author | wenzelm |
Mon, 20 Sep 2010 16:05:25 +0200 | |
changeset 39557 | fe5722fce758 |
parent 37109 | e67760c1b851 |
child 40026 | 8f8f18a88685 |
permissions | -rw-r--r-- |
37109 | 1 |
(* Title: HOLCF/ex/Pattern_Match.thy |
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Author: Brian Huffman |
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*) |
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header {* An experimental pattern-matching notation *} |
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theory Pattern_Match |
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imports HOLCF |
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begin |
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text {* FIXME: Find a proper way to un-hide constants. *} |
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abbreviation fail :: "'a match" |
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where "fail \<equiv> Fixrec.fail" |
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abbreviation succeed :: "'a \<rightarrow> 'a match" |
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where "succeed \<equiv> Fixrec.succeed" |
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abbreviation run :: "'a match \<rightarrow> 'a" |
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where "run \<equiv> Fixrec.run" |
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subsection {* Fatbar combinator *} |
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definition |
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fatbar :: "('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match) \<rightarrow> ('a \<rightarrow> 'b match)" 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 match, 'a \<rightarrow> 'b match] \<Rightarrow> 'a \<rightarrow> 'b match" (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 = succeed\<cdot>y \<Longrightarrow> (m \<parallel> ms)\<cdot>x = succeed\<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 = succeed\<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 match) \<Rightarrow> ('b \<rightarrow> 'c) \<rightarrow> ('a \<rightarrow> 'c match)" where |
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"branch p \<equiv> \<Lambda> r x. match_case\<cdot>fail\<cdot>(\<Lambda> y. succeed\<cdot>(r\<cdot>y))\<cdot>(p\<cdot>x)" |
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lemma branch_simps: |
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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 = succeed\<cdot>y \<Longrightarrow> branch p\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>y)" |
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by (simp_all add: branch_def) |
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lemma branch_succeed [simp]: "branch succeed\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>x)" |
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by (simp add: branch_def) |
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subsection {* Cases operator *} |
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definition |
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cases :: "'a match \<rightarrow> 'a::pcpo" where |
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"cases = match_case\<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_succeed [simp]: "cases\<cdot>(succeed\<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 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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translations |
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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) => (succeed) *) |
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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.succeed}), |
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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 succeed) (_variable x)" |
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subsection {* Pattern combinators for data constructors *} |
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types ('a, 'b) pat = "'a \<rightarrow> 'b match" |
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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>(x, y). |
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match_case\<cdot>fail\<cdot>(\<Lambda> a. match_case\<cdot>fail\<cdot>(\<Lambda> b. succeed\<cdot>(a, b))\<cdot>(p2\<cdot>y))\<cdot>(p1\<cdot>x))" |
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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>(x, y))" |
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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 succeed\<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 succeed\<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. succeed\<cdot>())" |
