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Datei: compatibility.pvs Sprache: PVS

Original von: PVS^©

%%-------------------** Term Rewriting System (TRS) **------------------------
%%
%% Authors         : Andre Luiz Galdino
%%                   Universidade Federal de Goiás - Brasil
%%
%%                         and
%%
%%                   Mauricio Ayala Rincon
%%                   Universidade de Brasília - Brasil
%%
%% Last Modified On: September 29, 2009
%%
%%----------------------------------------------------------------------------

compatibility[variable: TYPE+, symbol: TYPE+, arity: [symbol -> nat]]: THEORY

BEGIN

  IMPORTING replacement[variable,symbol, arity],
            finite_sets[(V)] as fsetvar,
            ars[term]


      r, s, t: VAR term
            R: VAR pred[[term, term]]
            x: VAR (V)
            n: VAR nat

%%%% Defining the set of all function symbols whose arity is n %%%%%%%%%%%%%%%%%

  arity_eq(n): TYPE = {f: symbol | arity(f) = n}

%%%% Defining, respectively, the concepts closed under operations, compatible %%
%%%% with operations, and compatible with contexts                            %%

close_op?(R): bool =
    FORALL ( n: nat, (f: arity_eq(n)), (st1, st2: fset.fs_len(n))):
      (FORALL (m: below[n]): R(st1(m), st2(m))
         => R(app(f, st1), app(f, st2)))


comp_op?(R): bool =
    FORALL (n: nat, i: below[n], (f: arity_eq(n)), (st1: fset.fs_len(n)), t):
       LET s = st1(i), st2 = replace(t, st1, i) IN
         R(s,t) =>  R(app(f,st1), app(f,st2))

comp_cont?(R): bool = FORALL (p: position), s: positionsOF(s)(p) =>
                        (FORALL r, t: R(r,t) =>
                           R(replaceTerm(s, r, p), replaceTerm(s, t, p)))

%%%% Properties %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

comp_op_iff_comp_cont: LEMMA comp_op?(R) <=> comp_cont?(R)

closure_comp_op: LEMMA comp_op?(R) =>
                 (comp_op?(TC(R)) & comp_op?(RTC(R)) & comp_op?(EC(R)))

closure_comp_cont: LEMMA comp_cont?(R) =>
                 (comp_cont?(TC(R)) & comp_cont?(RTC(R)) & comp_cont?(EC(R)))

END compatibility

¤ Dauer der Verarbeitung: 0.2 Sekunden (vorverarbeitet) ¤

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