src/HOL/Imperative_HOL/Heap_Monad.thy
author haftmann
Wed Sep 01 11:09:50 2010 +0200 (2010-09-01)
changeset 38968 e55deaa22fff
parent 38773 f9837065b5e8
child 39021 139aada5caf8
permissions -rw-r--r--
do not print object frame around Scala includes -- this is in the responsibility of the user
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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 Code_Natural
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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> execute c h = Some (r, h')"
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lemma crelI:
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  "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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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 [execute_simps]:
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  "execute (return x) = Some \<circ> Pair x"
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  by (simp add: return_def execute_simps)
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lemma success_returnI [success_intros]:
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  "success (return x) h"
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  by (rule successI) (simp add: execute_simps)
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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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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 [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 execute_simps)
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definition bind :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" where
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  [code del]: "bind 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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setup {*
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  Adhoc_Overloading.add_variant 
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    @{const_name Monad_Syntax.bind} @{const_name Heap_Monad.bind}
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*}
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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_case:
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  "execute (f \<guillemotright>= g) h = (case (execute f h) of
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    Some (x, h') \<Rightarrow> execute (g x) h' | None \<Rightarrow> None)"
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  by (simp 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 "execute f h = Some (x, h')"
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    and "execute (g x) h' = Some (y, h'')"
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  shows "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 execute_simps)
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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)
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lemma bind_bind [simp]: "(f \<guillemotright>= g) \<guillemotright>= k = (f :: 'a Heap) \<guillemotright>= (\<lambda>x. g x \<guillemotright>= k)"
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   320
  by (rule Heap_eqI) (simp add: bind_def execute_simps split: option.splits)
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   321
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   322
lemma raise_bind [simp]: "raise e \<guillemotright>= f = raise e"
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   323
  by (rule Heap_eqI) (simp add: execute_simps)
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   324
haftmann@26170
