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child 37845  b70d7a347964 
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 Monad_Syntax 
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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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using assms by (rule crelE) (simp add: success_def execute_simps) 
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37792  262 
definition bind :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" where 
263 
[code del]: "bind f g = Heap (\<lambda>h. case execute f h of 

37709  264 
Some (x, h') \<Rightarrow> execute (g x) h' 
265 
 None \<Rightarrow> None)" 

266 

37792  267 
setup {* 
268 
Adhoc_Overloading.add_variant 

37816  269 
@{const_name Monad_Syntax.bind} @{const_name Heap_Monad.bind} 
37792  270 
*} 
271 

37758  272 
lemma execute_bind [execute_simps]: 
37709  273 
"execute f h = Some (x, h') \<Longrightarrow> execute (f \<guillemotright>= g) h = execute (g x) h'" 
274 
"execute f h = None \<Longrightarrow> execute (f \<guillemotright>= g) h = None" 

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by (simp_all add: bind_def) 
37709  276 

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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  283 
by (auto intro!: successI elim!: successE simp add: bind_def) 
284 

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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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288 

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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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296 

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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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301 

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lemma execute_bind_eq_SomeI: 
37754  303 
assumes "Heap_Monad.execute f h = Some (x, h')" 
304 
and "Heap_Monad.execute (g x) h' = Some (y, h'')" 

305 
shows "Heap_Monad.execute (f \<guillemotright>= g) h = Some (y, h'')" 

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using assms by (simp add: bind_def) 
37754  307 

37709  308 
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  310 

311 
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  313 

37828  314 
lemma bind_bind [simp]: "(f \<guillemotright>= g) \<guillemotright>= k = (f :: 'a Heap) \<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  316 

317 
lemma raise_bind [simp]: "raise e \<guillemotright>= f = raise e" 

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by (rule Heap_eqI) (simp add: execute_simps) 
37709  319 

26170  320 

37758  321 
subsection {* Generic combinators *} 
26170  322 

37758  323 
subsubsection {* Assertions *} 
26170  324 

37709  325 
definition assert :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a Heap" where 
326 
"assert P x = (if P x then return x else raise ''assert'')" 

28742  327 

37758  328 
lemma execute_assert [execute_simps]: 
37754  329 
"P x \<Longrightarrow> execute (assert P x) h = Some (x, h)" 
330 
"\<not> P x \<Longrightarrow> execute (assert P x) h = None" 

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by (simp_all add: assert_def execute_simps) 
37754  332 

37758  333 
lemma success_assertI [success_intros]: 
334 
"P x \<Longrightarrow> success (assert P x) h" 

335 
by (rule successI) (simp add: execute_assert) 

336 

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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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340 

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lemma crel_assertE [crel_elims]: 
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342 
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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345 

28742  346 
lemma assert_cong [fundef_cong]: 
347 
assumes "P = P'" 

348 
assumes "\<And>x. P' x \<Longrightarrow> f x = f' x" 

349 
shows "(assert P x >>= f) = (assert P' x >>= f')" 

37754  350 
by (rule Heap_eqI) (insert assms, simp add: assert_def) 
28742  351 

37758  352 

353 
subsubsection {* Plain lifting *} 

354 

37754  355 
definition lift :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b Heap" where 
356 
"lift f = return o f" 

37709  357 

37754  358 
lemma lift_collapse [simp]: 
359 
"lift f x = return (f x)" 

360 
by (simp add: lift_def) 

37709  361 

37754  362 
lemma bind_lift: 
363 
"(f \<guillemotright>= lift g) = (f \<guillemotright>= (\<lambda>x. return (g x)))" 

364 
by (simp add: lift_def comp_def) 

37709  365 

37758  366 

367 
subsubsection {* Iteration  warning: this is rarely useful! *} 

368 

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primrec fold_map :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap" where 
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"fold_map f [] = return []" 
37792  371 
 "fold_map f (x # xs) = do { 
37709  372 
y \<leftarrow> f x; 
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373 
ys \<leftarrow> fold_map f xs; 
37709  374 
return (y # ys) 
37792  375 
}" 
37709  376 

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lemma fold_map_append: 
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378 
"fold_map f (xs @ ys) = fold_map f xs \<guillemotright>= (\<lambda>xs. fold_map f ys \<guillemotright>= (\<lambda>ys. return (xs @ ys)))" 
37754  379 
by (induct xs) simp_all 
380 

37758  381 
lemma execute_fold_map_unchanged_heap [execute_simps]: 
37754  382 
assumes "\<And>x. x \<in> set xs \<Longrightarrow> \<exists>y. execute (f x) h = Some (y, h)" 
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383 
shows "execute (fold_map f xs) h = 
37754  384 
Some (List.map (\<lambda>x. fst (the (execute (f x) h))) xs, h)" 
385 
using assms proof (induct xs) 

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case Nil show ?case by (simp add: execute_simps) 
37754  387 
next 
388 
case (Cons x xs) 

389 
from Cons.prems obtain y 

390 
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 = 
37754  392 
Some (map (\<lambda>x. fst (the (execute (f x) h))) xs, h)" by auto 
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ultimately show ?case by (simp, simp only: execute_bind(1), simp add: execute_simps) 
37754  394 
qed 
395 

26182  396 
subsection {* Code generator setup *} 
397 

398 
subsubsection {* Logical intermediate layer *} 

399 

37709  400 
primrec raise' :: "String.literal \<Rightarrow> 'a Heap" where 
401 
[code del, code_post]: "raise' (STR s) = raise s" 

26182  402 

37709  403 
lemma raise_raise' [code_inline]: 
404 
"raise s = raise' (STR s)" 

