author  krauss 
Wed, 13 Sep 2006 12:05:50 +0200  
changeset 20523  36a59e5d0039 
parent 20324  71d63a30cc96 
child 20536  f088edff8af8 
permissions  rwrr 
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(* Title: HOL/FunDef.thy 
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ID: $Id$ 

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Author: Alexander Krauss, TU Muenchen 

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A package for general recursive function definitions. 

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*) 

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theory FunDef 
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imports Accessible_Part Datatype Recdef 
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uses 
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("Tools/function_package/sum_tools.ML") 
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("Tools/function_package/fundef_common.ML") 
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("Tools/function_package/fundef_lib.ML") 
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("Tools/function_package/inductive_wrap.ML") 
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("Tools/function_package/context_tree.ML") 
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("Tools/function_package/fundef_prep.ML") 
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("Tools/function_package/fundef_proof.ML") 
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("Tools/function_package/termination.ML") 
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("Tools/function_package/mutual.ML") 
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("Tools/function_package/pattern_split.ML") 
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("Tools/function_package/fundef_package.ML") 
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("Tools/function_package/fundef_datatype.ML") 
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("Tools/function_package/auto_term.ML") 
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begin 
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lemma fundef_ex1_existence: 
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assumes f_def: "f \<equiv> \<lambda>x. THE y. (x,y)\<in>G" 
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assumes ex1: "\<exists>!y. (x,y)\<in>G" 
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shows "(x, f x)\<in>G" 
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by (simp only:f_def, rule theI', rule ex1) 
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lemma fundef_ex1_uniqueness: 
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assumes f_def: "f \<equiv> \<lambda>x. THE y. (x,y)\<in>G" 
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assumes ex1: "\<exists>!y. (x,y)\<in>G" 
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assumes elm: "(x, h x)\<in>G" 
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shows "h x = f x" 
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by (simp only:f_def, rule the1_equality[symmetric], rule ex1, rule elm) 
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lemma fundef_ex1_iff: 
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assumes f_def: "f \<equiv> \<lambda>x. THE y. (x,y)\<in>G" 
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assumes ex1: "\<exists>!y. (x,y)\<in>G" 
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shows "((x, y)\<in>G) = (f x = y)" 
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apply (auto simp:ex1 f_def the1_equality) 
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by (rule theI', rule ex1) 
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subsection {* Projections *} 
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consts 
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lpg::"(('a + 'b) * 'a) set" 
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rpg::"(('a + 'b) * 'b) set" 
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inductive lpg 
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intros 
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"(Inl x, x) : lpg" 
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inductive rpg 
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intros 
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"(Inr y, y) : rpg" 
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definition 
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"lproj x = (THE y. (x,y) : lpg)" 
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"rproj x = (THE y. (x,y) : rpg)" 
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lemma lproj_inl: 
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"lproj (Inl x) = x" 
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by (auto simp:lproj_def intro: the_equality lpg.intros elim: lpg.cases) 
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lemma rproj_inr: 
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"rproj (Inr x) = x" 
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by (auto simp:rproj_def intro: the_equality rpg.intros elim: rpg.cases) 
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use "Tools/function_package/sum_tools.ML" 
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use "Tools/function_package/fundef_common.ML" 
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use "Tools/function_package/fundef_lib.ML" 
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use "Tools/function_package/inductive_wrap.ML" 
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use "Tools/function_package/context_tree.ML" 
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use "Tools/function_package/fundef_prep.ML" 
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use "Tools/function_package/fundef_proof.ML" 
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use "Tools/function_package/termination.ML" 
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use "Tools/function_package/mutual.ML" 
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use "Tools/function_package/pattern_split.ML" 
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use "Tools/function_package/fundef_package.ML" 
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setup FundefPackage.setup 
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use "Tools/function_package/fundef_datatype.ML" 
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setup FundefDatatype.setup 
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use "Tools/function_package/auto_term.ML" 
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setup FundefAutoTerm.setup 
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lemmas [fundef_cong] = 
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let_cong if_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong 
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lemma split_cong[fundef_cong]: 
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"\<lbrakk> \<And>x y. (x, y) = q \<Longrightarrow> f x y = g x y; p = q \<rbrakk> 

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\<Longrightarrow> split f p = split g q" 

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by (auto simp:split_def) 

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end 