   325
haftmann@37758
   326
subsection {* Generic combinators *}
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   327
haftmann@37758
   328
subsubsection {* Assertions *}
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   329
haftmann@37709
   330
definition assert :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a Heap" where
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   331
  "assert P x = (if P x then return x else raise ''assert'')"
haftmann@28742
   332
haftmann@37758
   333
lemma execute_assert [execute_simps]:
haftmann@37754
   334
  "P x \<Longrightarrow> execute (assert P x) h = Some (x, h)"
haftmann@37754
   335
  "\<not> P x \<Longrightarrow> execute (assert P x) h = None"
haftmann@37787
   336
  by (simp_all add: assert_def execute_simps)
haftmann@37754
   337
haftmann@37758
   338
lemma success_assertI [success_intros]:
haftmann@37758
   339
  "P x \<Longrightarrow> success (assert P x) h"
haftmann@37758
   340
  by (rule successI) (simp add: execute_assert)
haftmann@37758
   341
haftmann@37771
   342
lemma crel_assertI [crel_intros]:
haftmann@37771
   343
  "P x \<Longrightarrow> h' = h \<Longrightarrow> r = x \<Longrightarrow> crel (assert P x) h h' r"
haftmann@37771
   344
  by (rule crelI) (simp add: execute_assert)
haftmann@37771
   345
 
haftmann@37771
   346
lemma crel_assertE [crel_elims]:
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   347
  assumes "crel (assert P x) h h' r"
haftmann@37771
   348
  obtains "P x" "r = x" "h' = h"
haftmann@37771
   349
  using assms by (rule crelE) (cases "P x", simp_all add: execute_assert success_def)
haftmann@37771
   350
haftmann@28742
   351
lemma assert_cong [fundef_cong]:
haftmann@28742
   352
  assumes "P = P'"
haftmann@28742
   353
  assumes "\<And>x. P' x \<Longrightarrow> f x = f' x"
haftmann@28742
   354
  shows "(assert P x >>= f) = (assert P' x >>= f')"
haftmann@37754
   355
  by (rule Heap_eqI) (insert assms, simp add: assert_def)
haftmann@28742
   356
haftmann@37758
   357
haftmann@37758
   358
subsubsection {* Plain lifting *}
haftmann@37758
   359
haftmann@37754
   360
definition lift :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b Heap" where
haftmann@37754
   361
  "lift f = return o f"
haftmann@37709
   362
haftmann@37754
   363
lemma lift_collapse [simp]:
haftmann@37754
   364
  "lift f x = return (f x)"
haftmann@37754
   365
  by (simp add: lift_def)
haftmann@37709
   366
haftmann@37754
   367
lemma bind_lift:
haftmann@37754
   368
  "(f \<guillemotright>= lift g) = (f \<guillemotright>= (\<lambda>x. return (g x)))"
haftmann@37754
   369
  by (simp add: lift_def comp_def)
haftmann@37709
   370
haftmann@37758
   371
haftmann@37758
   372
subsubsection {* Iteration -- warning: this is rarely useful! *}
haftmann@37758
   373
haftmann@37756
   374
primrec fold_map :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap" where
haftmann@37756
   375
  "fold_map f [] = return []"
krauss@37792
   376
| "fold_map f (x # xs) = do {
haftmann@37709
   377
     y \<leftarrow> f x;
haftmann@37756
   378
     ys \<leftarrow> fold_map f xs;
haftmann@37709
   379
     return (y # ys)
krauss@37792
   380
   }"
haftmann@37709
   381
haftmann@37756
   382
lemma fold_map_append:
haftmann@37756
   383
  "fold_map f (xs @ ys) = fold_map f xs \<guillemotright>= (\<lambda>xs. fold_map f ys \<guillemotright>= (\<lambda>ys. return (xs @ ys)))"
haftmann@37754
   384
  by (induct xs) simp_all
haftmann@37754
   385
haftmann@37758
   386
lemma execute_fold_map_unchanged_heap [execute_simps]:
haftmann@37754
   387
  assumes "\<And>x. x \<in> set xs \<Longrightarrow> \<exists>y. execute (f x) h = Some (y, h)"
haftmann@37756
   388
  shows "execute (fold_map f xs) h =
