(* File: TLA/Stfun.thy ID: $Id: Stfun.thy,v 1.6 2005/09/07 18:22:40 wenzelm Exp $ Author: Stephan Merz Copyright: 1998 University of Munich Theory Name: Stfun Logic Image: HOL States and state functions for TLA as an "intensional" logic. *) theory Stfun imports Intensional begin typedecl state instance state :: world .. types 'a stfun = "state => 'a" stpred = "bool stfun" consts (* Formalizing type "state" would require formulas to be tagged with their underlying state space and would result in a system that is much harder to use. (Unlike Hoare logic or Unity, TLA has quantification over state variables, and therefore one usually works with different state spaces within a single specification.) Instead, "state" is just an anonymous type whose only purpose is to provide "Skolem" constants. Moreover, we do not define a type of state variables separate from that of arbitrary state functions, again in order to simplify the definition of flexible quantification later on. Nevertheless, we need to distinguish state variables, mainly to define the enabledness of actions. The user identifies (tuples of) "base" state variables in a specification via the "meta predicate" basevars, which is defined here. *) stvars :: "'a stfun => bool" syntax "PRED" :: "lift => 'a" ("PRED _") "_stvars" :: "lift => bool" ("basevars _") translations "PRED P" => "(P::state => _)" "_stvars" == "stvars" defs (* Base variables may be assigned arbitrary (type-correct) values. Note that vs may be a tuple of variables. The correct identification of base variables is up to the user who must take care not to introduce an inconsistency. For example, "basevars (x,x)" would definitely be inconsistent. *) basevars_def: "stvars vs == range vs = UNIV" ML {* use_legacy_bindings (the_context ()) *} end
theorem basevars:
basevars vs ==> ∃u. vs u = c
theorem base_pair1:
basevars (x, y) ==> basevars x
theorem base_pair2:
basevars (x, y) ==> basevars y
theorem base_pair:
basevars (x, y) ==> basevars x ∧ basevars y
theorem unit_base:
basevars v
theorem baseE:
[| basevars vs; !!x. vs x = c ==> Q |] ==> Q