# HG changeset patch # User krauss # Date 1312274210 -7200 # Node ID 5cfc1c36ae97dd30c7841e07e7f06b0a5092f7eb # Parent 8c1dfd6c226215328a09e4fdc783049f4af50e42 moved recdef package to HOL/Library/Old_Recdef.thy diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Bali/Basis.thy --- a/src/HOL/Bali/Basis.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Bali/Basis.thy Tue Aug 02 10:36:50 2011 +0200 @@ -3,7 +3,7 @@ *) header {* Definitions extending HOL as logical basis of Bali *} -theory Basis imports Main begin +theory Basis imports Main "~~/src/HOL/Library/Old_Recdef" begin section "misc" diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Bali/Decl.thy --- a/src/HOL/Bali/Decl.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Bali/Decl.thy Tue Aug 02 10:36:50 2011 +0200 @@ -5,7 +5,8 @@ *} theory Decl -imports Term Table (** order is significant, because of clash for "var" **) +imports Term Table + (** order is significant, because of clash for "var" **) begin text {* diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Decision_Procs/Cooper.thy --- a/src/HOL/Decision_Procs/Cooper.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Decision_Procs/Cooper.thy Tue Aug 02 10:36:50 2011 +0200 @@ -3,7 +3,7 @@ *) theory Cooper -imports Complex_Main "~~/src/HOL/Library/Efficient_Nat" +imports Complex_Main "~~/src/HOL/Library/Efficient_Nat" "~~/src/HOL/Library/Old_Recdef" uses ("cooper_tac.ML") begin diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Decision_Procs/Ferrack.thy --- a/src/HOL/Decision_Procs/Ferrack.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Decision_Procs/Ferrack.thy Tue Aug 02 10:36:50 2011 +0200 @@ -4,7 +4,7 @@ theory Ferrack imports Complex_Main Dense_Linear_Order DP_Library - "~~/src/HOL/Library/Efficient_Nat" + "~~/src/HOL/Library/Efficient_Nat" "~~/src/HOL/Library/Old_Recdef" uses ("ferrack_tac.ML") begin diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Decision_Procs/MIR.thy --- a/src/HOL/Decision_Procs/MIR.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Decision_Procs/MIR.thy Tue Aug 02 10:36:50 2011 +0200 @@ -4,7 +4,7 @@ theory MIR imports Complex_Main Dense_Linear_Order DP_Library - "~~/src/HOL/Library/Efficient_Nat" + "~~/src/HOL/Library/Efficient_Nat" "~~/src/HOL/Library/Old_Recdef" uses ("mir_tac.ML") begin diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy --- a/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy Tue Aug 02 10:36:50 2011 +0200 @@ -6,7 +6,7 @@ theory Parametric_Ferrante_Rackoff imports Reflected_Multivariate_Polynomial Dense_Linear_Order DP_Library - "~~/src/HOL/Library/Efficient_Nat" + "~~/src/HOL/Library/Efficient_Nat" "~~/src/HOL/Library/Old_Recdef" begin subsection {* Terms *} diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Induct/Sexp.thy --- a/src/HOL/Induct/Sexp.