src/HOLCF/Fixrec.thy
author huffman
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fix output translation for Case syntax
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(*  Title:      HOLCF/Fixrec.thy
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    Author:     Amber Telfer and Brian Huffman
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*)
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header "Package for defining recursive functions in HOLCF"
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theory Fixrec
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imports Sprod Ssum Up One Tr Fix
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uses ("Tools/fixrec.ML")
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begin
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subsection {* Maybe monad type *}
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defaultsort cpo
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pcpodef (open) 'a maybe = "UNIV::(one ++ 'a u) set"
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by simp_all
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definition
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  fail :: "'a maybe" where
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  "fail = Abs_maybe (sinl\<cdot>ONE)"
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definition
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  return :: "'a \<rightarrow> 'a maybe" where
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  "return = (\<Lambda> x. Abs_maybe (sinr\<cdot>(up\<cdot>x)))"
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definition
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  maybe_when :: "'b \<rightarrow> ('a \<rightarrow> 'b) \<rightarrow> 'a maybe \<rightarrow> 'b::pcpo" where
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  "maybe_when = (\<Lambda> f r m. sscase\<cdot>(\<Lambda> x. f)\<cdot>(fup\<cdot>r)\<cdot>(Rep_maybe m))"
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lemma maybeE:
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  "\<lbrakk>p = \<bottom> \<Longrightarrow> Q; p = fail \<Longrightarrow> Q; \<And>x. p = return\<cdot>x \<Longrightarrow> Q\<rbrakk> \<Longrightarrow> Q"
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apply (unfold fail_def return_def)
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apply (cases p, rename_tac r)
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apply (rule_tac p=r in ssumE, simp add: Abs_maybe_strict)
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apply (rule_tac p=x in oneE, simp, simp)
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apply (rule_tac p=y in upE, simp, simp add: cont_Abs_maybe)
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done
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lemma return_defined [simp]: "return\<cdot>x \<noteq> \<bottom>"
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by (simp add: return_def cont_Abs_maybe Abs_maybe_defined)
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lemma fail_defined [simp]: "fail \<noteq> \<bottom>"
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by (simp add: fail_def Abs_maybe_defined)
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lemma return_eq [simp]: "(return\<cdot>x = return\<cdot>y) = (x = y)"
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by (simp add: return_def cont_Abs_maybe Abs_maybe_inject)
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lemma return_neq_fail [simp]:
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  "return\<cdot>x \<noteq> fail" "fail \<noteq> return\<cdot>x"
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by (simp_all add: return_def fail_def cont_Abs_maybe Abs_maybe_inject)
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lemma maybe_when_rews [simp]:
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  "maybe_when\<cdot>f\<cdot>r\<cdot>\<bottom> = \<bottom>"
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  "maybe_when\<cdot>f\<cdot>r\<cdot>fail = f"
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  "maybe_when\<cdot>f\<cdot>r\<cdot>(return\<cdot>x) = r\<cdot>x"
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by (simp_all add: return_def fail_def maybe_when_def cont_Rep_maybe
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                  cont2cont_LAM
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                  cont_Abs_maybe Abs_maybe_inverse Rep_maybe_strict)
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translations
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  "case m of XCONST fail \<Rightarrow> t1 | XCONST return\<cdot>x \<Rightarrow> t2"
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    == "CONST maybe_when\<cdot>t1\<cdot>(\<Lambda> x. t2)\<cdot>m"
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subsubsection {* Monadic bind operator *}
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definition
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  bind :: "'a maybe \<rightarrow> ('a \<rightarrow> 'b maybe) \<rightarrow> 'b maybe" where
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  "bind = (\<Lambda> m f. case m of fail \<Rightarrow> fail | return\<cdot>x \<Rightarrow> f\<cdot>x)"
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text {* monad laws *}
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lemma bind_strict [simp]: "bind\<cdot>\<bottom>\<cdot>f = \<bottom>"
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by (simp add: bind_def)
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lemma bind_fail [simp]: "bind\<cdot>fail\<cdot>f = fail"
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by (simp add: bind_def)
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lemma left_unit [simp]: "bind\<cdot>(return\<cdot>a)\<cdot>k = k\<cdot>a"
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by (simp add: bind_def)
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lemma right_unit [simp]: "bind\<cdot>m\<cdot>return = m"
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by (rule_tac p=m in maybeE, simp_all)
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lemma bind_assoc:
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 "bind\<cdot>(bind\<cdot>m\<cdot>k)\<cdot>h = bind\<cdot>m\<cdot>(\<Lambda> a. bind\<cdot>(k\<cdot>a)\<cdot>h)"
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by (rule_tac p=m in maybeE, simp_all)
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subsubsection {* Run operator *}
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definition
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  run :: "'a maybe \<rightarrow> 'a::pcpo" where
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  "run = maybe_when\<cdot>\<bottom>\<cdot>ID"
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text {* rewrite rules for run *}
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lemma run_strict [simp]: "run\<cdot>\<bottom> = \<bottom>"
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by (simp add: run_def)
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lemma run_fail [simp]: "run\<cdot>fail = \<bottom>"
