(*  Title:      HOL/Library/Old_Recdef.thy

     Author:     Konrad Slind and Markus Wenzel, TU Muenchen

 *)

 section \<open>TFL: recursive function definitions\<close>

 theory Old_Recdef

 imports Main

 keywords

   "recdef" :: thy_decl and

   "permissive" "congs" "hints"

 begin

 subsection \<open>Lemmas for TFL\<close>

 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_def: "cut f r x \<equiv> (\<lambda>y. if (y,x) \<in> r then f y else undefined)"

   unfolding cut_def .

 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 \<or> b) \<or> c == a \<or> (b \<or> c)"

   by simp

 lemma tfl_disjE: "P \<or> Q ==> P --> R ==> Q --> R ==> R"

   by blast

 lemma tfl_exE: "\<exists>x. P x ==> \<forall>x. P x --> Q ==> Q"

   by blast

 ML_file "old_recdef.ML"

 subsection \<open>Rule setup\<close>

 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 INF_cong SUP_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