An idea to implement manifest record fields:

record r : R := { c1 : T1 ; c2 : T2 with f c1 = g c2 }.

Only the syntactic sugar is actually missing!

diff --git a/helm/software/matita/tests/multiple_inheritance.ma b/helm/software/matita/tests/multiple_inheritance.ma
new file mode 100644 (file)
index 0000000..614f57c
--- /dev/null
+++ b/helm/software/matita/tests/multiple_inheritance.ma
@@ -0,0 +1,54 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/test/".
+
+include "logic/equality.ma".
+
+record R1 : Type := { C:> Type; plus: C \to C \to C}.
+record R2 : Type := { K:> Type; mult: K \to K \to K}.
+
+(* Missing syntactic sugar:
+   record R : Type := { r1 :> R1; r2 :> R2 with C r1 = K r2}
+*)
+record R : Type := { r1 :> R1; r2_ : R2; with_: C r1 = K r2_ }.
+
+(* This can be done automatically *)
+lemma r2 : R → R2.
+ intro;
+ apply mk_R2;
+ [ apply (C r)
+ | apply (eq_rect ? ? (λx.x → x → x));
+   [3: symmetry;
+       [2: apply (with_ r)
+       | skip
+       ]
+   | skip
+   | apply (mult (r2_ r))
+   ]
+ ].
+qed.
+coercion cic:/matita/test/r2.con.
+
+(* Let's play with it *)
+definition f ≝ λr:R.λx:r.plus ? (mult ? x x) x.
+
+axiom plus_idempotent: ∀r1:R1.∀x:r1. plus ? x x = x.
+axiom mult_idempotent: ∀r2:R2.∀x:r2. mult ? x x = x.
+
+lemma test: ∀r:R. ∀x:r. f ? x = x.
+ intros;
+ unfold f;
+ auto paramodulation.
+qed.
\ No newline at end of file