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Induct/Sexp.thy Tue Aug 02 10:36:50 2011 +0200 @@ -6,7 +6,7 @@ structures by hand. *) -theory Sexp imports Main begin +theory Sexp imports Main "~~/src/HOL/Library/Old_Recdef" begin type_synonym 'a item = "'a Datatype.item" abbreviation "Leaf == Datatype.Leaf" diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/IsaMakefile Tue Aug 02 10:36:50 2011 +0200 @@ -292,7 +292,6 @@ Quotient.thy \ Random.thy \ Random_Sequence.thy \ - Recdef.thy \ Record.thy \ Refute.thy \ Semiring_Normalization.thy \ @@ -359,7 +358,6 @@ Tools/Quotient/quotient_tacs.ML \ Tools/Quotient/quotient_term.ML \ Tools/Quotient/quotient_typ.ML \ - Tools/recdef.ML \ Tools/record.ML \ Tools/semiring_normalizer.ML \ Tools/Sledgehammer/async_manager.ML \ @@ -389,15 +387,6 @@ Tools/string_code.ML \ Tools/string_syntax.ML \ Tools/transfer.ML \ - Tools/TFL/casesplit.ML \ - Tools/TFL/dcterm.ML \ - Tools/TFL/post.ML \ - Tools/TFL/rules.ML \ - Tools/TFL/tfl.ML \ - Tools/TFL/thms.ML \ - Tools/TFL/thry.ML \ - Tools/TFL/usyntax.ML \ - Tools/TFL/utils.ML $(OUT)/HOL-Main: main.ML $(MAIN_DEPENDENCIES) @$(ISABELLE_TOOL) usedir -b -f main.ML -g true $(OUT)/Pure HOL-Main @@ -464,7 +453,8 @@ Library/List_lexord.thy Library/Mapping.thy Library/Monad_Syntax.thy \ Library/More_List.thy Library/More_Set.thy Library/Multiset.thy \ Library/Nat_Bijection.thy Library/Nested_Environment.thy \ - Library/Numeral_Type.thy Library/OptionalSugar.thy \ + Library/Numeral_Type.thy Library/Old_Recdef.thy \ + Library/OptionalSugar.thy \ Library/Order_Relation.thy Library/Permutation.thy \ Library/Permutations.thy Library/Poly_Deriv.thy \ Library/Polynomial.thy Library/Predicate_Compile_Quickcheck.thy \ @@ -486,7 +476,11 @@ Library/While_Combinator.thy Library/Zorn.thy \ $(SRC)/Tools/adhoc_overloading.ML Library/positivstellensatz.ML \ Library/reflection.ML Library/reify_data.ML \ - Library/document/root.bib Library/document/root.tex + Library/document/root.bib Library/document/root.tex \ + Tools/TFL/casesplit.ML Tools/TFL/dcterm.ML Tools/TFL/post.ML \ + Tools/TFL/rules.ML Tools/TFL/tfl.ML Tools/TFL/thms.ML \ + Tools/TFL/thry.ML Tools/TFL/usyntax.ML Tools/TFL/utils.ML \ + Tools/recdef.ML @cd Library; $(ISABELLE_TOOL) usedir -b $(OUT)/HOL HOL-Library diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Library/Library.thy --- a/src/HOL/Library/Library.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Library/Library.thy Tue Aug 02 10:36:50 2011 +0200 @@ -39,6 +39,7 @@ Multiset Nested_Environment Numeral_Type + Old_Recdef OptionalSugar Option_ord Permutation diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Library/More_List.thy --- a/src/HOL/Library/More_List.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Library/More_List.thy Tue Aug 02 10:36:50 2011 +0200 @@ -35,7 +35,7 @@ "fold f (rev xs) = foldr f xs" by (simp add: foldr_fold_rev) -lemma fold_cong [fundef_cong, recdef_cong]: +lemma fold_cong [fundef_cong]: "a = b \ xs = ys \ (\x. x \ set xs \ f x = g x) \ fold f xs a = fold g ys b" by (induct ys arbitrary: a b xs) simp_all diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Library/Old_Recdef.