haftmann@37754
   389
    Some (List.map (\<lambda>x. fst (the (execute (f x) h))) xs, h)"
haftmann@37754
   390
using assms proof (induct xs)
haftmann@37787
   391
  case Nil show ?case by (simp add: execute_simps)
haftmann@37754
   392
next
haftmann@37754
   393
  case (Cons x xs)
haftmann@37754
   394
  from Cons.prems obtain y
haftmann@37754
   395
    where y: "execute (f x) h = Some (y, h)" by auto
haftmann@37756
   396
  moreover from Cons.prems Cons.hyps have "execute (fold_map f xs) h =
haftmann@37754
   397
    Some (map (\<lambda>x. fst (the (execute (f x) h))) xs, h)" by auto
haftmann@37787
   398
  ultimately show ?case by (simp, simp only: execute_bind(1), simp add: execute_simps)
haftmann@37754
   399
qed
haftmann@37754
   400
haftmann@26182
   401
subsection {* Code generator setup *}
haftmann@26182
   402
haftmann@26182
   403
subsubsection {* Logical intermediate layer *}
haftmann@26182
   404
haftmann@37709
   405
primrec raise' :: "String.literal \<Rightarrow> 'a Heap" where
haftmann@37709
   406
  [code del, code_post]: "raise' (STR s) = raise s"
haftmann@26182
   407
haftmann@37709
   408
lemma raise_raise' [code_inline]:
haftmann@37709
   409
  "raise s = raise' (STR s)"
haftmann@37709
   410
  by simp
haftmann@26182
   411
haftmann@37709
   412
code_datatype raise' -- {* avoid @{const "Heap"} formally *}
haftmann@26182
   413
haftmann@26182
   414
haftmann@27707
   415
subsubsection {* SML and OCaml *}
haftmann@26182
   416
haftmann@26752
   417
code_type Heap (SML "unit/ ->/ _")
haftmann@37828
   418
code_const bind (SML "!(fn/ f'_/ =>/ fn/ ()/ =>/ f'_/ (_/ ())/ ())")
haftmann@27707
   419
code_const return (SML "!(fn/ ()/ =>/ _)")
haftmann@37709
   420
code_const Heap_Monad.raise' (SML "!(raise/ Fail/ _)")
haftmann@26182
   421
haftmann@37754
   422
code_type Heap (OCaml "unit/ ->/ _")
haftmann@37828
   423
code_const bind (OCaml "!(fun/ f'_/ ()/ ->/ f'_/ (_/ ())/ ())")
haftmann@27707
   424
code_const return (OCaml "!(fun/ ()/ ->/ _)")
haftmann@37828
   425
code_const Heap_Monad.raise' (OCaml "failwith")
haftmann@27707
   426
haftmann@37838
   427
haftmann@37838
   428
subsubsection {* Haskell *}
haftmann@37838
   429
haftmann@37838
   430
text {* Adaption layer *}
haftmann@37838
   431
haftmann@37838
   432
code_include Haskell "Heap"
haftmann@37838
   433
{*import qualified Control.Monad;
haftmann@37838
   434
import qualified Control.Monad.ST;
haftmann@37838
   435
import qualified Data.STRef;
haftmann@37838
   436
import qualified Data.Array.ST;
haftmann@37838
   437
haftmann@37964
   438
import Natural;
haftmann@37964
   439
haftmann@37838
   440
type RealWorld = Control.Monad.ST.RealWorld;
haftmann@37838
   441
type ST s a = Control.Monad.ST.ST s a;
haftmann@37838
   442
type STRef s a = Data.STRef.STRef s a;
haftmann@37964
   443
type STArray s a = Data.Array.ST.STArray s Natural a;
haftmann@37838
   444
haftmann@37838
   445
newSTRef = Data.STRef.newSTRef;
haftmann@37838
   446
readSTRef = Data.STRef.readSTRef;
haftmann@37838
   447
writeSTRef = Data.STRef.writeSTRef;
haftmann@37838
   448
haftmann@37964
   449
newArray :: Natural -> a -> ST s (STArray s a);
haftmann@37838
   450
newArray k = Data.Array.ST.newArray (0, k);
haftmann@37838
   451
haftmann@37838
   452
newListArray :: [a] -> ST s (STArray s a);
haftmann@37964
   453
newListArray xs = Data.Array.ST.newListArray (0, (fromInteger . toInteger . length) xs) xs;
haftmann@37838
   454
haftmann@37964
   455
newFunArray :: Natural -> (Natural -> a) -> ST s (STArray s a);
haftmann@37838
   456
newFunArray k f = Data.Array.ST.newListArray (0, k) (map f [0..k-1]);
haftmann@37838
   457
haftmann@37964
   458
lengthArray :: STArray s a -> ST s Natural;
