(* *)
(**************************************************************************)
-include "logic/pts.ma".
-ndefinition hint_declaration_Type0 ≝ λA:Type[0] .λa,b:A.a.
-ndefinition hint_declaration_Type1 ≝ λA:Type[1].λa,b:A.a.
-ndefinition hint_declaration_Type2 ≝ λa,b:Type[1].a.
-ndefinition hint_declaration_CProp0 ≝ λA:CProp[0].λa,b:A.a.
-ndefinition hint_declaration_CProp1 ≝ λA:CProp[1].λa,b:A.a.
-ndefinition hint_declaration_CProp2 ≝ λa,b:CProp[1].a.
-
-notation > "≔ (list0 (ident x : T )sep ,) ⊢ term 19 Px ≡ term 19 Py"
+(*
+
+Notation for hint declaration
+==============================
+
+The idea is to write a context, with abstraction first, then
+recursive calls (let-in) and finally the two equivalent terms.
+The context can be empty. Note the ; to begin the second part of
+the context (necessary even if the first part is empty).
+
+ unification hint PREC \coloneq
+ ID : TY, ..., ID : TY
+ ; ID \equest T, ..., ID \equest T
+ \vdash T1 \equiv T2
+
+With unidoce and some ASCII art it looks like the following:
+
+ unification hint PREC ≔ ID : TY, ..., ID : TY;
+ ID ≟ T, ..., ID ≟ T
+ (*---------------------*) ⊢
+ T1 ≡ T2
+
+The order of premises is relevant, since they are processed in order
+(left to right).
+
+*)
+
+(* 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 @{'hint_decl $Px $Py} rec acc @{ ∀${ident x}:$T.$acc } } }.
+ for @{ ${ fold right
+ @{ ${ default
+ @{ ${ fold right
+ @{ 'hint_decl $Px $Py }
+ rec acc1 @{ let ( ${ident U} : ?) ≝ $V in $acc1} } }
+ @{ 'hint_decl $Px $Py }
+ }
+ }
+ 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[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[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_Type1" 'hint_decl a b = (hint_declaration_Type1 ? a b).
interpretation "hint_decl_CProp1" 'hint_decl a b = (hint_declaration_CProp1 ? 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).
+
+(* 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.
+
+*)
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