src/HOL/Imperative_HOL/Heap_Monad.thy
author bulwahn
Wed Mar 31 16:44:41 2010 +0200 (2010-03-31)
changeset 36057 ca6610908ae9
parent 35423 6ef9525a5727
child 36078 59f6773a7d1d
permissions -rw-r--r--
adding MREC induction rule in Imperative HOL
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(*  Title:      HOL/Library/Heap_Monad.thy
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    Author:     John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen
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*)
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header {* A monad with a polymorphic heap *}
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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 combinators *}
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datatype exception = Exn
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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 + exception) \<times> heap"
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primrec
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  execute :: "'a Heap \<Rightarrow> heap \<Rightarrow> ('a + exception) \<times> heap" where
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  "execute (Heap f) = f"
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lemmas [code del] = execute.simps
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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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lemma Heap_eqI':
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  "(\<And>h. (\<lambda>x. execute (f x) h) = (\<lambda>y. execute (g y) h)) \<Longrightarrow> f = g"
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    by (auto simp: expand_fun_eq intro: Heap_eqI)
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lemma Heap_strip: "(\<And>f. PROP P f) \<equiv> (\<And>g. PROP P (Heap g))"
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proof
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  fix g :: "heap \<Rightarrow> ('a + exception) \<times> heap" 
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  assume "\<And>f. PROP P f"
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  then show "PROP P (Heap g)" .
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next
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  fix f :: "'a Heap" 
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  assume assm: "\<And>g. PROP P (Heap g)"
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  then have "PROP P (Heap (execute f))" .
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  then show "PROP P f" by simp
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qed
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definition
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  heap :: "(heap \<Rightarrow> 'a \<times> heap) \<Rightarrow> 'a Heap" where
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  [code del]: "heap f = Heap (\<lambda>h. apfst Inl (f h))"
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lemma execute_heap [simp]:
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  "execute (heap f) h = apfst Inl (f h)"
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  by (simp add: heap_def)
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definition
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  bindM :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" (infixl ">>=" 54) where
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  [code del]: "f >>= g = Heap (\<lambda>h. case execute f h of
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                  (Inl x, h') \<Rightarrow> execute (g x) h'
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                | r \<Rightarrow> r)"
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notation
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  bindM (infixl "\<guillemotright>=" 54)
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abbreviation
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  chainM :: "'a Heap \<Rightarrow> 'b Heap \<Rightarrow> 'b Heap"  (infixl ">>" 54) where
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  "f >> g \<equiv> f >>= (\<lambda>_. g)"
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notation
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  chainM (infixl "\<guillemotright>" 54)
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definition
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  return :: "'a \<Rightarrow> 'a Heap" where
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  [code del]: "return x = heap (Pair x)"
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lemma execute_return [simp]:
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  "execute (return x) h = apfst Inl (x, h)"
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  by (simp add: return_def)
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definition
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  raise :: "string \<Rightarrow> 'a Heap" where -- {* the string is just decoration *}
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  [code del]: "raise s = Heap (Pair (Inr Exn))"
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notation (latex output)
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  "raise" ("\<^raw:{\textsf{raise}}>")
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lemma execute_raise [simp]:
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  "execute (raise s) h = (Inr Exn, h)"
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  by (simp add: raise_def)
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subsubsection {* do-syntax *}
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text {*
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  We provide a convenient do-notation for monadic expressions
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  well-known from Haskell.  @{const Let} is printed
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  specially in do-expressions.
