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(* Title: HOL/TLA/Memory/ProcedureInterface.thy
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Author: Stephan Merz, University of Munich
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*)
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section \<open>Procedure interface for RPC-Memory components\<close>
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theory ProcedureInterface
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imports "../TLA" RPCMemoryParams
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begin
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typedecl ('a,'r) chan
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(* type of channels with argument type 'a and return type 'r.
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we model a channel as an array of variables (of type chan)
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rather than a single array-valued variable because the
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notation gets a little simpler.
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*)
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type_synonym ('a,'r) channel =" (PrIds \<Rightarrow> ('a,'r) chan) stfun"
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(* data-level functions *)
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consts
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cbit :: "('a,'r) chan \<Rightarrow> bit"
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rbit :: "('a,'r) chan \<Rightarrow> bit"
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arg :: "('a,'r) chan \<Rightarrow> 'a"
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res :: "('a,'r) chan \<Rightarrow> 'r"
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(* state functions *)
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definition caller :: "('a,'r) channel \<Rightarrow> (PrIds \<Rightarrow> (bit * 'a)) stfun"
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where "caller ch == \<lambda>s p. (cbit (ch s p), arg (ch s p))"
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definition rtrner :: "('a,'r) channel \<Rightarrow> (PrIds \<Rightarrow> (bit * 'r)) stfun"
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where "rtrner ch == \<lambda>s p. (rbit (ch s p), res (ch s p))"
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(* slice through array-valued state function *)
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definition slice :: "('a \<Rightarrow> 'b) stfun \<Rightarrow> 'a \<Rightarrow> 'b stfun"
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where "slice x i s \<equiv> x s i"
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syntax
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"_slice" :: "[lift, 'a] \<Rightarrow> lift" ("(_!_)" [70,70] 70)
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translations
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"_slice" \<rightleftharpoons> "CONST slice"
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(* state predicates *)
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definition Calling :: "('a,'r) channel \<Rightarrow> PrIds \<Rightarrow> stpred"
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where "Calling ch p == PRED cbit< ch!p > \<noteq> rbit< ch!p >"
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(* actions *)
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definition ACall :: "('a,'r) channel \<Rightarrow> PrIds \<Rightarrow> 'a stfun \<Rightarrow> action"
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where "ACall ch p v \<equiv> ACT
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\<not> $Calling ch p
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\<and> (cbit<ch!p>$ \<noteq> $rbit<ch!p>)
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\<and> (arg<ch!p>$ = $v)"
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definition AReturn :: "('a,'r) channel \<Rightarrow> PrIds \<Rightarrow> 'r stfun \<Rightarrow> action"
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where "AReturn ch p v == ACT
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$Calling ch p
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\<and> (rbit<ch!p>$ = $cbit<ch!p>)
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\<and> (res<ch!p>$ = $v)"
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syntax
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"_Call" :: "['a, 'b, lift] \<Rightarrow> lift" ("(Call _ _ _)" [90,90,90] 90)
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"_Return" :: "['a, 'b, lift] \<Rightarrow> lift" ("(Return _ _ _)" [90,90,90] 90)
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translations
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"_Call" \<rightleftharpoons> "CONST ACall"
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"_Return" \<rightleftharpoons> "CONST AReturn"
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(* temporal formulas *)
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definition PLegalCaller :: "('a,'r) channel \<Rightarrow> PrIds \<Rightarrow> temporal"
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where "PLegalCaller ch p == TEMP
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Init(\<not> Calling ch p)
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\<and> \<box>[\<exists>a. Call ch p a ]_((caller ch)!p)"
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definition LegalCaller :: "('a,'r) channel \<Rightarrow> temporal"
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where "LegalCaller ch == TEMP (\<forall>p. PLegalCaller ch p)"
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definition PLegalReturner :: "('a,'r) channel \<Rightarrow> PrIds \<Rightarrow> temporal"
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where "PLegalReturner ch p == TEMP \<box>[\<exists>v. Return ch p v ]_((rtrner ch)!p)"
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definition LegalReturner :: "('a,'r) channel \<Rightarrow> temporal"
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where "LegalReturner ch == TEMP (\<forall>p. PLegalReturner ch p)"
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declare slice_def [simp]
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lemmas Procedure_defs = caller_def rtrner_def Calling_def ACall_def AReturn_def
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PLegalCaller_def LegalCaller_def PLegalReturner_def LegalReturner_def
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(* Calls and returns change their subchannel *)
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lemma Call_changed: "\<turnstile> Call ch p v \<longrightarrow> <Call ch p v>_((caller ch)!p)"
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by (auto simp: angle_def ACall_def caller_def Calling_def)
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lemma Return_changed: "\<turnstile> Return ch p v \<longrightarrow> <Return ch p v>_((rtrner ch)!p)"
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by (auto simp: angle_def AReturn_def rtrner_def Calling_def)
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end
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