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by (simp add: run_def)
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lemma run_return [simp]: "run\<cdot>(return\<cdot>x) = x"
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by (simp add: run_def)
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subsubsection {* Monad plus operator *}
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definition
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  mplus :: "'a maybe \<rightarrow> 'a maybe \<rightarrow> 'a maybe" where
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  "mplus = (\<Lambda> m1 m2. case m1 of fail \<Rightarrow> m2 | return\<cdot>x \<Rightarrow> m1)"
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abbreviation
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  mplus_syn :: "['a maybe, 'a maybe] \<Rightarrow> 'a maybe"  (infixr "+++" 65)  where
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  "m1 +++ m2 == mplus\<cdot>m1\<cdot>m2"
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text {* rewrite rules for mplus *}
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lemma mplus_strict [simp]: "\<bottom> +++ m = \<bottom>"
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by (simp add: mplus_def)
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lemma mplus_fail [simp]: "fail +++ m = m"
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by (simp add: mplus_def)
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lemma mplus_return [simp]: "return\<cdot>x +++ m = return\<cdot>x"
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by (simp add: mplus_def)
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lemma mplus_fail2 [simp]: "m +++ fail = m"
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by (rule_tac p=m in maybeE, simp_all)
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lemma mplus_assoc: "(x +++ y) +++ z = x +++ (y +++ z)"
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by (rule_tac p=x in maybeE, simp_all)
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subsubsection {* Fatbar combinator *}
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definition
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  fatbar :: "('a \<rightarrow> 'b maybe) \<rightarrow> ('a \<rightarrow> 'b maybe) \<rightarrow> ('a \<rightarrow> 'b maybe)" where
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  "fatbar = (\<Lambda> a b x. a\<cdot>x +++ b\<cdot>x)"
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abbreviation
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  fatbar_syn :: "['a \<rightarrow> 'b maybe, 'a \<rightarrow> 'b maybe] \<Rightarrow> 'a \<rightarrow> 'b maybe" (infixr "\<parallel>" 60)  where
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  "m1 \<parallel> m2 == fatbar\<cdot>m1\<cdot>m2"
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lemma fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> (m \<parallel> ms)\<cdot>x = \<bottom>"
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by (simp add: fatbar_def)
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lemma fatbar2: "m\<cdot>x = fail \<Longrightarrow> (m \<parallel> ms)\<cdot>x = ms\<cdot>x"
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by (simp add: fatbar_def)
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lemma fatbar3: "m\<cdot>x = return\<cdot>y \<Longrightarrow> (m \<parallel> ms)\<cdot>x = return\<cdot>y"
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by (simp add: fatbar_def)
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lemmas fatbar_simps = fatbar1 fatbar2 fatbar3
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lemma run_fatbar1: "m\<cdot>x = \<bottom> \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = \<bottom>"
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by (simp add: fatbar_def)
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lemma run_fatbar2: "m\<cdot>x = fail \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = run\<cdot>(ms\<cdot>x)"
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by (simp add: fatbar_def)
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lemma run_fatbar3: "m\<cdot>x = return\<cdot>y \<Longrightarrow> run\<cdot>((m \<parallel> ms)\<cdot>x) = y"
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by (simp add: fatbar_def)
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lemmas run_fatbar_simps [simp] = run_fatbar1 run_fatbar2 run_fatbar3
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subsection {* Case branch combinator *}
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definition
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  branch :: "('a \<rightarrow> 'b maybe) \<Rightarrow> ('b \<rightarrow> 'c) \<rightarrow> ('a \<rightarrow> 'c maybe)" where
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  "branch p \<equiv> \<Lambda> r x. bind\<cdot>(p\<cdot>x)\<cdot>(\<Lambda> y. return\<cdot>(r\<cdot>y))"
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lemma branch_rews:
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  "p\<cdot>x = \<bottom> \<Longrightarrow> branch p\<cdot>r\<cdot>x = \<bottom>"
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  "p\<cdot>x = fail \<Longrightarrow> branch p\<cdot>r\<cdot>x = fail"
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  "p\<cdot>x = return\<cdot>y \<Longrightarrow> branch p\<cdot>r\<cdot>x = return\<cdot>(r\<cdot>y)"
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by (simp_all add: branch_def)
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lemma branch_return [simp]: "branch return\<cdot>r\<cdot>x = return\<cdot>(r\<cdot>x)"
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by (simp add: branch_def)
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subsubsection {* Cases operator *}
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definition
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  cases :: "'a maybe \<rightarrow> 'a::pcpo" where
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  "cases = maybe_when\<cdot>\<bottom>\<cdot>ID"
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text {* rewrite rules for cases *}
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lemma cases_strict [simp]: "cases\<cdot>\<bottom> = \<bottom>"
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by (simp add: cases_def)
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lemma cases_fail [simp]: "cases\<cdot>fail = \<bottom>"
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by (simp add: cases_def)
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lemma cases_return [simp]: "cases\<cdot>(return\<cdot>x) = x"
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by (simp add: cases_def)
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subsection {* Case syntax *}
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nonterminals
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  Case_syn  Cases_syn
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syntax
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  "_Case_syntax":: "['a, Cases_syn] => 'b"               ("(Case _ of/ _)" 10)