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*}
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nonterminals do_expr
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syntax
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  "_do" :: "do_expr \<Rightarrow> 'a"
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    ("(do (_)//done)" [12] 100)
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  "_bindM" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("_ <- _;//_" [1000, 13, 12] 12)
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  "_chainM" :: "'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("_;//_" [13, 12] 12)
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  "_let" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("let _ = _;//_" [1000, 13, 12] 12)
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  "_nil" :: "'a \<Rightarrow> do_expr"
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    ("_" [12] 12)
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syntax (xsymbols)
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  "_bindM" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("_ \<leftarrow> _;//_" [1000, 13, 12] 12)
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syntax (latex output)
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  "_do" :: "do_expr \<Rightarrow> 'a"
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    ("(\<^raw:{\textsf{do}}> (_))" [12] 100)
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  "_let" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
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    ("\<^raw:\textsf{let}> _ = _;//_" [1000, 13, 12] 12)
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notation (latex output)
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  "return" ("\<^raw:{\textsf{return}}>")
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translations
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  "_do f" => "f"
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  "_bindM x f g" => "f \<guillemotright>= (\<lambda>x. g)"
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  "_chainM f g" => "f \<guillemotright> g"
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  "_let x t f" => "CONST Let t (\<lambda>x. f)"
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  "_nil f" => "f"
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print_translation {*
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let
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  fun dest_abs_eta (Abs (abs as (_, ty, _))) =
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        let
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          val (v, t) = Syntax.variant_abs abs;
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        in (Free (v, ty), t) end
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    | dest_abs_eta t =
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        let
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          val (v, t) = Syntax.variant_abs ("", dummyT, t $ Bound 0);
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        in (Free (v, dummyT), t) end;
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  fun unfold_monad (Const (@{const_syntax bindM}, _) $ f $ g) =
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        let
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          val (v, g') = dest_abs_eta g;
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          val vs = fold_aterms (fn Free (v, _) => insert (op =) v | _ => I) v [];
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          val v_used = fold_aterms
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            (fn Free (w, _) => (fn s => s orelse member (op =) vs w) | _ => I) g' false;
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        in if v_used then
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          Const (@{syntax_const "_bindM"}, dummyT) $ v $ f $ unfold_monad g'
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        else
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          Const (@{syntax_const "_chainM"}, dummyT) $ f $ unfold_monad g'
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        end
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    | unfold_monad (Const (@{const_syntax chainM}, _) $ f $ g) =
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        Const (@{syntax_const "_chainM"}, dummyT) $ f $ unfold_monad g
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    | unfold_monad (Const (@{const_syntax Let}, _) $ f $ g) =
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        let
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          val (v, g') = dest_abs_eta g;
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        in Const (@{syntax_const "_let"}, dummyT) $ v $ f $ unfold_monad g' end
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    | unfold_monad (Const (@{const_syntax Pair}, _) $ f) =
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        Const (@{const_syntax return}, dummyT) $ f
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    | unfold_monad f = f;
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  fun contains_bindM (Const (@{const_syntax bindM}, _) $ _ $ _) = true
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    | contains_bindM (Const (@{const_syntax Let}, _) $ _ $ Abs (_, _, t)) =
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        contains_bindM t;
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  fun bindM_monad_tr' (f::g::ts) = list_comb
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    (Const (@{syntax_const "_do"}, dummyT) $
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      unfold_monad (Const (@{const_syntax bindM}, dummyT) $ f $ g), ts);
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  fun Let_monad_tr' (f :: (g as Abs (_, _, g')) :: ts) =
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    if contains_bindM g' then list_comb
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      (Const (@{syntax_const "_do"}, dummyT) $
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        unfold_monad (Const (@{const_syntax Let}, dummyT) $ f $ g), ts)
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    else raise Match;
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in
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 [(@{const_syntax bindM}, bindM_monad_tr'),
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  (@{const_syntax Let}, Let_monad_tr')]
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end;
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*}
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subsection {* Monad properties *}
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subsubsection {* Monad laws *}
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lemma return_bind: "return x \<guillemotright>= f = f x"