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Library/Old_Recdef.thy Tue Aug 02 10:36:50 2011 +0200 @@ -0,0 +1,214 @@ +(* Title: HOL/Library/Old_Recdef.thy + Author: Konrad Slind and Markus Wenzel, TU Muenchen +*) + +header {* TFL: recursive function definitions *} + +theory Old_Recdef +imports Main +uses + ("~~/src/HOL/Tools/TFL/casesplit.ML") + ("~~/src/HOL/Tools/TFL/utils.ML") + ("~~/src/HOL/Tools/TFL/usyntax.ML") + ("~~/src/HOL/Tools/TFL/dcterm.ML") + ("~~/src/HOL/Tools/TFL/thms.ML") + ("~~/src/HOL/Tools/TFL/rules.ML") + ("~~/src/HOL/Tools/TFL/thry.ML") + ("~~/src/HOL/Tools/TFL/tfl.ML") + ("~~/src/HOL/Tools/TFL/post.ML") + ("~~/src/HOL/Tools/recdef.ML") +begin + +inductive + wfrec_rel :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b => bool" + for R :: "('a * 'a) set" + and F :: "('a => 'b) => 'a => 'b" +where + wfrecI: "ALL z. (z, x) : R --> wfrec_rel R F z (g z) ==> + wfrec_rel R F x (F g x)" + +definition + cut :: "('a => 'b) => ('a * 'a)set => 'a => 'a => 'b" where + "cut f r x == (%y. if (y,x):r then f y else undefined)" + +definition + adm_wf :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => bool" where + "adm_wf R F == ALL f g x. + (ALL z. (z, x) : R --> f z = g z) --> F f x = F g x" + +definition + wfrec :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b" where + "wfrec R F == %x. THE y. wfrec_rel R (%f x. F (cut f R x) x) x y" + +subsection{*Well-Founded Recursion*} + +text{*cut*} + +lemma cuts_eq: "(cut f r x = cut g r x) = (ALL y. (y,x):r --> f(y)=g(y))" +by (simp add: fun_eq_iff cut_def) + +lemma cut_apply: "(x,a):r ==> (cut f r a)(x) = f(x)" +by (simp add: cut_def) + +text{*Inductive characterization of wfrec combinator; for details see: +John Harrison, "Inductive definitions: automation and application"*} + +lemma wfrec_unique: "[| adm_wf R F; wf R |] ==> EX! y. wfrec_rel R F x y" +apply (simp add: adm_wf_def) +apply (erule_tac a=x in wf_induct) +apply (rule ex1I) +apply (rule_tac g = "%x. THE y. wfrec_rel R F x y" in wfrec_rel.wfrecI) +apply (fast dest!: theI') +apply (erule wfrec_rel.cases, simp) +apply (erule allE, erule allE, erule allE, erule mp) +apply (fast intro: the_equality [symmetric]) +done + +lemma adm_lemma: "adm_wf R (%f x. F (cut f R x) x)" +apply (simp add: adm_wf_def) +apply (intro strip) +apply (rule cuts_eq [THEN iffD2, THEN subst], assumption) +apply (rule refl) +done + +lemma wfrec: "wf(r) ==> wfrec r H a = H (cut (wfrec r H) r a) a" +apply (simp add: wfrec_def) +apply (rule adm_lemma [THEN wfrec_unique, THEN the1_equality], assumption) +apply (rule wfrec_rel.wfrecI) +apply (intro strip) +apply (erule adm_lemma [THEN wfrec_unique, THEN theI']) +done + + +text{** This form avoids giant explosions in proofs. NOTE USE OF ==*} +lemma def_wfrec: "[| f==wfrec r H; wf(r) |] ==> f(a) = H (cut f r a) a" +apply auto +apply (blast intro: wfrec) +done + + +subsection {* Nitpick setup *} + +axiomatization wf_wfrec :: "('a \ 'a \ bool) \ (('a \ 'b) \ 'a \ 'b) \ 'a \ 'b" + +definition wf_wfrec' :: "('a \ 'a \ bool) \ (('a \ 'b) \ 'a \ 'b) \ 'a \ 'b" where +[nitpick_simp]: "wf_wfrec' R F x = F (cut (wf_wfrec R F) R x) x" + +definition wfrec' :: "('a \ 'a \ bool) \ (('a \ 'b) \ 'a \ 'b) \ 'a \ 'b" where +"wfrec' R F x \ if wf R then wf_wfrec' R F x + else THE y. wfrec_rel R (%f x. F (cut f R x) x) x y" + +setup {* + Nitpick_HOL.register_ersatz_global + [(@{const_name wf_wfrec}, @{const_name wf_wfrec'}), + (@{const_name wfrec}, @{const_name wfrec'})] +*} + +hide_const (open) wf_wfrec wf_wfrec' wfrec' +hide_fact (open) wf_wfrec'_def wfrec'_def + + +subsection {* Lemmas for TFL *} + +lemma tfl_wf_induct: "ALL R. wf R --> + (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))" +apply