then cat = cat / n(i)
if op$ = "^" 	then cat = cat ^ n(i)
if op$ = "max"	then cat = max(cat,n(i))
if op$ = "min"	then cat = min(cat,n(i))
if op$ = "avg"	then cat = cat + n(i)
if op$ = "cat"	then cat$ = cat$ + str$(n(i))

next i if op$ = "avg" then cat = cat / count if op$ = "cat" then cat = val(str$(n(1))+cat$) end function</lang> 

  +:  55
  -:  -53
  *:  3628800
  /:  2.75573205e-7
  ^:  1
min:  1
max:  10
avg:  5.5
cat:  12345678910

Rust

<lang rust>fn main() { 

   println!("Sum: {}", (1..10).fold(0, |acc, n| acc + n));
   println!("Product: {}", (1..10).fold(1, |acc, n| acc * n));
   let chars = ['a', 'b', 'c', 'd', 'e'];
   println!("Concatenation: {}",
            chars.iter().map(|&c| (c as u8 + 1) as char).collect::<String>());

}</lang>

Output:
Sum: 45
Product: 362880
Concatenation: bcdef

Scala

<lang scala>object Main extends App { 

 val a = Seq(1, 2, 3, 4, 5)
 println(s"Array       : ${a.mkString(", ")}")
 println(s"Sum         : ${a.sum}")
 println(s"Difference  : ${a.reduce { (x, y) => x - y }}")
 println(s"Product     : ${a.product}")
 println(s"Minimum     : ${a.min}")
 println(s"Maximum     : ${a.max}")

}</lang>

Scheme

Implementation

reduce implemented for a single list: <lang scheme>(define (reduce fn init lst) 

 (do ((val init (fn (car rem) val)) ; accumulated value passed as second argument
      (rem lst (cdr rem)))
   ((null? rem) val)))

(display (reduce + 0 '(1 2 3 4 5))) (newline) ; => 15 (display (reduce expt 2 '(3 4))) (newline)  ; => 262144</lang>

Using SRFI 1

There is also an implementation of fold and fold-right in SRFI-1, for lists.

These take a two-argument procedure: (lambda (value acc) ...) where value is the next value in the list, and acc is the accumulated value. The initial value is used for the first value of acc. 

> (import (srfi 1))
> (fold + 0 '(1 2 3 4 5))
15
> (fold expt 2 '(3 4)) ; => (expt 4 (expt 3 2))
262144
> (fold-right expt 2 '(3 4)) ; => (expt 3 (expt 4 2))
43046721

More than one list may be folded over, when the function is passed one item from each list plus the accumulated value: 

> (fold + 0 '(1 2 3) '(4 5 6)) ; add up all the numbers in all the lists
21

Sidef

<lang ruby>say (1..10 -> reduce('+')); say (1..10 -> reduce{|a,b| a + b});</lang>

Standard ML

<lang sml>- val nums = [1,2,3,4,5,6,7,8,9,10]; val nums = [1,2,3,4,5,6,7,8,9,10] : int list - val sum = foldl op+ 0 nums; val sum = 55 : int - val product = foldl op* 1 nums; val product = 3628800 : int</lang>

Swift

<lang swift>let nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

print(nums.reduce(0, +)) print(nums.reduce(1, *)) print(nums.reduce("", { $0 + String($1) }))</lang>

Output:
55
3628800
12345678910

Tailspin

It is probably easier to just write the whole thing as an inline transform rather than create a utility. <lang tailspin> [1..5] -> \(@: $(1); $(2..last)... -> @: $@ + $; $@!\) -> '$; ' -> !OUT::write [1..5] -> \(@: $(1); $(2..last)... -> @: $@ - $; $@!\) -> '$; ' -> !OUT::write [1..5] -> \(@: $(1); $(2..last)... -> @: $@ * $; $@!\) -> '$; ' -> !OUT::write </lang>

Output:
15
-13
120

If you really want to make a utility, it could look like this: <lang tailspin> templates fold&{op:} 

