161 lines
6.4 KiB
Plaintext
161 lines
6.4 KiB
Plaintext
(*
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* Copyright 2014, General Dynamics C4 Systems
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*
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* This software may be distributed and modified according to the terms of
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* the GNU General Public License version 2. Note that NO WARRANTY is provided.
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* See "LICENSE_GPLv2.txt" for details.
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*
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* @TAG(GD_GPL)
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*)
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theory SubMonad_R
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imports KHeap_R EmptyFail
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begin
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(* SubMonadLib *)
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lemma submonad_doMachineOp:
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"submonad ksMachineState (ksMachineState_update \<circ> K) \<top> doMachineOp"
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apply (unfold_locales)
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apply (clarsimp simp: ext stateAssert_def doMachineOp_def o_def gets_def
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get_def bind_def return_def submonad_fn_def)+
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done
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interpretation submonad_doMachineOp:
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submonad ksMachineState "(ksMachineState_update \<circ> K)" \<top> doMachineOp
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by (rule submonad_doMachineOp)
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lemma corres_machine_op:
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assumes P: "corres_underlying Id False True r \<top> \<top> x x'"
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shows "corres r \<top> \<top> (do_machine_op x) (doMachineOp x')"
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apply (rule corres_submonad [OF submonad_do_machine_op submonad_doMachineOp _ _ P])
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apply (simp_all add: state_relation_def swp_def)
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done
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lemma doMachineOp_mapM:
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assumes "\<And>x. empty_fail (m x)"
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shows "doMachineOp (mapM m l) = mapM (doMachineOp \<circ> m) l"
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apply (rule submonad_mapM [OF submonad_doMachineOp submonad_doMachineOp,
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simplified])
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apply (rule assms)
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done
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lemma doMachineOp_mapM_x:
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assumes "\<And>x. empty_fail (m x)"
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shows "doMachineOp (mapM_x m l) = mapM_x (doMachineOp \<circ> m) l"
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apply (rule submonad_mapM_x [OF submonad_doMachineOp submonad_doMachineOp,
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simplified])
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apply (rule assms)
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done
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lemma submonad_args_ksPSpace:
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"submonad_args ksPSpace (ksPSpace_update o (\<lambda>x _. x)) \<top>"
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by (simp add: submonad_args_def)
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context begin interpretation Arch . (*FIXME: arch_split*)
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definition
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"asUser_fetch \<equiv> \<lambda>t s. case (ksPSpace s t) of
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Some (KOTCB tcb) \<Rightarrow> (atcbContextGet o tcbArch) tcb
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| None \<Rightarrow> undefined"
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definition
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"asUser_replace \<equiv> \<lambda>t uc s.
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let obj = case (ksPSpace s t) of
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Some (KOTCB tcb) \<Rightarrow> Some (KOTCB (tcb \<lparr>tcbArch := atcbContextSet uc (tcbArch tcb)\<rparr>))
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| obj \<Rightarrow> obj
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in s \<lparr> ksPSpace := (ksPSpace s) (t := obj) \<rparr>"
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lemma threadGet_stateAssert_gets_asUser:
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"threadGet (atcbContextGet o tcbArch) t = do stateAssert (tcb_at' t) []; gets (asUser_fetch t) od"
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apply (rule is_stateAssert_gets [OF _ _ empty_fail_threadGet no_fail_threadGet])
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apply (clarsimp simp: threadGet_def liftM_def, wp)
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apply (simp add: threadGet_def liftM_def, wp getObject_tcb_at')
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apply (simp add: threadGet_def liftM_def, wp)
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apply (rule hoare_strengthen_post, wp getObject_obj_at')
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apply (simp add: objBits_def objBitsKO_def)+
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apply (clarsimp simp: obj_at'_def asUser_fetch_def projectKOs atcbContextGet_def)
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done
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lemma threadSet_modify_asUser:
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"tcb_at' t st \<Longrightarrow>
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threadSet (\<lambda>tcb. tcb\<lparr> tcbArch := atcbContextSet uc (tcbArch tcb)\<rparr>) t st = modify (asUser_replace t uc) st"
