src/HOL/Imperative_HOL/Heap_Monad.thy
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(*  Title:      HOL/Library/Heap_Monad.thy
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    Author:     John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen
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*)
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header {* A monad with a polymorphic heap and primitive reasoning infrastructure *}
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theory Heap_Monad
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imports Heap
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begin
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subsection {* The monad *}
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subsubsection {* Monad construction *}
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text {* Monadic heap actions either produce values
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  and transform the heap, or fail *}
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datatype 'a Heap = Heap "heap \<Rightarrow> ('a \<times> heap) option"
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primrec execute :: "'a Heap \<Rightarrow> heap \<Rightarrow> ('a \<times> heap) option" where
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  [code del]: "execute (Heap f) = f"
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lemma Heap_cases [case_names succeed fail]:
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  fixes f and h
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  assumes succeed: "\<And>x h'. execute f h = Some (x, h') \<Longrightarrow> P"
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  assumes fail: "execute f h = None \<Longrightarrow> P"
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  shows P
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  using assms by (cases "execute f h") auto
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lemma Heap_execute [simp]:
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  "Heap (execute f) = f" by (cases f) simp_all
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lemma Heap_eqI:
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  "(\<And>h. execute f h = execute g h) \<Longrightarrow> f = g"
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    by (cases f, cases g) (auto simp: expand_fun_eq)
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ML {* structure Execute_Simps = Named_Thms(
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  val name = "execute_simps"
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  val description = "simplification rules for execute"
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) *}
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setup Execute_Simps.setup
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lemma execute_Let [simp, execute_simps]:
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  "execute (let x = t in f x) = (let x = t in execute (f x))"
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  by (simp add: Let_def)
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subsubsection {* Specialised lifters *}
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definition tap :: "(heap \<Rightarrow> 'a) \<Rightarrow> 'a Heap" where
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  [code del]: "tap f = Heap (\<lambda>h. Some (f h, h))"
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lemma execute_tap [simp, execute_simps]:
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  "execute (tap f) h = Some (f h, h)"
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  by (simp add: tap_def)
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definition heap :: "(heap \<Rightarrow> 'a \<times> heap) \<Rightarrow> 'a Heap" where
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  [code del]: "heap f = Heap (Some \<circ> f)"
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lemma execute_heap [simp, execute_simps]:
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  "execute (heap f) = Some \<circ> f"
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  by (simp add: heap_def)
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definition guard :: "(heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> 'a \<times> heap) \<Rightarrow> 'a Heap" where
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  [code del]: "guard P f = Heap (\<lambda>h. if P h then Some (f h) else None)"
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lemma execute_guard [execute_simps]:
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  "\<not> P h \<Longrightarrow> execute (guard P f) h = None"
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  "P h \<Longrightarrow> execute (guard P f) h = Some (f h)"
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  by (simp_all add: guard_def)
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subsubsection {* Predicate classifying successful computations *}
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definition success :: "'a Heap \<Rightarrow> heap \<Rightarrow> bool" where
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  "success f h \<longleftrightarrow> execute f h \<noteq> None"
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lemma successI:
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  "execute f h \<noteq> None \<Longrightarrow> success f h"
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  by (simp add: success_def)
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lemma successE:
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  assumes "success f h"
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  obtains r h' where "r = fst (the (execute c h))"
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    and "h' = snd (the (execute c h))"
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    and "execute f h \<noteq> None"
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  using assms by (simp add: success_def)
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ML {* structure Success_Intros = Named_Thms(
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  val name = "success_intros"
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  val description = "introduction rules for success"
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) *}
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setup Success_Intros.setup
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lemma success_tapI [iff, success_intros]:
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  "success (tap f) h"
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  by (rule successI) simp
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lemma success_heapI [iff, success_intros]:
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  "success (heap f) h"
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  by (rule successI) simp
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lemma success_guardI [success_intros]:
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  "P h \<Longrightarrow> success (guard P f) h"
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  by (rule successI) (simp add: execute_guard)
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lemma success_LetI [success_intros]:
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  "x = t \<Longrightarrow> success (f x) h \<Longrightarrow> success (let x = t in f x) h"
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  by (simp add: Let_def)
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lemma success_ifI:
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  "(c \<Longrightarrow> success t h) \<Longrightarrow> (\<not> c \<Longrightarrow> success e h) \<Longrightarrow>
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    success (if c then t else e) h"
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  by (simp add: success_def)
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subsubsection {* Predicate for a simple relational calculus *}
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text {*
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  The @{text crel} predicate states that when a computation @{text c}
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  runs with the heap @{text h} will result in return value @{text r}
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  and a heap @{text "h'"}, i.e.~no exception occurs.
