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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  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 fun_of_seq 1.
  24
  25 notation < "hvbox((\lfloor term 19 p \rfloor) \sub ident i)" with precedence 90
  26 for @{ 'sequence (\lambda ${ident i} : $t . $p)}.
  27
  28 notation > "hvbox((\lfloor term 19 p \rfloor) \sub ident i)" with precedence 90
  29 for @{ 'sequence (\lambda ${ident i} . $p)}.
  30
  31 notation > "hvbox(\lfloor ident i, term 19 p \rfloor)" with precedence 90
  32 for @{ 'sequence (\lambda ${ident i} . $p)}.
  33
  34 notation "a \sub i" left associative with precedence 90
  35   for @{ 'sequence_appl $a $i }.
  36
  37 interpretation "sequence" 'sequence \eta.x = (mk_seq _ x).
  38 interpretation "sequence element" 'sequence_appl s i = (fun_of_seq _ s i).