(* Title: HOLCF/IOA/meta_theory/TLS.thy
ID: $Id$
Author: Olaf Müller
*)
header {* Temporal Logic of Steps -- tailored for I/O automata *}
theory TLS
imports IOA TL
begin
defaultsort type
types
('a, 's) ioa_temp = "('a option,'s)transition temporal"
('a, 's) step_pred = "('a option,'s)transition predicate"
's state_pred = "'s predicate"
consts
option_lift :: "('a => 'b) => 'b => ('a option => 'b)"
plift :: "('a => bool) => ('a option => bool)"
temp_sat :: "('a,'s)execution => ('a,'s)ioa_temp => bool" (infixr "|==" 22)
xt1 :: "'s predicate => ('a,'s)step_pred"
xt2 :: "'a option predicate => ('a,'s)step_pred"
validTE :: "('a,'s)ioa_temp => bool"
validIOA :: "('a,'s)ioa => ('a,'s)ioa_temp => bool"
mkfin :: "'a Seq => 'a Seq"
ex2seq :: "('a,'s)execution => ('a option,'s)transition Seq"
ex2seqC :: "('a,'s)pairs -> ('s => ('a option,'s)transition Seq)"
defs
mkfin_def:
"mkfin s == if Partial s then @t. Finite t & s = t @@ UU
else s"
option_lift_def:
"option_lift f s y == case y of None => s | Some x => (f x)"
(* plift is used to determine that None action is always false in
transition predicates *)
plift_def:
"plift P == option_lift P False"
temp_sat_def:
"ex |== P == ((ex2seq ex) |= P)"
xt1_def:
"xt1 P tr == P (fst tr)"
xt2_def:
"xt2 P tr == P (fst (snd tr))"
ex2seq_def:
"ex2seq ex == ((ex2seqC $(mkfin (snd ex))) (fst ex))"
ex2seqC_def:
"ex2seqC == (fix$(LAM h ex. (%s. case ex of
nil => (s,None,s)>>nil
| x##xs => (flift1 (%pr.
(s,Some (fst pr), snd pr)>> (h$xs) (snd pr))
$x)
)))"
validTE_def:
"validTE P == ! ex. (ex |== P)"
validIOA_def:
"validIOA A P == ! ex : executions A . (ex |== P)"
axioms
mkfin_UU:
"mkfin UU = nil"
mkfin_nil:
"mkfin nil =nil"
mkfin_cons:
"(mkfin (a>>s)) = (a>>(mkfin s))"
ML {* use_legacy_bindings (the_context ()) *}
end