annotate eq.urs @ 21:e7d64ea0f922

Variant.weaken, mp, and mapR
author Adam Chlipala <adam@chlipala.net>
date Thu, 05 Jan 2012 18:04:04 -0500
parents 799f43bce62b
children
rev   line source
adam@6 1 (** A constructor equality predicate *)
adam@6 2
adam@6 3 con eq :: K --> K -> K -> Type
adam@6 4
adam@6 5 val refl : K --> t ::: K -> eq t t
adam@6 6 val sym : K --> t1 ::: K -> t2 ::: K -> eq t1 t2 -> eq t2 t1
adam@6 7 val trans : K --> t1 ::: K -> t2 ::: K -> t3 ::: K -> eq t1 t2 -> eq t2 t3 -> eq t1 t3
adam@6 8
adam@6 9 val cast : K --> t1 ::: K -> t2 ::: K -> eq t1 t2 -> f :: (K -> Type) -> f t1 -> f t2
adam@6 10
adam@6 11 val fold : K --> tf :: ({K} -> Type) -> r ::: {K}
adam@6 12 -> (pre :: {K} -> nm :: Name -> v :: K -> post :: {K} -> [pre ~ post] => [[nm] ~ pre ++ post] =>
adam@6 13 eq r (pre ++ [nm = v] ++ post) -> tf post -> tf ([nm = v] ++ post))
adam@6 14 -> tf [] -> folder r -> tf r
adam@6 15
adam@6 16 val foldUR : tr :: Type -> tf :: ({Unit} -> Type) -> r ::: {Unit}
adam@6 17 -> (pre :: {Unit} -> nm :: Name -> post :: {Unit} -> [pre ~ post] => [[nm] ~ pre ++ post] =>
adam@6 18 eq r (pre ++ [nm] ++ post) -> tr -> tf post -> tf ([nm] ++ post))
adam@6 19 -> tf [] -> folder r -> $(mapU tr r) -> tf r
adam@6 20
adam@6 21 val foldR : K --> tr :: (K -> Type) -> tf :: ({K} -> Type) -> r ::: {K}
adam@6 22 -> (pre :: {K} -> nm :: Name -> t :: K -> post :: {K} -> [pre ~ post] => [[nm] ~ pre ++ post] =>
adam@6 23 eq r (pre ++ [nm = t] ++ post) -> tr t -> tf post -> tf ([nm = t] ++ post))
adam@6 24 -> tf [] -> folder r -> $(map tr r) -> tf r
adam@6 25
adam@6 26 val foldR2 : K --> tr1 :: (K -> Type) -> tr2 :: (K -> Type) -> tf :: ({K} -> Type) -> r ::: {K}
adam@6 27 -> (pre :: {K} -> nm :: Name -> t :: K -> post :: {K} -> [pre ~ post] => [[nm] ~ pre ++ post] =>
adam@6 28 eq r (pre ++ [nm = t] ++ post) -> tr1 t -> tr2 t -> tf post -> tf ([nm = t] ++ post))
adam@6 29 -> tf [] -> folder r -> $(map tr1 r) -> $(map tr2 r) -> tf r
adam@6 30
adam@6 31 val foldR3 : K --> tr1 :: (K -> Type) -> tr2 :: (K -> Type) -> tr3 :: (K -> Type) -> tf :: ({K} -> Type) -> r ::: {K}
adam@6 32 -> (pre :: {K} -> nm :: Name -> t :: K -> post :: {K} -> [pre ~ post] => [[nm] ~ pre ++ post] =>
adam@6 33 eq r (pre ++ [nm = t] ++ post) -> tr1 t -> tr2 t -> tr3 t -> tf post -> tf ([nm = t] ++ post))
adam@6 34 -> tf [] -> folder r -> $(map tr1 r) -> $(map tr2 r) -> $(map tr3 r) -> tf r
adam@6 35
adam@6 36 val foldR4 : K --> tr1 :: (K -> Type) -> tr2 :: (K -> Type) -> tr3 :: (K -> Type) -> tr4 :: (K -> Type) -> tf :: ({K} -> Type) -> r ::: {K}
adam@6 37 -> (pre :: {K} -> nm :: Name -> t :: K -> post :: {K} -> [pre ~ post] => [[nm] ~ pre ++ post] =>
adam@6 38 eq r (pre ++ [nm = t] ++ post) -> tr1 t -> tr2 t -> tr3 t -> tr4 t -> tf post -> tf ([nm = t] ++ post))
adam@6 39 -> tf [] -> folder r -> $(map tr1 r) -> $(map tr2 r) -> $(map tr3 r) -> $(map tr4 r) -> tf r
adam@6 40
adam@6 41 val mp : K --> tr :: (K -> Type) -> tf :: (K -> Type) -> r ::: {K}
adam@6 42 -> (nm :: Name -> t :: K -> rest :: {K} -> [[nm] ~ rest] =>
adam@6 43 eq r ([nm = t] ++ rest) -> tr t -> tf t)
adam@6 44 -> folder r -> $(map tr r) -> $(map tf r)