author  haftmann 
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child 37792  ba0bc31b90d7 
permissions  rwrr 
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(* Title: HOL/Imperative_HOL/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 [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 [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 [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 [success_intros]: 
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"success (tap f) h" 
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by (rule successI) (simp add: execute_simps) 
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lemma success_heapI [success_intros]: 
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"success (heap f) h" 
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by (rule successI) (simp add: execute_simps) 
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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 execute_simps) 
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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 simp add: execute_simps) 
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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 execute_simps) 
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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 add: execute_simps) 
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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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226 

37758  227 

228 
subsubsection {* Monad combinators *} 

26170  229 

37709  230 
definition return :: "'a \<Rightarrow> 'a Heap" where 
26170  231 
[code del]: "return x = heap (Pair x)" 
232 

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lemma execute_return [execute_simps]: 
37709  234 
"execute (return x) = Some \<circ> Pair x" 
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by (simp add: return_def execute_simps) 
26170  236 

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lemma success_returnI [success_intros]: 
37758  238 
"success (return x) h" 
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by (rule successI) (simp add: execute_simps) 
37758  240 

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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 add: execute_simps) 
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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 add: execute_simps) 
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37709  250 
definition raise :: "string \<Rightarrow> 'a Heap" where  {* the string is just decoration *} 
251 
[code del]: "raise s = Heap (\<lambda>_. None)" 

26170  252 

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lemma execute_raise [execute_simps]: 
37709  254 
"execute (raise s) = (\<lambda>_. None)" 
26170  255 
by (simp add: raise_def) 
256 

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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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261 

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definition bind :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" (infixl ">>=" 54) where 
37709  263 
[code del]: "f >>= g = Heap (\<lambda>h. case execute f h of 
264 
Some (x, h') \<Rightarrow> execute (g x) h' 

265 
 None \<Rightarrow> None)" 

266 

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notation bind (infixl "\<guillemotright>=" 54) 
37709  268 

37758  269 
lemma execute_bind [execute_simps]: 
37709  270 
"execute f h = Some (x, h') \<Longrightarrow> execute (f \<guillemotright>= g) h = execute (g x) h'" 
271 
"execute f h = None \<Longrightarrow> execute (f \<guillemotright>= g) h = None" 

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by (simp_all add: bind_def) 
37709  273 

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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" 
37758  280 
by (auto intro!: successI elim!: successE simp add: bind_def) 
281 

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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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285 

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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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293 

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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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298 

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lemma execute_bind_eq_SomeI: 
37754  300 
assumes "Heap_Monad.execute f h = Some (x, h')" 
301 
and "Heap_Monad.execute (g x) h' = Some (y, h'')" 

302 
shows "Heap_Monad.execute (f \<guillemotright>= g) h = Some (y, h'')" 

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using assms by (simp add: bind_def) 
37754  304 

37709  305 
lemma return_bind [simp]: "return x \<guillemotright>= f = f x" 
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by (rule Heap_eqI) (simp add: execute_bind execute_simps) 
37709  307 

308 
lemma bind_return [simp]: "f \<guillemotright>= return = f" 

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by (rule Heap_eqI) (simp add: bind_def execute_simps split: option.splits) 
37709  310 

311 
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 execute_simps split: option.splits) 
37709  313 

314 
lemma raise_bind [simp]: "raise e \<guillemotright>= f = raise e" 

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by (rule Heap_eqI) (simp add: execute_simps) 
37709  316 

37754  317 
abbreviation chain :: "'a Heap \<Rightarrow> 'b Heap \<Rightarrow> 'b Heap" (infixl ">>" 54) where 
37709  318 
"f >> g \<equiv> f >>= (\<lambda>_. g)" 
319 

37754  320 
notation chain (infixl "\<guillemotright>" 54) 
37709  321 

26170  322 

323 
subsubsection {* dosyntax *} 

324 

325 
text {* 

326 
We provide a convenient donotation for monadic expressions 

327 
wellknown from Haskell. @{const Let} is printed 

328 
specially in doexpressions. 