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  by (simp add: bindM_def return_def)
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lemma bind_return: "f \<guillemotright>= return = f"
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proof (rule Heap_eqI)
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  fix h
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  show "execute (f \<guillemotright>= return) h = execute f h"
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    by (auto simp add: bindM_def return_def split: sum.splits prod.splits)
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qed
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lemma bind_bind: "(f \<guillemotright>= g) \<guillemotright>= h = f \<guillemotright>= (\<lambda>x. g x \<guillemotright>= h)"
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  by (rule Heap_eqI) (auto simp add: bindM_def split: split: sum.splits prod.splits)
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lemma bind_bind': "f \<guillemotright>= (\<lambda>x. g x \<guillemotright>= h x) = f \<guillemotright>= (\<lambda>x. g x \<guillemotright>= (\<lambda>y. return (x, y))) \<guillemotright>= (\<lambda>(x, y). h x y)"
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  by (rule Heap_eqI) (auto simp add: bindM_def split: split: sum.splits prod.splits)
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lemma raise_bind: "raise e \<guillemotright>= f = raise e"
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  by (simp add: raise_def bindM_def)
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lemmas monad_simp = return_bind bind_return bind_bind raise_bind
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subsection {* Generic combinators *}
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definition
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  liftM :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b Heap"
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where
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  "liftM f = return o f"
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definition
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  compM :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> ('b \<Rightarrow> 'c Heap) \<Rightarrow> 'a \<Rightarrow> 'c Heap" (infixl ">>==" 54)
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where
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  "(f >>== g) = (\<lambda>x. f x \<guillemotright>= g)"
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notation
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  compM (infixl "\<guillemotright>==" 54)
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lemma liftM_collapse: "liftM f x = return (f x)"
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  by (simp add: liftM_def)
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lemma liftM_compM: "liftM f \<guillemotright>== g = g o f"
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  by (auto intro: Heap_eqI' simp add: expand_fun_eq liftM_def compM_def bindM_def)
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lemma compM_return: "f \<guillemotright>== return = f"
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  by (simp add: compM_def monad_simp)
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lemma compM_compM: "(f \<guillemotright>== g) \<guillemotright>== h = f \<guillemotright>== (g \<guillemotright>== h)"
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  by (simp add: compM_def monad_simp)
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lemma liftM_bind:
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  "(\<lambda>x. liftM f x \<guillemotright>= liftM g) = liftM (\<lambda>x. g (f x))"
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  by (rule Heap_eqI') (simp add: monad_simp liftM_def bindM_def)
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lemma liftM_comp:
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  "liftM f o g = liftM (f o g)"
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  by (rule Heap_eqI') (simp add: liftM_def)
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lemmas monad_simp' = monad_simp liftM_compM compM_return
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  compM_compM liftM_bind liftM_comp
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primrec 
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  mapM :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap"
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where
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  "mapM f [] = return []"
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  | "mapM f (x#xs) = do y \<leftarrow> f x;
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                        ys \<leftarrow> mapM f xs;
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                        return (y # ys)
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                     done"
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primrec
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  foldM :: "('a \<Rightarrow> 'b \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b \<Rightarrow> 'b Heap"
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where
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  "foldM f [] s = return s"
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  | "foldM f (x#xs) s = f x s \<guillemotright>= foldM f xs"
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definition
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  assert :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a Heap"
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where
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  "assert P x = (if P x then return x else raise (''assert''))"
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lemma assert_cong [fundef_cong]:
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  assumes "P = P'"
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  assumes "\<And>x. P' x \<Longrightarrow> f x = f' x"
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  shows "(assert P x >>= f) = (assert P' x >>= f')"
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  using assms by (auto simp add: assert_def return_bind raise_bind)
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subsubsection {* A monadic combinator for simple recursive functions *}
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text {* Using a locale to fix arguments f and g of MREC *}
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locale mrec =
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fixes
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  f :: "'a => ('b + 'a) Heap"
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  and g :: "'a => 'a => 'b => 'b Heap"
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begin
