add transpose

default.nix

@@ -4,12 +4,13 @@ let
 
   inherit (nixpkgs) pkgs;
 
-  f = { mkDerivation, base, singletons, stdenv }:
+  f = { mkDerivation, base, integer-gmp, singletons, stdenv }:
       mkDerivation {
         pname = "Interlude";
         version = "0.1.0.0";
         src = ./.;
-        libraryHaskellDepends = [ base singletons ];
+        libraryHaskellDepends = [ base integer-gmp singletons ];
+        description = "My take on Prelude";
         license = stdenv.lib.licenses.gpl3;
       };
 

src/Data/Vec.hs

@@ -168,6 +168,16 @@ intercalate ∷ Vec a n → Vec (Vec a n) m → Vec a ((m :+ Pred m) :× n)
 intercalate xs xss = concat (intersperse xs xss)
 
 
+-- | The 'transpose' function transposes the rows and columns of its argument.
+-- For example,
+--
+-- > transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]]
+--
+transpose ∷ SingI n ⇒ Vec (Vec a n) m → Vec (Vec a m) n
+transpose Nil = replicate Nil
+transpose (xs :- xss) = zipWith (:-) xs (transpose xss)
+
+
 -- | 'foldl' applied to a binary operator, a starting value
 -- and a 'Vec' reduces the vector to a single value obtained
 -- by sequentially applying the operation from the left to the right.
@@ -214,11 +224,16 @@ concatMap ∷ (a → Vec b n) → Vec a m → Vec b (m :× n)
 concatMap f = concat ∘ map f
 
 
--- | Applied to a singleton natural @n@ and a value produces
+-- | Applied to a a value produces a vector obtained by
--- a vector obtained by duplicating the value @n@ times
+-- duplicating the value @n@ times.
-replicate ∷ Sℕ n → a → Vec a n
+replicate ∷ ∀ a n. SingI n ⇒ a → Vec a n
-replicate SZ     _ = Nil
+replicate = replicate' (sing ∷ Sℕ n)
-replicate (SS n) a = a :- replicate n a
+
+
+-- | 'replicate' variant with an explicit length argument.
+replicate' ∷ Sℕ n → a → Vec a n
+replicate' SZ     _ = Nil
+replicate' (SS n) a = a :- replicate' n a
 
 
 -- | 'and' returns the conjunction of a container of bools.
@@ -233,14 +248,14 @@ or = foldr₁ (∨)
 
 -- | Determines whether any element of the structure satisfies the predicate.
 any ∷ (a → 𝔹) → Vec a n → 𝔹
-any _ Nil = T
+any _ Nil       = F
-any p xs  = or (map p xs)
+any p (x :- xs) = or (map p (x :- xs))
 
 
 -- | Determines whether all elements of the structure satisfy the predicate.
 all ∷ (a → 𝔹) → Vec a n → 𝔹
-all _ Nil = T
+all _ Nil       = T
-all p xs  = and (map p xs)
+all p (x :- xs) = and (map p (x :- xs))
 
 
 -- | The 'sum' function computes the sum of the numbers of a vector.
@@ -266,4 +281,3 @@ drop ∷ Sℕ n → Vec a m → Vec a (m :- n)
 drop SZ     x         = x
 drop (SS n) (x :- xs) = drop n xs
 
-