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RE: [Caml-list] really HO Functions
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 Date: 2004-09-30 (17:30) From: Harrison, John R Subject: RE: [Caml-list] really HO Functions
```| I've just had a look through some real programs that I've written and
the
| answer is definitely yes. I use them quite a lot. For >2 they are
mainly 3,
| sometimes 4 and I haven't seen any >4.

I haven't actually checked, but I suspect I'd find something similar.
There may
be an interesting psychological observation to be made here: most people
find
very high-order functions intellectually unmanageable.

Something similar is usually acknowledged in logic with respect to long
quantifier alternations (for all x there exists a y such that for all z,
...).
I believe I once saw a provocative claim by Kreisel that most
mathematical
concepts are in fact only invented in order to hide complicated
quantifier
alternations.

John.

-----Original Message-----
From: owner-caml-list@pauillac.inria.fr
[mailto:owner-caml-list@pauillac.inria.fr] On Behalf Of Jon Harrop
Sent: Wednesday, September 29, 2004 3:31 PM
To: caml-list
Subject: Re: [Caml-list] really HO Functions

On Wednesday 29 September 2004 19:48, Radu Grigore wrote:
> My question is: are there functions of level >= 2 used in practice
> (e.g. (('a -> 'b -> 'a) -> 'a -> 'b list -> 'a) -> 'c)?

I've just had a look through some real programs that I've written and
the
answer is definitely yes. I use them quite a lot. For >2 they are mainly
3,
sometimes 4 and I haven't seen any >4.

> If so, are
> there any typical ones that appear in many applications (maybe not as
> widespread like map & company but at least of comparable usefulness)?

I seem to use them when I write generic functions which are later
specialised.

> One example of a level 2 function (stolen from a recent post by Jon
> Harrop) is this:
>   let sum fold = fold (+);;

Funny to think that this function is still state-of-the-art Java and
C++. ;-)

Cheers,
Jon.

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