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function (default "\<lambda>(x,h). (Inr Exn, undefined)") 
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  mrec 
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where
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  "mrec x h = 
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   (case Heap_Monad.execute (f x) h of
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     (Inl (Inl r), h') \<Rightarrow> (Inl r, h')
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   | (Inl (Inr s), h') \<Rightarrow> 
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          (case mrec s h' of
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             (Inl z, h'') \<Rightarrow> Heap_Monad.execute (g x s z) h''
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           | (Inr e, h'') \<Rightarrow> (Inr e, h''))
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   | (Inr e, h') \<Rightarrow> (Inr e, h')
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   )"
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by auto
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lemma graph_implies_dom:
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  "mrec_graph x y \<Longrightarrow> mrec_dom x"
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apply (induct rule:mrec_graph.induct) 
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apply (rule accpI)
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apply (erule mrec_rel.cases)
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by simp
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lemma mrec_default: "\<not> mrec_dom (x, h) \<Longrightarrow> mrec x h = (Inr Exn, undefined)"
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  unfolding mrec_def 
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  by (rule fundef_default_value[OF mrec_sumC_def graph_implies_dom, of _ _ "(x, h)", simplified])
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lemma mrec_di_reverse: 
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  assumes "\<not> mrec_dom (x, h)"
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  shows "
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   (case Heap_Monad.execute (f x) h of
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     (Inl (Inl r), h') \<Rightarrow> False
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   | (Inl (Inr s), h') \<Rightarrow> \<not> mrec_dom (s, h')
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   | (Inr e, h') \<Rightarrow> False
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   )" 
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using assms
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by (auto split:prod.splits sum.splits)
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 (erule notE, rule accpI, elim mrec_rel.cases, simp)+
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lemma mrec_rule:
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  "mrec x h = 
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   322
   (case Heap_Monad.execute (f x) h of
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   323
     (Inl (Inl r), h') \<Rightarrow> (Inl r, h')
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   324
   | (Inl (Inr s), h') \<Rightarrow> 
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   325
          (case mrec s h' of
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   326
             (Inl z, h'') \<Rightarrow> Heap_Monad.execute (g x s z) h''
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   327
           | (Inr e, h'') \<Rightarrow> (Inr e, h''))
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   328
   | (Inr e, h') \<Rightarrow> (Inr e, h')
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   329
   )"
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   330
apply (cases "mrec_dom (x,h)", simp)
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   331
apply (frule mrec_default)
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   332
apply (frule mrec_di_reverse, simp)
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   333
by (auto split: sum.split prod.split simp: mrec_default)
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   334
bulwahn@34051
   335
bulwahn@34051
   336
definition
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  "MREC x = Heap (mrec x)"
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   338
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   339
lemma MREC_rule:
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  "MREC x = 
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   341
  (do y \<leftarrow> f x;
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   342
                (case y of 
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   343
                Inl r \<Rightarrow> return r
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   344
              | Inr s \<Rightarrow> 
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   345
                do z \<leftarrow> MREC s ;
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   346
                   g x s z
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   347
                done) done)"
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   348
  unfolding MREC_def
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   349
  unfolding bindM_def return_def
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   350
  apply simp
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   351
  apply (rule ext)
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   352
  apply (unfold mrec_rule[of x])
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   353
  by (auto split:prod.splits sum.splits)
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   354
bulwahn@36057
   355
bulwahn@36057
   356
lemma MREC_pinduct:
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  assumes "Heap_Monad.execute (MREC x) h = (Inl r, h')"
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   358
  assumes non_rec_case: "\<And> x h h' r. Heap_Monad.execute (f x) h = (Inl (Inl r), h') \<Longrightarrow> P x h h' r"
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   359
  assumes rec_case: "\<And> x h h1 h2 h' s z r. Heap_Monad.execute (f x) h = (Inl (Inr s), h1) \<Longrightarrow> Heap_Monad.execute (MREC s) h1 = (Inl z, h2) \<Longrightarrow> P s h1 h2 z
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   360
    \<Longrightarrow> Heap_Monad.execute (g x s z) h2 = (Inl r, h') \<Longrightarrow> P x h h' r"
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   361
  shows "P x h h' r"
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   362
proof -
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   363
  from assms(1) have mrec: "mrec x h = (Inl r, h')"
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   364
    unfolding MREC_def execute.simps .