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*}  
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definition crel :: "'a Heap \<Rightarrow> heap \<Rightarrow> heap \<Rightarrow> 'a \<Rightarrow> bool" where
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  crel_def: "crel c h h' r \<longleftrightarrow> Heap_Monad.execute c h = Some (r, h')"
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lemma crelI:
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  "Heap_Monad.execute c h = Some (r, h') \<Longrightarrow> crel c h h' r"
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  by (simp add: crel_def)
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lemma crelE:
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  assumes "crel c h h' r"
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  obtains "r = fst (the (execute c h))"
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    and "h' = snd (the (execute c h))"
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    and "success c h"
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proof (rule that)
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  from assms have *: "execute c h = Some (r, h')" by (simp add: crel_def)
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  then show "success c h" by (simp add: success_def)
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  from * have "fst (the (execute c h)) = r" and "snd (the (execute c h)) = h'"
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    by simp_all
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  then show "r = fst (the (execute c h))"
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    and "h' = snd (the (execute c h))" by simp_all
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qed
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lemma crel_success:
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  "crel c h h' r \<Longrightarrow> success c h"
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  by (simp add: crel_def success_def)
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lemma success_crelE:
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  assumes "success c h"
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  obtains r h' where "crel c h h' r"
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  using assms by (auto simp add: crel_def success_def)
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lemma crel_deterministic:
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  assumes "crel f h h' a"
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    and "crel f h h'' b"
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  shows "a = b" and "h' = h''"
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  using assms unfolding crel_def by auto
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ML {* structure Crel_Intros = Named_Thms(
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  val name = "crel_intros"
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  val description = "introduction rules for crel"
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) *}
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ML {* structure Crel_Elims = Named_Thms(
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  val name = "crel_elims"
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  val description = "elimination rules for crel"
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) *}
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setup "Crel_Intros.setup #> Crel_Elims.setup"
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lemma crel_LetI [crel_intros]:
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  assumes "x = t" "crel (f x) h h' r"
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  shows "crel (let x = t in f x) h h' r"
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  using assms by simp
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lemma crel_LetE [crel_elims]:
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  assumes "crel (let x = t in f x) h h' r"
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  obtains "crel (f t) h h' r"
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  using assms by simp
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lemma crel_ifI:
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  assumes "c \<Longrightarrow> crel t h h' r"
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    and "\<not> c \<Longrightarrow> crel e h h' r"
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  shows "crel (if c then t else e) h h' r"
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  by (cases c) (simp_all add: assms)
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lemma crel_ifE:
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  assumes "crel (if c then t else e) h h' r"
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  obtains "c" "crel t h h' r"
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    | "\<not> c" "crel e h h' r"
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  using assms by (cases c) simp_all
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lemma crel_tapI [crel_intros]:
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  assumes "h' = h" "r = f h"
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  shows "crel (tap f) h h' r"
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  by (rule crelI) (simp add: assms)
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lemma crel_tapE [crel_elims]:
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  assumes "crel (tap f) h h' r"
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  obtains "h' = h" and "r = f h"
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  using assms by (rule crelE) auto
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lemma crel_heapI [crel_intros]:
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  assumes "h' = snd (f h)" "r = fst (f h)"
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  shows "crel (heap f) h h' r"
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  by (rule crelI) (simp add: assms)
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lemma crel_heapE [crel_elims]:
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  assumes "crel (heap f) h h' r"
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  obtains "h' = snd (f h)" and "r = fst (f h)"
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  using assms by (rule crelE) simp
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lemma crel_guardI [crel_intros]:
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  assumes "P h" "h' = snd (f h)" "r = fst (f h)"
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  shows "crel (guard P f) h h' r"
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  by (rule crelI) (simp add: assms execute_simps)
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lemma crel_guardE [crel_elims]:
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  assumes "crel (guard P f) h h' r"
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  obtains "h' = snd (f h)" "r = fst (f h)" "P h"
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  using assms by (rule crelE)
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    (auto simp add: execute_simps elim!: successE, cases "P h", auto simp add: execute_simps)
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subsubsection {* Monad combinators *}
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definition return :: "'a \<Rightarrow> 'a Heap" where
