copied Cyril's monoid_enriched_cat.v to enriched_cat.v

Author: ptorrx

tests/enriched_cat.v

@@ -1,3 +1,74 @@
 (* testing enriched categories *)
 
+From HB Require Import structures.
+From Coq Require Import ssreflect ssrfun.
+
+HB.mixin Record isQuiver Obj := { hom : Obj -> Obj -> Type }.
+
+HB.structure Definition Quiver := { Obj of isQuiver Obj }.
+
+HB.mixin Record isMon A := {
+    zero  : A;
+    add   : A -> A -> A;
+    addrA : associative add;
+    add0r : left_id zero add;
+    addr0 : right_id zero add;
+  }.
+
+HB.structure
+  Definition Monoid := { A of isMon A }.
+
+(**)
+HB.mixin Record hom_isMonT T of Quiver T :=
+    { private : forall A B, isMon (@hom T A B) }.
+
+HB.structure
+  Definition Monoid_enriched_quiverT :=
+  { Obj of isQuiver Obj & hom_isMonT Obj }.
+
+(**)
+
+
+Fail HB.structure
+  Definition Monoid_enriched_quiver :=
+    { Obj of isQuiver Obj &
+             (forall A B : Obj, isMon (@hom (Quiver.clone Obj _) A B)) }.
+
+(* Step 0: define a wrapper predicate in coq-elpi *)
+(* 5 lines of documentation + 1 line of elpi code in structure.v
+  `pred wrapper-mixin o:mixinname, o:gref, o:mixinname`
+*)
+(* Step 1: add a wrapper attribute to declare wrappers,
+    they should index:
+    - the wrapped mixin (`isMon`)
+    - the wrapper mixin (`hom_isMon`)
+    - the new subject (`hom`)
+  This attribute will add an entry in the `wrapper-mixin` database.
+  As an addition substep, we should check that the wrapper has
+  exactly one field, which is the wrapped mixin.
+  *)
+#[wrapper]
+HB.mixin Record hom_isMon T of Quiver T :=
+    { private : forall A B, isMon (@hom T A B) }.
+    
+(* Step 2: at structure declaration, export the main and only projection
+   of each declared wrapper as an instance of the wrapped structure on
+   its subject *)
+HB.structure
+  Definition Monoid_enriched_quiver :=
+    { Obj of isQuiver Obj & hom_isMon Obj }.
+
+HB.instance Definition _ (T : Monoid_enriched_quiver.type) (A B : T) :
+  isMon (@hom T A B) := @private T A B.
+
+  (* each instance of isMon should be tried as an instance of hom_isMon *)
+
+(* Step 3: for each instance of a wrapped mixin on a subject known 
+  to be wrapped, automatically produce an instance of the wrapper mixin too. *)
+HB.instance Definition _ := isQuiver.Build Type (fun A B => A -> B).
+Fail HB.instance Definition homTypeMon (A B : Quiver.type) := isMon.Build (hom A B) (* ... *).
+(* This last command should create a `Monoid_enriched_quiver`, in order to do so it should
+  automatically instanciate the wrapper `hom_isMon`:
+  HB.instance Definition _ := hom_isMon.Build Type homTypeMon.
+ *)