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  "_Case1"      :: "['a, 'b] => Case_syn"                ("(2_ =>/ _)" 10)
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  ""            :: "Case_syn => Cases_syn"               ("_")
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  "_Case2"      :: "[Case_syn, Cases_syn] => Cases_syn"  ("_/ | _")
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syntax (xsymbols)
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  "_Case1"      :: "['a, 'b] => Case_syn"                ("(2_ \<Rightarrow>/ _)" 10)
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translations
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  "_Case_syntax x ms" == "CONST Fixrec.cases\<cdot>(ms\<cdot>x)"
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  "_Case2 m ms" == "m \<parallel> ms"
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text {* Parsing Case expressions *}
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syntax
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  "_pat" :: "'a"
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  "_variable" :: "'a"
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  "_noargs" :: "'a"
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  "_Case1 p r" => "CONST branch (_pat p)\<cdot>(_variable p r)"
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  "_variable (_args x y) r" => "CONST csplit\<cdot>(_variable x (_variable y r))"
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  "_variable _noargs r" => "CONST unit_when\<cdot>r"
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parse_translation {*
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(* rewrite (_pat x) => (return) *)
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(* rewrite (_variable x t) => (Abs_CFun (%x. t)) *)
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 [(@{syntax_const "_pat"}, fn _ => Syntax.const @{const_syntax Fixrec.return}),
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  mk_binder_tr (@{syntax_const "_variable"}, @{const_syntax Abs_CFun})];
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*}
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text {* Printing Case expressions *}
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syntax
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  "_match" :: "'a"
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print_translation {*
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  let
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    fun dest_LAM (Const (@{const_syntax Rep_CFun},_) $ Const (@{const_syntax unit_when},_) $ t) =
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          (Syntax.const @{syntax_const "_noargs"}, t)
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    |   dest_LAM (Const (@{const_syntax Rep_CFun},_) $ Const (@{const_syntax csplit},_) $ t) =
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          let
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            val (v1, t1) = dest_LAM t;
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            val (v2, t2) = dest_LAM t1;
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          in (Syntax.const @{syntax_const "_args"} $ v1 $ v2, t2) end
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    |   dest_LAM (Const (@{const_syntax Abs_CFun},_) $ t) =
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          let
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            val abs =
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              case t of Abs abs => abs
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                | _ => ("x", dummyT, incr_boundvars 1 t $ Bound 0);
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            val (x, t') = atomic_abs_tr' abs;
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          in (Syntax.const @{syntax_const "_variable"} $ x, t') end
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    |   dest_LAM _ = raise Match; (* too few vars: abort translation *)
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    fun Case1_tr' [Const(@{const_syntax branch},_) $ p, r] =
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          let val (v, t) = dest_LAM r in
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            Syntax.const @{syntax_const "_Case1"} $
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              (Syntax.const @{syntax_const "_match"} $ p $ v) $ t
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          end;
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  in [(@{const_syntax Rep_CFun}, Case1_tr')] end;
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*}
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translations
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  "x" <= "_match (CONST Fixrec.return) (_variable x)"
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subsection {* Pattern combinators for data constructors *}
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types ('a, 'b) pat = "'a \<rightarrow> 'b maybe"
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definition
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  cpair_pat :: "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a \<times> 'b, 'c \<times> 'd) pat" where
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  "cpair_pat p1 p2 = (\<Lambda>\<langle>x, y\<rangle>.
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    bind\<cdot>(p1\<cdot>x)\<cdot>(\<Lambda> a. bind\<cdot>(p2\<cdot>y)\<cdot>(\<Lambda> b. return\<cdot>\<langle>a, b\<rangle>)))"
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definition
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  spair_pat ::
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  "('a, 'c) pat \<Rightarrow> ('b, 'd) pat \<Rightarrow> ('a::pcpo \<otimes> 'b::pcpo, 'c \<times> 'd) pat" where
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  "spair_pat p1 p2 = (\<Lambda>(:x, y:). cpair_pat p1 p2\<cdot>\<langle>x, y\<rangle>)"
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definition
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  sinl_pat :: "('a, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where
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  "sinl_pat p = sscase\<cdot>p\<cdot>(\<Lambda> x. fail)"
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definition
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  sinr_pat :: "('b, 'c) pat \<Rightarrow> ('a::pcpo \<oplus> 'b::pcpo, 'c) pat" where
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  "sinr_pat p = sscase\<cdot>(\<Lambda> x. fail)\<cdot>p"
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definition
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  up_pat :: "('a, 'b) pat \<Rightarrow> ('a u, 'b) pat" where
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  "up_pat p = fup\<cdot>p"
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definition
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  TT_pat :: "(tr, unit) pat" where
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  "TT_pat = (\<Lambda> b. If b then return\<cdot>() else fail fi)"