clarify +apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast) +done + +lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)" +apply clarify +apply (rule cut_apply, assumption) +done + +lemma tfl_wfrec: + "ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)" +apply clarify +apply (erule wfrec) +done + +lemma tfl_eq_True: "(x = True) --> x" + by blast + +lemma tfl_rev_eq_mp: "(x = y) --> y --> x"; + by blast + +lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)" + by blast + +lemma tfl_P_imp_P_iff_True: "P ==> P = True" + by blast + +lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)" + by blast + +lemma tfl_disj_assoc: "(a \ b) \ c == a \ (b \ c)" + by simp + +lemma tfl_disjE: "P \ Q ==> P --> R ==> Q --> R ==> R" + by blast + +lemma tfl_exE: "\x. P x ==> \x. P x --> Q ==> Q" + by blast + +use "~~/src/HOL/Tools/TFL/casesplit.ML" +use "~~/src/HOL/Tools/TFL/utils.ML" +use "~~/src/HOL/Tools/TFL/usyntax.ML" +use "~~/src/HOL/Tools/TFL/dcterm.ML" +use "~~/src/HOL/Tools/TFL/thms.ML" +use "~~/src/HOL/Tools/TFL/rules.ML" +use "~~/src/HOL/Tools/TFL/thry.ML" +use "~~/src/HOL/Tools/TFL/tfl.ML" +use "~~/src/HOL/Tools/TFL/post.ML" +use "~~/src/HOL/Tools/recdef.ML" +setup Recdef.setup + +text {*Wellfoundedness of @{text same_fst}*} + +definition + same_fst :: "('a => bool) => ('a => ('b * 'b)set) => (('a*'b)*('a*'b))set" +where + "same_fst P R == {((x',y'),(x,y)) . x'=x & P x & (y',y) : R x}" + --{*For @{text rec_def} declarations where the first n parameters + stay unchanged in the recursive call. *} + +lemma same_fstI [intro!]: + "[| P x; (y',y) : R x |] ==> ((x,y'),(x,y)) : same_fst P R" +by (simp add: same_fst_def) + +lemma wf_same_fst: + assumes prem: "(!!x. P x ==> wf(R x))" + shows "wf(same_fst P R)" +apply (simp cong del: imp_cong add: wf_def same_fst_def) +apply (intro strip) +apply (rename_tac a b) +apply (case_tac "wf (R a)") + apply (erule_tac a = b in wf_induct, blast) +apply (blast intro: prem) +done + +text {*Rule setup*} + +lemmas [recdef_simp] = + inv_image_def + measure_def + lex_prod_def + same_fst_def + less_Suc_eq [THEN iffD2] + +lemmas [recdef_cong] = + if_cong let_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong + map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong + +lemmas [recdef_wf] = + wf_trancl + wf_less_than + wf_lex_prod + wf_inv_image + wf_measure + wf_measures + wf_pred_nat + wf_same_fst + wf_empty + +end diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/List.thy --- a/src/HOL/List.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/List.thy Tue Aug 02 10:36:50 2011 +0200 @@ -5,7 +5,7 @@ header {* The datatype of finite lists *} theory List -imports Plain Presburger Recdef Code_Numeral Quotient ATP +imports Plain Presburger Code_Numeral Quotient ATP uses ("Tools/list_code.ML") ("Tools/list_to_set_comprehension.ML") @@ -800,7 +800,7 @@ lemma map_eq_conv[simp]: "(map f xs = map g xs) = (!x : set xs. f x = g x)" by (induct xs) auto -lemma map_cong [fundef_cong, recdef_cong]: +lemma map_cong [fundef_cong]: "xs = ys \ (\x. x \ set ys \ f x = g x) \ map f xs = map g ys" by simp @@ -1237,7 +1237,7 @@ (\us vs. ys = us @ x # vs \ (\u\set us. \ P u) \ P x \ xs = filter P vs)" by(auto dest:Cons_eq_filterD) -lemma