add permutations

src/Data/Vec.hs

@@ -179,6 +179,20 @@ transpose (xs :- xss) = gcastWith proof (zipWith (:-) xs (transpose xss))
   where proof = min_self (sLength xs)
 
 
+-- | The 'permutations' function returns the vector of all permutations of the argument.
+--
+-- > permutations "abc" ≡ ["abc","bac","cba","bca","cab","acb"]
+permutations ∷ Vec a n → Vec (Vec a n) (Fact n)
+permutations Nil       = Nil:-Nil
+permutations (x:-Nil)  = (x:-Nil):-Nil
+permutations xs@(_:-_) = concatMap (\(y,ys) → map (y:-) (permutations ys)) (select xs)
+  where
+    select ∷ Vec a n → Vec (a, Vec a (Pred n)) n
+    select Nil            = Nil
+    select (x:-Nil)       = (x, Nil) :- Nil
+    select (x:-xs@(_:-_)) = (x,xs) :- map (\(y,ys) → (y, x:-ys)) (select xs)
+
+
 -- | '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.