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definition
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  FF_pat :: "(tr, unit) pat" where
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  "FF_pat = (\<Lambda> b. If b then fail else return\<cdot>() fi)"
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definition
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  ONE_pat :: "(one, unit) pat" where
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  "ONE_pat = (\<Lambda> ONE. return\<cdot>())"
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text {* Parse translations (patterns) *}
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translations
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  "_pat (XCONST cpair\<cdot>x\<cdot>y)" => "CONST cpair_pat (_pat x) (_pat y)"
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  "_pat (XCONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)"
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  "_pat (XCONST sinl\<cdot>x)" => "CONST sinl_pat (_pat x)"
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  "_pat (XCONST sinr\<cdot>x)" => "CONST sinr_pat (_pat x)"
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  "_pat (XCONST up\<cdot>x)" => "CONST up_pat (_pat x)"
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  "_pat (XCONST TT)" => "CONST TT_pat"
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  "_pat (XCONST FF)" => "CONST FF_pat"
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  "_pat (XCONST ONE)" => "CONST ONE_pat"
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text {* CONST version is also needed for constructors with special syntax *}
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translations
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  "_pat (CONST cpair\<cdot>x\<cdot>y)" => "CONST cpair_pat (_pat x) (_pat y)"
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  "_pat (CONST spair\<cdot>x\<cdot>y)" => "CONST spair_pat (_pat x) (_pat y)"
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text {* Parse translations (variables) *}
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translations
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  "_variable (XCONST cpair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
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  "_variable (XCONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
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  "_variable (XCONST sinl\<cdot>x) r" => "_variable x r"
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  "_variable (XCONST sinr\<cdot>x) r" => "_variable x r"
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  "_variable (XCONST up\<cdot>x) r" => "_variable x r"
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  "_variable (XCONST TT) r" => "_variable _noargs r"
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  "_variable (XCONST FF) r" => "_variable _noargs r"
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  "_variable (XCONST ONE) r" => "_variable _noargs r"
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translations
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  "_variable (CONST cpair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
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  "_variable (CONST spair\<cdot>x\<cdot>y) r" => "_variable (_args x y) r"
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text {* Print translations *}
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translations
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  "CONST cpair\<cdot>(_match p1 v1)\<cdot>(_match p2 v2)"
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      <= "_match (CONST cpair_pat p1 p2) (_args v1 v2)"
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  "CONST spair\<cdot>(_match p1 v1)\<cdot>(_match p2 v2)"
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      <= "_match (CONST spair_pat p1 p2) (_args v1 v2)"
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  "CONST sinl\<cdot>(_match p1 v1)" <= "_match (CONST sinl_pat p1) v1"
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  "CONST sinr\<cdot>(_match p1 v1)" <= "_match (CONST sinr_pat p1) v1"
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  "CONST up\<cdot>(_match p1 v1)" <= "_match (CONST up_pat p1) v1"
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  "CONST TT" <= "_match (CONST TT_pat) _noargs"
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  "CONST FF" <= "_match (CONST FF_pat) _noargs"
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  "CONST ONE" <= "_match (CONST ONE_pat) _noargs"
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lemma cpair_pat1:
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  "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>\<langle>x, y\<rangle> = \<bottom>"
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apply (simp add: branch_def cpair_pat_def)
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   356
apply (rule_tac p="p\<cdot>x" in maybeE, simp_all)
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done
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lemma cpair_pat2:
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  "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>\<langle>x, y\<rangle> = fail"
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apply (simp add: branch_def cpair_pat_def)
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apply (rule_tac p="p\<cdot>x" in maybeE, simp_all)
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   363
done
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   364
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lemma cpair_pat3:
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  "branch p\<cdot>r\<cdot>x = return\<cdot>s \<Longrightarrow>
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   367
   branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>\<langle>x, y\<rangle> = branch q\<cdot>s\<cdot>y"
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   368
apply (simp add: branch_def cpair_pat_def)
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   369
apply (rule_tac p="p\<cdot>x" in maybeE, simp_all)
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   370
apply (rule_tac p="q\<cdot>y" in maybeE, simp_all)
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   371
done
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   372
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lemmas cpair_pat [simp] =
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  cpair_pat1 cpair_pat2 cpair_pat3
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lemma spair_pat [simp]:
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  "branch (spair_pat p1 p2)\<cdot>r\<cdot>\<bottom> = \<bottom>"
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   378
  "\<lbrakk>x \<noteq> \<bottom>; y \<noteq> \<bottom>\<rbrakk>
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   379
     \<Longrightarrow> branch (spair_pat p1 p2)\<cdot>r\<cdot>(:x, y:) =
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   380
         branch (cpair_pat p1 p2)\<cdot>r\<cdot>\<langle>x, y\<rangle>"