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   365
  from mrec have dom: "mrec_dom (x, h)"
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   366
    apply -
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   367
    apply (rule ccontr)
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   368
    apply (drule mrec_default) by auto
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   369
  from mrec have h'_r: "h' = (snd (mrec x h))" "r = (Sum_Type.Projl (fst (mrec x h)))"
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   370
    by auto
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   371
  from mrec have "P x h (snd (mrec x h)) (Sum_Type.Projl (fst (mrec x h)))"
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   372
  proof (induct arbitrary: r h' rule: mrec.pinduct[OF dom])
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   373
    case (1 x h)
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   374
    obtain rr h' where "mrec x h = (rr, h')" by fastsimp
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   375
    obtain fret h1 where exec_f: "Heap_Monad.execute (f x) h = (fret, h1)" by fastsimp
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   376
    show ?case
bulwahn@36057
   377
    proof (cases fret)
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   378
      case (Inl a)
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   379
      note Inl' = this
bulwahn@36057
   380
      show ?thesis
bulwahn@36057
   381
      proof (cases a)
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   382
        case (Inl aa)
bulwahn@36057
   383
        from this Inl' 1(1) exec_f mrec non_rec_case show ?thesis
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   384
          by auto
bulwahn@36057
   385
      next
bulwahn@36057
   386
        case (Inr b)
bulwahn@36057
   387
        note Inr' = this
bulwahn@36057
   388
        obtain ret_mrec h2 where mrec_rec: "mrec b h1 = (ret_mrec, h2)" by fastsimp
bulwahn@36057
   389
        from this Inl 1(1) exec_f mrec show ?thesis
bulwahn@36057
   390
        proof (cases "ret_mrec")
bulwahn@36057
   391
          case (Inl aaa)
bulwahn@36057
   392
          from this mrec exec_f Inl' Inr' 1(1) mrec_rec 1(2)[OF exec_f Inl' Inr', of "aaa" "h2"] 1(3)
bulwahn@36057
   393
            show ?thesis
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   394
              apply auto
bulwahn@36057
   395
              apply (rule rec_case)
bulwahn@36057
   396
              unfolding MREC_def by auto
bulwahn@36057
   397
        next
bulwahn@36057
   398
          case (Inr b)
bulwahn@36057
   399
          from this Inl 1(1) exec_f mrec Inr' mrec_rec 1(3) show ?thesis by auto
bulwahn@36057
   400
        qed
bulwahn@36057
   401
      qed
bulwahn@36057
   402
    next
bulwahn@36057
   403
      case (Inr b)
bulwahn@36057
   404
      from this 1(1) mrec exec_f 1(3) show ?thesis by simp
bulwahn@36057
   405
    qed
bulwahn@36057
   406
  qed
bulwahn@36057
   407
  from this h'_r show ?thesis by simp
bulwahn@36057
   408
qed
bulwahn@36057
   409
bulwahn@36057
   410
end
bulwahn@36057
   411
bulwahn@36057
   412
text {* Providing global versions of the constant and the theorems *}
bulwahn@36057
   413
bulwahn@36057
   414
abbreviation "MREC == mrec.MREC"
bulwahn@36057
   415
lemmas MREC_rule = mrec.MREC_rule
bulwahn@36057
   416
lemmas MREC_pinduct = mrec.MREC_pinduct
bulwahn@36057
   417
haftmann@26170
   418
hide (open) const heap execute
haftmann@26170
   419
haftmann@26182
   420
haftmann@26182
   421
subsection {* Code generator setup *}
haftmann@26182
   422
haftmann@26182
   423
subsubsection {* Logical intermediate layer *}
haftmann@26182
   424
haftmann@26182
   425
definition
haftmann@31205
   426
  Fail :: "String.literal \<Rightarrow> exception"
haftmann@26182
   427
where
haftmann@28562
   428
  [code del]: "Fail s = Exn"
haftmann@26182
   429
haftmann@26182
   430
definition
haftmann@26182
   431
  raise_exc :: "exception \<Rightarrow> 'a Heap"
haftmann@26182
   432
where
haftmann@28562
   433
  [code del]: "raise_exc e = raise []"
haftmann@26182
   434
haftmann@32069
   435
lemma raise_raise_exc [code, code_unfold]:
haftmann@26182
   436
  "raise s = raise_exc (Fail (STR s))"
haftmann@26182
   437
  unfolding Fail_def raise_exc_def raise_def ..