haftmann@37838
   459
lengthArray a = Control.Monad.liftM snd (Data.Array.ST.getBounds a);
haftmann@37838
   460
haftmann@37964
   461
readArray :: STArray s a -> Natural -> ST s a;
haftmann@37838
   462
readArray = Data.Array.ST.readArray;
haftmann@37838
   463
haftmann@37964
   464
writeArray :: STArray s a -> Natural -> a -> ST s ();
haftmann@37838
   465
writeArray = Data.Array.ST.writeArray;*}
haftmann@37838
   466
haftmann@37838
   467
code_reserved Haskell Heap
haftmann@37838
   468
haftmann@37838
   469
text {* Monad *}
haftmann@37838
   470
haftmann@37838
   471
code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _")
haftmann@37838
   472
code_monad bind Haskell
haftmann@37838
   473
code_const return (Haskell "return")
haftmann@37838
   474
code_const Heap_Monad.raise' (Haskell "error")
haftmann@37838
   475
haftmann@37838
   476
haftmann@37838
   477
subsubsection {* Scala *}
haftmann@37838
   478
haftmann@37842
   479
code_include Scala "Heap"
haftmann@38968
   480
{*object Heap {
haftmann@38968
   481
  def bind[A, B](f: Unit => A, g: A => Unit => B): Unit => B = (_: Unit) => g (f ()) ()
haftmann@38968
   482
}
haftmann@37842
   483
haftmann@37842
   484
class Ref[A](x: A) {
haftmann@37842
   485
  var value = x
haftmann@37842
   486
}
haftmann@37842
   487
haftmann@37842
   488
object Ref {
haftmann@38771
   489
  def apply[A](x: A): Ref[A] =
haftmann@38771
   490
    new Ref[A](x)
haftmann@38771
   491
  def lookup[A](r: Ref[A]): A =
haftmann@38771
   492
    r.value
haftmann@38771
   493
  def update[A](r: Ref[A], x: A): Unit =
haftmann@38771
   494
    { r.value = x }
haftmann@37842
   495
}
haftmann@37842
   496
haftmann@37964
   497
object Array {
haftmann@38968
   498
  import collection.mutable.ArraySeq
haftmann@38968
   499
  def alloc[A](n: Natural)(x: A): ArraySeq[A] =
haftmann@38771
   500
    ArraySeq.fill(n.as_Int)(x)
haftmann@38968
   501
  def make[A](n: Natural)(f: Natural => A): ArraySeq[A] =
haftmann@38968
   502
    ArraySeq.tabulate(n.as_Int)((k: Int) => f(Natural(k)))
haftmann@38968
   503
  def len[A](a: ArraySeq[A]): Natural =
haftmann@38968
   504
    Natural(a.length)
haftmann@38968
   505
  def nth[A](a: ArraySeq[A], n: Natural): A =
haftmann@38771
   506
    a(n.as_Int)
haftmann@38968
   507
  def upd[A](a: ArraySeq[A], n: Natural, x: A): Unit =
haftmann@38771
   508
    a.update(n.as_Int, x)
haftmann@38771
   509
  def freeze[A](a: ArraySeq[A]): List[A] =
haftmann@38771
   510
    a.toList
haftmann@38968
   511
}
haftmann@38968
   512
*}
haftmann@37842
   513
haftmann@38968
   514
code_reserved Scala Heap Ref Array
haftmann@37838
   515
haftmann@37838
   516
code_type Heap (Scala "Unit/ =>/ _")
haftmann@38771
   517
code_const bind (Scala "Heap.bind")
haftmann@37842
   518
code_const return (Scala "('_: Unit)/ =>/ _")
haftmann@37845
   519
code_const Heap_Monad.raise' (Scala "!error((_))")
haftmann@37838
   520
haftmann@37838
   521
haftmann@37838
   522
subsubsection {* Target variants with less units *}
haftmann@37838
   523
haftmann@31871
   524
setup {*
haftmann@31871
   525
haftmann@31871
   526
let
haftmann@27707
   527
haftmann@31871
   528
open Code_Thingol;
haftmann@31871
   529
haftmann@31871
   530
fun imp_program naming =
haftmann@27707
   531
haftmann@31871
   532
  let
haftmann@31871
   533
    fun is_const c = case lookup_const naming c
haftmann@31871
   534
     of SOME c' => (fn c'' => c' = c'')
haftmann@31871
   535
      | NONE => K false;
haftmann@37756
   536
    val is_bind = is_const @{const_name bind};
haftmann@31871
   537
    val is_return = is_const @{const_name return};
haftmann@31893
   538
    val dummy_name = "";
haftmann@31893
   539
    val dummy_case_term = IVar NONE;
