[Haskell-cafe] Hello and type-level SKI

[Tslil Clingman]

Greetings all,

I've been reading this list for a short while and I thought I'd like to
begin to contribute where possible. This message pretty much serves to
say:

- Hello, Haskell!
- This community is great, and it's always been a great pleasure to read
  the newsgroup(s)
- Here is a small and likely multiply re-re-discovered `proof' of why the type
  system is Turing Complete

> {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies,
>   FlexibleInstances, FlexibleContexts, UndecidableInstances #-}

> data S2 x y
> data S1 x
> data S
> data K1 x
> data K
> data I
 
> class Apply a b c | a b -> c
> instance Apply K x (K1 x)
> instance Apply S x (S1 x)
> instance Apply (S1 x) y (S2 x y)
> instance Apply I x x
> instance Apply (K1 x) y x
> instance (Apply x z xz, Apply y z yz, Apply xz yz a) => Apply (S2 x y) z a

> -- The core function
> apply :: (Apply a b c) => a -> b -> c
> apply _ _ = undefined
> -- Hereendeththelesson --

> -- For `ease of use', but not strictly necessary
> data X
> data Y
> data Z
> s = undefined :: S
> k = undefined :: K
> i = undefined :: I
> x = undefined :: X
> y = undefined :: Y
> z = undefined :: Z
> -- Example
> reverse = apply (apply s (apply k (apply s i))) k

I just thought I'd share this snippet here, but if this is not the right
place, or it's too long or something please don't hesitate to let me know.

Thanks for your attention,
Yours &c.,
Tslil
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