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apply (rule is_modify [OF _ empty_fail_threadSet no_fail_threadSet])
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apply (clarsimp simp: threadSet_def setObject_def split_def
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updateObject_default_def)
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apply wp
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apply (rule_tac Q="\<lambda>rv. obj_at' (op = rv) t and (op = st)" in hoare_post_imp)
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apply (clarsimp simp: asUser_replace_def Let_def obj_at'_def
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projectKOs fun_upd_def
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split: option.split kernel_object.split)
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apply (wp getObject_obj_at' | clarsimp simp: objBits_def objBitsKO_def atcbContextSet_def)+
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done
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lemma atcbContext_get_eq[simp] : "atcbContextGet (atcbContextSet x atcb) = x"
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by(simp add: atcbContextGet_def atcbContextSet_def)
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lemma atcbContext_set_eq[simp] : "atcbContextSet (atcbContextGet t) t = t"
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by (cases t, simp add: atcbContextGet_def atcbContextSet_def)
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lemma atcbContext_set_set[simp] : "atcbContextSet x (atcbContextSet y atcb) = atcbContextSet x atcb"
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by (cases atcb ,simp add: atcbContextSet_def)
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lemma submonad_asUser:
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"submonad (asUser_fetch t) (asUser_replace t) (tcb_at' t) (asUser t)"
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apply (unfold_locales)
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apply (clarsimp simp: asUser_fetch_def asUser_replace_def
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Let_def obj_at'_def projectKOs
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split: kernel_object.split option.split)
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apply (clarsimp simp: asUser_replace_def Let_def
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split: kernel_object.split option.split)
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apply (rename_tac tcb)
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apply (case_tac tcb, simp)
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apply (clarsimp simp: asUser_fetch_def asUser_replace_def Let_def
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fun_upd_idem
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split: kernel_object.splits option.splits)
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apply (rename_tac tcb)
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apply (case_tac tcb, simp add: map_upd_triv atcbContextSet_def)
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apply (clarsimp simp: obj_at'_def asUser_replace_def
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Let_def projectKOs atcbContextSet_def
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split: kernel_object.splits option.splits)
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apply (rename_tac tcb)
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apply (case_tac tcb, simp add: objBitsKO_def ps_clear_def)
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apply (rule ext)
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apply (clarsimp simp: submonad_fn_def asUser_def bind_assoc split_def)
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apply (subst threadGet_stateAssert_gets_asUser, simp add: bind_assoc, rule ext)
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apply (rule bind_apply_cong [OF refl])+
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apply (rule bind_apply_cong [OF threadSet_modify_asUser])
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apply (clarsimp simp: in_monad stateAssert_def select_f_def)
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apply (rule refl)
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done
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end
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global_interpretation submonad_asUser:
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submonad "asUser_fetch t" "asUser_replace t" "tcb_at' t" "asUser t"
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by (rule submonad_asUser)
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lemma asUser_doMachineOp_comm:
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"\<lbrakk> empty_fail m; empty_fail m' \<rbrakk> \<Longrightarrow>
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do x \<leftarrow> asUser t m; y \<leftarrow> doMachineOp m'; n x y od =
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do y \<leftarrow> doMachineOp m'; x \<leftarrow> asUser t m; n x y od"
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apply (rule submonad_comm [OF submonad.axioms(1) [OF submonad_asUser]
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submonad.axioms(1) [OF submonad_doMachineOp]])
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apply (simp add: submonad.fn_is_sm [OF submonad_asUser])
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apply (simp add: submonad.fn_is_sm [OF submonad_doMachineOp])
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apply (simp add: asUser_replace_def Let_def)
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apply simp
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apply (rule refl)
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apply assumption+
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done
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lemma doMachineOp_nosch [wp]:
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"\<lbrace>\<lambda>s. P (ksSchedulerAction s)\<rbrace> doMachineOp m \<lbrace>\<lambda>rv s. P (ksSchedulerAction s)\<rbrace>"
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apply (simp add: doMachineOp_def split_def)
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apply (wp select_f_wp)
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apply simp
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done
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end
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