haftmann@26182
   438
haftmann@26182
   439
hide (open) const Fail raise_exc
haftmann@26182
   440
haftmann@26182
   441
haftmann@27707
   442
subsubsection {* SML and OCaml *}
haftmann@26182
   443
haftmann@26752
   444
code_type Heap (SML "unit/ ->/ _")
haftmann@26182
   445
code_const Heap (SML "raise/ (Fail/ \"bare Heap\")")
haftmann@27826
   446
code_const "op \<guillemotright>=" (SML "!(fn/ f'_/ =>/ fn/ ()/ =>/ f'_/ (_/ ())/ ())")
haftmann@27707
   447
code_const return (SML "!(fn/ ()/ =>/ _)")
haftmann@26182
   448
code_const "Heap_Monad.Fail" (SML "Fail")
haftmann@27707
   449
code_const "Heap_Monad.raise_exc" (SML "!(fn/ ()/ =>/ raise/ _)")
haftmann@26182
   450
haftmann@26182
   451
code_type Heap (OCaml "_")
haftmann@26182
   452
code_const Heap (OCaml "failwith/ \"bare Heap\"")
haftmann@27826
   453
code_const "op \<guillemotright>=" (OCaml "!(fun/ f'_/ ()/ ->/ f'_/ (_/ ())/ ())")
haftmann@27707
   454
code_const return (OCaml "!(fun/ ()/ ->/ _)")
haftmann@26182
   455
code_const "Heap_Monad.Fail" (OCaml "Failure")
haftmann@27707
   456
code_const "Heap_Monad.raise_exc" (OCaml "!(fun/ ()/ ->/ raise/ _)")
haftmann@27707
   457
haftmann@31871
   458
setup {*
haftmann@31871
   459
haftmann@31871
   460
let
haftmann@27707
   461
haftmann@31871
   462
open Code_Thingol;
haftmann@31871
   463
haftmann@31871
   464
fun imp_program naming =
haftmann@27707
   465
haftmann@31871
   466
  let
haftmann@31871
   467
    fun is_const c = case lookup_const naming c
haftmann@31871
   468
     of SOME c' => (fn c'' => c' = c'')
haftmann@31871
   469
      | NONE => K false;
haftmann@31871
   470
    val is_bindM = is_const @{const_name bindM};
haftmann@31871
   471
    val is_return = is_const @{const_name return};
haftmann@31893
   472
    val dummy_name = "";
haftmann@31871
   473
    val dummy_type = ITyVar dummy_name;
haftmann@31893
   474
    val dummy_case_term = IVar NONE;
haftmann@31871
   475
    (*assumption: dummy values are not relevant for serialization*)
haftmann@31871
   476
    val unitt = case lookup_const naming @{const_name Unity}
haftmann@31871
   477
     of SOME unit' => IConst (unit', (([], []), []))
haftmann@31871
   478
      | NONE => error ("Must include " ^ @{const_name Unity} ^ " in generated constants.");
haftmann@31871
   479
    fun dest_abs ((v, ty) `|=> t, _) = ((v, ty), t)
haftmann@31871
   480
      | dest_abs (t, ty) =
haftmann@31871
   481
          let
haftmann@31871
   482
            val vs = fold_varnames cons t [];
haftmann@31871
   483
            val v = Name.variant vs "x";
haftmann@31871
   484
            val ty' = (hd o fst o unfold_fun) ty;
haftmann@31893
   485
          in ((SOME v, ty'), t `$ IVar (SOME v)) end;
haftmann@31871
   486
    fun force (t as IConst (c, _) `$ t') = if is_return c
haftmann@31871
   487
          then t' else t `$ unitt
haftmann@31871
   488
      | force t = t `$ unitt;
haftmann@31871
   489
    fun tr_bind' [(t1, _), (t2, ty2)] =
haftmann@31871
   490
      let
haftmann@31871
   491
        val ((v, ty), t) = dest_abs (t2, ty2);
haftmann@31871
   492
      in ICase (((force t1, ty), [(IVar v, tr_bind'' t)]), dummy_case_term) end
haftmann@31871
   493
    and tr_bind'' t = case unfold_app t
haftmann@31871
   494
         of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if is_bindM c
haftmann@31871
   495
              then tr_bind' [(x1, ty1), (x2, ty2)]
haftmann@31871
   496
              else force t
haftmann@31871
   497
          | _ => force t;
haftmann@31893
   498
    fun imp_monad_bind'' ts = (SOME dummy_name, dummy_type) `|=> ICase (((IVar (SOME dummy_name), dummy_type),
haftmann@31871
   499
      [(unitt, tr_bind' ts)]), dummy_case_term)
haftmann@31871
   500
    and imp_monad_bind' (const as (c, (_, tys))) ts = if is_bindM c then case (ts, tys)
haftmann@31871
   501
       of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)]
