--- a/src/HOL/IOA/meta_theory/IOA.thy Wed Jun 21 15:14:58 1995 +0200
+++ b/src/HOL/IOA/meta_theory/IOA.thy Wed Jun 21 15:47:10 1995 +0200
@@ -63,9 +63,9 @@
defs
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))"
+ "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"
@@ -73,9 +73,9 @@
trans_of_def "trans_of == (snd o snd)"
ioa_def
- "IOA(ioa) == (is_asig(asig_of(ioa)) & \
- \ (~ starts_of(ioa) = {}) & \
- \ state_trans (asig_of ioa) (trans_of ioa))"
+ "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:
@@ -83,15 +83,15 @@
* Finite executions have None actions from some point on.
*******)
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))"
+ "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(ioa) == {e. snd e 0:starts_of(ioa) & \
-\ is_execution_fragment ioa e}"
+ "executions(ioa) == {e. snd e 0:starts_of(ioa) &
+ is_execution_fragment ioa e}"
reachable_def
@@ -103,10 +103,10 @@
(* Restrict the trace to those members of the set s *)
filter_oseq_def
- "filter_oseq p s == \
-\ (%i.case s(i) \
-\ of None => None \
-\ | Some(x) => if p x then Some x else None)"
+ "filter_oseq p s ==
+ (%i.case s(i)
+ of None => None
+ | Some(x) => if p x then Some x else None)"
mk_trace_def
@@ -115,13 +115,13 @@
(* Does an ioa have an execution with the given trace *)
has_trace_def
- "has_trace ioa b == \
-\ (? ex:executions(ioa). b = mk_trace ioa (fst ex))"
+ "has_trace ioa b ==
+ (? ex:executions(ioa). b = mk_trace ioa (fst ex))"
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) "
+ "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 *)
@@ -134,10 +134,10 @@
*)
compat_asigs_def
- "compat_asigs a1 a2 == \
- \ (((outputs(a1) Int outputs(a2)) = {}) & \
- \ ((internals(a1) Int actions(a2)) = {}) & \
- \ ((internals(a2) Int actions(a1)) = {}))"
+ "compat_asigs a1 a2 ==
+ (((outputs(a1) Int outputs(a2)) = {}) &
+ ((internals(a1) Int actions(a2)) = {}) &
+ ((internals(a2) Int actions(a1)) = {}))"
compat_ioas_def
@@ -145,52 +145,52 @@
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))))"
+ "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
- "(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))})"
+ "(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 asig actns == \
-\ (inputs(asig) Int actns, outputs(asig) Int actns, \
-\ internals(asig) Un (externals(asig) - actns))"
+ "restrict_asig asig actns ==
+ (inputs(asig) Int actns, outputs(asig) Int actns,
+ internals(asig) Un (externals(asig) - actns))"
restrict_def
- "restrict ioa actns == \
-\ (restrict_asig (asig_of ioa) actns, starts_of(ioa), trans_of(ioa))"
+ "restrict ioa actns ==
+ (restrict_asig (asig_of ioa) actns, starts_of(ioa), trans_of(ioa))"
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))"
+ "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 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)})"
+"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