54 lines
1.5 KiB
Plaintext
54 lines
1.5 KiB
Plaintext
module Case3
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data Nat : U where
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Z : Nat
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S : Nat -> Nat
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data Vect : Nat -> U -> U where
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Nil : {a : U} -> Vect Z a
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_::_ : {a : U} -> {k : Nat} -> a -> Vect k a -> Vect (S k) a
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infixr 5 _::_
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head : {a : U} {k : Nat} -> Vect (S k) a -> a
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head (x :: xs) = x
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-- These came from a Conor McBride lecture where they use SHE
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vapp : {s t: U} {k : Nat} -> Vect k (s -> t) -> Vect k s -> Vect k t
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vapp (f :: fs) (t :: ts) = f t :: vapp fs ts
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vapp Nil Nil = Nil
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vec : { a : U } -> (n : Nat) -> a -> Vect n a
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vec Z x = Nil
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vec (S k) x = x :: vec k x
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-- And then typeclass, which I don't have yet. I'll add a few underlying functions
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fmap : {a b : U} {n : Nat} -> (a -> b) -> Vect n a -> Vect n b
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fmap f Nil = Nil
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fmap f (x :: xs) = (f x :: fmap f xs)
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pure : {a : U} {n : Nat} -> a -> Vect n a
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pure {a} {n} = vec n
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_<*>_ : {s t: U} {k : Nat} -> Vect k (s -> t) -> Vect k s -> Vect k t
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_<*>_ = vapp
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-- and idiom brackets (maybe someday)
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-- I'll add foldl
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foldl : {acc el : U} {n : Nat} -> (acc -> el -> acc) -> acc -> Vect n el -> acc
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foldl f acc Nil = acc
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foldl f acc (x :: xs) = foldl f (f acc x) xs
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zipWith : {a b c : U} {m : Nat} -> (a -> b -> c) -> Vect m a -> Vect m b -> Vect m c
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zipWith f Nil Nil = Nil
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zipWith f (x :: xs) (y :: ys) = f x y :: zipWith f xs ys
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transpose : {a : U} {m n : Nat} -> Vect m (Vect n a) -> Vect n (Vect m a)
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-- TODO Doesn't work without the (forced) Z, investigate
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transpose {a} {Z} {n} Nil = vec n Nil
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transpose {a} {S k} {n} (x :: xs) = zipWith (_::_) x (transpose xs)
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