haftmann@31871
   502
        | ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] `$ t3
haftmann@31871
   503
        | (ts, _) => imp_monad_bind (eta_expand 2 (const, ts))
haftmann@31871
   504
      else IConst const `$$ map imp_monad_bind ts
haftmann@31871
   505
    and imp_monad_bind (IConst const) = imp_monad_bind' const []
haftmann@31871
   506
      | imp_monad_bind (t as IVar _) = t
haftmann@31871
   507
      | imp_monad_bind (t as _ `$ _) = (case unfold_app t
haftmann@31871
   508
         of (IConst const, ts) => imp_monad_bind' const ts
haftmann@31871
   509
          | (t, ts) => imp_monad_bind t `$$ map imp_monad_bind ts)
haftmann@31871
   510
      | imp_monad_bind (v_ty `|=> t) = v_ty `|=> imp_monad_bind t
haftmann@31871
   511
      | imp_monad_bind (ICase (((t, ty), pats), t0)) = ICase
haftmann@31871
   512
          (((imp_monad_bind t, ty),
haftmann@31871
   513
            (map o pairself) imp_monad_bind pats),
haftmann@31871
   514
              imp_monad_bind t0);
haftmann@28663
   515
haftmann@31871
   516
  in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end;
haftmann@27707
   517
haftmann@27707
   518
in
haftmann@27707
   519
haftmann@31871
   520
Code_Target.extend_target ("SML_imp", ("SML", imp_program))
haftmann@31871
   521
#> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program))
haftmann@27707
   522
haftmann@27707
   523
end
haftmann@31871
   524
haftmann@27707
   525
*}
haftmann@27707
   526
haftmann@26182
   527
code_reserved OCaml Failure raise
haftmann@26182
   528
haftmann@26182
   529
haftmann@26182
   530
subsubsection {* Haskell *}
haftmann@26182
   531
haftmann@26182
   532
text {* Adaption layer *}
haftmann@26182
   533
haftmann@29793
   534
code_include Haskell "Heap"
haftmann@26182
   535
{*import qualified Control.Monad;
haftmann@26182
   536
import qualified Control.Monad.ST;
haftmann@26182
   537
import qualified Data.STRef;
haftmann@26182
   538
import qualified Data.Array.ST;
haftmann@26182
   539
haftmann@27695
   540
type RealWorld = Control.Monad.ST.RealWorld;
haftmann@26182
   541
type ST s a = Control.Monad.ST.ST s a;
haftmann@26182
   542
type STRef s a = Data.STRef.STRef s a;
haftmann@27673
   543
type STArray s a = Data.Array.ST.STArray s Int a;
haftmann@26182
   544
haftmann@26182
   545
newSTRef = Data.STRef.newSTRef;
haftmann@26182
   546
readSTRef = Data.STRef.readSTRef;
haftmann@26182
   547
writeSTRef = Data.STRef.writeSTRef;
haftmann@26182
   548
haftmann@27673
   549
newArray :: (Int, Int) -> a -> ST s (STArray s a);
haftmann@26182
   550
newArray = Data.Array.ST.newArray;
haftmann@26182
   551
haftmann@27673
   552
newListArray :: (Int, Int) -> [a] -> ST s (STArray s a);
haftmann@26182
   553
newListArray = Data.Array.ST.newListArray;
haftmann@26182
   554
haftmann@27673
   555
lengthArray :: STArray s a -> ST s Int;
haftmann@27673
   556
lengthArray a = Control.Monad.liftM snd (Data.Array.ST.getBounds a);
haftmann@26182
   557
haftmann@27673
   558
readArray :: STArray s a -> Int -> ST s a;
haftmann@26182
   559
readArray = Data.Array.ST.readArray;
haftmann@26182
   560
haftmann@27673
   561
writeArray :: STArray s a -> Int -> a -> ST s ();
haftmann@26182
   562
writeArray = Data.Array.ST.writeArray;*}
haftmann@26182
   563
haftmann@29793
   564
code_reserved Haskell Heap
haftmann@26182
   565
haftmann@26182
   566
text {* Monad *}
haftmann@26182
   567
haftmann@29793
   568
code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _")
haftmann@27695
   569
code_const Heap (Haskell "error/ \"bare Heap\"")
haftmann@28145
   570
code_monad "op \<guillemotright>=" Haskell
haftmann@26182
   571
code_const return (Haskell "return")
haftmann@26182
   572
code_const "Heap_Monad.Fail" (Haskell "_")
haftmann@26182
   573
code_const "Heap_Monad.raise_exc" (Haskell "error")
haftmann@26182
   574
haftmann@26170
   575
end