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  [code del]: "return x = heap (Pair x)"
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lemma execute_return [simp, execute_simps]:
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  "execute (return x) = Some \<circ> Pair x"
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  by (simp add: return_def)
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lemma success_returnI [iff, success_intros]:
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  "success (return x) h"
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  by (rule successI) simp
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lemma crel_returnI [crel_intros]:
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  "h = h' \<Longrightarrow> crel (return x) h h' x"
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  by (rule crelI) simp
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lemma crel_returnE [crel_elims]:
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  assumes "crel (return x) h h' r"
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  obtains "r = x" "h' = h"
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  using assms by (rule crelE) simp
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definition raise :: "string \<Rightarrow> 'a Heap" where -- {* the string is just decoration *}
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  [code del]: "raise s = Heap (\<lambda>_. None)"
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lemma execute_raise [simp, execute_simps]:
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  "execute (raise s) = (\<lambda>_. None)"
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  by (simp add: raise_def)
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lemma crel_raiseE [crel_elims]:
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  assumes "crel (raise x) h h' r"
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  obtains "False"
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  using assms by (rule crelE) (simp add: success_def)
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definition bind :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" (infixl ">>=" 54) where
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  [code del]: "f >>= g = Heap (\<lambda>h. case execute f h of
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                  Some (x, h') \<Rightarrow> execute (g x) h'
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                | None \<Rightarrow> None)"
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notation bind (infixl "\<guillemotright>=" 54)
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lemma execute_bind [execute_simps]:
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  "execute f h = Some (x, h') \<Longrightarrow> execute (f \<guillemotright>= g) h = execute (g x) h'"
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  "execute f h = None \<Longrightarrow> execute (f \<guillemotright>= g) h = None"
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  by (simp_all add: bind_def)
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lemma execute_bind_success:
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  "success f h \<Longrightarrow> execute (f \<guillemotright>= g) h = execute (g (fst (the (execute f h)))) (snd (the (execute f h)))"
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  by (cases f h rule: Heap_cases) (auto elim!: successE simp add: bind_def)
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lemma success_bind_executeI:
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  "execute f h = Some (x, h') \<Longrightarrow> success (g x) h' \<Longrightarrow> success (f \<guillemotright>= g) h"
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  by (auto intro!: successI elim!: successE simp add: bind_def)
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lemma success_bind_crelI [success_intros]:
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  "crel f h h' x \<Longrightarrow> success (g x) h' \<Longrightarrow> success (f \<guillemotright>= g) h"
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  by (auto simp add: crel_def success_def bind_def)
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lemma crel_bindI [crel_intros]:
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  assumes "crel f h h' r" "crel (g r) h' h'' r'"
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  shows "crel (f \<guillemotright>= g) h h'' r'"
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  using assms
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  apply (auto intro!: crelI elim!: crelE successE)
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  apply (subst execute_bind, simp_all)
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  done
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lemma crel_bindE [crel_elims]:
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  assumes "crel (f \<guillemotright>= g) h h'' r'"
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  obtains h' r where "crel f h h' r" "crel (g r) h' h'' r'"
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  using assms by (auto simp add: crel_def bind_def split: option.split_asm)
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lemma execute_bind_eq_SomeI:
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  assumes "Heap_Monad.execute f h = Some (x, h')"
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    and "Heap_Monad.execute (g x) h' = Some (y, h'')"
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  shows "Heap_Monad.execute (f \<guillemotright>= g) h = Some (y, h'')"
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  using assms by (simp add: bind_def)
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lemma return_bind [simp]: "return x \<guillemotright>= f = f x"
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  by (rule Heap_eqI) (simp add: execute_bind)
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lemma bind_return [simp]: "f \<guillemotright>= return = f"
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  by (rule Heap_eqI) (simp add: bind_def split: option.splits)
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lemma bind_bind [simp]: "(f \<guillemotright>= g) \<guillemotright>= k = f \<guillemotright>= (\<lambda>x. g x \<guillemotright>= k)"
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  by (rule Heap_eqI) (simp add: bind_def split: option.splits)
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lemma raise_bind [simp]: "raise e \<guillemotright>= f = raise e"
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  by (rule Heap_eqI) (simp add: execute_bind)
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abbreviation chain :: "'a Heap \<Rightarrow> 'b Heap \<Rightarrow> 'b Heap"  (infixl ">>" 54) where
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  "f >> g \<equiv> f >>= (\<lambda>_. g)"
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notation chain (infixl "\<guillemotright>" 54)
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subsubsection {* do-syntax *}
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text {*
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  We provide a convenient do-notation for monadic expressions
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  well-known from Haskell.  @{const Let} is printed
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  specially in do-expressions.
