Theory Old_Recdef

(*  Title:      HOL/Library/Old_Recdef.thy
    Author:     Konrad Slind and Markus Wenzel, TU Muenchen
*)

section TFL: recursive function definitions

theory Old_Recdef
imports Main
keywords
  "recdef" :: thy_defn and
  "permissive" "congs" "hints"
begin

subsection Lemmas for TFL

lemma tfl_wf_induct: "R. wf R 
       (P. (x. (y. (y,x)R  P y)  P x)  (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  (λy. if (y,x)  r then f y else undefined)"
  unfolding cut_def .

lemma tfl_cut_apply: "f R. (x,a)R  (cut f R a)(x) = f(x)"
apply clarify
apply (rule cut_apply, assumption)
done

lemma tfl_wfrec:
     "M R f. (f=wfrec R M)  wf R  (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

ML_file old_recdef.ML


subsection 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 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