Add curhnum

import churnNum

import churnNum

Add combinators

Add combinators

app/Main.hs

@@ -1,6 +1,7 @@
 module Main where
 
 import           Base
+import           ChurchNum
 import           Lib
 
 main :: IO ()

src/Base.hs

@@ -1,3 +1,4 @@
+{-# LANGUAGE NoImplicitPrelude #-}
 module Base (
   identity,
   constant,

src/ChurchNum.hs

@@ -0,0 +1,53 @@
+module ChurchNum (
+  zero, -- point free
+  one,  -- point free
+  two,  -- point free
+  inc,  -- point free
+  dec ,
+  add,
+  sub,
+  mul,  -- point free
+  church,
+  unchurch,-- point free
+  isZero
+) where
+
+import           Base
+import           Combinators
+
+-- zero :: p2 -> t3 -> t3
+zero = Base.flip constant
+
+-- one :: (t1 -> t2) -> t1 -> t2
+one = apply
+
+-- two :: (t -> t) -> t -> t
+-- @help: can't figure out point free version (cause s-combinator is not)
+-- two x y = x $ x y
+two = s Base.compose identity
+
+-- inc :: Num a => a -> a
+inc = (+1)
+
+-- dec :: Num a => a -> a
+-- dec x = x - 1
+dec = Base.flip (-) 1
+
+-- add :: Num a => a -> a -> a
+add = (+)
+
+-- sub :: Num a => a -> a -> a
+sub = (-)
+
+-- mult :: Num a => a -> a -> a
+mul a b = church a (+b) 0
+
+-- church :: (Eq t1, Num t1) => t1 -> (t2 -> t2) -> t2 -> t2
+church 0 = zero
+church n = \f x -> f $ church (n -1 ) f x
+
+-- unchurch :: ((Integer -> Integer) -> Integer -> t3) -> t3
+unchurch = Base.flip ($ (1 +)) 0
+
+-- isZero :: (Eq a, Num a) => a -> Bool
+isZero = (==) 0

src/Combinators.hs

@@ -0,0 +1,5 @@
+module Combinators where
+
+s f g x = f x (g x) -- S-combinator
+identity x = x -- I-combinator
+constant x y = y -- K -combinator