2016 Update
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Tina Müller
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7965 changed files with 139854 additions and 31002 deletions
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@ -1,15 +1,18 @@
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While implementing a recursive function, it often happens that we must resort to a separate "helper function" to handle the actual recursion.
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While implementing a recursive function, it often happens that we must resort to a separate ''helper function'' to handle the actual recursion.
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This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), cause unwanted side-effects, and/or the function doesn't have the right arguments and/or return values.
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This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), causing unwanted side-effects, and/or the function doesn't have the right arguments and/or return values.
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So we end up inventing some silly name like "foo2" or "foo_helper". I have always found it painful to come up with a proper name, and see a quite some disadvantages:
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So we end up inventing some silly name like '''foo2''' or '''foo_helper'''. I have always found it painful to come up with a proper name, and see some disadvantages:
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* You have to think up a name, which then pollutes the namespace
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* A function is created which is called from nowhere else
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* The program flow in the source code is interrupted
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::* You have to think up a name, which then pollutes the namespace
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::* Function is created which is called from nowhere else
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::* The program flow in the source code is interrupted
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Some languages allow you to embed recursion directly in-place. This might work via a label, a local ''gosub'' instruction, or some special keyword.
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Some languages allow you to embed recursion directly in-place. This might work via a label, a local ''gosub'' instruction, or some special keyword.
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Anonymous recursion can also be accomplished using the [[Y combinator]].
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Anonymous recursion can also be accomplished using the [[Y combinator]].
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If possible, demonstrate this by writing the recursive version of the fibonacci function (see [[Fibonacci sequence]]) which checks for a negative argument before doing the actual recursion.
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;Task:
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If possible, demonstrate this by writing the recursive version of the fibonacci function (see [[Fibonacci sequence]]) which checks for a negative argument before doing the actual recursion.
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<br><br>
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15
Task/Anonymous-recursion/ALGOL-68/anonymous-recursion.alg
Normal file
15
Task/Anonymous-recursion/ALGOL-68/anonymous-recursion.alg
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@ -0,0 +1,15 @@
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PROC fibonacci = ( INT x )INT:
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IF x < 0
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THEN
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print( ( "negative parameter to fibonacci", newline ) );
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stop
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ELSE
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PROC actual fibonacci = ( INT n )INT:
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IF n < 2
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THEN
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n
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ELSE
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actual fibonacci( n - 1 ) + actual fibonacci( n - 2 )
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FI;
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actual fibonacci( x )
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FI;
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@ -1,13 +1,20 @@
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#define system.
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#define extensions.
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#import system.
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#import extensions.
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#symbol fibo = (:n)
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[
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(n < 0)
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? [ #throw InvalidArgumentException new &message:"Must be non negative". ].
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#class(extension)mathOp
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{
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#method fib
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[
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(self < 0)
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? [ #throw InvalidArgumentException new &message:"Must be non negative". ].
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^ { eval:n [ ^ (n > 1) ? [ ($self:(n - 2)) + ($self:(n - 1)) ] ! [ n ]. ] }:n.
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].
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^ control eval:self &for:
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(:n)
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[
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(n > 1) ? [ this eval:(n - 2) + this eval:(n - 1) ] ! [ n ]
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].
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]
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}
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#symbol program =
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[
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@ -15,7 +22,7 @@
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[
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console writeLiteral:"fib(":i:")=".
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console writeLine:(fibo:i) | if &InvalidArgumentError: e
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console writeLine:(i fib) | if &InvalidArgumentError: e
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[
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console writeLine:"invalid".
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].
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7
Task/Anonymous-recursion/Io/anonymous-recursion.io
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7
Task/Anonymous-recursion/Io/anonymous-recursion.io
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fib := method(x,
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if(x < 0, Exception raise("Negative argument not allowed!"))
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fib2 := method(n,
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if(n < 2, n, fib2(n-1) + fib2(n-2))
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)
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fib2(x floor)
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)
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13
Task/Anonymous-recursion/REXX/anonymous-recursion-1.rexx
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13
Task/Anonymous-recursion/REXX/anonymous-recursion-1.rexx
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/*REXX program to show anonymous recursion (of a function or subroutine). */
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numeric digits 1e6 /*in case the user goes ka-razy. */
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parse arg x . /*obtain the optional argument from CL.*/
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if x=='' | x=="," then x=12 /*Not specified? Then use the default.*/
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w=length(x) /*W: used for formatting the output. */
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do j=0 to x; jj=right(j, w) /*use the argument as an upper limit.*/
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say 'fibonacci('jj") =" fib(j) /*show the Fibonacci sequence: 0 ──► x */
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end /*j*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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fib: procedure; parse arg z; if z>=0 then return .(z)
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say "***error*** argument can't be negative."; exit
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.: procedure; parse arg #; if #<2 then return #; return .(#-1) + .(#-2)
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14
Task/Anonymous-recursion/REXX/anonymous-recursion-2.rexx
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14
Task/Anonymous-recursion/REXX/anonymous-recursion-2.rexx
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/*REXX program to show anonymous recursion of a function or subroutine with memoization.*/
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numeric digits 1e6 /*in case the user goes ka-razy. */
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parse arg x . /*obtain the optional argument from CL.*/
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if x=='' | x=="," then x=12 /*Not specified? Then use the default.*/
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@.=.; @.0=0; @.1=1 /*used to implement memoization for FIB*/
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w=length(x) /*W: used for formatting the output. */
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do j=0 to x; jj=right(j, w) /*use the argument as an upper limit.*/
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say 'fibonacci('jj") =" fib(j) /*show the Fibonacci sequence: 0 ──► x */
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end /*j*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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fib: procedure expose @.; arg z; if z>=0 then return .(z)
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say "***error*** argument can't be negative."; exit
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.: procedure expose @.; arg #; if @.#\==. then return @.#; @.#=.(#-1)+.(#-2); return @.#
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@ -1,11 +0,0 @@
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/*REXX program to show anonymous recursion (of a function/subroutine). */
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numeric digits 1e6 /*in case the user goes kaa-razy.*/
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do j=0 to word(arg(1) 12, 1) /*use argument or the default: 12*/
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say 'fibonacci('j") =" fib(j) /*show Fibonacci sequence: 0──►x */
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end /*j*/
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────subroutines─────────────────────────*/
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fib: procedure; if arg(1)>=0 then return .(arg(1))
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say "***error!*** argument can't be negative."; exit
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.:procedure; arg _; if _<2 then return _; return .(_-1)+.(_-2)
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@ -0,0 +1,12 @@
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10 INPUT "Enter a number: ";n
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20 LET t=0
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30 GO SUB 60
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40 PRINT t
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50 STOP
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60 LET nold1=1: LET nold2=0
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70 IF n<0 THEN PRINT "Positive argument required!": RETURN
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80 IF n=0 THEN LET t=nold2: RETURN
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90 IF n=1 THEN LET t=nold1: RETURN
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100 LET t=nold2+nold1
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110 IF n>2 THEN LET n=n-1: LET nold2=nold1: LET nold1=t: GO SUB 100
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120 RETURN
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