Make everything relevant.

Too few proofs were relevant. Now they are.

1 files changed, 43 insertions, 0 deletions

diff --git a/src/Inky/Data/SnocList.idr b/src/Inky/Data/SnocList.idr
new file mode 100644
index 0000000..494e8cc
--- /dev/null
+++ b/src/Inky/Data/SnocList.idr
@@ -0,0 +1,43 @@
+module Inky.Data.SnocList
+
+import public Data.SnocList
+import public Data.SnocList.Operations
+
+import Inky.Decidable.Maybe
+
+public export
+data LengthOf : SnocList a -> Type where
+  Z : LengthOf [<]
+  S : LengthOf sx -> LengthOf (sx :< x)
+
+%name LengthOf len
+
+public export
+lengthOfAppend : LengthOf sx -> LengthOf sy -> LengthOf (sx ++ sy)
+lengthOfAppend len1 Z = len1
+lengthOfAppend len1 (S len2) = S (lengthOfAppend len1 len2)
+
+public export
+lengthOf : (sx : SnocList a) -> LengthOf sx
+lengthOf [<] = Z
+lengthOf (sx :< x) = S (lengthOf sx)
+
+export
+lengthUnique : (len1, len2 : LengthOf sx) -> len1 = len2
+lengthUnique Z Z = Refl
+lengthUnique (S len1) (S len2) = cong S $ lengthUnique len1 len2
+
+export
+isSnoc : (sx : SnocList a) -> Proof (SnocList a, a) (\syy => sx = fst syy :< snd syy) (sx = [<])
+isSnoc [<] = Nothing `Because` Refl
+isSnoc (sx :< x) = Just (sx, x) `Because` Refl
+
+public export
+replicate : Nat -> a -> SnocList a
+replicate 0 x = [<]
+replicate (S n) x = replicate n x :< x
+
+public export
+lengthOfReplicate : (n : Nat) -> (0 x : a) -> LengthOf (replicate n x)
+lengthOfReplicate 0 x = Z
+lengthOfReplicate (S k) x = S (lengthOfReplicate k x)