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*}
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nonterminals do_expr
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syntax
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  "_do" :: "do_expr \<Rightarrow> 'a"
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    ("(do (_)//done)" [12] 100)
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  "_bind" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("_ <- _;//_" [1000, 13, 12] 12)
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  "_chain" :: "'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("_;//_" [13, 12] 12)
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  "_let" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("let _ = _;//_" [1000, 13, 12] 12)
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  "_nil" :: "'a \<Rightarrow> do_expr"
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    ("_" [12] 12)
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syntax (xsymbols)
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  "_bind" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("_ \<leftarrow> _;//_" [1000, 13, 12] 12)
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translations
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  "_do f" => "f"
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  "_bind x f g" => "f \<guillemotright>= (\<lambda>x. g)"
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  "_chain f g" => "f \<guillemotright> g"
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  "_let x t f" => "CONST Let t (\<lambda>x. f)"
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  "_nil f" => "f"
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print_translation {*
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let
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  fun dest_abs_eta (Abs (abs as (_, ty, _))) =
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        let
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          val (v, t) = Syntax.variant_abs abs;
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        in (Free (v, ty), t) end
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    | dest_abs_eta t =
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        let
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          val (v, t) = Syntax.variant_abs ("", dummyT, t $ Bound 0);
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        in (Free (v, dummyT), t) end;
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  fun unfold_monad (Const (@{const_syntax bind}, _) $ f $ g) =
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        let
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          val (v, g') = dest_abs_eta g;
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          val vs = fold_aterms (fn Free (v, _) => insert (op =) v | _ => I) v [];
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          val v_used = fold_aterms
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            (fn Free (w, _) => (fn s => s orelse member (op =) vs w) | _ => I) g' false;
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        in if v_used then
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          Const (@{syntax_const "_bind"}, dummyT) $ v $ f $ unfold_monad g'
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        else
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          Const (@{syntax_const "_chain"}, dummyT) $ f $ unfold_monad g'
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        end
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    | unfold_monad (Const (@{const_syntax chain}, _) $ f $ g) =
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        Const (@{syntax_const "_chain"}, dummyT) $ f $ unfold_monad g
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    | unfold_monad (Const (@{const_syntax Let}, _) $ f $ g) =
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        let
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          val (v, g') = dest_abs_eta g;
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        in Const (@{syntax_const "_let"}, dummyT) $ v $ f $ unfold_monad g' end
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    | unfold_monad (Const (@{const_syntax Pair}, _) $ f) =
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        Const (@{const_syntax return}, dummyT) $ f
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    | unfold_monad f = f;
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  fun contains_bind (Const (@{const_syntax bind}, _) $ _ $ _) = true
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    | contains_bind (Const (@{const_syntax Let}, _) $ _ $ Abs (_, _, t)) =
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        contains_bind t;
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  fun bind_monad_tr' (f::g::ts) = list_comb
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    (Const (@{syntax_const "_do"}, dummyT) $
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      unfold_monad (Const (@{const_syntax bind}, dummyT) $ f $ g), ts);
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  fun Let_monad_tr' (f :: (g as Abs (_, _, g')) :: ts) =
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    if contains_bind g' then list_comb
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      (Const (@{syntax_const "_do"}, dummyT) $
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        unfold_monad (Const (@{const_syntax Let}, dummyT) $ f $ g), ts)
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    else raise Match;
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in
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 [(@{const_syntax bind}, bind_monad_tr'),
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  (@{const_syntax Let}, Let_monad_tr')]
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end;
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*}
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subsection {* Generic combinators *}
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subsubsection {* Assertions *}
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definition assert :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a Heap" where
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  "assert P x = (if P x then return x else raise ''assert'')"
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lemma execute_assert [execute_simps]:
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  "P x \<Longrightarrow> execute (assert P x) h = Some (x, h)"
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  "\<not> P x \<Longrightarrow> execute (assert P x) h = None"
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  by (simp_all add: assert_def)
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lemma success_assertI [success_intros]:
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  "P x \<Longrightarrow> success (assert P x) h"
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  by (rule successI) (simp add: execute_assert)
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lemma crel_assertI [crel_intros]:
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  "P x \<Longrightarrow> h' = h \<Longrightarrow> r = x \<Longrightarrow> crel (assert P x) h h' r"
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  by (rule crelI) (simp add: execute_assert)
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   423
 
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lemma crel_assertE [crel_elims]:
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  assumes "crel (assert P x) h h' r"
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  obtains "P x" "r = x" "h' = h"
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  using assms by (rule crelE) (cases "P x", simp_all add: execute_assert success_def)
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   428