329 
*} 

330 

331 
nonterminals do_expr 

332 

333 
syntax 

334 
"_do" :: "do_expr \<Rightarrow> 'a" 

335 
("(do (_)//done)" [12] 100) 

37754  336 
"_bind" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr" 
26170  337 
("_ < _;//_" [1000, 13, 12] 12) 
37754  338 
"_chain" :: "'a \<Rightarrow> do_expr \<Rightarrow> do_expr" 
26170  339 
("_;//_" [13, 12] 12) 
340 
"_let" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr" 

341 
("let _ = _;//_" [1000, 13, 12] 12) 

342 
"_nil" :: "'a \<Rightarrow> do_expr" 

343 
("_" [12] 12) 

344 

345 
syntax (xsymbols) 

37754  346 
"_bind" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr" 
26170  347 
("_ \<leftarrow> _;//_" [1000, 13, 12] 12) 
348 

349 
translations 

28145  350 
"_do f" => "f" 
37754  351 
"_bind x f g" => "f \<guillemotright>= (\<lambda>x. g)" 
352 
"_chain f g" => "f \<guillemotright> g" 

26170  353 
"_let x t f" => "CONST Let t (\<lambda>x. f)" 
354 
"_nil f" => "f" 

355 

356 
print_translation {* 

357 
let 

358 
fun dest_abs_eta (Abs (abs as (_, ty, _))) = 

359 
let 

360 
val (v, t) = Syntax.variant_abs abs; 

28145  361 
in (Free (v, ty), t) end 
26170  362 
 dest_abs_eta t = 
363 
let 

364 
val (v, t) = Syntax.variant_abs ("", dummyT, t $ Bound 0); 

28145  365 
in (Free (v, dummyT), t) end; 
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fun unfold_monad (Const (@{const_syntax bind}, _) $ f $ g) = 
26170  367 
let 
28145  368 
val (v, g') = dest_abs_eta g; 
369 
val vs = fold_aterms (fn Free (v, _) => insert (op =) v  _ => I) v []; 

26170  370 
val v_used = fold_aterms 
28145  371 
(fn Free (w, _) => (fn s => s orelse member (op =) vs w)  _ => I) g' false; 
26170  372 
in if v_used then 
37754  373 
Const (@{syntax_const "_bind"}, dummyT) $ v $ f $ unfold_monad g' 
26170  374 
else 
37754  375 
Const (@{syntax_const "_chain"}, dummyT) $ f $ unfold_monad g' 
26170  376 
end 
37754  377 
 unfold_monad (Const (@{const_syntax chain}, _) $ f $ g) = 
378 
Const (@{syntax_const "_chain"}, dummyT) $ f $ unfold_monad g 

26170  379 
 unfold_monad (Const (@{const_syntax Let}, _) $ f $ g) = 
380 
let 

28145  381 
val (v, g') = dest_abs_eta g; 
35113  382 
in Const (@{syntax_const "_let"}, dummyT) $ v $ f $ unfold_monad g' end 
26170  383 
 unfold_monad (Const (@{const_syntax Pair}, _) $ f) = 
28145  384 
Const (@{const_syntax return}, dummyT) $ f 
26170  385 
 unfold_monad f = f; 
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386 
fun contains_bind (Const (@{const_syntax bind}, _) $ _ $ _) = true 
37754  387 
 contains_bind (Const (@{const_syntax Let}, _) $ _ $ Abs (_, _, t)) = 
388 
contains_bind t; 

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fun bind_monad_tr' (f::g::ts) = list_comb 
35113  390 
(Const (@{syntax_const "_do"}, dummyT) $ 
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unfold_monad (Const (@{const_syntax bind}, dummyT) $ f $ g), ts); 
35113  392 
fun Let_monad_tr' (f :: (g as Abs (_, _, g')) :: ts) = 
37754  393 
if contains_bind g' then list_comb 
35113  394 
(Const (@{syntax_const "_do"}, dummyT) $ 
395 
unfold_monad (Const (@{const_syntax Let}, dummyT) $ f $ g), ts) 

28145  396 
else raise Match; 
35113  397 
in 
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398 
[(@{const_syntax bind}, bind_monad_tr'), 
35113  399 
(@{const_syntax Let}, Let_monad_tr')] 
400 
end; 

26170  401 
*} 
402 

403 

37758  404 
subsection {* Generic combinators *} 
26170  405 

37758  406 
subsubsection {* Assertions *} 
26170  407 

37709  408 
definition assert :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a Heap" where 
409 
"assert P x = (if P x then return x else raise ''assert'')" 

28742  410 

37758  411 
lemma execute_assert [execute_simps]: 
37754  412 
"P x \<Longrightarrow> execute (assert P x) h = Some (x, h)" 
413 
"\<not> P x \<Longrightarrow> execute (assert P x) h = None" 

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by (simp_all add: assert_def execute_simps) 
37754  415 

37758  416 
lemma success_assertI [success_intros]: 
417 
"P x \<Longrightarrow> success (assert P x) h" 

418 
by (rule successI) (simp add: execute_assert) 

419 

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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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422 
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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425 
assumes "crel (assert P x) h h' r" 
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426 
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 

28742  429 
lemma assert_cong [fundef_cong]: 
430 
assumes "P = P'" 