filter_cong[fundef_cong, recdef_cong]: +lemma filter_cong[fundef_cong]: "xs = ys \ (\x. x \ set ys \ P x = Q x) \ filter P xs = filter Q ys" apply simp apply(erule thin_rl) @@ -2003,12 +2003,12 @@ apply(auto) done -lemma takeWhile_cong [fundef_cong, recdef_cong]: +lemma takeWhile_cong [fundef_cong]: "[| l = k; !!x. x : set l ==> P x = Q x |] ==> takeWhile P l = takeWhile Q k" by (induct k arbitrary: l) (simp_all) -lemma dropWhile_cong [fundef_cong, recdef_cong]: +lemma dropWhile_cong [fundef_cong]: "[| l = k; !!x. x : set l ==> P x = Q x |] ==> dropWhile P l = dropWhile Q k" by (induct k arbitrary: l, simp_all) @@ -2349,12 +2349,12 @@ shows "foldl (\s x. f x s) (h s) xs = h (foldl (\s x. g x s) s xs)" by (rule sym, insert assms, induct xs arbitrary: s) (simp_all add: fun_eq_iff) -lemma foldl_cong [fundef_cong, recdef_cong]: +lemma foldl_cong [fundef_cong]: "[| a = b; l = k; !!a x. x : set l ==> f a x = g a x |] ==> foldl f a l = foldl g b k" by (induct k arbitrary: a b l) simp_all -lemma foldr_cong [fundef_cong, recdef_cong]: +lemma foldr_cong [fundef_cong]: "[| a = b; l = k; !!a x. x : set l ==> f x a = g x a |] ==> foldr f l a = foldr g k b" by (induct k arbitrary: a b l) simp_all @@ -4586,7 +4586,7 @@ definition "measures fs = inv_image (lex less_than) (%a. map (%f. f a) fs)" -lemma wf_measures[recdef_wf, simp]: "wf (measures fs)" +lemma wf_measures[simp]: "wf (measures fs)" unfolding measures_def by blast diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/MicroJava/J/TypeRel.thy --- a/src/HOL/MicroJava/J/TypeRel.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/MicroJava/J/TypeRel.thy Tue Aug 02 10:36:50 2011 +0200 @@ -4,7 +4,7 @@ header {* \isaheader{Relations between Java Types} *} -theory TypeRel imports Decl begin +theory TypeRel imports Decl "~~/src/HOL/Library/Old_Recdef" begin -- "direct subclass, cf. 8.1.3" diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/NanoJava/TypeRel.thy --- a/src/HOL/NanoJava/TypeRel.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/NanoJava/TypeRel.thy Tue Aug 02 10:36:50 2011 +0200 @@ -4,7 +4,7 @@ header "Type relations" -theory TypeRel imports Decl begin +theory TypeRel imports Decl "~~/src/HOL/Library/Old_Recdef" begin consts subcls1 :: "(cname \ cname) set" --{* subclass *} diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Nitpick.thy --- a/src/HOL/Nitpick.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Nitpick.thy Tue Aug 02 10:36:50 2011 +0200 @@ -82,15 +82,6 @@ definition wf' :: "('a \ 'a \ bool) \ bool" where "wf' r \ acyclic r \ (finite r \ unknown)" -axiomatization wf_wfrec :: "('a \ 'a \ bool) \ (('a \ 'b) \ 'a \ 'b) \ 'a \ 'b" - -definition wf_wfrec' :: "('a \ 'a \ bool) \ (('a \ 'b) \ 'a \ 'b) \ 'a \ 'b" where -[nitpick_simp]: "wf_wfrec' R F x = F (Recdef.cut (wf_wfrec R F) R x) x" - -definition wfrec' :: "('a \ 'a \ bool) \ (('a \ 'b) \ 'a \ 'b) \ 'a \ 'b" where -"wfrec' R F x \ if wf R then wf_wfrec' R F x - else THE y. wfrec_rel R (%f x. F (Recdef.cut f R x) x) x y" - definition card' :: "('a \ bool) \ nat" where "card' A \ if finite A then length (SOME xs. set xs = A \ distinct xs) else 0" @@ -238,14 +229,14 @@ setup {* Nitpick_Isar.setup *} hide_const (open) unknown is_unknown