 @: $(1);
 $(2..last)... -> @: [$@, $] -> op;
 $@ !

end fold

templates add 

 $(1) + $(2) !

end add

templates mul 

 $(1) * $(2) !

end mul

[1..5] -> fold&{op:add} -> '$; ' -> !OUT::write

[1..5] -> fold&{op:mul} -> '$; ' -> !OUT::write </lang>

Output:
15
120

Tcl

Tcl does not come with a built-in fold command, but it is easy to construct: <lang tcl>proc fold {lambda zero list} { 

   set accumulator $zero
   foreach item $list {

set accumulator [apply $lambda $accumulator $item] 

   }
   return $accumulator

}</lang> Demonstrating: <lang tcl>set 1to5 {1 2 3 4 5}

puts [fold {{a b} {expr {$a+$b}}} 0 $1to5] puts [fold {{a b} {expr {$a*$b}}} 1 $1to5] puts [fold {{a b} {return $a,$b}} x $1to5]</lang>

Output:
15
120
x,1,2,3,4,5

Note that these particular operations would more conventionally be written as: <lang tcl>puts [::tcl::mathop::+ {*}$1to5] puts [::tcl::mathop::* {*}$1to5] puts x,[join $1to5 ,]</lang> But those are not general catamorphisms.

VBA

<lang vb>Public Sub reduce() 

   s = [{1,2,3,4,5}]
   Debug.Print WorksheetFunction.Sum(s)
   Debug.Print WorksheetFunction.Product(s)

End Sub</lang>

WDTE

Translated from the JavaScript ES6 example with a few modifications.

<lang WDTE>let a => import 'arrays'; let s => import 'stream'; let str => import 'strings';

  1. Sum of [1, 10]:

let nums => [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]; a.stream nums -> s.reduce 0 + -- io.writeln io.stdout;

  1. As an alternative to an array, a range stream can be used. Here's the product of [1, 11):

s.range 1 11 -> s.reduce 1 * -- io.writeln io.stdout;

  1. And here's a concatenation:

s.range 1 11 -> s.reduce (str.format '{}{}') -- io.writeln io.stdout;</lang>

Wortel

You can reduce an array with the !/ operator. <lang wortel>!/ ^+ [1 2 3] ; returns 6</lang> If you want to reduce with an initial value, you'll need the @fold operator. <lang wortel>@fold ^+ 1 [1 2 3] ; returns 7</lang>

Output:
55
3628800
12345678910

Wren

<lang ecmascript>var a = [1, 2, 3, 4, 5] var sum = a.reduce { |acc, i| acc + i } var prod = a.reduce { |acc, i| acc * i } var sumSq = a.reduce { |acc, i| acc + i*i } System.print(a) System.print("Sum is %(sum)") System.print("Product is %(prod)") System.print("Sum of squares is %(sumSq)")</lang>

Output:
[1, 2, 3, 4, 5]
Sum is 15
Product is 120
Sum of squares is 55

zkl

Most sequence objects in zkl have a reduce method. <lang zkl>T("foo","bar").reduce(fcn(p,n){p+n}) //--> "foobar" "123four5".reduce(fcn(p,c){p+(c.matches("[0-9]") and c or 0)}, 0) //-->11 File("foo.zkl").reduce('+(1).fpM("0-"),0) //->5 (lines in file)</lang>

ZX Spectrum Basic

Translation of: BBC_BASIC

<lang zxbasic>10 DIM a(5) 20 FOR i=1 TO 5 30 READ a(i) 40 NEXT i 50 DATA 1,2,3,4,5 60 LET o$="+": GO SUB 1000: PRINT tmp 70 LET o$="-": GO SUB 1000: PRINT tmp 80 LET o$="*": GO SUB 1000: PRINT tmp 90 STOP 1000 REM Reduce 1010 LET tmp=a(1) 1020 FOR i=2 TO 5 1030 LET tmp=VAL ("tmp"+o$+"a(i)") 1040 NEXT i 1050 RETURN </lang>

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