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text {* Parse translations (patterns) *} |
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translations |
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"_pat (XCONST Pair x 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 Pair x 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 Pair x 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 Pair x 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 Pair (_match p1 v1) (_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>(x, y) = \<bottom>" |
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apply (simp add: branch_def cpair_pat_def) |
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apply (cases "p\<cdot>x", 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>(x, y) = fail" |
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apply (simp add: branch_def cpair_pat_def) |
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apply (cases "p\<cdot>x", simp_all) |
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done |
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lemma cpair_pat3: |
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"branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow> |
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branch (cpair_pat p q)\<cdot>(csplit\<cdot>r)\<cdot>(x, y) = branch q\<cdot>s\<cdot>y" |
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apply (simp add: branch_def cpair_pat_def) |
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apply (cases "p\<cdot>x", simp_all) |
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apply (cases "q\<cdot>y", simp_all) |
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done |
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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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"\<lbrakk>x \<noteq> \<bottom>; y \<noteq> \<bottom>\<rbrakk> |
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\<Longrightarrow> branch (spair_pat p1 p2)\<cdot>r\<cdot>(:x, y:) = |
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branch (cpair_pat p1 p2)\<cdot>r\<cdot>(x, y)" |
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by (simp_all add: branch_def spair_pat_def) |
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lemma sinl_pat [simp]: |
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"branch (sinl_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>" |
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"x \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = branch p\<cdot>r\<cdot>x" |
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"y \<noteq> \<bottom> \<Longrightarrow> branch (sinl_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = fail" |
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by (simp_all add: branch_def sinl_pat_def) |
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lemma sinr_pat [simp]: |
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"branch (sinr_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>" |
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"x \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinl\<cdot>x) = fail" |
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"y \<noteq> \<bottom> \<Longrightarrow> branch (sinr_pat p)\<cdot>r\<cdot>(sinr\<cdot>y) = branch p\<cdot>r\<cdot>y" |
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by (simp_all add: branch_def sinr_pat_def) |
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lemma up_pat [simp]: |
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"branch (up_pat p)\<cdot>r\<cdot>\<bottom> = \<bottom>" |
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"branch (up_pat p)\<cdot>r\<cdot>(up\<cdot>x) = branch p\<cdot>r\<cdot>x" |
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by (simp_all add: branch_def up_pat_def) |
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lemma TT_pat [simp]: |
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"branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>" |
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"branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = succeed\<cdot>r" |
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"branch TT_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = fail" |
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by (simp_all add: branch_def TT_pat_def) |
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lemma FF_pat [simp]: |
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"branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>" |
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"branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>TT = fail" |
