isabelle: comparison src/HOL/IOA/IOA.thy

equal deleted inserted replaced

-:bd49e10bbd24
+:aa3833fb7bee
 (*  Title:      HOL/IOA/IOA.thy
 ID:         $Id$
 Author:     Tobias Nipkow & Konrad Slind
 Copyright   1994  TU Muenchen
-The I/O automata of Lynch and Tuttle.
 *)
-IOA = Asig +
+header {* The I/O automata of Lynch and Tuttle *}
+theory IOA
+imports Asig
+begin
 types
 'a seq            =   "nat => 'a"
 'a oseq           =   "nat => 'a option"
 ('a,'b)execution  =   "'a oseq * 'b seq"
 trans_of   ::"('action,'state)ioa => ('action,'state)transition set"
 IOA        ::"('action,'state)ioa => bool"
 (* Executions, schedules, and traces *)
-is_execution_fragment,
+is_execution_fragment ::"[('action,'state)ioa, ('action,'state)execution] => bool"
 has_execution ::"[('action,'state)ioa, ('action,'state)execution] => bool"
 executions    :: "('action,'state)ioa => ('action,'state)execution set"
 mk_trace  :: "[('action,'state)ioa, 'action oseq] => 'action oseq"
 reachable     :: "[('action,'state)ioa, 'state] => bool"
 invariant     :: "[('action,'state)ioa, 'state=>bool] => bool"
 (* binary composition of action signatures and automata *)
 compat_asigs ::"['action signature, 'action signature] => bool"
 asig_comp    ::"['action signature, 'action signature] => 'action signature"
 compat_ioas  ::"[('action,'s)ioa, ('action,'t)ioa] => bool"
-"||"         ::"[('a,'s)ioa, ('a,'t)ioa] => ('a,'s*'t)ioa"  (infixr 10)
+par         ::"[('a,'s)ioa, ('a,'t)ioa] => ('a,'s*'t)ioa"  (infixr "||" 10)
 (* Filtering and hiding *)
 filter_oseq  :: "('a => bool) => 'a oseq => 'a oseq"
 restrict_asig :: "['a signature, 'a set] => 'a signature"
 (* Instantiation of abstract IOA by concrete actions *)
 rename:: "('a, 'b)ioa => ('c => 'a option) => ('c,'b)ioa"
 defs
-state_trans_def
+state_trans_def:
 "state_trans asig R ==
 (!triple. triple:R --> fst(snd(triple)):actions(asig)) &
 (!a. (a:inputs(asig)) --> (!s1. ? s2. (s1,a,s2):R))"
-asig_of_def   "asig_of == fst"
+asig_of_def:   "asig_of == fst"
-starts_of_def "starts_of == (fst o snd)"
+starts_of_def: "starts_of == (fst o snd)"
-trans_of_def  "trans_of == (snd o snd)"
+trans_of_def:  "trans_of == (snd o snd)"
-ioa_def
+ioa_def:
 "IOA(ioa) == (is_asig(asig_of(ioa))      &
 (~ starts_of(ioa) = {})    &
 state_trans (asig_of ioa) (trans_of ioa))"
 (* An execution fragment is modelled with a pair of sequences:
 * the first is the action options, the second the state sequence.
 * Finite executions have None actions from some point on.
 *******)
-is_execution_fragment_def
+is_execution_fragment_def:
 "is_execution_fragment A ex ==
 let act = fst(ex); state = snd(ex)
 in !n a. (act(n)=None --> state(Suc(n)) = state(n)) &
 (act(n)=Some(a) --> (state(n),a,state(Suc(n))):trans_of(A))"
-executions_def
+executions_def:
 "executions(ioa) == {e. snd e 0:starts_of(ioa) &
 is_execution_fragment ioa e}"
-reachable_def
+reachable_def:
 "reachable ioa s == (? ex:executions(ioa). ? n. (snd ex n) = s)"
-invariant_def "invariant A P == (!s. reachable A s --> P(s))"
+invariant_def: "invariant A P == (!s. reachable A s --> P(s))"
 (* Restrict the trace to those members of the set s *)
-filter_oseq_def
+filter_oseq_def:
 "filter_oseq p s ==
 (%i. case s(i)
 of None => None
 | Some(x) => if p x then Some x else None)"
-mk_trace_def
+mk_trace_def:
 "mk_trace(ioa) == filter_oseq(%a. a:externals(asig_of(ioa)))"
 (* Does an ioa have an execution with the given trace *)
-has_trace_def
+has_trace_def:
 "has_trace ioa b ==
 (? ex:executions(ioa). b = mk_trace ioa (fst ex))"
-normal_form_def
+normal_form_def:
 "NF(tr) == @nf. ? f. mono(f) & (!i. nf(i)=tr(f(i))) &
 (!j. j ~: range(f) --> nf(j)= None) &
 (!i. nf(i)=None --> (nf (Suc i)) = None)   "
 (* All the traces of an ioa *)
-traces_def
+traces_def:
 "traces(ioa) == {trace. ? tr. trace=NF(tr) & has_trace ioa tr}"
 (*
-traces_def
+traces_def:
 "traces(ioa) == {tr. has_trace ioa tr}"
 *)
-compat_asigs_def
+compat_asigs_def:
 "compat_asigs a1 a2 ==
 (((outputs(a1) Int outputs(a2)) = {}) &
 ((internals(a1) Int actions(a2)) = {}) &
 ((internals(a2) Int actions(a1)) = {}))"
-compat_ioas_def
+compat_ioas_def:
 "compat_ioas ioa1 ioa2 == compat_asigs (asig_of(ioa1)) (asig_of(ioa2))"
-asig_comp_def
+asig_comp_def:
 "asig_comp a1 a2 ==
 (((inputs(a1) Un inputs(a2)) - (outputs(a1) Un outputs(a2)),
 (outputs(a1) Un outputs(a2)),
 (internals(a1) Un internals(a2))))"
-par_def
+par_def:
 "(ioa1 || ioa2) ==
 (asig_comp (asig_of ioa1) (asig_of ioa2),
 {pr. fst(pr):starts_of(ioa1) & snd(pr):starts_of(ioa2)},
 {tr. let s = fst(tr); a = fst(snd(tr)); t = snd(snd(tr))
 in (a:actions(asig_of(ioa1)) | a:actions(asig_of(ioa2))) &
 (if a:actions(asig_of(ioa1)) then
 (fst(s),a,fst(t)):trans_of(ioa1)
 else fst(t) = fst(s))
 &
 (if a:actions(asig_of(ioa2)) then
 (snd(s),a,snd(t)):trans_of(ioa2)
 else snd(t) = snd(s))})"
-restrict_asig_def
+restrict_asig_def:
 "restrict_asig asig actns ==
 (inputs(asig) Int actns, outputs(asig) Int actns,
 internals(asig) Un (externals(asig) - actns))"
-restrict_def
+restrict_def:
 "restrict ioa actns ==
 (restrict_asig (asig_of ioa) actns, starts_of(ioa), trans_of(ioa))"
-ioa_implements_def
+ioa_implements_def:
 "ioa_implements ioa1 ioa2 ==
 ((inputs(asig_of(ioa1)) = inputs(asig_of(ioa2))) &
 (outputs(asig_of(ioa1)) = outputs(asig_of(ioa2))) &
 traces(ioa1) <= traces(ioa2))"
-rename_def
+rename_def:
 "rename ioa ren ==
 (({b. ? x. Some(x)= ren(b) & x : inputs(asig_of(ioa))},
 {b. ? x. Some(x)= ren(b) & x : outputs(asig_of(ioa))},
 {b. ? x. Some(x)= ren(b) & x : internals(asig_of(ioa))}),
 starts_of(ioa)   ,
 {tr. let s = fst(tr); a = fst(snd(tr));  t = snd(snd(tr))
 in
 ? x. Some(x) = ren(a) & (s,x,t):trans_of(ioa)})"
-end
+ML {* use_legacy_bindings (the_context ()) *}
+end

changeset 17288	aa3833fb7bee
parent 11482	ec2c382ff4f0
child 19801	b2af2549efd1