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lemma assert_cong [fundef_cong]:
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   430
  assumes "P = P'"
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  assumes "\<And>x. P' x \<Longrightarrow> f x = f' x"
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  shows "(assert P x >>= f) = (assert P' x >>= f')"
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  by (rule Heap_eqI) (insert assms, simp add: assert_def)
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   434
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   435
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   436
subsubsection {* Plain lifting *}
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   437
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definition lift :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b Heap" where
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  "lift f = return o f"
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lemma lift_collapse [simp]:
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  "lift f x = return (f x)"
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  by (simp add: lift_def)
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   444
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lemma bind_lift:
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  "(f \<guillemotright>= lift g) = (f \<guillemotright>= (\<lambda>x. return (g x)))"
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  by (simp add: lift_def comp_def)
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subsubsection {* Iteration -- warning: this is rarely useful! *}
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   451
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   452
primrec fold_map :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap" where
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  "fold_map f [] = return []"
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| "fold_map f (x # xs) = do
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     y \<leftarrow> f x;
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     ys \<leftarrow> fold_map f xs;
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     return (y # ys)
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   458
   done"
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   459
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   460
lemma fold_map_append:
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  "fold_map f (xs @ ys) = fold_map f xs \<guillemotright>= (\<lambda>xs. fold_map f ys \<guillemotright>= (\<lambda>ys. return (xs @ ys)))"
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  by (induct xs) simp_all
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   463
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lemma execute_fold_map_unchanged_heap [execute_simps]:
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  assumes "\<And>x. x \<in> set xs \<Longrightarrow> \<exists>y. execute (f x) h = Some (y, h)"
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  shows "execute (fold_map f xs) h =
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    Some (List.map (\<lambda>x. fst (the (execute (f x) h))) xs, h)"
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   468
using assms proof (induct xs)
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  case Nil show ?case by simp
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   470
next
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  case (Cons x xs)
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   472
  from Cons.prems obtain y
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   473
    where y: "execute (f x) h = Some (y, h)" by auto
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  moreover from Cons.prems Cons.hyps have "execute (fold_map f xs) h =
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    Some (map (\<lambda>x. fst (the (execute (f x) h))) xs, h)" by auto
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   476
  ultimately show ?case by (simp, simp only: execute_bind(1), simp)
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   477
qed
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   478
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   479
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   480
subsubsection {* A monadic combinator for simple recursive functions *}
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   482
text {* Using a locale to fix arguments f and g of MREC *}
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   483
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   484
locale mrec =
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   485
  fixes f :: "'a \<Rightarrow> ('b + 'a) Heap"
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   486
  and g :: "'a \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> 'b Heap"
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   487
begin
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   488
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   489
function (default "\<lambda>(x, h). None") mrec :: "'a \<Rightarrow> heap \<Rightarrow> ('b \<times> heap) option" where
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   490
  "mrec x h = (case execute (f x) h of
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   491
     Some (Inl r, h') \<Rightarrow> Some (r, h')
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   492
   | Some (Inr s, h') \<Rightarrow> (case mrec s h' of
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   493
             Some (z, h'') \<Rightarrow> execute (g x s z) h''
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   494
           | None \<Rightarrow> None)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   495
   | None \<Rightarrow> None)"
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   496
by auto
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   497
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   498
lemma graph_implies_dom:
35423
6ef9525a5727 eliminated hard tabs;
wenzelm
parents: 35113
diff changeset
   499
  "mrec_graph x y \<Longrightarrow> mrec_dom x"
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   500
apply (induct rule:mrec_graph.induct) 
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   501
apply (rule accpI)
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   502
apply (erule mrec_rel.cases)
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   503
by simp
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   504
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   505
lemma mrec_default: "\<not> mrec_dom (x, h) \<Longrightarrow> mrec x h = None"
35423
6ef9525a5727 eliminated hard tabs;
wenzelm
parents: 35113
diff changeset
   506
  unfolding mrec_def 
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   507
  by (rule fundef_default_value[OF mrec_sumC_def graph_implies_dom, of _ _ "(x, h)", simplified])
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   508
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   509
lemma mrec_di_reverse: 
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   510
  assumes "\<not> mrec_dom (x, h)"
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   511
  shows "
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   512
   (case execute (f x) h of
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   513
     Some (Inl r, h') \<Rightarrow> False
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   514
   | Some (Inr s, h') \<Rightarrow> \<not> mrec_dom (s, h')
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   515
   | None \<Rightarrow> False
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   516
   )" 
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   517
using assms apply (auto split: option.split sum.split)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   518