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"branch FF_pat\<cdot>(unit_when\<cdot>r)\<cdot>FF = succeed\<cdot>r" |
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by (simp_all add: branch_def FF_pat_def) |
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lemma ONE_pat [simp]: |
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"branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>\<bottom> = \<bottom>" |
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"branch ONE_pat\<cdot>(unit_when\<cdot>r)\<cdot>ONE = succeed\<cdot>r" |
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by (simp_all add: branch_def ONE_pat_def) |
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subsection {* Wildcards, as-patterns, and lazy patterns *} |
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definition |
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wild_pat :: "'a \<rightarrow> unit match" where |
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"wild_pat = (\<Lambda> x. succeed\<cdot>())" |
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definition |
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as_pat :: "('a \<rightarrow> 'b match) \<Rightarrow> 'a \<rightarrow> ('a \<times> 'b) match" where |
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"as_pat p = (\<Lambda> x. match_case\<cdot>fail\<cdot>(\<Lambda> a. succeed\<cdot>(x, a))\<cdot>(p\<cdot>x))" |
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definition |
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lazy_pat :: "('a \<rightarrow> 'b::pcpo match) \<Rightarrow> ('a \<rightarrow> 'b match)" where |
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"lazy_pat p = (\<Lambda> x. succeed\<cdot>(cases\<cdot>(p\<cdot>x)))" |
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text {* Parse translations (patterns) *} |
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translations |
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"_pat _" => "CONST wild_pat" |
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text {* Parse translations (variables) *} |
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translations |
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"_variable _ r" => "_variable _noargs r" |
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text {* Print translations *} |
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translations |
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"_" <= "_match (CONST wild_pat) _noargs" |
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lemma wild_pat [simp]: "branch wild_pat\<cdot>(unit_when\<cdot>r)\<cdot>x = succeed\<cdot>r" |
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by (simp add: branch_def wild_pat_def) |
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lemma as_pat [simp]: |
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"branch (as_pat p)\<cdot>(csplit\<cdot>r)\<cdot>x = branch p\<cdot>(r\<cdot>x)\<cdot>x" |
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apply (simp add: branch_def as_pat_def) |
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apply (cases "p\<cdot>x", simp_all) |
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done |
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lemma lazy_pat [simp]: |
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"branch p\<cdot>r\<cdot>x = \<bottom> \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)" |
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"branch p\<cdot>r\<cdot>x = fail \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>(r\<cdot>\<bottom>)" |
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"branch p\<cdot>r\<cdot>x = succeed\<cdot>s \<Longrightarrow> branch (lazy_pat p)\<cdot>r\<cdot>x = succeed\<cdot>s" |
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apply (simp_all add: branch_def lazy_pat_def) |
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apply (cases "p\<cdot>x", simp_all)+ |
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done |
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subsection {* Examples *} |
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term "Case t of (:up\<cdot>(sinl\<cdot>x), sinr\<cdot>y:) \<Rightarrow> (x, y)" |
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term "\<Lambda> t. Case t of up\<cdot>(sinl\<cdot>a) \<Rightarrow> a | up\<cdot>(sinr\<cdot>b) \<Rightarrow> b" |
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term "\<Lambda> t. Case t of (:up\<cdot>(sinl\<cdot>_), sinr\<cdot>x:) \<Rightarrow> x" |
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subsection {* ML code for generating definitions *} |
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ML {* |