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   381
by (simp_all add: branch_def spair_pat_def)
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   382
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   383
lemma sinl_pat [simp]:
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   384
  "branch (sinl_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
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   385
  "x \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = branch p\<cdot>r\<cdot>x"
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   386
  "y \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = fail"
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   387
by (simp_all add: branch_def sinl_pat_def)
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   388
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   389
lemma sinr_pat [simp]:
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   390
  "branch (sinr_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
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   391
  "x \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = fail"
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   392
  "y \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = branch p\<cdot>r\<cdot>y"
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   393
by (simp_all add: branch_def sinr_pat_def)
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   394
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   395
lemma up_pat [simp]:
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   396
  "branch (up_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>"
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   397
  "branch (up_pat p)\<cdot>r\<cdot>(up\<cdot>x) = branch p\<cdot>r\<cdot>x"
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   398
by (simp_all add: branch_def up_pat_def)
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diff changeset
   399
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   400
lemma TT_pat [simp]:
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   401
  "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
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   402
  "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = return\<cdot>r"
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   403
  "branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = fail"
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diff changeset
   404
by (simp_all add: branch_def TT_pat_def)
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   405
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   406
lemma FF_pat [simp]:
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   407
  "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
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diff changeset
   408
  "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = fail"
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   409
  "branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = return\<cdot>r"
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diff changeset
   410
by (simp_all add: branch_def FF_pat_def)
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diff changeset
   411
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   412
lemma ONE_pat [simp]:
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   413
  "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>"
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diff changeset
   414
  "branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>ONE = return\<cdot>r"
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diff changeset
   415
by (simp_all add: branch_def ONE_pat_def)
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diff changeset
   416
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   417
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   418
subsection {* Wildcards, as-patterns, and lazy patterns *}
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   419
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   420
syntax
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   421
  "_as_pat" :: "[idt, 'a] \<Rightarrow> 'a" (infixr "\<as>" 10)
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   422
  "_lazy_pat" :: "'a \<Rightarrow> 'a" ("\<lazy> _" [1000] 1000)
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   423
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   424
definition
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   425
  wild_pat :: "'a \<rightarrow> unit maybe" where
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   426
  "wild_pat = (\<Lambda> x. return\<cdot>())"
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diff changeset
   427
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   428
definition
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   429
  as_pat :: "('a \<rightarrow> 'b maybe) \<Rightarrow> 'a \<rightarrow> ('a \<times> 'b) maybe" where
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   430
  "as_pat p = (\<Lambda> x. bind\<cdot>(p\<cdot>x)\<cdot>(\<Lambda> a. return\<cdot>\<langle>x, a\<rangle>))"
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diff changeset
   431
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diff changeset
   432
definition
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   433
  lazy_pat :: "('a \<rightarrow> 'b::pcpo maybe) \<Rightarrow> ('a \<rightarrow> 'b maybe)" where
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   434
  "lazy_pat p = (\<Lambda> x. return\<cdot>(cases\<cdot>(p\<cdot>x)))"
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diff changeset
   435
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   436
text {* Parse translations (patterns) *}
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diff changeset
   437
translations
26046
1624b3304bb9 fix broken syntax translations
huffman
parents: 25158
diff changeset
   438
  "_pat _" => "CONST wild_pat"
1624b3304bb9 fix broken syntax translations
huffman
parents: 25158
diff changeset
   439
  "_pat (_as_pat x y)" => "CONST as_pat (_pat y)"
1624b3304bb9 fix broken syntax translations
huffman
parents: 25158
diff changeset
   440
  "_pat (_lazy_pat x)" => "CONST lazy_pat (_pat x)"
18293
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   441
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   442
text {* Parse translations (variables) *}
18112
dc1d6f588204 reimplemented Case syntax using print/parse translations; moved as-patterns to separate section
huffman
parents: 18110
diff changeset
   443
translations
29322
ae6f2b1559fa renamed syntax constant "_var" to "_variable", to avoid clash with internal token marker;
wenzelm
parents: 29141
diff changeset
   444
  "_variable _ r" => "_variable _noargs r"
ae6f2b1559fa renamed syntax constant "_var" to "_variable", to avoid clash with internal token marker;
wenzelm
parents: 29141
diff changeset
   445
  "_variable (_as_pat x y) r" => "_variable (_args x y) r"
ae6f2b1559fa renamed syntax constant "_var" to "_variable", to avoid clash with internal token marker;
wenzelm
parents: 29141
diff changeset
   446
  "_variable (_lazy_pat x) r" => "_variable x r"
