70 lines
2.3 KiB
Plaintext
70 lines
2.3 KiB
Plaintext
(*
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* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*)
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theory IndirectCalls
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imports
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"PrettyProgs"
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begin
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definition
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lookup_proc :: "(string \<Rightarrow> 'proc_addr) \<Rightarrow> ('proc_id \<rightharpoonup> string)
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\<Rightarrow> 'proc_addr \<Rightarrow> 'proc_id"
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where
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"lookup_proc symtab naming x
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= (THE pid. naming pid \<noteq> None \<and> symtab (the (naming pid)) = x)"
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definition
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lookup_proc_safe :: "(string \<Rightarrow> 'proc_addr) \<Rightarrow> ('proc_id \<rightharpoonup> string)
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\<Rightarrow> 'proc_addr \<Rightarrow> bool"
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where
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"lookup_proc_safe symtab naming x
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= (card {pid. naming pid \<noteq> None \<and> symtab (the (naming pid)) = x} = 1)"
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definition
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procs_consistent :: "(string \<Rightarrow> 'proc_addr) \<Rightarrow> ('proc_nm \<rightharpoonup> string)
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\<Rightarrow> bool"
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where
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"procs_consistent symtab naming
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= (finite (dom naming)
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\<and> (\<forall>x y nm nm'. naming x = Some nm \<and> naming y = Some nm'
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\<and> symtab nm = symtab nm'
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\<longrightarrow> x = y))"
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lemma procs_consistent_eq:
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"\<lbrakk> naming proc = Some nm; procs_consistent symtab naming; addr = symtab nm \<rbrakk>
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\<Longrightarrow> lookup_proc symtab naming addr = proc"
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apply (clarsimp simp: procs_consistent_def lookup_proc_def)
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apply (rule the_equality)
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apply clarsimp
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apply clarsimp
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done
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lemma procs_consistent_safe:
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"\<lbrakk> naming proc = Some nm; procs_consistent symtab naming; addr = symtab nm \<rbrakk>
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\<Longrightarrow> lookup_proc_safe symtab naming addr"
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apply (clarsimp simp: procs_consistent_def lookup_proc_safe_def)
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apply (rule trans, rule arg_cong[where f=card and y="{proc}"])
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apply auto
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done
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lemma hoare_indirect_call_procs_consistent:
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"\<lbrakk> naming proc = Some nm;
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\<Gamma> \<turnstile> P (call initf proc ret c) Q, A \<rbrakk>
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\<Longrightarrow> \<Gamma> \<turnstile> ({s. procs_consistent symtab naming \<and> x_fn s = symtab nm} \<inter> P)
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(dynCall initf (\<lambda>s. lookup_proc symtab naming (x_fn s))
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ret c) Q, A"
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apply (rule hoare_complete, drule hoare_sound)
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apply (clarsimp simp: cvalid_def HoarePartialDef.valid_def)
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apply (erule exec_dynCall_Normal_elim)
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apply (simp add: procs_consistent_eq)
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apply blast
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done
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end
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