src/HOL/Library/Old_Recdef.thy
 author wenzelm Fri Jun 19 20:14:50 2015 +0200 (2015-06-19) changeset 60523 be2d9f5ddc76 parent 60520 09fc5eaa21ce child 67091 1393c2340eec permissions -rw-r--r--
discontinued unused 'defer_recdef';
1 (*  Title:      HOL/Library/Old_Recdef.thy
2     Author:     Konrad Slind and Markus Wenzel, TU Muenchen
3 *)
5 section \<open>TFL: recursive function definitions\<close>
7 theory Old_Recdef
8 imports Main
9 keywords
10   "recdef" :: thy_decl and
11   "permissive" "congs" "hints"
12 begin
14 subsection \<open>Lemmas for TFL\<close>
16 lemma tfl_wf_induct: "ALL R. wf R -->
17        (ALL P. (ALL x. (ALL y. (y,x):R --> P y) --> P x) --> (ALL x. P x))"
18 apply clarify
19 apply (rule_tac r = R and P = P and a = x in wf_induct, assumption, blast)
20 done
22 lemma tfl_cut_def: "cut f r x \<equiv> (\<lambda>y. if (y,x) \<in> r then f y else undefined)"
23   unfolding cut_def .
25 lemma tfl_cut_apply: "ALL f R. (x,a):R --> (cut f R a)(x) = f(x)"
26 apply clarify
27 apply (rule cut_apply, assumption)
28 done
30 lemma tfl_wfrec:
31      "ALL M R f. (f=wfrec R M) --> wf R --> (ALL x. f x = M (cut f R x) x)"
32 apply clarify
33 apply (erule wfrec)
34 done
36 lemma tfl_eq_True: "(x = True) --> x"
37   by blast
39 lemma tfl_rev_eq_mp: "(x = y) --> y --> x"
40   by blast
42 lemma tfl_simp_thm: "(x --> y) --> (x = x') --> (x' --> y)"
43   by blast
45 lemma tfl_P_imp_P_iff_True: "P ==> P = True"
46   by blast
48 lemma tfl_imp_trans: "(A --> B) ==> (B --> C) ==> (A --> C)"
49   by blast
51 lemma tfl_disj_assoc: "(a \<or> b) \<or> c == a \<or> (b \<or> c)"
52   by simp
54 lemma tfl_disjE: "P \<or> Q ==> P --> R ==> Q --> R ==> R"
55   by blast
57 lemma tfl_exE: "\<exists>x. P x ==> \<forall>x. P x --> Q ==> Q"
58   by blast
60 ML_file "old_recdef.ML"
63 subsection \<open>Rule setup\<close>
65 lemmas [recdef_simp] =
66   inv_image_def
67   measure_def
68   lex_prod_def
69   same_fst_def
70   less_Suc_eq [THEN iffD2]
72 lemmas [recdef_cong] =
73   if_cong let_cong image_cong INF_cong SUP_cong bex_cong ball_cong imp_cong
74   map_cong filter_cong takeWhile_cong dropWhile_cong foldl_cong foldr_cong
76 lemmas [recdef_wf] =
77   wf_trancl
78   wf_less_than
79   wf_lex_prod
80   wf_inv_image
81   wf_measure
82   wf_measures
83   wf_pred_nat
84   wf_same_fst
85   wf_empty
87 end