18293
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   447
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   448
text {* Print translations *}
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   449
translations
26046
1624b3304bb9 fix broken syntax translations
huffman
parents: 25158
diff changeset
   450
  "_" <= "_match (CONST wild_pat) _noargs"
29322
ae6f2b1559fa renamed syntax constant "_var" to "_variable", to avoid clash with internal token marker;
wenzelm
parents: 29141
diff changeset
   451
  "_as_pat x (_match p v)" <= "_match (CONST as_pat p) (_args (_variable x) v)"
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   452
  "_lazy_pat (_match p v)" <= "_match (CONST lazy_pat p) v"
18293
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   453
19327
4565e230e6eb lazy patterns in lambda abstractions
huffman
parents: 19104
diff changeset
   454
text {* Lazy patterns in lambda abstractions *}
4565e230e6eb lazy patterns in lambda abstractions
huffman
parents: 19104
diff changeset
   455
translations
28891
f199def7a6a5 separate run and cases combinators
huffman
parents: 26046
diff changeset
   456
  "_cabs (_lazy_pat p) r" == "CONST Fixrec.cases oo (_Case1 (_lazy_pat p) r)"
19327
4565e230e6eb lazy patterns in lambda abstractions
huffman
parents: 19104
diff changeset
   457
18293
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   458
lemma wild_pat [simp]: "branch wild_pat\<cdot>(unit_when\<cdot>r)\<cdot>x = return\<cdot>r"
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   459
by (simp add: branch_def wild_pat_def)
18112
dc1d6f588204 reimplemented Case syntax using print/parse translations; moved as-patterns to separate section
huffman
parents: 18110
diff changeset
   460
18293
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   461
lemma as_pat [simp]:
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   462
  "branch (as_pat p)\<cdot>(csplit\<cdot>r)\<cdot>x = branch p\<cdot>(r\<cdot>x)\<cdot>x"
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   463
apply (simp add: branch_def as_pat_def)
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   464
apply (rule_tac p="p\<cdot>x" in maybeE, simp_all)
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   465
done
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   466
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   467
lemma lazy_pat [simp]:
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   468
  "branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = return\<cdot>(r\<cdot>\<bottom>)"
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   469
  "branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = return\<cdot>(r\<cdot>\<bottom>)"
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   470
  "branch p\<cdot>r\<cdot>x = return\<cdot>s \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = return\<cdot>s"
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   471
apply (simp_all add: branch_def lazy_pat_def)
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   472
apply (rule_tac [!] p="p\<cdot>x" in maybeE, simp_all)
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   473
done
4eaa654c92f2 reimplement Case expression pattern matching to support lazy patterns
huffman
parents: 18112
diff changeset
   474
18112
dc1d6f588204 reimplemented Case syntax using print/parse translations; moved as-patterns to separate section
huffman
parents: 18110
diff changeset
   475
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   476
subsection {* Match functions for built-in types *}
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   477
16776
a3899ac14a1c generalized types of monadic operators to class cpo; added match function for UU
huffman
parents: 16758
diff changeset
   478
defaultsort pcpo
a3899ac14a1c generalized types of monadic operators to class cpo; added match function for UU
huffman
parents: 16758
diff changeset
   479
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   480
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   481
  match_UU :: "'a \<rightarrow> 'c maybe \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   482
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   483
  "match_UU = strictify\<cdot>(\<Lambda> x k. fail)"
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   484
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   485
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   486
  match_cpair :: "'a::cpo \<times> 'b::cpo \<rightarrow> ('a \<rightarrow> 'b \<rightarrow> 'c maybe) \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   487
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   488
  "match_cpair = (\<Lambda> x k. csplit\<cdot>k\<cdot>x)"
16776
a3899ac14a1c generalized types of monadic operators to class cpo; added match function for UU
huffman
parents: 16758
diff changeset
   489
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   490
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   491
  match_spair :: "'a \<otimes> 'b \<rightarrow> ('a \<rightarrow> 'b \<rightarrow> 'c maybe) \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   492
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   493
  "match_spair = (\<Lambda> x k. ssplit\<cdot>k\<cdot>x)"
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   494
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   495
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   496
  match_sinl :: "'a \<oplus> 'b \<rightarrow> ('a \<rightarrow> 'c maybe) \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   497
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   498
  "match_sinl = (\<Lambda> x k. sscase\<cdot>k\<cdot>(\<Lambda> b. fail)\<cdot>x)"
16551
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   499
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   500
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   501
  match_sinr :: "'a \<oplus> 'b \<rightarrow> ('b \<rightarrow> 'c maybe) \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   502
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   503
  "match_sinr = (\<Lambda> x k. sscase\<cdot>(\<Lambda> a. fail)\<cdot>k\<cdot>x)"
16551
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   504
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   505
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   506
  match_up :: "'a::cpo u \<rightarrow> ('a \<rightarrow> 'c maybe) \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   507
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   508
  "match_up = (\<Lambda> x k. fup\<cdot>k\<cdot>x)"
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   509
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   510
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   511
  match_ONE :: "one \<rightarrow> 'c maybe \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   512
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   513
  "match_ONE = (\<Lambda> ONE k. k)"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   514
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   515
definition
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   516