apply (rule ccontr)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   519
apply (erule notE, rule accpI, elim mrec_rel.cases, auto)+
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   520
done
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   521
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   522
lemma mrec_rule:
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   523
  "mrec x h = 
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   524
   (case execute (f x) h of
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   525
     Some (Inl r, h') \<Rightarrow> Some (r, h')
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   526
   | Some (Inr s, h') \<Rightarrow> 
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   527
          (case mrec s h' of
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   528
             Some (z, h'') \<Rightarrow> execute (g x s z) h''
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   529
           | None \<Rightarrow> None)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   530
   | None \<Rightarrow> None
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   531
   )"
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   532
apply (cases "mrec_dom (x,h)", simp)
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   533
apply (frule mrec_default)
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   534
apply (frule mrec_di_reverse, simp)
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   535
by (auto split: sum.split option.split simp: mrec_default)
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   536
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   537
definition
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   538
  "MREC x = Heap (mrec x)"
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   539
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   540
lemma MREC_rule:
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   541
  "MREC x = 
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   542
  (do y \<leftarrow> f x;
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   543
                (case y of 
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   544
                Inl r \<Rightarrow> return r
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   545
              | Inr s \<Rightarrow> 
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   546
                do z \<leftarrow> MREC s ;
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   547
                   g x s z
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   548
                done) done)"
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   549
  unfolding MREC_def
37756
59caa6180fff avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents: 37754
diff changeset
   550
  unfolding bind_def return_def
34051
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   551
  apply simp
1a82e2e29d67 added Imperative_HOL examples; added tail-recursive combinator for monadic heap functions; adopted code generation of references; added lemmas
bulwahn
parents: 32069
diff changeset
   552
  apply (rule ext)
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   553
  apply (unfold mrec_rule[of x])
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   554
  by (auto split: option.splits prod.splits sum.splits)
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   555
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   556
lemma MREC_pinduct:
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   557
  assumes "execute (MREC x) h = Some (r, h')"
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   558
  assumes non_rec_case: "\<And> x h h' r. execute (f x) h = Some (Inl r, h') \<Longrightarrow> P x h h' r"
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   559
  assumes rec_case: "\<And> x h h1 h2 h' s z r. execute (f x) h = Some (Inr s, h1) \<Longrightarrow> execute (MREC s) h1 = Some (z, h2) \<Longrightarrow> P s h1 h2 z
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   560
    \<Longrightarrow> execute (g x s z) h2 = Some (r, h') \<Longrightarrow> P x h h' r"
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   561
  shows "P x h h' r"
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   562
proof -
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   563
  from assms(1) have mrec: "mrec x h = Some (r, h')"
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   564
    unfolding MREC_def execute.simps .
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   565
  from mrec have dom: "mrec_dom (x, h)"
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   566
    apply -
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   567
    apply (rule ccontr)
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   568
    apply (drule mrec_default) by auto
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   569
  from mrec have h'_r: "h' = snd (the (mrec x h))" "r = fst (the (mrec x h))"
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   570
    by auto
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   571
  from mrec have "P x h (snd (the (mrec x h))) (fst (the (mrec x h)))"
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   572
  proof (induct arbitrary: r h' rule: mrec.pinduct[OF dom])
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   573
    case (1 x h)
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   574
    obtain rr h' where "the (mrec x h) = (rr, h')" by fastsimp
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   575
    show ?case
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   576
    proof (cases "execute (f x) h")
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   577
      case (Some result)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   578
      then obtain a h1 where exec_f: "execute (f x) h = Some (a, h1)" by fastsimp
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   579
      note Inl' = this
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   580
      show ?thesis
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   581
      proof (cases a)
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   582
        case (Inl aa)
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   583
        from this Inl' 1(1) exec_f mrec non_rec_case show ?thesis
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   584
          by auto
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   585
      next
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   586
        case (Inr b)
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   587
        note Inr' = this
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   588
        show ?thesis
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   589
        proof (cases "mrec b h1")
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   590
          case (Some result)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   591
          then obtain aaa h2 where mrec_rec: "mrec b h1 = Some (aaa, h2)" by fastsimp
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   592
          moreover from this have "P b h1 (snd (the (mrec b h1))) (fst (the (mrec b h1)))"
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   593
            apply (intro 1(2))
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   594
            apply (auto simp add: Inr Inl')
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   595
            done
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   596
          moreover note mrec mrec_rec exec_f Inl' Inr' 1(1) 1(3)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   597
          ultimately show ?thesis
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   598
            apply auto
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   599
            apply (rule rec_case)
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   600
            apply auto
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   601
            unfolding MREC_def by auto
