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3 (*      ||M||                                                             *)
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11 (*        v         GNU General Public License Version 2                  *)
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14
15 (* ********************************************************************** *)
16 (*                          Progetto FreeScale                            *)
17 (*                                                                        *)
18 (*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
19 (*   Sviluppo: 2008-2010                                                  *)
20 (*                                                                        *)
21 (* ********************************************************************** *)
22
23 include "common/theory.ma".
24
25 (* coppia dipendente *)
26
27 ninductive sigma (A:Type) (P:A → Type) : Type ≝
28     sigma_intro: ∀x:A.P x → sigma A P.
29
30 notation < "hvbox(\Sigma ident i opt (: tx) break . p)"
31   right associative with precedence 20
32 for @{ 'Sigma ${default
33   @{\lambda ${ident i} : $tx. $p}  
34   @{\lambda ${ident i} . $p}}}.
35
36 notation > "\Sigma list1 ident x sep , opt (: T). term 19 Px"
37   with precedence 20
38   for ${ default
39           @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}:$T.$acc)} } }
40           @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}.$acc)} } }
41        }.
42
43 notation "\ll term 19 a, break term 19 b \gg"
44 with precedence 90 for @{'dependent_pair (λx:?.? x) $a $b}.
45 interpretation "dependent pair" 'dependent_pair \eta.c a b = (sigma_intro ? c a b).
46
47 interpretation "sigma" 'Sigma \eta.x = (sigma ? x).
48
49 ndefinition sigmaFst ≝
50 λT:Type.λf:T → Type.λs:sigma T f.match s with [ sigma_intro x _ ⇒ x ].
51 ndefinition sigmaSnd ≝
52 λT:Type.λf:T → Type.λs:sigma T f.match s return λs.f (sigmaFst ?? s) with [ sigma_intro _ x ⇒ x ].