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Re: curried fns
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Date: 1995-11-21 (10:52)
From: Pierre Weis <Pierre.Weis@i...>
Subject: Re: curried fns

> Something I sometimes wonder about is which of the following is more
> efficient. Perhaps a CAML Light expert can comment.
>   let map f =
>     let rec mapf l =
>       match l with
>         [] -> []
>       | (x::t) -> let y = f x in y::(mapf t) in
>     mapf;;
> or
>   let rec map f l =
>     match l with
>       [] -> []
>     | (x::t) -> let y = f x in y::(map f t);;

The answer is clearly: this is compiler dependent!

The first definition is a strange view of map as a (non-recursive)
function that compute a looping function. The second definition is
more natural and properly exposes that map gets two arguments. If there
are no efficiency reasons to prefer the first form I definitively
prefer the second ``natural'' definition.

The problem is more generally ``how to define functions with 2
arguments'': there is no syntactic way to define functions with
multiple arguments in Caml. Thus the user has to encode it, either via
curryfication or via tuples (let f x y = ... or let f (x,y) = ...).
Naive compilation of these two encodings is not efficient, let's
explain why.

Suppose f defined as

   let f x y = body
or equivalently
   let f = function x -> function y -> body.

As is explicit on this expanded form, f can be partially applied: if
e1 evaluates to v1, then the expression f e1 evaluates to a closure
with code part (function y -> body) and environment part (x, v1).
Thus the naive compilation of ``f e1 e2'' (or equivalently (f e1) e2)
starts by calling f with argument v1, then f builds and returns the
intermediate closure, and this closure is then  applied to (the value
of) e2. This is inefficient, since we perform 2 function calls and
vaste memory to build this intermediate closure which is immediately
applied and becomes garbage.

Now suppose f be defined as

  let f (x, y) = body

the naive evaluation of f (e1, e2) is now:
1) evaluate e1 and e2 leading to v1 and v2
2) build the tuple (e1, e2)
3) call f with this tuple.

Here we perform only one function call, but once again we build an
intermediate data structure to call the function, and this data
structure becomes garbage as soon as entering the function.

A clever way of compiling one of this two forms is necessary since
functions with multiple arguments are mandatory and heavily used. This
is a bit difficult but the idea is mainly the following:
 - for curried functions directly call their body when they are
applied with all their arguments (complete applications).
 - for functions with tuples directly call their body without
constructing the tuple (these functions are always completely applied).

Since curried functions are a bit more powerful, since they can be
partially applied, we may suppose that users will adopt this way of
encoding multiple arguments. Thus, generally speaking Caml compilers
optimize the curried form of encoding. These optimizations are not
always as efficient as the scheme described above, but compilation of
currification is definitively better than tupling for Caml Light,
Caml Special Light, Bigloo and Camlot. Caml compilers generally do not
optimize tupling.

We may now discuss the efficiency of your example.
The naive form:
   let rec map f l =
     match l with
       [] -> []
     | (x::t) -> let y = f x in y::(map f t);;
exposes that map has two arguments. Thus a compiler that optimizes
complete application of curried functions will efficiently compile the
recursive call. On the other hand a naive compiler will build the
partial intermediate closure for each recursive call.

On the other hand, with the first encoding:
   let map f =
     let rec mapf l =
       match l with
         [] -> []
       | (x::t) -> let y = f x in y::(mapf t) in
the optimizing compiler may fail to recognize that map may be
optimized as a curried functions with two arguments: it will instead
compute a closure for mapf, and generally speaking a closure is less
efficiently applied.
An interesting case: the Bigloo compiler performs a so-called
$\eta$-optimization that automatically rewrite this code to (an
equivalent of) the first natural one!

The naive compiler will compile naively as usual, but now your code
effectively require to compute the intermediate closure only once,
when partially applying map to f. Hence recursive calls to mapf will
save this extra closure construction, and the second form will be a
bit more efficient.

In conclusion: prefer the natural encoding, it is clearer and
compilers are designed to optimize natural code.

Pierre Weis
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