krauss@44013: (* Title: HOL/Library/Old_Recdef.thy wenzelm@10773: Author: Konrad Slind and Markus Wenzel, TU Muenchen wenzelm@12023: *) wenzelm@5123: wenzelm@12023: header {* TFL: recursive function definitions *} wenzelm@7701: krauss@44013: theory Old_Recdef krauss@44014: imports Wfrec wenzelm@46947: keywords "recdef" :: thy_decl and "permissive" "congs" "hints" haftmann@16417: uses krauss@44013: ("~~/src/HOL/Tools/TFL/casesplit.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/utils.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/usyntax.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/dcterm.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/thms.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/rules.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/thry.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/tfl.ML") krauss@44013: ("~~/src/HOL/Tools/TFL/post.ML") krauss@44013: ("~~/src/HOL/Tools/recdef.ML") nipkow@15131: begin wenzelm@10773: krauss@44013: subsection {* Lemmas for TFL *} krauss@44013: krauss@26748: lemma tfl_wf_induct: "ALL R. wf R --> krauss@26748: (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))" krauss@26748: apply clarify krauss@26748: apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast) krauss@26748: done krauss@26748: krauss@26748: lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)" krauss@26748: apply clarify krauss@26748: apply (rule cut_apply, assumption) krauss@26748: done krauss@26748: krauss@26748: lemma tfl_wfrec: krauss@26748: "ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)" krauss@26748: apply clarify krauss@26748: apply (erule wfrec) krauss@26748: done krauss@26748: wenzelm@10773: lemma tfl_eq_True: "(x = True) --> x" wenzelm@10773: by blast wenzelm@10773: wenzelm@46947: lemma tfl_rev_eq_mp: "(x = y) --> y --> x" wenzelm@10773: by blast wenzelm@10773: wenzelm@10773: lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)" wenzelm@10773: by blast wenzelm@6438: wenzelm@10773: lemma tfl_P_imp_P_iff_True: "P ==> P = True" wenzelm@10773: by blast wenzelm@10773: wenzelm@10773: lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)" wenzelm@10773: by blast wenzelm@10773: wenzelm@12023: lemma tfl_disj_assoc: "(a \ b) \ c == a \ (b \ c)" wenzelm@10773: by simp wenzelm@10773: wenzelm@12023: lemma tfl_disjE: "P \ Q ==> P --> R ==> Q --> R ==> R" wenzelm@10773: by blast wenzelm@10773: wenzelm@12023: lemma tfl_exE: "\x. P x ==> \x. P x --> Q ==> Q" wenzelm@10773: by blast wenzelm@10773: krauss@44013: use "~~/src/HOL/Tools/TFL/casesplit.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/utils.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/usyntax.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/dcterm.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/thms.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/rules.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/thry.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/tfl.ML" krauss@44013: use "~~/src/HOL/Tools/TFL/post.ML" krauss@44013: use "~~/src/HOL/Tools/recdef.ML" haftmann@31723: setup Recdef.setup wenzelm@6438: krauss@44014: subsection {* Rule setup *} krauss@32244: wenzelm@9855: lemmas [recdef_simp] = wenzelm@9855: inv_image_def wenzelm@9855: measure_def wenzelm@9855: lex_prod_def nipkow@11284: same_fst_def wenzelm@9855: less_Suc_eq [THEN iffD2] wenzelm@9855: wenzelm@23150: lemmas [recdef_cong] = krauss@22622: if_cong let_cong image_cong INT_cong UN_cong bex_cong ball_cong imp_cong krauss@44013: map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong wenzelm@9855: wenzelm@9855: lemmas [recdef_wf] = wenzelm@9855: wf_trancl wenzelm@9855: wf_less_than wenzelm@9855: wf_lex_prod wenzelm@9855: wf_inv_image wenzelm@9855: wf_measure krauss@44013: wf_measures wenzelm@9855: wf_pred_nat nipkow@10653: wf_same_fst wenzelm@9855: wf_empty wenzelm@9855: wenzelm@6438: end