Question

As far as I know recursion is very elegant but unefficient in OOP and procedural programming (see the wonderful “High Order perl”, Mark Jason Dominus). I had some informations that in functional programming recursion is fast – keeping its elegance and simplicity. Could someone confirm and possibly amplify this? I am thinking in terms of XSLT and Haskell (high on my next-language-to-learn list)

Thanks

Daniel

Answer 1

Tail recursion is iteration in any decent functional language implementation. Here’s an example using GHC Haskell. A simple program to add a sequence of numbers. It begins as the composition of several recursive functions:

import qualified Data.Vector as U

main = print (U.sum (U.enumFromTo 1 (10000000 :: Int)))

Which the compiler optimizes into a single tail recursive function (in a source-to-source transformation):

loop x y = case y <= y 10000000 of
      False -> x
      True  -> loop (x + y) (y + 1)

This recursive function is then compiled into a straight forward loop:

loop:
    .Lc216:
            cmpq $10000000,%rsi
            jle .Lc219
            movq %r14,%rbx
            movq (%rbp),%rax
            jmp *(%rax)
    .Lc219:
            addq %rsi,%r14
            incq %rsi
            jmp loop

Or with the GHC LLVM backend, additional optimizations are applied to the imperative representation of the program:

    loop:
        leaq    1(%rsi), %rax
        addq    %rsi, %r14
        cmpq    $10000001, %rax
        jge     .LBB1_5
        addq    $2, %rsi
        addq    %rax, %r14
    test:                                # %tailrecurse
        cmpq    $10000001, %rsi
        jl      loop

Note how the tail recursive label is tagged.

So we had a pipeline of recursive functions, which were compiled to a single tail recursive function, which was compiled to a single imperative loop using no stack. And 8 instructions in the end.

And that is why both function composition, and recursion, are extremely efficient in good, optimizing function languages.