[haskell] redoing Hlist.hs

cpp/tmp/README.org

@@ -0,0 +1 @@
+Template metaprogramming in C++

cpp/tmp/factorial.cpp

@@ -0,0 +1,46 @@
+#include<iostream>
+#include<list>
+
+template<unsigned n>
+struct factorial {
+  enum { val = n * factorial<n-1>::val };
+};
+
+template<>
+struct factorial<0> {
+  enum { val = 1 };
+};
+
+
+int main() {
+  std::cout << factorial<0>::val << std::endl;
+  std::cout << factorial<1>::val << std::endl;
+  std::cout << factorial<2>::val << std::endl;
+  std::cout << factorial<3>::val << std::endl;
+  std::cout << factorial<4>::val << std::endl;
+  std::cout << factorial<5>::val << std::endl;
+  std::cout << factorial<6>::val << std::endl;
+  std::cout << factorial<7>::val << std::endl;
+  std::cout << factorial<8>::val << std::endl;
+  std::cout << factorial<9>::val << std::endl;
+  std::cout << factorial<10>::val << std::endl;
+  std::cout << factorial<11>::val << std::endl;
+  std::cout << factorial<12>::val << std::endl;
+}
+
+// Output
+/*
+1
+1
+2
+6
+24
+120
+720
+5040
+40320
+362880
+3628800
+39916800
+479001600
+*/

haskell/Hlist-orig.hs

@@ -0,0 +1,57 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE TypeFamilies #-}
+
+
+-- -- Method 1
+-- data family Hlist (l :: [*])
+-- data instance Hlist '[] = HNil
+-- data instance Hlist (t ': ts) = HCons t (Hlist ts)
+
+-- hd :: Hlist (t ': ts) -> t  
+-- hd (HCons x _) = x
+
+-- tl :: Hlist (t ': ts) -> Hlist ts
+-- tl (HCons _ xs) = xs
+
+-- idx :: Hlist ts -> (n :: Int) -> (ts '!! n)
+
+-- -- Can't make it work
+-- -- app :: Hlist ts1 -> Hlist ts2 -> Hlist (ts1 '++ ts2)
+-- -- app HNil hls2 = hls2
+
+-- -- Can't make it work
+-- -- len :: Hlist ts -> Int
+-- -- len HNil = 0
+-- -- len (HCons _ xs) = 1 + (len xs)
+
+
+-- -- Method 2 ??
+-- data HNil = HNil
+-- data HCons a b = HCons a b 
+
+-- a = HCons 3 HNil 
+-- b = HCons 3 (HCons True HNil)
+  
+
+
+-- -- Method 3
+-- data Hlist :: [*] -> * where
+--   HNil :: Hlist '[]
+--   HCons :: t -> Hlist ts -> Hlist (t : ts)
+
+-- data Member x (l':ls) where
+--   First :: Member x (l:ls)
+--   Next :: Member x ls -> Member x (l:ls)
+
+-- data Member x (l':ls) where
+--   First :: Member x (l:ls)
+--   Next :: Member x ls -> Member x (l:ls)
+
+-- len :: Hlist ts -> Int
+-- len HNil = 0
+-- len (HCons _ xs) = 1 + (len xs)
+
+-- a = HCons 3 HNil 
+-- b = HCons 3 (HCons True HNil)

haskell/Hlist.hs

@@ -1,57 +1,58 @@
 {-# LANGUAGE DataKinds #-}
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE GADTs #-}          -- Enabled by default apparently
+{-# LANGUAGE TypeOperators #-}  -- Enabled by default apparently
 {-# LANGUAGE TypeFamilies #-}
 
-
--- -- Method 1
--- data family Hlist (l :: [*])
--- data instance Hlist '[] = HNil
--- data instance Hlist (t ': ts) = HCons t (Hlist ts)
-
--- hd :: Hlist (t ': ts) -> t  
--- hd (HCons x _) = x
-
--- tl :: Hlist (t ': ts) -> Hlist ts
--- tl (HCons _ xs) = xs
-
--- idx :: Hlist ts -> (n :: Int) -> (ts '!! n)
-
--- -- Can't make it work
--- -- app :: Hlist ts1 -> Hlist ts2 -> Hlist (ts1 '++ ts2)
--- -- app HNil hls2 = hls2
-
--- -- Can't make it work
--- -- len :: Hlist ts -> Int
--- -- len HNil = 0
--- -- len (HCons _ xs) = 1 + (len xs)
-
-
--- -- Method 2 ??
--- data HNil = HNil
--- data HCons a b = HCons a b 
-
--- a = HCons 3 HNil 
--- b = HCons 3 (HCons True HNil)
-  
-
-
--- Method 3
 data Hlist :: [*] -> * where
   HNil :: Hlist '[]
   HCons :: t -> Hlist ts -> Hlist (t : ts)
 
-data Member x (l':ls) where
-  First :: Member x (l:ls)
-  Next :: Member x ls -> Member x (l:ls)
+data Member :: a -> [*] -> * where 
+  First :: Member x (x':l)
+  Next :: Member x l -> Member x (x':l)
 
 -- data Member x (l':ls) where
 --   First :: Member x (l:ls)
 --   Next :: Member x ls -> Member x (l:ls)
 
--- len :: Hlist ts -> Int
--- len HNil = 0
--- len (HCons _ xs) = 1 + (len xs)
+hd :: Hlist (t ': ts) -> t  
+hd (HCons x _) = x
 
--- a = HCons 3 HNil 
--- b = HCons 3 (HCons True HNil)
+tl :: Hlist (t ': ts) -> Hlist ts
+tl (HCons _ xs) = xs
+
+len :: Hlist ts -> Int
+len HNil = 0
+len (HCons _ xs) = 1 + (len xs)
+
+type family (++) (l1 :: [*]) (l2 :: [*]) where
+  '[] ++ y = y
+  (x':xs) ++ y = x':(xs ++ y)
+
+cat :: Hlist ts1 -> Hlist ts2 -> Hlist (ts1 ++ ts2)  
+cat HNil y = y
+cat (HCons x xs) y = HCons x (cat xs y)
+
+
+
+
+-- Example hlists
+a = HCons 3 HNil 
+b = HCons 3 (HCons True HNil)
+-- λ> a
+-- a :: Hlist '[Integer]
+-- λ> b
+-- b :: Hlist '[Integer, Bool]
+-- λ> tl a
+--
+-- tl a :: Hlist '[]
+-- λ> tl b
+-- tl b :: Hlist '[Bool]
+-- λ> hd a
+-- 3
+-- λ> hd (tl b)
+-- True
+-- λ> hd $ tl (tl b)  -- Error
+--
+-- λ> cat b b
+-- cat b b :: Hlist '[Integer, Bool, Integer, Bool]