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-rw-r--r--lib/ur/top.urs31
1 files changed, 31 insertions, 0 deletions
diff --git a/lib/ur/top.urs b/lib/ur/top.urs
index 50526f43..75d85fcd 100644
--- a/lib/ur/top.urs
+++ b/lib/ur/top.urs
@@ -21,21 +21,34 @@ end
val not : bool -> bool
+(* Type-level identity function *)
con id = K ==> fn t :: K => t
+
+(* Type-level function which yields the value-level record
+ described by the given type-level record *)
con record = fn t :: {Type} => $t
+
con fst = K1 ==> K2 ==> fn t :: (K1 * K2) => t.1
con snd = K1 ==> K2 ==> fn t :: (K1 * K2) => t.2
con fst3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.1
con snd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.2
con thd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.3
+(* Convert a record of n Units into a type-level record where
+ each field has the same value (which describes a uniformly
+ typed record) *)
con mapU = K ==> fn f :: K => map (fn _ :: Unit => f)
+(* Existential type former *)
con ex :: K --> (K -> Type) -> Type
+(* Introduction of existential type *)
val ex_intro : K --> tf :: (K -> Type) -> choice :: K -> tf choice -> ex tf
+
+(* Eliminator for existential type *)
val ex_elim : K --> tf ::: (K -> Type) -> ex tf -> res ::: Type -> (choice :: K -> tf choice -> res) -> res
+(* Composition of ordinary (value-level) functions *)
val compose : t1 ::: Type -> t2 ::: Type -> t3 ::: Type
-> (t2 -> t3) -> (t1 -> t2) -> (t1 -> t3)
@@ -45,37 +58,52 @@ val read_option : t ::: Type -> read t -> read (option t)
val txt : t ::: Type -> ctx ::: {Unit} -> use ::: {Type} -> show t -> t
-> xml ctx use []
+(* Given a polymorphic type (tf) and a means of constructing
+ "default" values of tf applied to arbitrary arguments,
+ constructs records consisting of those "default" values *)
val map0 : K --> tf :: (K -> Type)
-> (t :: K -> tf t)
-> r ::: {K} -> folder r -> $(map tf r)
+
+(* Given two polymorphic types (tf1 and tf2) and a means of
+ converting from tf1 t to tf2 t for arbitrary t,
+ converts records of tf1's to records of tf2's *)
val mp : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type)
-> (t ::: K -> tf1 t -> tf2 t)
-> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r)
+
+(* Two-argument conversion form of mp *)
val map2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf :: (K -> Type)
-> (t ::: K -> tf1 t -> tf2 t -> tf t)
-> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf r)
+
+(* Three-argument conversion form of mp *)
val map3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type) -> tf :: (K -> Type)
-> (t ::: K -> tf1 t -> tf2 t -> tf3 t -> tf t)
-> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> $(map tf r)
+(* Fold along a uniformly (homogenously) typed record *)
val foldUR : tf :: Type -> tr :: ({Unit} -> Type)
-> (nm :: Name -> rest :: {Unit}
-> [[nm] ~ rest] =>
tf -> tr rest -> tr ([nm] ++ rest))
-> tr [] -> r ::: {Unit} -> folder r -> $(mapU tf r) -> tr r
+(* Fold (generalized safe zip) along two equal-length uniformly-typed records *)
val foldUR2 : tf1 :: Type -> tf2 :: Type -> tr :: ({Unit} -> Type)
-> (nm :: Name -> rest :: {Unit}
-> [[nm] ~ rest] =>
tf1 -> tf2 -> tr rest -> tr ([nm] ++ rest))
-> tr [] -> r ::: {Unit} -> folder r -> $(mapU tf1 r) -> $(mapU tf2 r) -> tr r
+(* Fold along a heterogenously-typed record *)
val foldR : K --> tf :: (K -> Type) -> tr :: ({K} -> Type)
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>
tf t -> tr rest -> tr ([nm = t] ++ rest))
-> tr [] -> r ::: {K} -> folder r -> $(map tf r) -> tr r
+(* Fold (generalized safe zip) along two heterogenously-typed records *)
val foldR2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type)
-> tr :: ({K} -> Type)
-> (nm :: Name -> t :: K -> rest :: {K}
@@ -84,6 +112,7 @@ val foldR2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type)
-> tr []
-> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> tr r
+(* Fold (generalized safe zip) along three heterogenously-typed records *)
val foldR3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type)
-> tr :: ({K} -> Type)
-> (nm :: Name -> t :: K -> rest :: {K}
@@ -92,11 +121,13 @@ val foldR3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type
-> tr []
-> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> tr r
+(* Generate some XML by mapping over a uniformly-typed record *)
val mapUX : tf :: Type -> ctx :: {Unit}
-> (nm :: Name -> rest :: {Unit} -> [[nm] ~ rest] =>
tf -> xml ctx [] [])
-> r ::: {Unit} -> folder r -> $(mapU tf r) -> xml ctx [] []
+(* Generate some XML by mapping over a heterogenously-typed record *)
val mapX : K --> tf :: (K -> Type) -> ctx :: {Unit}
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>