]> matita.cs.unibo.it Git - helm.git/blob - helm/software/matita/contribs/assembly/compiler/sigma.ma
nasty change in the lexer/parser:
[helm.git] / helm / software / matita / contribs / assembly / compiler / sigma.ma
1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 (* ********************************************************************** *)
16 (*                                                                        *)
17 (* Sviluppato da:                                                         *)
18 (*   Cosimo Oliboni, oliboni@cs.unibo.it                                  *)
19 (*                                                                        *)
20 (* ********************************************************************** *)
21
22 (* coppia dipendente *)
23
24 inductive sigma (A:Type) (P:A → Type) : Type ≝
25     sigma_intro: ∀x:A.P x → sigma A P.
26
27 notation < "hvbox(\Sigma ident i opt (: tx) break . p)"
28   right associative with precedence 20
29 for @{ 'Sigma ${default
30   @{\lambda ${ident i} : $tx. $p}  
31   @{\lambda ${ident i} . $p}}}.
32
33 notation > "\Sigma list1 ident x sep , opt (: T). term 19 Px"
34   with precedence 20
35   for ${ default
36           @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}:$T.$acc)} } }
37           @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}.$acc)} } }
38        }.
39
40 notation "\ll term 19 a, break term 19 b \gg"
41 with precedence 90 for @{'dependent_pair (λx:?.? x) $a $b}.
42 interpretation "dependent pair" 'dependent_pair \eta.c a b = (sigma_intro ? c a b).
43
44 interpretation "sigma" 'Sigma \eta.x = (sigma ? x).
45
46 definition sigmaFst ≝
47 λT:Type.λf:T → Type.λs:sigma T f.match s with [ sigma_intro x _ ⇒ x ].
48 definition sigmaSnd ≝
49 λT:Type.λf:T → Type.λs:sigma T f.match s return λs.f (sigmaFst ?? s) with [ sigma_intro _ x ⇒ x ].