Bug fixed: the debrujinate function (hence the one to compute objects height)

[helm.git] / helm / software / components / ng_refiner / esempio.ma

diff --git a/helm/software/components/ng_refiner/esempio.ma b/helm/software/components/ng_refiner/esempio.ma
index 613448a61a1a59b18cde474687b6973c44a4395f..8f9604a8524817acdbc1489a7613b43239981310 100644 (file)
--- a/helm/software/components/ng_refiner/esempio.ma
+++ b/helm/software/components/ng_refiner/esempio.ma
@@ -15,15 +15,53 @@
 include "nat/plus.ma".
 
 definition hole : ∀A:Type.A → A ≝ λA.λx.x.
+definition id : ∀A:Type.A → A ≝ λA.λx.x.
 
+(* Common case in dama, reduction with metas
+inductive list : Type := nil : list | cons : nat -> list -> list.
+let rec len l := match l with [ nil => O | cons _ l => S (len l) ].
+axiom lt : nat -> nat -> Prop.
+axiom foo : ∀x. Not (lt (hole ? x) (hole ? O)) = (lt x (len nil) -> False).
+*) 
+
+(* meta1 Vs meta2 with different contexts
 axiom foo: 
   ∀P:Type.∀f:P→P→Prop.∀x:P.
    (λw. ((∀e:P.f x (w x)) = (∀y:P. f x (hole ? y)))) 
-   (λw:P.hole ? w). (* OK *)
-   
+   (λw:P.hole ? w). 
+*)
+
+(* meta1 Vs meta1 with different local contexts
 axiom foo: 
   ∀P:Type.∀f:P→P→P.∀x,y:P. 
-    (λw.(f x (w x) = f x (w y))) (λw:P.hole ? w). (* OK, restringe Rel1 *)
+    (λw.(f x (w x) = f x (w y))) (λw:P.hole ? w).
+*)
+
+(* meta Vs term && term Vs meta with different local ctx
+axiom foo: 
+  ∀P:Type.∀f:P→P→P.∀x,y:P.
+    (λw.(f (w x) (hole ? x) = f x (w y))) (λw:P.hole ? w).
+*)
+
+(* occur check
+axiom foo: 
+  ∀P:Type.∀f:P→P→P.∀x,y:P.
+    (λw.(f x (f (w x) x) = f x (w y))) (λw:P.hole ? w).
+*)
+
+(* unifying the type of (y ?) with (Q x) we instantiate ? to x
+axiom foo: 
+  ∀P:Type.∀Q:P→Type.∀f:∀x:P.Q x→P→P.∀x:P.∀y:∀x.Q x.
+    (λw.(f w (y w) x = (id ? f) x (hole ? (y x)) x)) (hole ? x).
+*)  
+   
+alias num (instance 0) = "natural number".
+axiom foo: (100+111) = (100+110). 
+
+
+    (id ?(id ?(id ?(id ? (100+100))))) =
+    (id ?(id ?(id ?(id ? (99+100))))).[3:
+    apply (refl_eq nat (id ?(id ?(id ?(id ? (98+102+?))))));
 
 axiom foo: (λx,y.(λz. z (x+y) + z x) (λw:nat.hole ? w)) = λx,y.x. (* OK *)
 axiom foo: (λx,y.(λz. z x + z (x+y)) (λw:nat.hole ? w)) = λx,y.x. (* KO, delift rels only *)