431 
assumes "\<And>x. P' x \<Longrightarrow> f x = f' x" 

432 
shows "(assert P x >>= f) = (assert P' x >>= f')" 

37754  433 
by (rule Heap_eqI) (insert assms, simp add: assert_def) 
28742  434 

37758  435 

436 
subsubsection {* Plain lifting *} 

437 

37754  438 
definition lift :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b Heap" where 
439 
"lift f = return o f" 

37709  440 

37754  441 
lemma lift_collapse [simp]: 
442 
"lift f x = return (f x)" 

443 
by (simp add: lift_def) 

37709  444 

37754  445 
lemma bind_lift: 
446 
"(f \<guillemotright>= lift g) = (f \<guillemotright>= (\<lambda>x. return (g x)))" 

447 
by (simp add: lift_def comp_def) 

37709  448 

37758  449 

450 
subsubsection {* Iteration  warning: this is rarely useful! *} 

451 

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primrec fold_map :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap" where 
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453 
"fold_map f [] = return []" 
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454 
 "fold_map f (x # xs) = do 
37709  455 
y \<leftarrow> f x; 
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456 
ys \<leftarrow> fold_map f xs; 
37709  457 
return (y # ys) 
458 
done" 

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)))" 
37754  462 
by (induct xs) simp_all 
463 

37758  464 
lemma execute_fold_map_unchanged_heap [execute_simps]: 
37754  465 
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 = 
37754  467 
Some (List.map (\<lambda>x. fst (the (execute (f x) h))) xs, h)" 
468 
using assms proof (induct xs) 

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469 
case Nil show ?case by (simp add: execute_simps) 
37754  470 
next 
471 
case (Cons x xs) 

472 
from Cons.prems obtain y 

473 
where y: "execute (f x) h = Some (y, h)" by auto 

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474 
moreover from Cons.prems Cons.hyps have "execute (fold_map f xs) h = 
37754  475 
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 add: execute_simps) 
37754  477 
qed 
478 

26182  479 
subsection {* Code generator setup *} 
480 

481 
subsubsection {* Logical intermediate layer *} 

482 

37709  483 
primrec raise' :: "String.literal \<Rightarrow> 'a Heap" where 
484 
[code del, code_post]: "raise' (STR s) = raise s" 

26182  485 

37709  486 
lemma raise_raise' [code_inline]: 
487 
"raise s = raise' (STR s)" 

488 
by simp 

26182  489 

37709  490 
code_datatype raise'  {* avoid @{const "Heap"} formally *} 
26182  491 

492 

27707  493 
subsubsection {* SML and OCaml *} 
26182  494 

26752  495 
code_type Heap (SML "unit/ >/ _") 
27826  496 
code_const "op \<guillemotright>=" (SML "!(fn/ f'_/ =>/ fn/ ()/ =>/ f'_/ (_/ ())/ ())") 
27707  497 
code_const return (SML "!(fn/ ()/ =>/ _)") 
37709  498 
code_const Heap_Monad.raise' (SML "!(raise/ Fail/ _)") 
26182  499 

37754  500 
code_type Heap (OCaml "unit/ >/ _") 
27826  501 
code_const "op \<guillemotright>=" (OCaml "!(fun/ f'_/ ()/ >/ f'_/ (_/ ())/ ())") 
27707  502 
code_const return (OCaml "!(fun/ ()/ >/ _)") 
37709  503 
code_const Heap_Monad.raise' (OCaml "failwith/ _") 
27707  504 

31871  505 
setup {* 
506 

507 
let 

27707  508 

31871  509 
open Code_Thingol; 
510 

511 
fun imp_program naming = 

27707  512 

31871  513 
let 
514 
fun is_const c = case lookup_const naming c 

515 
of SOME c' => (fn c'' => c' = c'') 

516 
 NONE => K false; 

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val is_bind = is_const @{const_name bind}; 
31871  518 
val is_return = is_const @{const_name return}; 
31893  519 
val dummy_name = ""; 
31871  520 
val dummy_type = ITyVar dummy_name; 
31893  521 
val dummy_case_term = IVar NONE; 
31871  522 
(*assumption: dummy values are not relevant for serialization*) 
523 
val unitt = case lookup_const naming @{const_name Unity} 

524 
of SOME unit' => IConst (unit', (([], []), [])) 

525 
 NONE => error ("Must include " ^ @{const_name Unity} ^ " in generated constants."); 

526 
fun dest_abs ((v, ty) `=> t, _) = ((v, ty), t) 

527 
 dest_abs (t, ty) = 

528 
let 

529 
val vs = fold_varnames cons t []; 