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local open HOLCF_Library in |
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val beta_rules = |
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@{thms beta_cfun cont_id cont_const cont2cont_Rep_CFun cont2cont_LAM'} @ |
|
364 |
@{thms cont2cont_fst cont2cont_snd cont2cont_Pair}; |
|
365 |
||
366 |
val beta_ss = HOL_basic_ss addsimps (simp_thms @ beta_rules); |
|
367 |
||
368 |
fun define_consts |
|
369 |
(specs : (binding * term * mixfix) list) |
|
370 |
(thy : theory) |
|
371 |
: (term list * thm list) * theory = |
|
372 |
let |
|
373 |
fun mk_decl (b, t, mx) = (b, fastype_of t, mx); |
|
374 |
val decls = map mk_decl specs; |
|
375 |
val thy = Cont_Consts.add_consts decls thy; |
|
376 |
fun mk_const (b, T, mx) = Const (Sign.full_name thy b, T); |
|
377 |
val consts = map mk_const decls; |
|
378 |
fun mk_def c (b, t, mx) = |
|
379 |
(Binding.suffix_name "_def" b, Logic.mk_equals (c, t)); |
|
380 |
val defs = map2 mk_def consts specs; |
|
381 |
val (def_thms, thy) = |
|
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
37109
diff
changeset
|
382 |
Global_Theory.add_defs false (map Thm.no_attributes defs) thy; |
37109 | 383 |
in |
384 |
((consts, def_thms), thy) |
|
385 |
end; |
|
386 |
||
387 |
fun prove |
|
388 |
(thy : theory) |
|
389 |
(defs : thm list) |
|
390 |
(goal : term) |
|
391 |
(tacs : {prems: thm list, context: Proof.context} -> tactic list) |
|
392 |
: thm = |
|
393 |
let |
|
394 |
fun tac {prems, context} = |
|
395 |
rewrite_goals_tac defs THEN |
|
396 |
EVERY (tacs {prems = map (rewrite_rule defs) prems, context = context}) |
|
397 |
in |
|
398 |
Goal.prove_global thy [] [] goal tac |
|
399 |
end; |
|
400 |
||
401 |
fun get_vars_avoiding |
|
402 |
(taken : string list) |
|
403 |
(args : (bool * typ) list) |
|
404 |
: (term list * term list) = |
|
405 |
let |
|
406 |
val Ts = map snd args; |
|
407 |
val ns = Name.variant_list taken (Datatype_Prop.make_tnames Ts); |
|
408 |
val vs = map Free (ns ~~ Ts); |
|
409 |
val nonlazy = map snd (filter_out (fst o fst) (args ~~ vs)); |
|
410 |
in |
|
411 |
(vs, nonlazy) |
|
412 |
end; |
|
413 |
||
414 |
(******************************************************************************) |
|
415 |
(************** definitions and theorems for pattern combinators **************) |
|
416 |
(******************************************************************************) |
|
417 |
||
418 |
fun add_pattern_combinators |
|
419 |
(bindings : binding list) |
|
420 |
(spec : (term * (bool * typ) list) list) |
|
421 |
(lhsT : typ) |
|
422 |
(exhaust : thm) |
|
423 |
(case_const : typ -> term) |
|
424 |
(case_rews : thm list) |
|
425 |
(thy : theory) = |
|
426 |
let |
|
427 |
||
428 |
(* utility functions *) |
|
429 |
fun mk_pair_pat (p1, p2) = |
|
430 |
let |
|
431 |
val T1 = fastype_of p1; |
|
432 |
val T2 = fastype_of p2; |
|
433 |
val (U1, V1) = apsnd dest_matchT (dest_cfunT T1); |
|
434 |
val (U2, V2) = apsnd dest_matchT (dest_cfunT T2); |
|
435 |
val pat_typ = [T1, T2] ---> |
|
436 |
(mk_prodT (U1, U2) ->> mk_matchT (mk_prodT (V1, V2))); |
|
437 |
val pat_const = Const (@{const_name cpair_pat}, pat_typ); |
|
438 |
in |
|
439 |
pat_const $ p1 $ p2 |
|
440 |
end; |
|
441 |
fun mk_tuple_pat [] = succeed_const HOLogic.unitT |
|
442 |
| mk_tuple_pat ps = foldr1 mk_pair_pat ps; |
|
443 |
fun branch_const (T,U,V) = |
|
444 |
Const (@{const_name branch}, |
|
445 |
(T ->> mk_matchT U) --> (U ->> V) ->> T ->> mk_matchT V); |
|
446 |
||
447 |
(* define pattern combinators *) |
|
448 |
local |
|
449 |
val tns = map (fst o dest_TFree) (snd (dest_Type lhsT)); |
|
450 |
||
451 |
fun pat_eqn (i, (bind, (con, args))) : binding * term * mixfix = |
|
452 |
let |
|
453 |
val pat_bind = Binding.suffix_name "_pat" bind; |
|
454 |
val Ts = map snd args; |
|
455 |
val Vs = |
|
456 |
(map (K "'t") args) |
|
457 |
|> Datatype_Prop.indexify_names |
|
458 |
|> Name.variant_list tns |
|
459 |
|> map (fn t => TFree (t, @{sort pcpo})); |
|
460 |
val patNs = Datatype_Prop.indexify_names (map (K "pat") args); |
|
461 |
val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs; |
|
462 |
val pats = map Free (patNs ~~ patTs); |
|
463 |
val fail = mk_fail (mk_tupleT Vs); |
|
464 |
val (vs, nonlazy) = get_vars_avoiding patNs args; |
|
465 |
val rhs = big_lambdas vs (mk_tuple_pat pats ` mk_tuple vs); |
|
466 |
fun one_fun (j, (_, args')) = |
|
467 |
let |
|
468 |
val (vs', nonlazy) = get_vars_avoiding patNs args'; |
|
469 |
in if i = j then rhs else big_lambdas vs' fail end; |
|
470 |
val funs = map_index one_fun spec; |
|
471 |
val body = list_ccomb (case_const (mk_matchT (mk_tupleT Vs)), funs); |
|
472 |
in |
|
473 |
(pat_bind, lambdas pats body, NoSyn) |
|
474 |
end; |
|
475 |
in |
|
476 |
val ((pat_consts, pat_defs), thy) = |
|
