helm/software/matita/contribs/dama/dama/sequence.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "nat/nat.ma".
  16
  17 inductive sequence (O:Type) : Type ≝
  18  | mk_seq : (nat → O) → sequence O.
  19
  20 definition fun_of_seq: ∀O:Type.sequence O → nat → O ≝
  21   λO.λx:sequence O.match x with [ mk_seq f ⇒ f ].
  22
  23 coercion cic:/matita/dama/sequence/fun_of_seq.con 1.
  24
  25 notation < "hvbox((\lfloor p \rfloor) \sub ident i)"
  26   left associative with precedence 70
  27 for @{ 'sequence (\lambda ${ident i} : $t . $p)}.
  28
  29 notation > "hvbox((\lfloor p \rfloor) \sub ident i)"
  30   left associative with precedence 70
  31 for @{ 'sequence (\lambda ${ident i} . $p)}.
  32
  33 notation > "hvbox(\lfloor ident i, p \rfloor)"
  34   left associative with precedence 70
  35 for @{ 'sequence (\lambda ${ident i} . $p)}.
  36
  37 notation "a \sub i" left associative with precedence 70
  38   for @{ 'sequence_appl $a $i }.
  39
  40 interpretation "sequence" 'sequence \eta.x = (mk_seq _ x).
  41 interpretation "sequence element" 'sequence_appl s i = (fun_of_seq _ s i).