more work on coercions composition

[helm.git] / helm / software / matita / tests / ng_coercions.ma

diff --git a/helm/software/matita/tests/ng_coercions.ma b/helm/software/matita/tests/ng_coercions.ma
index 1a16862670a8b6fa809a8517ac38df4a657881aa..3e22b3410b426b980396440ed8673c0a8c244cca 100644 (file)
--- a/helm/software/matita/tests/ng_coercions.ma
+++ b/helm/software/matita/tests/ng_coercions.ma
@@ -12,19 +12,51 @@
 (*                                                                        *)
 (**************************************************************************)
 
-axiom A : Type.
-axiom B : Type.
-axiom C : Type.
+include "ng_pts.ma".
 
-axiom f : A → B.
-axiom g : B → C.
+(* easy *)
+naxiom T : Type.
+naxiom S : Type.
+naxiom R : Type.
+naxiom U : Type.
+naxiom c : T → S.
+naxiom c1 : S → R.
+naxiom c2 : R → U.
 
-(* nlemma xxx : ∀P:C → Prop. ∀x:A. P x. *)  
+ncoercion foo1 : ∀_t:T.S ≝ c on _t : T to S.
+ncoercion foo2 : ∀_r:R.U ≝ c2 on _r : R to U.
+ncoercion foo3 : ∀_s:S.R ≝ c1 on _s : S to R.
 
-coercion f. coercion g.
+(* another *)
 
-axiom T : Type.
+naxiom nat : Type.
+naxiom A : nat → Type. 
+naxiom B : nat → Type.
+naxiom C : nat → Type.
+naxiom D : nat → Type.
+naxiom a :  ∀n:nat. A n → B n.
+naxiom a1 : ∀n:nat. B n → C n.
+naxiom a2 : ∀n:nat. C n → D n.
 
-axiom h : A → T. coercion h. 
+ncoercion foo1 : ∀n:nat. ∀_a:A n. B n ≝ a  on _a : A ? to B ?.
+ncoercion foo2 : ∀n:nat. ∀_c:C n. D n ≝ a2 on _c : C ? to D ?.
+ncoercion foo3 : ∀n:nat. ∀_b:B n. C n ≝ a1 on _b : B ? to C ?.
 
-nlemma xxx : ∀P:C → Prop. ∀x:A. P x.  
\ No newline at end of file
+naxiom cx : ∀n,m:nat. B n → C m.
+
+ncoercion foo3 : ∀n,m:nat. ∀_b:B n. C m ≝ cx on _b : B ? to C ?.
+
+naxiom Suc : nat → nat.
+naxiom cs : ∀n:nat. B n → C (Suc n).
+
+ncoercion foo3 : ∀n:nat. ∀_b:B n. C (Suc n) ≝ cs on _b : B ? to C ?.
+
+(* funclass *)
+naxiom Y : Type.
+naxiom W : Type.
+naxiom X : Type.
+naxiom f : Y → W.
+naxiom g : W → X → X → X.
+
+ncoercion foo : ∀_y:Y. W ≝ f on _y : Y to W. 
+ncoercion foo : ∀_w:W. X → X → X ≝ g on _w : W to Π_.Π_.?.