freescale porting

[helm.git] / helm / software / matita / contribs / ng_assembly2 / common / sigma.ma

diff --git a/helm/software/matita/contribs/ng_assembly2/common/sigma.ma b/helm/software/matita/contribs/ng_assembly2/common/sigma.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                          Progetto FreeScale                            *)
+(*                                                                        *)
+(*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
+(*   Sviluppo: 2008-2010                                                  *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "common/theory.ma".
+
+(* coppia dipendente *)
+
+ninductive sigma (A:Type) (P:A → Type) : Type ≝
+    sigma_intro: ∀x:A.P x → sigma A P.
+
+notation < "hvbox(\Sigma ident i opt (: tx) break . p)"
+  right associative with precedence 20
+for @{ 'Sigma ${default
+  @{\lambda ${ident i} : $tx. $p}  
+  @{\lambda ${ident i} . $p}}}.
+
+notation > "\Sigma list1 ident x sep , opt (: T). term 19 Px"
+  with precedence 20
+  for ${ default
+          @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}:$T.$acc)} } }
+          @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}.$acc)} } }
+       }.
+
+notation "\ll term 19 a, break term 19 b \gg"
+with precedence 90 for @{'dependent_pair (λx:?.? x) $a $b}.
+interpretation "dependent pair" 'dependent_pair \eta.c a b = (sigma_intro ? c a b).
+
+interpretation "sigma" 'Sigma \eta.x = (sigma ? x).
+
+ndefinition sigmaFst ≝
+λT:Type.λf:T → Type.λs:sigma T f.match s with [ sigma_intro x _ ⇒ x ].
+ndefinition sigmaSnd ≝
+λT:Type.λf:T → Type.λs:sigma T f.match s return λs.f (sigmaFst ?? s) with [ sigma_intro _ x ⇒ x ].