  match_TT :: "tr \<rightarrow> 'c maybe \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   517
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   518
  "match_TT = (\<Lambda> x k. If x then k else fail fi)"
18094
404f298220af simplify definitions
huffman
parents: 16779
diff changeset
   519
 
25131
2c8caac48ade modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents: 23152
diff changeset
   520
definition
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   521
  match_FF :: "tr \<rightarrow> 'c maybe \<rightarrow> 'c maybe"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   522
where
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   523
  "match_FF = (\<Lambda> x k. If x then fail else k fi)"
16460
72a08d509d62 added match functions for ONE, TT, and FF; added theorem mplus_fail2
huffman
parents: 16417
diff changeset
   524
16776
a3899ac14a1c generalized types of monadic operators to class cpo; added match function for UU
huffman
parents: 16758
diff changeset
   525
lemma match_UU_simps [simp]:
31008
b8f4e351b5bf add proper support for bottom-patterns in fixrec package
huffman
parents: 30914
diff changeset
   526
  "match_UU\<cdot>\<bottom>\<cdot>k = \<bottom>"
b8f4e351b5bf add proper support for bottom-patterns in fixrec package
huffman
parents: 30914
diff changeset
   527
  "x \<noteq> \<bottom> \<Longrightarrow> match_UU\<cdot>x\<cdot>k = fail"
b8f4e351b5bf add proper support for bottom-patterns in fixrec package
huffman
parents: 30914
diff changeset
   528
by (simp_all add: match_UU_def)
16776
a3899ac14a1c generalized types of monadic operators to class cpo; added match function for UU
huffman
parents: 16758
diff changeset
   529
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   530
lemma match_cpair_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   531
  "match_cpair\<cdot>\<langle>x, y\<rangle>\<cdot>k = k\<cdot>x\<cdot>y"
33401
fc43fa403a69 add fixrec support for HOL pair constructor patterns
huffman
parents: 31738
diff changeset
   532
  "match_cpair\<cdot>(x, y)\<cdot>k = k\<cdot>x\<cdot>y"
fc43fa403a69 add fixrec support for HOL pair constructor patterns
huffman
parents: 31738
diff changeset
   533
by (simp_all add: match_cpair_def)
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   534
16551
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   535
lemma match_spair_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   536
  "\<lbrakk>x \<noteq> \<bottom>; y \<noteq> \<bottom>\<rbrakk> \<Longrightarrow> match_spair\<cdot>(:x, y:)\<cdot>k = k\<cdot>x\<cdot>y"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   537
  "match_spair\<cdot>\<bottom>\<cdot>k = \<bottom>"
16551
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   538
by (simp_all add: match_spair_def)
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   539
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   540
lemma match_sinl_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   541
  "x \<noteq> \<bottom> \<Longrightarrow> match_sinl\<cdot>(sinl\<cdot>x)\<cdot>k = k\<cdot>x"
30914
ceeb5f2eac75 fix too-specific types in lemmas match_{sinl,sinr}_simps
huffman
parents: 30912
diff changeset
   542
  "y \<noteq> \<bottom> \<Longrightarrow> match_sinl\<cdot>(sinr\<cdot>y)\<cdot>k = fail"
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   543
  "match_sinl\<cdot>\<bottom>\<cdot>k = \<bottom>"
16551
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   544
by (simp_all add: match_sinl_def)
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   545
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   546
lemma match_sinr_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   547
  "x \<noteq> \<bottom> \<Longrightarrow> match_sinr\<cdot>(sinl\<cdot>x)\<cdot>k = fail"
30914
ceeb5f2eac75 fix too-specific types in lemmas match_{sinl,sinr}_simps
huffman
parents: 30912
diff changeset
   548
  "y \<noteq> \<bottom> \<Longrightarrow> match_sinr\<cdot>(sinr\<cdot>y)\<cdot>k = k\<cdot>y"
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   549
  "match_sinr\<cdot>\<bottom>\<cdot>k = \<bottom>"
16551
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   550
by (simp_all add: match_sinr_def)
7abf8a713613 added match functions for spair, sinl, sinr
huffman
parents: 16463
diff changeset
   551
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   552
lemma match_up_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   553
  "match_up\<cdot>(up\<cdot>x)\<cdot>k = k\<cdot>x"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   554
  "match_up\<cdot>\<bottom>\<cdot>k = \<bottom>"
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   555
by (simp_all add: match_up_def)
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   556
16460
72a08d509d62 added match functions for ONE, TT, and FF; added theorem mplus_fail2
huffman
parents: 16417
diff changeset
   557
lemma match_ONE_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   558
  "match_ONE\<cdot>ONE\<cdot>k = k"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   559
  "match_ONE\<cdot>\<bottom>\<cdot>k = \<bottom>"
18094
404f298220af simplify definitions
huffman
parents: 16779
diff changeset
   560
by (simp_all add: match_ONE_def)
16460
72a08d509d62 added match functions for ONE, TT, and FF; added theorem mplus_fail2
huffman
parents: 16417
diff changeset
   561
72a08d509d62 added match functions for ONE, TT, and FF; added theorem mplus_fail2
huffman
parents: 16417
diff changeset
   562
lemma match_TT_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   563
  "match_TT\<cdot>TT\<cdot>k = k"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   564
  "match_TT\<cdot>FF\<cdot>k = fail"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   565
  "match_TT\<cdot>\<bottom>\<cdot>k = \<bottom>"
18094
404f298220af simplify definitions
huffman
parents: 16779
diff changeset
   566
by (simp_all add: match_TT_def)
16460
72a08d509d62 added match functions for ONE, TT, and FF; added theorem mplus_fail2
huffman
parents: 16417
diff changeset
   567
72a08d509d62 added match functions for ONE, TT, and FF; added theorem mplus_fail2
huffman
parents: 16417
diff changeset
   568
lemma match_FF_simps [simp]:
30912
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   569
  "match_FF\<cdot>FF\<cdot>k = k"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   570
  "match_FF\<cdot>TT\<cdot>k = fail"
4022298c1a86 change definition of match combinators for fixrec package
huffman
parents: 30131
diff changeset
   571
  "match_FF\<cdot>\<bottom>\<cdot>k = \<bottom>"
18094
404f298220af simplify definitions
huffman
parents: 16779
diff changeset
   572
by (simp_all add: match_FF_def)
16460
72a08d509d62 added match functions for ONE, TT, and FF; added theorem mplus_fail2
huffman
parents: 16417
diff changeset
   573
16401
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   574
subsection {* Mutual recursion *}
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   575
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   576
text {*
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   577
  The following rules are used to prove unfolding theorems from
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   578
  fixed-point definitions of mutually recursive functions.