bisim bisim_iterator_max Quot safe_The - FunBox PairBox Word prod refl' wf' wf_wfrec wf_wfrec' wfrec' card' setsum' + FunBox PairBox Word prod refl' wf' card' setsum' fold_graph' nat_gcd nat_lcm int_gcd int_lcm Frac Abs_Frac Rep_Frac zero_frac one_frac num denom norm_frac frac plus_frac times_frac uminus_frac number_of_frac inverse_frac less_frac less_eq_frac of_frac hide_type (open) iota bisim_iterator fun_box pair_box unsigned_bit signed_bit word hide_fact (open) Ex1_unfold rtrancl_unfold rtranclp_unfold tranclp_unfold - prod_def refl'_def wf'_def wf_wfrec'_def wfrec'_def card'_def setsum'_def + prod_def refl'_def wf'_def card'_def setsum'_def fold_graph'_def The_psimp Eps_psimp unit_case_unfold nat_case_unfold list_size_simp nat_gcd_def nat_lcm_def int_gcd_def int_lcm_def Frac_def zero_frac_def one_frac_def num_def denom_def norm_frac_def frac_def diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Recdef.thy --- a/src/HOL/Recdef.thy Tue Aug 02 10:03:14 2011 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,189 +0,0 @@ -(* Title: HOL/Recdef.thy - Author: Konrad Slind and Markus Wenzel, TU Muenchen -*) - -header {* TFL: recursive function definitions *} - -theory Recdef -imports Plain Hilbert_Choice -uses - ("Tools/TFL/casesplit.ML") - ("Tools/TFL/utils.ML") - ("Tools/TFL/usyntax.ML") - ("Tools/TFL/dcterm.ML") - ("Tools/TFL/thms.ML") - ("Tools/TFL/rules.ML") - ("Tools/TFL/thry.ML") - ("Tools/TFL/tfl.ML") - ("Tools/TFL/post.ML") - ("Tools/recdef.ML") -begin - -inductive - wfrec_rel :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b => bool" - for R :: "('a * 'a) set" - and F :: "('a => 'b) => 'a => 'b" -where - wfrecI: "ALL z. (z, x) : R --> wfrec_rel R F z (g z) ==> - wfrec_rel R F x (F g x)" - -definition - cut :: "('a => 'b) => ('a * 'a)set => 'a => 'a => 'b" where - "cut f r x == (%y. if (y,x):r then f y else undefined)" - -definition - adm_wf :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => bool" where - "adm_wf R F == ALL f g x. - (ALL z. (z, x) : R --> f z = g z) --> F f x = F g x" - -definition - wfrec :: "('a * 'a) set => (('a => 'b) => 'a => 'b) => 'a => 'b" where - "wfrec R F == %x. THE y. wfrec_rel R (%f x. F (cut f R x) x) x y" - -subsection{*Well-Founded Recursion*} - -text{*cut*} - -lemma cuts_eq: "(cut f r x = cut g r x) = (ALL y. (y,x):r --> f(y)=g(y))" -by (simp add: fun_eq_iff cut_def) - -lemma cut_apply: "(x,a):r ==> (cut f r a)(x) = f(x)" -by (simp add: cut_def) - -text{*Inductive characterization of wfrec combinator; for details see: -John Harrison, "Inductive definitions: automation and application"*} - -lemma wfrec_unique: "[| adm_wf R F; wf R |] ==> EX! y. wfrec_rel R F x y" -apply (simp add: adm_wf_def) -apply (erule_tac a=x in wf_induct) -apply (rule ex1I) -apply (rule_tac g = "%x. THE y. wfrec_rel R F x y" in wfrec_rel.wfrecI) -apply (fast dest!: theI') -apply (erule wfrec_rel.cases, simp) -apply (erule allE, erule allE, erule allE, erule mp) -apply (fast intro: the_equality [symmetric]) -done - -lemma adm_lemma: "adm_wf R (%f x. F (cut f R x) x)" -apply (simp add: adm_wf_def) -apply (intro strip) -apply (rule cuts_eq [THEN iffD2, THEN subst], assumption) -apply (rule refl) -done - -lemma wfrec: "wf(r) ==> wfrec r