(*
File: TLA/Action.thy
Author: Stephan Merz
Copyright: 1998 University of Munich
Theory Name: Action
Logic Image: HOL
Define the action level of TLA as an Isabelle theory.
*)
Action = Intensional + Stfun +
(** abstract syntax **)
types
'a trfun = "(state * state) => 'a"
action = bool trfun
instance
"*" :: (world, world) world
consts
(** abstract syntax **)
before :: 'a stfun => 'a trfun
after :: 'a stfun => 'a trfun
unch :: 'a stfun => action
SqAct :: [action, 'a stfun] => action
AnAct :: [action, 'a stfun] => action
enabled :: action => stpred
(** concrete syntax **)
syntax
(* Syntax for writing action expressions in arbitrary contexts *)
"ACT" :: lift => 'a ("(ACT _)")
"_before" :: lift => lift ("($_)" [100] 99)
"_after" :: lift => lift ("(_$)" [100] 99)
"_unchanged" :: lift => lift ("(unchanged _)" [100] 99)
(*** Priming: same as "after" ***)
"_prime" :: lift => lift ("(_`)" [100] 99)
"_SqAct" :: [lift, lift] => lift ("([_]'_(_))" [0,1000] 99)
"_AnAct" :: [lift, lift] => lift ("(<_>'_(_))" [0,1000] 99)
"_Enabled" :: lift => lift ("(Enabled _)" [100] 100)
translations
"ACT A" => "(A::state*state => _)"
"_before" == "before"
"_after" => "_prime"
"_unchanged" == "unch"
"_prime" == "after"
"_SqAct" == "SqAct"
"_AnAct" == "AnAct"
"_Enabled" == "enabled"
"w |= [A]_v" <= "_SqAct A v w"
"w |= <A>_v" <= "_AnAct A v w"
"s |= Enabled A" <= "_Enabled A s"
"w |= unchanged f" <= "_unchanged f w"
rules
unl_before "(ACT $v) (s,t) == v s"
unl_after "(ACT v`) (s,t) == v t"
unchanged_def "(s,t) |= unchanged v == (v t = v s)"
square_def "ACT [A]_v == ACT (A | unchanged v)"
angle_def "ACT <A>_v == ACT (A & ~ unchanged v)"
enabled_def "s |= Enabled A == EX u. (s,u) |= A"
end