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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* 
+
+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 
+               @{ ${ 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 "basics/pts.ma".
+
+definition hint_declaration_Type0  ≝  λA:Type[0] .λa,b:A.Prop.
+definition hint_declaration_Type1  ≝  λA:Type[1].λa,b:A.Prop.
+definition hint_declaration_Type2  ≝  λa,b:Type[2].Prop.
+definition hint_declaration_CProp0 ≝  λA:CProp[0].λa,b:A.Prop.
+definition hint_declaration_CProp1 ≝  λA:CProp[1].λa,b:A.Prop.
+definition 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
+record solution2 (S : Type[2]) (s : S) : Type[3] ≝ {
+  target2 : Type[2];
+  result2  : target2
+}.
+
+record solution1 (S : Type[1]) (s : S) : Type[2] ≝ {
+  target1 : Type[1];
+  result1  : target1
+}.
+
+coercion nonunifcoerc1 : ∀S:Type[1].∀s:S.∀l:solution1 S s. target1 S s l ≝ result1 
+ on s : ? to target1 ???.
+
+coercion nonunifcoerc2 : ∀S:Type[2].∀s:S.∀l:solution2 S s. target2 S s l ≝ result2
+ on s : ? to target2 ???.
+*)
+
+(* Example of a non uniform coercion declaration 
+   
+     Type[0]              setoid
+                >--->     
+     MR                   R  
+
+   provided MR = carr R
+
+unification hint 0 ≔ R : setoid;
+   MR ≟ carr R, 
+   sol ≟ mk_solution1 Type[0] MR setoid R 
+(* ---------------------------------------- *) ⊢ 
+   setoid ≡ target1 ? MR sol.
+
+*)
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