3 Notation for hint declaration
4 ==============================
6 The idea is to write a context, with abstraction first, then
7 recursive calls (let-in) and finally the two equivalent terms.
8 The context can be empty. Note the ; to begin the second part of
9 the context (necessary even if the first part is empty).
11 unification hint PREC \coloneq
13 ; ID \equest T, ..., ID \equest T
16 With unidoce and some ASCII art it looks like the following:
18 unification hint PREC ≔ ID : TY, ..., ID : TY;
20 (*---------------------*) ⊢
23 The order of premises is relevant, since they are processed in order
28 (* it seems unbelivable, but it works! *)
29 notation > "≔ (list0 ( (list1 (ident x) sep , ) opt (: T) ) sep ,) opt (; (list1 (ident U ≟ term 19 V ) sep ,)) ⊢ term 19 Px ≡ term 19 Py"
34 @{ 'hint_decl $Px $Py }
35 rec acc1 @{ let ( ${ident U} : ?) ≝ $V in $acc1} } }
36 @{ 'hint_decl $Px $Py }
40 ${ fold right @{ $acc } rec acc2
41 @{ ∀${ident x}:${ default @{ $T } @{ ? } }.$acc2 } }
45 include "basics/pts.ma".
47 definition hint_declaration_Type0 ≝ λA:Type[0] .λa,b:A.Prop.
48 definition hint_declaration_Type1 ≝ λA:Type[1].λa,b:A.Prop.
49 definition hint_declaration_Type2 ≝ λa,b:Type[2].Prop.
50 definition hint_declaration_CProp0 ≝ λA:CProp[0].λa,b:A.Prop.
51 definition hint_declaration_CProp1 ≝ λA:CProp[1].λa,b:A.Prop.
52 definition hint_declaration_CProp2 ≝ λa,b:CProp[2].Prop.
54 interpretation "hint_decl_Type2" 'hint_decl a b = (hint_declaration_Type2 a b).
55 interpretation "hint_decl_CProp2" 'hint_decl a b = (hint_declaration_CProp2 a b).
56 interpretation "hint_decl_Type1" 'hint_decl a b = (hint_declaration_Type1 ? a b).
57 interpretation "hint_decl_CProp1" 'hint_decl a b = (hint_declaration_CProp1 ? a b).
58 interpretation "hint_decl_CProp0" 'hint_decl a b = (hint_declaration_CProp0 ? a b).
59 interpretation "hint_decl_Type0" 'hint_decl a b = (hint_declaration_Type0 ? a b).
61 (* Non uniform coercions support
62 record solution2 (S : Type[2]) (s : S) : Type[3] ≝ {
67 record solution1 (S : Type[1]) (s : S) : Type[2] ≝ {
72 coercion nonunifcoerc1 : ∀S:Type[1].∀s:S.∀l:solution1 S s. target1 S s l ≝ result1
73 on s : ? to target1 ???.
75 coercion nonunifcoerc2 : ∀S:Type[2].∀s:S.∀l:solution2 S s. target2 S s l ≝ result2
76 on s : ? to target2 ???.
79 (* Example of a non uniform coercion declaration
87 unification hint 0 ≔ R : setoid;
89 sol ≟ mk_solution1 Type[0] MR setoid R
90 (* ---------------------------------------- *) ⊢
91 setoid ≡ target1 ? MR sol.