530 
val v = Name.variant vs "x"; 

531 
val ty' = (hd o fst o unfold_fun) ty; 

31893  532 
in ((SOME v, ty'), t `$ IVar (SOME v)) end; 
31871  533 
fun force (t as IConst (c, _) `$ t') = if is_return c 
534 
then t' else t `$ unitt 

535 
 force t = t `$ unitt; 

536 
fun tr_bind' [(t1, _), (t2, ty2)] = 

537 
let 

538 
val ((v, ty), t) = dest_abs (t2, ty2); 

539 
in ICase (((force t1, ty), [(IVar v, tr_bind'' t)]), dummy_case_term) end 

540 
and tr_bind'' t = case unfold_app t 

37754  541 
of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if is_bind c 
31871  542 
then tr_bind' [(x1, ty1), (x2, ty2)] 
543 
else force t 

544 
 _ => force t; 

31893  545 
fun imp_monad_bind'' ts = (SOME dummy_name, dummy_type) `=> ICase (((IVar (SOME dummy_name), dummy_type), 
31871  546 
[(unitt, tr_bind' ts)]), dummy_case_term) 
37754  547 
and imp_monad_bind' (const as (c, (_, tys))) ts = if is_bind c then case (ts, tys) 
31871  548 
of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] 
549 
 ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] `$ t3 

550 
 (ts, _) => imp_monad_bind (eta_expand 2 (const, ts)) 

551 
else IConst const `$$ map imp_monad_bind ts 

552 
and imp_monad_bind (IConst const) = imp_monad_bind' const [] 

553 
 imp_monad_bind (t as IVar _) = t 

554 
 imp_monad_bind (t as _ `$ _) = (case unfold_app t 

555 
of (IConst const, ts) => imp_monad_bind' const ts 

556 
 (t, ts) => imp_monad_bind t `$$ map imp_monad_bind ts) 

557 
 imp_monad_bind (v_ty `=> t) = v_ty `=> imp_monad_bind t 

558 
 imp_monad_bind (ICase (((t, ty), pats), t0)) = ICase 

559 
(((imp_monad_bind t, ty), 

560 
(map o pairself) imp_monad_bind pats), 

561 
imp_monad_bind t0); 

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562 

31871  563 
in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end; 
27707  564 

565 
in 

566 

31871  567 
Code_Target.extend_target ("SML_imp", ("SML", imp_program)) 
568 
#> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program)) 

27707  569 

570 
end 

31871  571 

27707  572 
*} 
573 

26182  574 

575 
subsubsection {* Haskell *} 

576 

577 
text {* Adaption layer *} 

578 

29793  579 
code_include Haskell "Heap" 
26182  580 
{*import qualified Control.Monad; 
581 
import qualified Control.Monad.ST; 

582 
import qualified Data.STRef; 

583 
import qualified Data.Array.ST; 

584 

27695  585 
type RealWorld = Control.Monad.ST.RealWorld; 
26182  586 
type ST s a = Control.Monad.ST.ST s a; 
587 
type STRef s a = Data.STRef.STRef s a; 

27673  588 
type STArray s a = Data.Array.ST.STArray s Int a; 
26182  589 

590 
newSTRef = Data.STRef.newSTRef; 

591 
readSTRef = Data.STRef.readSTRef; 

592 
writeSTRef = Data.STRef.writeSTRef; 

593 

27673  594 
newArray :: (Int, Int) > a > ST s (STArray s a); 
26182  595 
newArray = Data.Array.ST.newArray; 
596 

27673  597 
newListArray :: (Int, Int) > [a] > ST s (STArray s a); 
26182  598 
newListArray = Data.Array.ST.newListArray; 
599 

27673  600 
lengthArray :: STArray s a > ST s Int; 
601 
lengthArray a = Control.Monad.liftM snd (Data.Array.ST.getBounds a); 

26182  602 

27673  603 
readArray :: STArray s a > Int > ST s a; 
26182  604 
readArray = Data.Array.ST.readArray; 
605 

27673  606 
writeArray :: STArray s a > Int > a > ST s (); 
26182  607 
writeArray = Data.Array.ST.writeArray;*} 
608 

29793  609 
code_reserved Haskell Heap 
26182  610 

611 
text {* Monad *} 

612 

29793  613 
code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _") 
28145  614 
code_monad "op \<guillemotright>=" Haskell 
26182  615 
code_const return (Haskell "return") 
37709  616 
code_const Heap_Monad.raise' (Haskell "error/ _") 
26182  617 

37758  618 
hide_const (open) Heap heap guard raise' fold_map 
37724  619 

26170  620 
end 