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wreczek/ChurchNumerals.hs

Created January 26, 2018 13:37
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ChurchNumerals.hs
{-# LANGUAGE RankNTypes #-}
module ChurchNumerals
( church, unchurch, zero, one, two, three, four,
five, six, seven, eight, nine, ten
) where
-- we define natural numbers of Church
type Church a = (a -> a) -> a -> a
-- converting functions
church:: Integer -> Church Integer
church 0 = \f x -> x
church n = \f x -> f(church(n-1) f x)
unchurch:: Church Integer -> Integer
unchurch cn = cn(+1) 0
--
zero :: Church x
zero= \f x -> x
one :: Church x
one= \f x -> f $ x
two :: Church x
two= \f x -> f . f $ x
three :: Church x
three= \f x-> f.f.f$x
four :: Church x
four= \f x-> f.f.f.f$x
five :: Church x
five= \f x -> f.f.f.f.f$x
six :: Church x
six= \f x-> f.f.f.f.f.f$x
seven :: Church x
seven= \f x-> f.f.f.f.f.f.f$x
eight :: Church x
eight= \f x-> f.f.f.f.f.f.f.f$x
nine :: Church x
nine= \f x-> f.f.f.f.f.f.f.f.f$x
ten :: Church x
ten= \f x->f.f.f.f.f.f.f.f.f.f$x
--kazdy nastepny liczebnik Churcha dodatkowo mozemy
-- utworzyc poprzez operacje arytmetyczne z modulu Calculation
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