(*---------------------*) ⊢
T1 ≡ T2
+The order of premises is relevant, since they are processed in order
+(left to right).
+
*)
-notation > "≔ (list0 ( ident x : T ) sep ,) opt (; (list1 (ident U ≟ term 90 V ) sep ,)) ⊢ term 19 Px ≡ term 19 Py"
+(* it seems unbelivable, but it works! *)
+notation > "≔ (list0 ( (list1 (ident x) sep , ) opt (: T) ) sep ,) opt (; (list1 (ident U ≟ term 19 V ) sep ,)) ⊢ term 19 Px ≡ term 19 Py"
with precedence 90
for @{ ${ fold right
@{ ${ default
@{ 'hint_decl $Px $Py }
}
}
- rec acc @{ ∀${ident x}:$T.$acc } } }.
+ rec acc @{
+ ${ fold right @{ $acc } rec acc2
+ @{ ∀${ident x}:${ default @{ $T } @{ ? } }.$acc2 } }
+ }
+ }}.
include "logic/pts.ma".
ndefinition hint_declaration_Type0 ≝ λA:Type[0] .λa,b:A.Prop.
ndefinition hint_declaration_Type1 ≝ λA:Type[1].λa,b:A.Prop.
-ndefinition hint_declaration_Type2 ≝ λa,b:Type[1].Prop.
+ndefinition hint_declaration_Type2 ≝ λa,b:Type[2].Prop.
ndefinition hint_declaration_CProp0 ≝ λA:CProp[0].λa,b:A.Prop.
ndefinition hint_declaration_CProp1 ≝ λA:CProp[1].λa,b:A.Prop.
-ndefinition hint_declaration_CProp2 ≝ λa,b:CProp[1].Prop.
+ndefinition hint_declaration_CProp2 ≝ λa,b:CProp[2].Prop.
interpretation "hint_decl_Type2" 'hint_decl a b = (hint_declaration_Type2 a b).
interpretation "hint_decl_CProp2" 'hint_decl a b = (hint_declaration_CProp2 a b).
interpretation "hint_decl_CProp0" 'hint_decl a b = (hint_declaration_CProp0 ? a b).
interpretation "hint_decl_Type0" 'hint_decl a b = (hint_declaration_Type0 ? a b).
-(* little test
-naxiom A : Type[0].
-naxiom C : A → A → Type[0].
-ndefinition D ≝ C.
-alias symbol "hint_decl" = "hint_decl_Type1".
-unification hint 0 ≔
- X : A, Y : A ; Z ≟ X, W ≟ Y ⊢ C X Y ≡ D Z W.
-
-*)
+(* Non uniform coercions support *)
+nrecord lock2 (S : Type[2]) (s : S) : Type[3] ≝ {
+ force2 : Type[2];
+ lift2 : force2
+}.
+
+nrecord lock1 (S : Type[1]) (s : S) : Type[2] ≝ {
+ force1 : Type[1];
+ lift1 : force1
+}.
+
+ncoercion lift1 : ∀S:Type[1].∀s:S.∀l:lock1 S s. force1 S s l ≝ lift1
+ on s : ? to force1 ???.
+
+ncoercion lift2 : ∀S:Type[2].∀s:S.∀l:lock2 S s. force2 S s l ≝ lift2
+ on s : ? to force2 ???.
+
+(* Example of a non uniform coercion declaration
+
+ Type[0] setoid
+ >--->
+ MR R
+
+ provided MR = carr R
+
+unification hint 0 ≔ R : setoid;
+ MR ≟ carr R,
+ lock ≟ mk_lock1 Type[0] MR setoid R
+(* ---------------------------------------- *) ⊢
+ setoid ≡ force1 ? MR lock.
+
+*)
\ No newline at end of file