H a = H (cut (wfrec r H) r a) a" -apply (simp add: wfrec_def) -apply (rule adm_lemma [THEN wfrec_unique, THEN the1_equality], assumption) -apply (rule wfrec_rel.wfrecI) -apply (intro strip) -apply (erule adm_lemma [THEN wfrec_unique, THEN theI']) -done - - -text{** This form avoids giant explosions in proofs. NOTE USE OF ==*} -lemma def_wfrec: "[| f==wfrec r H; wf(r) |] ==> f(a) = H (cut f r a) a" -apply auto -apply (blast intro: wfrec) -done - - -lemma tfl_wf_induct: "ALL R. wf R --> - (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))" -apply clarify -apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast) -done - -lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)" -apply clarify -apply (rule cut_apply, assumption) -done - -lemma tfl_wfrec: - "ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)" -apply clarify -apply (erule wfrec) -done - -lemma tfl_eq_True: "(x = True) --> x" - by blast - -lemma tfl_rev_eq_mp: "(x = y) --> y --> x"; - by blast - -lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)" - by blast - -lemma tfl_P_imp_P_iff_True: "P ==> P = True" - by blast - -lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)" - by blast - -lemma tfl_disj_assoc: "(a \ b) \ c == a \ (b \ c)" - by simp - -lemma tfl_disjE: "P \ Q ==> P --> R ==> Q --> R ==> R" - by blast - -lemma tfl_exE: "\x. P x ==> \x. P x --> Q ==> Q" - by blast - -use "Tools/TFL/casesplit.ML" -use "Tools/TFL/utils.ML" -use "Tools/TFL/usyntax.ML" -use "Tools/TFL/dcterm.ML" -use "Tools/TFL/thms.ML" -use "Tools/TFL/rules.ML" -use "Tools/TFL/thry.ML" -use "Tools/TFL/tfl.ML" -use "Tools/TFL/post.ML" -use "Tools/recdef.ML" -setup Recdef.setup - -text {*Wellfoundedness of @{text same_fst}*} - -definition - same_fst :: "('a => bool) => ('a => ('b * 'b)set) => (('a*'b)*('a*'b))set" -where - "same_fst P R == {((x',y'),(x,y)) . x'=x & P x & (y',y) : R x}" - --{*For @{text rec_def} declarations where the first n parameters - stay unchanged in the recursive call. *} - -lemma same_fstI [intro!]: - "[| P x; (y',y) : R x |] ==> ((x,y'),(x,y)) : same_fst P R" -by (simp add: same_fst_def) - -lemma wf_same_fst: - assumes prem: "(!!x. P x ==> wf(R x))" - shows "wf(same_fst P R)" -apply (simp cong del: imp_cong add: wf_def same_fst_def) -apply (intro strip) -apply (rename_tac a b) -apply (case_tac "wf (R a)") - apply (erule_tac a = b in wf_induct, blast) -apply (blast intro: prem) -done - -text {*Rule setup*} - -lemmas [recdef_simp] = - inv_image_def - measure_def - lex_prod_def - same_fst_def - less_Suc_eq [THEN iffD2] - -lemmas [recdef_cong] = - if_cong let_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong - -lemmas [recdef_wf] = - wf_trancl - wf_less_than - wf_lex_prod - wf_inv_image - wf_measure - wf_pred_nat - wf_same_fst - wf_empty - -end diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Subst/Unify.thy --- a/src/HOL/Subst/Unify.