Quelle csequence_list.pvs Sprache: PVS

%-----------------------------------------------------------------------------
% Conversions between sequences of countable length and the prelude list type.
%
% Author: Jerry James <loganjerry@gmail.com>
%
% This file and its accompanying proof file are distributed under the CC0 1.0
% Universal license: http://creativecommons.org/publicdomain/zero/1.0/.
%
% Version history:
%   2007 Feb 14: PVS 4.0 version
%   2011 May  6: PVS 5.0 version
%   2013 Jan 14: PVS 6.0 version
%-----------------------------------------------------------------------------
csequence_list[T: TYPE]: THEORY
BEGIN

  IMPORTING list[T], list_props[T], csequence_nth[T]

  n: VAR nat
  l: VAR list
  fseq: VAR finite_csequence

  % Convert a list to a finite_csequence
  from_list(l): RECURSIVE finite_csequence =
    IF null?(l) THEN empty_cseq ELSE add(car(l), from_list(cdr(l))) ENDIF
     MEASURE l BY <<

  from_list_length: THEOREM FORALL l: length(from_list(l)) = length(l)

  from_list_index: THEOREM
    FORALL l, n: index?(from_list(l))(n) IFF n < length(l)

  from_list_nth: THEOREM
    FORALL l, (n: below[length(l)]): nth(from_list(l), n) = nth(l, n)

  % Convert a finite_csequence to a list
  to_list(fseq): RECURSIVE list =
    IF empty?(fseq) THEN null
    ELSE cons(first(fseq), to_list(rest(fseq)))
    ENDIF
     MEASURE length(fseq)

  to_list_length: THEOREM FORALL fseq: length(to_list(fseq)) = length(fseq)

  to_list_index: THEOREM
    FORALL fseq, n: n < length(to_list(fseq)) IFF index?(fseq)(n)

  to_list_nth: THEOREM
    FORALL fseq, (n: indexes(fseq)): nth(to_list(fseq), n) = nth(fseq, n)

  % Applying both conversions gives you back what you started with

  to_from_list: THEOREM FORALL l: to_list(from_list(l)) = l

  from_to_list: THEOREM FORALL fseq: from_list(to_list(fseq)) = fseq

END csequence_list

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