# Catamorphism

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

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.

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

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);

```

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(Mul'Access, (1,2,3,4)), Width => 3);
```

end Catamorphism;</lang>

Output:
`  1  4 10 24`

## 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"}`

## 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```

## 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```

## 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(sub, 5, nums));
printf("%d\n", reduce(mul, 5, nums));
return 0;
```

}</lang>

Output:
```15
-13
120```

## 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```

## 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>

## 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 3.2 : <lang elena>import system'collections. import system'routines. import extensions. import extensions'text.

program = [

```   var numbers := 1 to:10 repeat(:n)( n ); summarize(ArrayList new).

var summary := numbers accumulate(Variable new:0) with(:a:b)( a + b ).

var product := numbers accumulate(Variable new:1) with(:a:b)( a * b ).

var concatenation := numbers accumulate(String new) with(:a:b)( a literal + b literal ).

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

].</lang>

Output:
```55 362880 123456789
```

## 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

<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
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
```
```     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
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```

<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:

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 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];

```   return a + b;
```

}

function mul(a, b) {

```   return a * b;
```

}

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

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

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

Output:
```15
-13
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}

```  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
```

## 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>

## 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", "rod", "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", "rod", "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(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;
```

``` 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(@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>

## Perl 6

Works with: Rakudo version 2015.12

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>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>

## 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

Output:
```15
-13
120
```

## 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

SWI-Prolog has native foldl in version 6.3.1
Module lambda was written by Ulrich Neumerkel and can be found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl <lang Prolog>:- use_module(library(lambda)).

% foldl is now a predicate of SWI-Prolog 6.3.1 % 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.
```

## Python

<lang python>>>> 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>

<lang python>from functools import reduce from operator import add, mul

nums = range(1,11)

product = reduce(mul, nums)

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

print(summation, product, concatenation)</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>

## REXX

This REXX example is modeled after the Perl 6 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 a list of arguments.*/
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 a list of arguments.*/
do k=2  to words(\$);    !=abs(word(\$, k));  if !=0  then return 0
x=x*! / GCD(x, !)              /*have  GCD do the heavy lifting.*/
end   /*k*/
return x</lang>
```
output:

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
```

## 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```

## 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.

## 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>

## 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>