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   579
*}
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   580
31095
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   581
lemma Pair_equalI: "\<lbrakk>x \<equiv> fst p; y \<equiv> snd p\<rbrakk> \<Longrightarrow> (x, y) \<equiv> p"
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   582
by simp
16401
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   583
31095
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   584
lemma Pair_eqD1: "(x, y) = (x', y') \<Longrightarrow> x = x'"
16401
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   585
by simp
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   586
31095
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   587
lemma Pair_eqD2: "(x, y) = (x', y') \<Longrightarrow> y = y'"
16401
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   588
by simp
57c35ede00b9 fixrec package now handles mutually-recursive definitions
huffman
parents: 16229
diff changeset
   589
31095
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   590
lemma def_cont_fix_eq:
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   591
  "\<lbrakk>f \<equiv> fix\<cdot>(Abs_CFun F); cont F\<rbrakk> \<Longrightarrow> f = F f"
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   592
by (simp, subst fix_eq, simp)
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   593
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   594
lemma def_cont_fix_ind:
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   595
  "\<lbrakk>f \<equiv> fix\<cdot>(Abs_CFun F); cont F; adm P; P \<bottom>; \<And>x. P x \<Longrightarrow> P (F x)\<rbrakk> \<Longrightarrow> P f"
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   596
by (simp add: fix_ind)
b79d140f6d0b simplify fixrec proofs for mutually-recursive definitions; generate better fixpoint induction rules
huffman
parents: 31008
diff changeset
   597
16463
342d74ca8815 fixrec shows unsolved subgoals when proofs of rewrites fail
huffman
parents: 16460
diff changeset
   598
text {* lemma for proving rewrite rules *}
342d74ca8815 fixrec shows unsolved subgoals when proofs of rewrites fail
huffman
parents: 16460
diff changeset
   599
342d74ca8815 fixrec shows unsolved subgoals when proofs of rewrites fail
huffman
parents: 16460
diff changeset
   600
lemma ssubst_lhs: "\<lbrakk>t = s; P s = Q\<rbrakk> \<Longrightarrow> P t = Q"
342d74ca8815 fixrec shows unsolved subgoals when proofs of rewrites fail
huffman
parents: 16460
diff changeset
   601
by simp
342d74ca8815 fixrec shows unsolved subgoals when proofs of rewrites fail
huffman
parents: 16460
diff changeset
   602
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   603
16758
c32334d98fcd fix typo
huffman
parents: 16754
diff changeset
   604
subsection {* Initializing the fixrec package *}
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   605
31738
7b9b9ba532ca discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents: 31095
diff changeset
   606
use "Tools/fixrec.ML"
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   607
31738
7b9b9ba532ca discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents: 31095
diff changeset
   608
setup {* Fixrec.setup *}
30131
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   609
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   610
setup {*
31738
7b9b9ba532ca discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents: 31095
diff changeset
   611
  Fixrec.add_matchers
30131
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   612
    [ (@{const_name up}, @{const_name match_up}),
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   613
      (@{const_name sinl}, @{const_name match_sinl}),
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   614
      (@{const_name sinr}, @{const_name match_sinr}),
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   615
      (@{const_name spair}, @{const_name match_spair}),
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   616
      (@{const_name cpair}, @{const_name match_cpair}),
33401
fc43fa403a69 add fixrec support for HOL pair constructor patterns
huffman
parents: 31738
diff changeset
   617
      (@{const_name Pair}, @{const_name match_cpair}),
30131
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   618
      (@{const_name ONE}, @{const_name match_ONE}),
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   619
      (@{const_name TT}, @{const_name match_TT}),
31008
b8f4e351b5bf add proper support for bottom-patterns in fixrec package
huffman
parents: 30914
diff changeset
   620
      (@{const_name FF}, @{const_name match_FF}),
b8f4e351b5bf add proper support for bottom-patterns in fixrec package
huffman
parents: 30914
diff changeset
   621
      (@{const_name UU}, @{const_name match_UU}) ]
30131
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   622
*}
6be1be402ef0 use TheoryData to keep track of pattern match combinators
huffman
parents: 29530
diff changeset
   623
28891
f199def7a6a5 separate run and cases combinators
huffman
parents: 26046
diff changeset
   624
hide (open) const return bind fail run cases
19104
7d69b6d7b8f1 use qualified name for return
huffman
parents: 19092
diff changeset
   625
33425
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   626
lemmas [fixrec_simp] =
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   627
  run_strict run_fail run_return
33429
42d7b6b4992b add more fixrec_simp rules
huffman
parents: 33425
diff changeset
   628
  mplus_strict mplus_fail mplus_return
33425
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   629
  spair_strict_iff
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   630
  sinl_defined_iff
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   631
  sinr_defined_iff
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   632
  up_defined
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   633
  ONE_defined
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   634
  dist_eq_tr(1,2)
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   635
  match_UU_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   636
  match_cpair_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   637
  match_spair_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   638
  match_sinl_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   639
  match_sinr_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   640
  match_up_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   641
  match_ONE_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   642
  match_TT_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   643
  match_FF_simps
7e4f3c66190d add fixrec_simp attribute and method (eventually to replace fixpat)
huffman
parents: 33401
diff changeset
   644
16221
879400e029bf New theory with lemmas for the fixrec package
huffman
parents:
diff changeset
   645
end