405 
by simp 

26182  406 

37709  407 
code_datatype raise'  {* avoid @{const "Heap"} formally *} 
26182  408 

409 

27707  410 
subsubsection {* SML and OCaml *} 
26182  411 

26752  412 
code_type Heap (SML "unit/ >/ _") 
37828  413 
code_const bind (SML "!(fn/ f'_/ =>/ fn/ ()/ =>/ f'_/ (_/ ())/ ())") 
27707  414 
code_const return (SML "!(fn/ ()/ =>/ _)") 
37709  415 
code_const Heap_Monad.raise' (SML "!(raise/ Fail/ _)") 
26182  416 

37754  417 
code_type Heap (OCaml "unit/ >/ _") 
37828  418 
code_const bind (OCaml "!(fun/ f'_/ ()/ >/ f'_/ (_/ ())/ ())") 
27707  419 
code_const return (OCaml "!(fun/ ()/ >/ _)") 
37828  420 
code_const Heap_Monad.raise' (OCaml "failwith") 
27707  421 

37838  422 

423 
subsubsection {* Haskell *} 

424 

425 
text {* Adaption layer *} 

426 

427 
code_include Haskell "Heap" 

428 
{*import qualified Control.Monad; 

429 
import qualified Control.Monad.ST; 

430 
import qualified Data.STRef; 

431 
import qualified Data.Array.ST; 

432 

433 
type RealWorld = Control.Monad.ST.RealWorld; 

434 
type ST s a = Control.Monad.ST.ST s a; 

435 
type STRef s a = Data.STRef.STRef s a; 

436 
type STArray s a = Data.Array.ST.STArray s Int a; 

437 

438 
newSTRef = Data.STRef.newSTRef; 

439 
readSTRef = Data.STRef.readSTRef; 

440 
writeSTRef = Data.STRef.writeSTRef; 

441 

442 
newArray :: Int > a > ST s (STArray s a); 

443 
newArray k = Data.Array.ST.newArray (0, k); 

444 

445 
newListArray :: [a] > ST s (STArray s a); 

446 
newListArray xs = Data.Array.ST.newListArray (0, length xs) xs; 

447 

448 
newFunArray :: Int > (Int > a) > ST s (STArray s a); 

449 
newFunArray k f = Data.Array.ST.newListArray (0, k) (map f [0..k1]); 

450 

451 
lengthArray :: STArray s a > ST s Int; 

452 
lengthArray a = Control.Monad.liftM snd (Data.Array.ST.getBounds a); 

453 

454 
readArray :: STArray s a > Int > ST s a; 

455 
readArray = Data.Array.ST.readArray; 

456 

457 
writeArray :: STArray s a > Int > a > ST s (); 

458 
writeArray = Data.Array.ST.writeArray;*} 

459 

460 
code_reserved Haskell Heap 

461 

462 
text {* Monad *} 

463 

464 
code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _") 

465 
code_monad bind Haskell 

466 
code_const return (Haskell "return") 

467 
code_const Heap_Monad.raise' (Haskell "error") 

468 

469 

470 
subsubsection {* Scala *} 

471 

37842  472 
code_include Scala "Heap" 
473 
{*def bind[A, B](f: Unit => A, g: A => Unit => B): Unit => B = (_: Unit) => g (f ()) () 

474 

475 
class Ref[A](x: A) { 

476 
var value = x 

477 
} 

478 

479 
object Ref { 

480 
def apply[A](x: A): Ref[A] = new Ref[A](x) 

481 
} 

482 

483 
def lookup[A](r: Ref[A]): A = r.value 

484 

485 
def update[A](r: Ref[A], x: A): Unit = { r.value = x }*} 

37838  486 

487 
code_reserved Scala Heap 

488 

489 
code_type Heap (Scala "Unit/ =>/ _") 

37842  490 
code_const bind (Scala "!Heap.bind((_), (_))") 
491 
code_const return (Scala "('_: Unit)/ =>/ _") 

37838  492 
code_const Heap_Monad.raise' (Scala "!error(_)") 
493 

494 

495 
subsubsection {* Target variants with less units *} 

496 

31871  497 
setup {* 
498 

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let 

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open Code_Thingol; 
502 

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fun imp_program naming = 

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let 
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fun is_const c = case lookup_const naming c 

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

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 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

509 
val is_bind = is_const @{const_name bind}; 
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val is_return = is_const @{const_name return}; 
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val dummy_name = ""; 
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val dummy_type = ITyVar dummy_name; 
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val dummy_case_term = IVar NONE; 
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(*assumption: dummy values are not relevant for serialization*) 
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val unitt = case lookup_const naming @{const_name Unity} 

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

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

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

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 dest_abs (t, ty) = 

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let 

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val vs = fold_varnames cons t []; 

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val v = Name.variant vs "x"; 

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

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

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 force t = t `$ unitt; 

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

529 
let 

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

531 
in ICase (((force t1, ty), [(IVar v, tr_bind'' t)]), dummy_case_term) end 

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and tr_bind'' t = case unfold_app t 

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

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 _ => force t; 

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

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

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else IConst const `$$ map imp_monad_bind ts 

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

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 imp_monad_bind (t as IVar _) = t 

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

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

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

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

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

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(((imp_monad_bind t, ty), 

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(map o pairself) imp_monad_bind pats), 

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imp_monad_bind t0); 

28663
bd8438543bf2
code identifier namings are no longer imperative
haftmann
parents:
28562
diff
changeset

554 

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in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end; 
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in 

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

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#> Code_Target.extend_target ("Scala_imp", ("Scala", imp_program)) 
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end 

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*} 
566 

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37758  568 
hide_const (open) Heap heap guard raise' fold_map 
37724  569 

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end 