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   602
        next
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   603
          case None
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   604
          from this 1(1) exec_f mrec Inr' 1(3) show ?thesis by auto
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   605
        qed
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   606
      qed
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   607
    next
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   608
      case None
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   609
      from this 1(1) mrec 1(3) show ?thesis by simp
36057
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   610
    qed
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   611
  qed
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   612
  from this h'_r show ?thesis by simp
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   613
qed
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   614
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   615
end
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   616
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   617
text {* Providing global versions of the constant and the theorems *}
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   618
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   619
abbreviation "MREC == mrec.MREC"
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   620
lemmas MREC_rule = mrec.MREC_rule
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   621
lemmas MREC_pinduct = mrec.MREC_pinduct
ca6610908ae9 adding MREC induction rule in Imperative HOL
bulwahn
parents: 35423
diff changeset
   622
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   623
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   624
subsection {* Code generator setup *}
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   625
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   626
subsubsection {* Logical intermediate layer *}
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   627
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   628
primrec raise' :: "String.literal \<Rightarrow> 'a Heap" where
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   629
  [code del, code_post]: "raise' (STR s) = raise s"
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   630
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   631
lemma raise_raise' [code_inline]:
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   632
  "raise s = raise' (STR s)"
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   633
  by simp
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   634
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   635
code_datatype raise' -- {* avoid @{const "Heap"} formally *}
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   636
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   637
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   638
subsubsection {* SML and OCaml *}
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   639
26752
6b276119139b corrected ML semantics
haftmann
parents: 26182
diff changeset
   640
code_type Heap (SML "unit/ ->/ _")
27826
4e50590ea9bc changed code setup
haftmann
parents: 27707
diff changeset
   641
code_const "op \<guillemotright>=" (SML "!(fn/ f'_/ =>/ fn/ ()/ =>/ f'_/ (_/ ())/ ())")
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   642
code_const return (SML "!(fn/ ()/ =>/ _)")
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   643
code_const Heap_Monad.raise' (SML "!(raise/ Fail/ _)")
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   644
37754
683d1e1bc234 guard combinator
haftmann
parents: 37724
diff changeset
   645
code_type Heap (OCaml "unit/ ->/ _")
27826
4e50590ea9bc changed code setup
haftmann
parents: 27707
diff changeset
   646
code_const "op \<guillemotright>=" (OCaml "!(fun/ f'_/ ()/ ->/ f'_/ (_/ ())/ ())")
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   647
code_const return (OCaml "!(fun/ ()/ ->/ _)")
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   648
code_const Heap_Monad.raise' (OCaml "failwith/ _")
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   649
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   650
setup {*
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   651
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   652
let
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   653
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   654
open Code_Thingol;
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   655
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   656
fun imp_program naming =
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   657
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   658
  let
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   659
    fun is_const c = case lookup_const naming c
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   660
     of SOME c' => (fn c'' => c' = c'')
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   661
      | NONE => K false;
37756
59caa6180fff avoid slightly odd "M" suffix; rename mapM to fold_map (fold_map_abort would be more correct, though)
haftmann
parents: 37754
diff changeset
   662
    val is_bind = is_const @{const_name bind};
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   663
    val is_return = is_const @{const_name return};
31893
7d8a89390cbf adaptated to changes in term representation
haftmann
parents: 31871
diff changeset
   664
    val dummy_name = "";
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   665
    val dummy_type = ITyVar dummy_name;
31893
7d8a89390cbf adaptated to changes in term representation
haftmann
parents: 31871
diff changeset
   666
    val dummy_case_term = IVar NONE;
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   667
    (*assumption: dummy values are not relevant for serialization*)
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   668
    val unitt = case lookup_const naming @{const_name Unity}
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   669
     of SOME unit' => IConst (unit', (([], []), []))
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   670
      | NONE => error ("Must include " ^ @{const_name Unity} ^ " in generated constants.");
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   671
    fun dest_abs ((v, ty) `|=> t, _) = ((v, ty), t)
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   672
      | dest_abs (t, ty) =
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   673
          let
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   674
            val vs = fold_varnames cons t [];
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   675
            val v = Name.variant vs "x";
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   676
            val ty' = (hd o fst o unfold_fun) ty;
31893
7d8a89390cbf adaptated to changes in term representation
haftmann
parents: 31871
diff changeset
   677
          in ((SOME v, ty'), t `$ IVar (SOME v)) end;
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   678
    fun force (t as IConst (c, _) `$ t') = if is_return c
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   679
          then t' else t `$ unitt
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   680
      | force t = t `$ unitt;
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   681
    fun tr_bind' [(t1, _), (t2, ty2)] =
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   682
      let
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   683
        val ((v, ty), t) = dest_abs (t2, ty2);
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   684
      in ICase (((force t1, ty), [(IVar v, tr_bind'' t)]), dummy_case_term) end
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   685
    and tr_bind'' t = case unfold_app t
37754
683d1e1bc234 guard combinator
haftmann
parents: 37724
diff changeset
   686
         of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if is_bind c
