From e2334196ba49e5db3f90545d97cea2c9b5652adf Mon Sep 17 00:00:00 2001
From: Vasiliy Vanchuk <v.vanchuk@tut.by>
Date: Wed, 2 May 2018 10:28:20 +0400
Subject: [PATCH 1/5] Add Base.hs

---
 app/Main.hs |  3 ++-
 src/Base.hs | 25 +++++++++++++++++++++++++
 2 files changed, 27 insertions(+), 1 deletion(-)
 create mode 100644 src/Base.hs

diff --git a/app/Main.hs b/app/Main.hs
index de1c1ab..a2e2765 100644
--- a/app/Main.hs
+++ b/app/Main.hs
@@ -1,6 +1,7 @@
 module Main where
 
-import Lib
+import           Base
+import           Lib
 
 main :: IO ()
 main = someFunc
diff --git a/src/Base.hs b/src/Base.hs
new file mode 100644
index 0000000..30a1cd0
--- /dev/null
+++ b/src/Base.hs
@@ -0,0 +1,25 @@
+module Base (
+  identity,
+  constant,
+  apply,
+  compose,
+  flip
+) where
+
+-- | Identity function.
+-- id :: a -> a
+-- identity = \x -> x
+identity x = x
+
+-- | Constant function.
+-- const :: a -> b -> a
+constant = \x y -> x
+
+-- apply :: (t1 -> t2) -> t1 -> t2
+apply = \f x -> f x
+
+-- compose :: (t1 -> t2) -> (t3 -> t1) -> t3 -> t2
+compose = \x y z -> x ( y (z))
+
+-- flip :: (a -> b -> c) -> b -> a -> c
+flip = \f x y -> f y x

From 1cc58057089640664dbaf46dfc46bcdd4c87ad2c Mon Sep 17 00:00:00 2001
From: Vasiliy Vanchuk <v.vanchuk@tut.by>
Date: Wed, 2 May 2018 11:40:06 +0400
Subject: [PATCH 2/5] Rewrite some functions

---
 src/Base.hs | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/src/Base.hs b/src/Base.hs
index 30a1cd0..a64fc92 100644
--- a/src/Base.hs
+++ b/src/Base.hs
@@ -13,13 +13,17 @@ identity x = x
 
 -- | Constant function.
 -- const :: a -> b -> a
-constant = \x y -> x
+-- constant = \x y -> x
+constant x y = x
 
 -- apply :: (t1 -> t2) -> t1 -> t2
-apply = \f x -> f x
+-- apply = \f x -> f x
+apply f x = f x
 
 -- compose :: (t1 -> t2) -> (t3 -> t1) -> t3 -> t2
-compose = \x y z -> x ( y (z))
+-- compose = \x y z -> x ( y (z))
+compose x y z = x ( y ( z ) )
 
 -- flip :: (a -> b -> c) -> b -> a -> c
-flip = \f x y -> f y x
+-- flip = \f x y -> f y x
+flip f x y = f y x

From 53d8eca9822e98ed2253189d3859f31a85cb91dd Mon Sep 17 00:00:00 2001
From: Vasiliy Vanchuk <v.vanchuk@tut.by>
Date: Tue, 8 May 2018 14:15:16 +0400
Subject: [PATCH 3/5] Add curhnum

import churnNum

import churnNum

Add combinators

Add combinators
---
 app/Main.hs        |  1 +
 src/Base.hs        |  1 +
 src/ChurchNum.hs   | 53 ++++++++++++++++++++++++++++++++++++++++++++++
 src/Combinators.hs |  5 +++++
 4 files changed, 60 insertions(+)
 create mode 100644 src/ChurchNum.hs
 create mode 100644 src/Combinators.hs

diff --git a/app/Main.hs b/app/Main.hs
index a2e2765..7338a82 100644
--- a/app/Main.hs
+++ b/app/Main.hs
@@ -1,6 +1,7 @@
 module Main where
 
 import           Base
+import           ChurchNum
 import           Lib
 
 main :: IO ()
diff --git a/src/Base.hs b/src/Base.hs
index a64fc92..4f0bbc5 100644
--- a/src/Base.hs
+++ b/src/Base.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE NoImplicitPrelude #-}
 module Base (
   identity,
   constant,
diff --git a/src/ChurchNum.hs b/src/ChurchNum.hs
new file mode 100644
index 0000000..ee980f0
--- /dev/null
+++ b/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
diff --git a/src/Combinators.hs b/src/Combinators.hs
new file mode 100644
index 0000000..88490ff
--- /dev/null
+++ b/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

From 0eac1bdd431fdf7fe571d1d0144ea402a834047c Mon Sep 17 00:00:00 2001
From: Vasiliy Vanchuk <v.vanchuk@tut.by>
Date: Tue, 8 May 2018 15:37:42 +0400
Subject: [PATCH 4/5] Add ChurchBool