477 |
define_consts (map_index pat_eqn (bindings ~~ spec)) thy |
|
478 |
end; |
|
479 |
||
480 |
(* syntax translations for pattern combinators *) |
|
481 |
local |
|
482 |
open Syntax |
|
483 |
fun syntax c = Syntax.mark_const (fst (dest_Const c)); |
|
484 |
fun app s (l, r) = Syntax.mk_appl (Constant s) [l, r]; |
|
485 |
val capp = app @{const_syntax Rep_CFun}; |
|
486 |
val capps = Library.foldl capp |
|
487 |
||
488 |
fun app_var x = Syntax.mk_appl (Constant "_variable") [x, Variable "rhs"]; |
|
489 |
fun app_pat x = Syntax.mk_appl (Constant "_pat") [x]; |
|
490 |
fun args_list [] = Constant "_noargs" |
|
491 |
| args_list xs = foldr1 (app "_args") xs; |
|
492 |
fun one_case_trans (pat, (con, args)) = |
|
493 |
let |
|
494 |
val cname = Constant (syntax con); |
|
495 |
val pname = Constant (syntax pat); |
|
496 |
val ns = 1 upto length args; |
|
497 |
val xs = map (fn n => Variable ("x"^(string_of_int n))) ns; |
|
498 |
val ps = map (fn n => Variable ("p"^(string_of_int n))) ns; |
|
499 |
val vs = map (fn n => Variable ("v"^(string_of_int n))) ns; |
|
500 |
in |
|
501 |
[ParseRule (app_pat (capps (cname, xs)), |
|
502 |
mk_appl pname (map app_pat xs)), |
|
503 |
ParseRule (app_var (capps (cname, xs)), |
|
504 |
app_var (args_list xs)), |
|
505 |
PrintRule (capps (cname, ListPair.map (app "_match") (ps,vs)), |
|
506 |
app "_match" (mk_appl pname ps, args_list vs))] |
|
507 |
end; |
|
508 |
val trans_rules : Syntax.ast Syntax.trrule list = |
|
509 |
maps one_case_trans (pat_consts ~~ spec); |
|
510 |
in |
|
511 |
val thy = Sign.add_trrules_i trans_rules thy; |
|
512 |
end; |
|
513 |
||
514 |
(* prove strictness and reduction rules of pattern combinators *) |
|
515 |
local |
|
516 |
val tns = map (fst o dest_TFree) (snd (dest_Type lhsT)); |
|
517 |
val rn = Name.variant tns "'r"; |
|
518 |
val R = TFree (rn, @{sort pcpo}); |
|
519 |
fun pat_lhs (pat, args) = |
|
520 |
let |
|
521 |
val Ts = map snd args; |
|
522 |
val Vs = |
|
523 |
(map (K "'t") args) |
|
524 |
|> Datatype_Prop.indexify_names |
|
525 |
|> Name.variant_list (rn::tns) |
|
526 |
|> map (fn t => TFree (t, @{sort pcpo})); |
|
527 |
val patNs = Datatype_Prop.indexify_names (map (K "pat") args); |
|
528 |
val patTs = map2 (fn T => fn V => T ->> mk_matchT V) Ts Vs; |
|
529 |
val pats = map Free (patNs ~~ patTs); |
|
530 |
val k = Free ("rhs", mk_tupleT Vs ->> R); |
|
531 |
val branch1 = branch_const (lhsT, mk_tupleT Vs, R); |
|
532 |
val fun1 = (branch1 $ list_comb (pat, pats)) ` k; |
|
533 |
val branch2 = branch_const (mk_tupleT Ts, mk_tupleT Vs, R); |
|
534 |
val fun2 = (branch2 $ mk_tuple_pat pats) ` k; |
|
535 |
val taken = "rhs" :: patNs; |
|
536 |
in (fun1, fun2, taken) end; |
|
537 |
fun pat_strict (pat, (con, args)) = |
|
538 |
let |
|
539 |
val (fun1, fun2, taken) = pat_lhs (pat, args); |
|
540 |
val defs = @{thm branch_def} :: pat_defs; |
|
541 |
val goal = mk_trp (mk_strict fun1); |
|
542 |
val rules = @{thms match_case_simps} @ case_rews; |
|
543 |
val tacs = [simp_tac (beta_ss addsimps rules) 1]; |
|
544 |
in prove thy defs goal (K tacs) end; |
|
545 |
fun pat_apps (i, (pat, (con, args))) = |
|
546 |
let |
|
547 |
val (fun1, fun2, taken) = pat_lhs (pat, args); |
|
548 |
fun pat_app (j, (con', args')) = |
|
549 |
let |
|
550 |
val (vs, nonlazy) = get_vars_avoiding taken args'; |
|
551 |
val con_app = list_ccomb (con', vs); |
|
552 |
val assms = map (mk_trp o mk_defined) nonlazy; |
|
553 |
val rhs = if i = j then fun2 ` mk_tuple vs else mk_fail R; |
|
554 |
val concl = mk_trp (mk_eq (fun1 ` con_app, rhs)); |
|
555 |
val goal = Logic.list_implies (assms, concl); |
|
556 |
val defs = @{thm branch_def} :: pat_defs; |
|
557 |
val rules = @{thms match_case_simps} @ case_rews; |
|
558 |
val tacs = [asm_simp_tac (beta_ss addsimps rules) 1]; |
|
559 |
in prove thy defs goal (K tacs) end; |
|
560 |
in map_index pat_app spec end; |
|
561 |
in |
|
562 |
val pat_stricts = map pat_strict (pat_consts ~~ spec); |
|
563 |
val pat_apps = flat (map_index pat_apps (pat_consts ~~ spec)); |
|
564 |
end; |
|
565 |
||
566 |
in |
|
567 |
(pat_stricts @ pat_apps, thy) |
|
568 |
end |
|
569 |
||
570 |
end |
|
571 |
*} |
|
572 |
||
573 |
(* |
|
574 |
Cut from HOLCF/Tools/domain_constructors.ML |
|
575 |
in function add_domain_constructors: |
|
576 |
||
577 |
( * define and prove theorems for pattern combinators * ) |
|
578 |
val (pat_thms : thm list, thy : theory) = |
|
579 |
let |
|
580 |
val bindings = map #1 spec; |
|
581 |
fun prep_arg (lazy, sel, T) = (lazy, T); |
|
582 |
fun prep_con c (b, args, mx) = (c, map prep_arg args); |
|
583 |
val pat_spec = map2 prep_con con_consts spec; |
|
584 |
in |
|
585 |
add_pattern_combinators bindings pat_spec lhsT |
|
586 |
exhaust case_const cases thy |
|
587 |
end |
|
588 |
||
589 |
*) |
|
590 |
||
591 |
end |