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[Haskell-cafe] Naive booleans and numbers - type-checking fails

Subject: [Haskell-cafe] Naive booleans and numbers - type-checking fails
From: Dušan Kolář
Date: Sun, 24 Jan 2010 20:01:09 +0100
Dear cafe,

I'm trying to prepare a naive definition of booleans, numbers and some helper functions such a way, so that definition in lambda-calculus can be used in a straightforward way in Haskell. I was caught in trouble quite soon during change of lambda-expressions to Haskell - defining prefn as a helper for prev. When using Haskell-ish if-then-else then there is no problem (the code commented out), while using defined if-then-else (mif), the type-checking fails, but just for this case! Other simple tests are OK for the mif. Do I need some extra option for type-checker, or is it a principal failure (infinite type is reported) - I'm running ghci 6.10.4.
> mtrue  x y = x
> mfalse x y = y

> m0 f n = n
> m1 f n = f n
> m2 f n = f (f n)

> msucc x g m = x g (g m)
> iszero m = m (\_ -> mfalse) mtrue

> mif c t f = c t f
> mpair f s = \e -> e f s
> mfst p = p mtrue
> msnd p = p mfalse

> -- mprefn f p = if mex True False then mth else mel
> mprefn f p = mif mex mth mel
>   where
>     mex = mfst p
>     mth = mpair mfalse (msnd p)
>     mel = mpair mfalse (f (msnd p))


Please, change of definitions is not a solution, I'm trying to follow available resources, so using something else is not an option. :-(
Thanks for any help

  Dusan

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