First version of PTS

[helm.git] / helm / software / matita / nlibrary / hints_declaration.ma

diff --git a/helm/software/matita/nlibrary/hints_declaration.ma b/helm/software/matita/nlibrary/hints_declaration.ma
index 29d17382b420c8bf99803ce7f212ef4e8f5482db..f91949be9f383f6b749be8388c414d795a3036a5 100644 (file)
--- a/helm/software/matita/nlibrary/hints_declaration.ma
+++ b/helm/software/matita/nlibrary/hints_declaration.ma
@@ -12,21 +12,68 @@
 (*                                                                        *)
 (**************************************************************************)
 
-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       
+
+*)
+   
+(* it seems unbelivable, but it works! *)
+notation > "≔ (list0 ( (list1 (ident x) sep , ) opt (: T) ) sep ,) opt (; (list1 (ident U ≟ term 90 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).
+
+(* 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, R : A, Y ;  Z ≟ X, W ≟ Y ⊢ C X Y ≡ D Z W.
+*)