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   687
              then tr_bind' [(x1, ty1), (x2, ty2)]
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   688
              else force t
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   689
          | _ => force t;
31893
7d8a89390cbf adaptated to changes in term representation
haftmann
parents: 31871
diff changeset
   690
    fun imp_monad_bind'' ts = (SOME dummy_name, dummy_type) `|=> ICase (((IVar (SOME dummy_name), dummy_type),
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   691
      [(unitt, tr_bind' ts)]), dummy_case_term)
37754
683d1e1bc234 guard combinator
haftmann
parents: 37724
diff changeset
   692
    and imp_monad_bind' (const as (c, (_, tys))) ts = if is_bind c then case (ts, tys)
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   693
       of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)]
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   694
        | ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] `$ t3
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   695
        | (ts, _) => imp_monad_bind (eta_expand 2 (const, ts))
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   696
      else IConst const `$$ map imp_monad_bind ts
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   697
    and imp_monad_bind (IConst const) = imp_monad_bind' const []
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   698
      | imp_monad_bind (t as IVar _) = t
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   699
      | imp_monad_bind (t as _ `$ _) = (case unfold_app t
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   700
         of (IConst const, ts) => imp_monad_bind' const ts
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   701
          | (t, ts) => imp_monad_bind t `$$ map imp_monad_bind ts)
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   702
      | imp_monad_bind (v_ty `|=> t) = v_ty `|=> imp_monad_bind t
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   703
      | imp_monad_bind (ICase (((t, ty), pats), t0)) = ICase
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   704
          (((imp_monad_bind t, ty),
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   705
            (map o pairself) imp_monad_bind pats),
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   706
              imp_monad_bind t0);
28663
bd8438543bf2 code identifier namings are no longer imperative
haftmann
parents: 28562
diff changeset
   707
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   708
  in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end;
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   709
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   710
in
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   711
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   712
Code_Target.extend_target ("SML_imp", ("SML", imp_program))
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   713
#> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program))
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   714
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   715
end
31871
cc1486840914 streamlined code
haftmann
parents: 31724
diff changeset
   716
27707
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   717
*}
54bf1fea9252 SML_imp, OCaml_imp
haftmann
parents: 27695
diff changeset
   718
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   719
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   720
subsubsection {* Haskell *}
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   721
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   722
text {* Adaption layer *}
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   723
29793
86cac1fab613 changed name space policy for Haskell includes
haftmann
parents: 29399
diff changeset
   724
code_include Haskell "Heap"
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   725
{*import qualified Control.Monad;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   726
import qualified Control.Monad.ST;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   727
import qualified Data.STRef;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   728
import qualified Data.Array.ST;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   729
27695
033732c90ebd Haskell now living in the RealWorld
haftmann
parents: 27673
diff changeset
   730
type RealWorld = Control.Monad.ST.RealWorld;
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   731
type ST s a = Control.Monad.ST.ST s a;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   732
type STRef s a = Data.STRef.STRef s a;
27673
52056ddac194 fixed code generator setup
haftmann
parents: 26753
diff changeset
   733
type STArray s a = Data.Array.ST.STArray s Int a;
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   734
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   735
newSTRef = Data.STRef.newSTRef;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   736
readSTRef = Data.STRef.readSTRef;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   737
writeSTRef = Data.STRef.writeSTRef;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   738
27673
52056ddac194 fixed code generator setup
haftmann
parents: 26753
diff changeset
   739
newArray :: (Int, Int) -> a -> ST s (STArray s a);
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   740
newArray = Data.Array.ST.newArray;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   741
27673
52056ddac194 fixed code generator setup
haftmann
parents: 26753
diff changeset
   742
newListArray :: (Int, Int) -> [a] -> ST s (STArray s a);
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   743
newListArray = Data.Array.ST.newListArray;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   744
27673
52056ddac194 fixed code generator setup
haftmann
parents: 26753
diff changeset
   745
lengthArray :: STArray s a -> ST s Int;
52056ddac194 fixed code generator setup
haftmann
parents: 26753
diff changeset
   746
lengthArray a = Control.Monad.liftM snd (Data.Array.ST.getBounds a);
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   747
27673
52056ddac194 fixed code generator setup
haftmann
parents: 26753
diff changeset
   748
readArray :: STArray s a -> Int -> ST s a;
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   749
readArray = Data.Array.ST.readArray;
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   750
27673
52056ddac194 fixed code generator setup
haftmann
parents: 26753
diff changeset
   751
writeArray :: STArray s a -> Int -> a -> ST s ();
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   752
writeArray = Data.Array.ST.writeArray;*}
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   753
29793
86cac1fab613 changed name space policy for Haskell includes
haftmann
parents: 29399
diff changeset
   754
code_reserved Haskell Heap
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   755
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   756
text {* Monad *}
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   757
29793
86cac1fab613 changed name space policy for Haskell includes
haftmann
parents: 29399
diff changeset
   758
code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _")
28145
af3923ed4786 dropped "run" marker in monad syntax
haftmann
parents: 28054
diff changeset
   759
code_monad "op \<guillemotright>=" Haskell
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   760
code_const return (Haskell "return")
37709
70fafefbcc98 simplified representation of monad type
haftmann
parents: 37591
diff changeset
   761
code_const Heap_Monad.raise' (Haskell "error/ _")
26182
8262ec0e8782 added code generator setup
haftmann
parents: 26170
diff changeset
   762
37758
bf86a65403a8 pervasive success combinator
haftmann
parents: 37756
diff changeset
   763
hide_const (open) Heap heap guard raise' fold_map
37724
haftmann
parents: 37709
diff changeset
   764
26170
66e6b967ccf1 added theories for imperative HOL
haftmann
parents:
diff changeset
   765
end