---
 app/Main.hs       |  1 +
 src/ChurchBool.hs | 31 +++++++++++++++++++++++++++++++
 src/ChurchNum.hs  |  4 ++--
 3 files changed, 34 insertions(+), 2 deletions(-)
 create mode 100644 src/ChurchBool.hs

diff --git a/app/Main.hs b/app/Main.hs
index 7338a82..7aa6020 100644
--- a/app/Main.hs
+++ b/app/Main.hs
@@ -1,6 +1,7 @@
 module Main where
 
 import           Base
+import           ChurchBool
 import           ChurchNum
 import           Lib
 
diff --git a/src/ChurchBool.hs b/src/ChurchBool.hs
new file mode 100644
index 0000000..2a7409e
--- /dev/null
+++ b/src/ChurchBool.hs
@@ -0,0 +1,31 @@
+module ChurchBool  where
+import           Base
+import           ChurchNum
+
+-- true :: p1 -> p2 -> p1
+true a b = a
+
+-- false :: p1 -> p2 -> p2
+false a b = b
+
+-- cond :: (t1 -> t2 -> t3) -> t1 -> t2 -> t3
+-- cond = identity
+cond a b c = a b c
+
+-- ((p2 -> p1 -> p3 -> p3) -> (p4 -> p5 -> p4) -> t) -> t
+isZero n = n (Base.constant false) true
+
+-- toNum :: (((t1 -> t2) -> t1 -> t2) -> (p2 -> t3 -> t3) -> t) -> t
+toChurchNum x  = x one zero
+-- unchurch $ toChurchNum $ ChurchBool.isZero zero
+
+-- (t1 -> (p1 -> p2 -> p2) -> t2)
+  -- -> ((p3 -> p4 -> p3) -> (p5 -> p6 -> p6) -> t1) -> t2
+and' a b = cond a (cond b true false) false
+
+-- ((p1 -> p2 -> p1) -> t1 -> t2)
+-- -> ((p3 -> p4 -> p3) -> (p5 -> p6 -> p6) -> t1) -> t2
+or' a b = cond a true (cond b true false)
+
+-- not' :: ((p1 -> p2 -> p2) -> (p3 -> p4 -> p3) -> t) -> t
+not' a = cond a false true
diff --git a/src/ChurchNum.hs b/src/ChurchNum.hs
index ee980f0..5e3bd62 100644
--- a/src/ChurchNum.hs
+++ b/src/ChurchNum.hs
@@ -16,7 +16,7 @@ import           Base
 import           Combinators
 
 -- zero :: p2 -> t3 -> t3
-zero = Base.flip constant
+zero = Base.flip Base.constant
 
 -- one :: (t1 -> t2) -> t1 -> t2
 one = apply
@@ -24,7 +24,7 @@ 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
+two = s Base.compose Base.identity
 
 -- inc :: Num a => a -> a
 inc = (+1)

From 21a905d988f7d6f17e758b895916811af95d77b3 Mon Sep 17 00:00:00 2001
From: Vasiliy Vanchuk <v.vanchuk@tut.by>
Date: Tue, 8 May 2018 16:24:17 +0400
Subject: [PATCH 5/5] Add tuples

---
 app/Main.hs  |  1 +
 src/Tuple.hs | 24 ++++++++++++++++++++++++
 2 files changed, 25 insertions(+)
 create mode 100644 src/Tuple.hs

diff --git a/app/Main.hs b/app/Main.hs
index 7aa6020..1623b4b 100644
--- a/app/Main.hs
+++ b/app/Main.hs
@@ -4,6 +4,7 @@ import           Base
 import           ChurchBool
 import           ChurchNum
 import           Lib
+import           Tuple
 
 main :: IO ()
 main = someFunc
diff --git a/src/Tuple.hs b/src/Tuple.hs
new file mode 100644
index 0000000..af2a810
--- /dev/null
+++ b/src/Tuple.hs
@@ -0,0 +1,24 @@
+module Tuple where
+
+import           Base
+
+constant' = Base.constant
+flip' = Base.flip
+
+-- tuple' :: t1 -> t2 -> (t1 -> t2 -> t3) -> t3
+tuple' a b f = f a b
+
+-- first' :: ((p1 -> p2 -> p1) -> b) -> b
+first' = ($ constant')
+
+-- second' :: ((p2 -> t3 -> t3) -> t) -> t
+second' t = t $ flip' constant'
+
+-- swap' :: ((p2 -> p2 -> p2) -> t1) -> (t1 -> t1 -> t2) -> t2
+swap' t = tuple' (second' t) (first' t)
+
+-- curry' :: (((t1 -> t2 -> t3) -> t3) -> t4) -> t1 -> t2 -> t4
+curry' f = f $ tuple'
+
+-- t1 -> (t1 -> t2) -> t2
+uncurry' f t = t f