haftmann@31871
   540
    (*assumption: dummy values are not relevant for serialization*)
haftmann@38057
   541
    val (unitt, unitT) = case lookup_const naming @{const_name Unity}
haftmann@38057
   542
     of SOME unit' => (IConst (unit', (([], []), [])), the (lookup_tyco naming @{type_name unit}) `%% [])
haftmann@31871
   543
      | NONE => error ("Must include " ^ @{const_name Unity} ^ " in generated constants.");
haftmann@31871
   544
    fun dest_abs ((v, ty) `|=> t, _) = ((v, ty), t)
haftmann@31871
   545
      | dest_abs (t, ty) =
haftmann@31871
   546
          let
haftmann@31871
   547
            val vs = fold_varnames cons t [];
haftmann@31871
   548
            val v = Name.variant vs "x";
haftmann@31871
   549
            val ty' = (hd o fst o unfold_fun) ty;
haftmann@31893
   550
          in ((SOME v, ty'), t `$ IVar (SOME v)) end;
haftmann@31871
   551
    fun force (t as IConst (c, _) `$ t') = if is_return c
haftmann@31871
   552
          then t' else t `$ unitt
haftmann@31871
   553
      | force t = t `$ unitt;
haftmann@38385
   554
    fun tr_bind'' [(t1, _), (t2, ty2)] =
haftmann@31871
   555
      let
haftmann@31871
   556
        val ((v, ty), t) = dest_abs (t2, ty2);
haftmann@38385
   557
      in ICase (((force t1, ty), [(IVar v, tr_bind' t)]), dummy_case_term) end
haftmann@38385
   558
    and tr_bind' t = case unfold_app t
haftmann@38386
   559
     of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if is_bind c
haftmann@38386
   560
          then tr_bind'' [(x1, ty1), (x2, ty2)]
haftmann@38386
   561
          else force t
haftmann@38386
   562
      | _ => force t;
haftmann@38057
   563
    fun imp_monad_bind'' ts = (SOME dummy_name, unitT) `|=> ICase (((IVar (SOME dummy_name), unitT),
haftmann@38385
   564
      [(unitt, tr_bind'' ts)]), dummy_case_term)
haftmann@38385
   565
    fun imp_monad_bind' (const as (c, (_, tys))) ts = if is_bind c then case (ts, tys)
haftmann@31871
   566
       of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)]
haftmann@31871
   567
        | ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] `$ t3
haftmann@31871
   568
        | (ts, _) => imp_monad_bind (eta_expand 2 (const, ts))
haftmann@31871
   569
      else IConst const `$$ map imp_monad_bind ts
haftmann@31871
   570
    and imp_monad_bind (IConst const) = imp_monad_bind' const []
haftmann@31871
   571
      | imp_monad_bind (t as IVar _) = t
haftmann@31871
   572
      | imp_monad_bind (t as _ `$ _) = (case unfold_app t
haftmann@31871
   573
         of (IConst const, ts) => imp_monad_bind' const ts
haftmann@31871
   574
          | (t, ts) => imp_monad_bind t `$$ map imp_monad_bind ts)
haftmann@31871
   575
      | imp_monad_bind (v_ty `|=> t) = v_ty `|=> imp_monad_bind t
haftmann@31871
   576
      | imp_monad_bind (ICase (((t, ty), pats), t0)) = ICase
haftmann@31871
   577
          (((imp_monad_bind t, ty),
haftmann@31871
   578
            (map o pairself) imp_monad_bind pats),
haftmann@31871
   579
              imp_monad_bind t0);
haftmann@28663
   580
haftmann@31871
   581
  in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end;
haftmann@27707
   582
haftmann@27707
   583
in
haftmann@27707
   584
haftmann@31871
   585
Code_Target.extend_target ("SML_imp", ("SML", imp_program))
haftmann@31871
   586
#> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program))
haftmann@37838
   587
#> Code_Target.extend_target ("Scala_imp", ("Scala", imp_program))
haftmann@27707
   588
haftmann@27707
   589
end
haftmann@31871
   590
haftmann@27707
   591
*}
haftmann@27707
   592
haftmann@26182
   593
haftmann@37758
   594
hide_const (open) Heap heap guard raise' fold_map
haftmann@37724
   595
haftmann@26170
   596
end