test for step 0 of CoREACT

Author: gares

_CoqProject.test-suite

@@ -80,6 +80,7 @@ tests/hnf.v
 tests/fun_instance.v
 tests/issue284.v
 tests/issue287.v
+tests/monoid_law_structure.v
 
 -R tests HB.tests
 -R examples HB.examples

tests/monoid_law_structure.v

@@ -0,0 +1,18 @@
+From HB Require Import structures.
+
+HB.mixin Record isMonLaw T (e : T) (op : T -> T -> T) := {
+  opmA : forall a b c, op (op a b) c = op a (op b c);
+  op1m : forall x, op e x = x;
+  opm1 : forall x, op x e = x;
+}.
+
+HB.structure Definition MonLaw T e := { op of isMonLaw T e op }.
+
+HB.mixin Record isPreMonoid T := {
+  zero : T;
+  add : T -> T -> T;
+}.
+HB.structure Definition PreMonoid := { T of isPreMonoid T }.
+
+HB.structure Definition Monoid :=
+  { T of isPreMonoid T & isMonLaw T zero add }.