[Caml-list] fixpoint

[Caml-list] fixpoint

[John Max Skaller]

Excuse dumb question about lambda calculus.
I'm using a typed lambda calculus for a kinding system
(the types are TYPE, TYPE->TYPE etc).
I'm uncertain how to handle recursion though.
Example:

    list a = 1 + a * list a

or

    list = fix f . fun a. 1 + a * f a

now we need:

    list int = 1 + int * list int

or

    list int = fix x . 1 + int * x

which suggests the following reduction:

    fix f . fun x . e ==> fix z . e [f x -> z]

Well, the rule works in this case. Will it always work?

-- 
John Max Skaller, mailto:skaller@ozemail.com.au
snail:10/1 Toxteth Rd, Glebe, NSW 2037, Australia.
voice:61-2-9660-0850



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Re: [Caml-list] fixpoint

[John Max Skaller]

John Max Skaller wrote:

Woops:

> which suggests the following reduction:
>
>    fix f . fun x . e ==> fix z . e [f x -> z]
>
> Well, the rule works in this case. Will it always work?
>
I meant:

    fix f. fun x . e ==> fun x. fix z . e [f x -> z] (* z not occuring 
in e *)

ie. the fix and fun binders swap around with the substitution.
I should also have noted that obviously this only works if it is
done at the right time, eg in

    fix g. (fun x (fun f ( f x) g) x)

the inner redex must be reduced first.

-- 
John Max Skaller, mailto:skaller@ozemail.com.au
snail:10/1 Toxteth Rd, Glebe, NSW 2037, Australia.
voice:61-2-9660-0850




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To unsubscribe, mail caml-list-request@inria.fr Archives: http://caml.inria.fr
Bug reports: http://caml.inria.fr/bin/caml-bugs FAQ: http://caml.inria.fr/FAQ/
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