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[helm.git] / helm / matita / contribs / PREDICATIVE-TOPOLOGY / domain_defs.ma

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_defs.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_defs.ma
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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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs".
+
+include "class_defs.ma".
+
+(* QUANTIFICATION DOMAINS
+   - These are the categories on which we allow quantification
+   - We set up single quantifiers, parametric on the domain, so they
+     already have the properties  that usually are axiomatized inside the 
+     domain structure. This makes domains easier to use
+*)
+
+record Domain: Type \def {
+   qd:> Class
+}.
+
+(* internal universal quantification *)
+inductive dall (D:Domain) (P:D \to Prop) : Prop \def
+   | dall_intro: (\forall d:D. cin D d \to P d) \to dall D P.
+
+(* internal existential quantification *)
+inductive dex (D:Domain) (P:D \to Prop) : Prop \def
+   | dex_intro: \forall d:D. cin D d \land P d \to dex D P.
+
+(* notations **************************************************************)
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "internal for all" 'iforall \eta.x =
+  (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/dall.ind#xpointer(1/1) _ x).
+
+notation > "hvbox(\iforall ident i opt (: ty) break . p)"
+  right associative with precedence 20
+for @{ 'iforall ${default
+  @{\lambda ${ident i} : $ty. $p)}
+  @{\lambda ${ident i} . $p}}}.
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "internal exists" 'dexists \eta.x =
+  (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/dex.ind#xpointer(1/1) _ x).
+
+notation > "hvbox(\iexists ident i opt (: ty) break . p)"
+  right associative with precedence 20
+for @{ 'dexists ${default
+  @{\lambda ${ident i} : $ty. $p)}
+  @{\lambda ${ident i} . $p}}}.