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Subst/Unify.thy Tue Aug 02 10:36:50 2011 +0200 @@ -6,7 +6,7 @@ header {* Unification Algorithm *} theory Unify -imports Unifier +imports Unifier "~~/src/HOL/Library/Old_Recdef" begin subsection {* Substitution and Unification in Higher-Order Logic. *} diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Tools/Nitpick/nitpick_hol.ML --- a/src/HOL/Tools/Nitpick/nitpick_hol.ML Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Tools/Nitpick/nitpick_hol.ML Tue Aug 02 10:36:50 2011 +0200 @@ -1779,7 +1779,7 @@ "too many nested definitions (" ^ string_of_int depth ^ ") while expanding " ^ quote s) - else if s = @{const_name wfrec'} then + else if s = "Old_Recdef.wfrec'" (* FIXME unchecked! *) then (do_term (depth + 1) Ts (s_betapplys Ts (def, ts)), []) else if not unfold andalso size_of_term def > def_inline_threshold () then @@ -1873,9 +1873,7 @@ [(@{const_name card}, @{const_name card'}), (@{const_name setsum}, @{const_name setsum'}), (@{const_name fold_graph}, @{const_name fold_graph'}), - (@{const_name wf}, @{const_name wf'}), - (@{const_name wf_wfrec}, @{const_name wf_wfrec'}), - (@{const_name wfrec}, @{const_name wfrec'})] + (@{const_name wf}, @{const_name wf'})] fun ersatz_table ctxt = (basic_ersatz_table @ #ersatz_table (Data.get (Context.Proof ctxt))) diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Tools/TFL/rules.ML --- a/src/HOL/Tools/TFL/rules.ML Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Tools/TFL/rules.ML Tue Aug 02 10:36:50 2011 +0200 @@ -445,7 +445,7 @@ fun is_cong thm = case (Thm.prop_of thm) of (Const("==>",_)$(Const(@{const_name Trueprop},_)$ _) $ - (Const("==",_) $ (Const (@{const_name Recdef.cut},_) $ f $ R $ a $ x) $ _)) => false + (Const("==",_) $ (Const (@{const_name Old_Recdef.cut},_) $ f $ R $ a $ x) $ _)) => false | _ => true; @@ -645,7 +645,7 @@ end; fun restricted t = is_some (USyntax.find_term - (fn (Const(@{const_name Recdef.cut},_)) =>true | _ => false) + (fn (Const(@{const_name Old_Recdef.cut},_)) =>true | _ => false) t) fun CONTEXT_REWRITE_RULE (func, G, cut_lemma, congs) th = diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/Tools/recdef.ML --- a/src/HOL/Tools/recdef.ML Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/Tools/recdef.ML Tue Aug 02 10:36:50 2011 +0200 @@ -182,7 +182,7 @@ (** add_recdef(_i) **) -fun requires_recdef thy = Theory.requires thy "Recdef" "recursive functions"; +fun requires_recdef thy = Theory.requires thy "Old_Recdef" "recursive functions"; fun gen_add_recdef tfl_fn prep_att prep_hints not_permissive raw_name R eq_srcs hints thy = let diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/ex/InductiveInvariant.thy --- a/src/HOL/ex/InductiveInvariant.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/ex/InductiveInvariant.thy Tue Aug 02 10:36:50 2011 +0200 @@ -4,7 +4,7 @@ header {* Some of the results in Inductive Invariants for Nested Recursion *} -theory InductiveInvariant imports Main begin +theory InductiveInvariant imports "~~/src/HOL/Library/Old_Recdef" begin text {* A formalization of some of the results in \emph{Inductive Invariants for Nested Recursion}, by Sava Krsti\'{c} and John diff -r 8c1dfd6c2262 -r 5cfc1c36ae97 src/HOL/ex/Recdefs.thy --- a/src/HOL/ex/Recdefs.thy Tue Aug 02 10:03:14 2011 +0200 +++ b/src/HOL/ex/Recdefs.thy Tue Aug 02 10:36:50 2011 +0200 @@ -7,7 +7,7 @@ header {* Examples of recdef definitions *} -theory Recdefs imports Main begin +theory Recdefs imports "~~/src/HOL/Library/Old_Recdef" begin consts fact :: "nat => nat" recdef fact less_than