2 imports Interpret.Interpret
3 (** )"../BridgeJEdit/BridgeJEdit" ( *activate after devel.of BridgeJEdit*)
4 (**) "../BridgeLibisabelle/BridgeLibisabelle" (*remove after devel.of BridgeJEdit*)
5 (* ^^^ for KEStore_Elems.add_thes *)
7 subsection \<open>theorems for Base_Tools\<close>
9 lemma real_unari_minus: "Not (a is_num) ==> - a = (-1) * (a::real)" by auto
10 (*lemma real_unari_minus: "- a = (-1) * (a::real)" by auto LOOPS WITH NUMERALS*)
11 (*Semiring_Normalization.comm_ring_1_class.ring_normalization_rules(1)*)
13 (* should be in Rational.thy, but needed for asms in e.g. d2_pqformula1 in PolyEq, RootEq... *)
14 lemma radd_left_cancel_le: "((k::real) + m \<le> k + n) = (m \<le> n)" by auto
15 (*Groups.ordered_ab_semigroup_add_imp_le_class.add_le_cancel_left*)
17 thm "Fields.linordered_field_class.mult_imp_le_div_pos" (*0 < ?y \<Longrightarrow> ?z * ?y \<le> ?x \<Longrightarrow> ?z \<le> ?x / ?y*)
19 axiomatization where (*for evaluating the assumptions of conditional rules*)
20 (* should be in Rational.thy, but needed for asms in e.g. d2_pqformula1 in PolyEq, RootEq... *)
21 rat_leq1: "0 \<noteq> b \<Longrightarrow> 0 \<noteq> d \<Longrightarrow> (a / b \<le> c / d) = (a * d \<le> b * c)"(*Quickcheck found a counterexample*) and
22 rat_leq2: "0 \<noteq> d \<Longrightarrow> (a \<le> c / d) = (a * d \<le> c)"(*Quickcheck found a counterexample*) and
23 rat_leq3: "0 \<noteq> b \<Longrightarrow> (a / b \<le> c ) = (a \<le> b * c)"(*Quickcheck found a counterexample*)
26 subsection \<open>setup for ML-functions\<close>
27 text \<open>required by "eval_binop" below\<close>
28 calculation occurs_in = \<open>Prog_Expr.eval_occurs_in "#occurs_in_"\<close>
29 calculation some_occur_in = \<open>Prog_Expr.eval_some_occur_in "#some_occur_in_"\<close>
30 calculation is_atom = \<open>Prog_Expr.eval_is_atom "#is_atom_"\<close>
31 calculation is_even = \<open>Prog_Expr.eval_is_even "#is_even_"\<close>
32 calculation le (less) = \<open>Prog_Expr.eval_equ "#less_"\<close>
33 calculation leq (less_eq) = \<open>Prog_Expr.eval_equ "#less_equal_"\<close>
34 calculation ident = \<open>Prog_Expr.eval_ident "#ident_"\<close>
35 calculation equal (HOL.eq) = \<open>Prog_Expr.eval_equal "#equal_"\<close>
36 calculation PLUS (plus) = \<open>(**)eval_binop "#add_"\<close>
37 calculation MINUS (minus) = \<open>(**)eval_binop "#sub_"\<close>
38 calculation TIMES (times) = \<open>(**)eval_binop "#mult_"\<close>
39 calculation DIVIDE (divide) = \<open>Prog_Expr.eval_cancel "#divide_e"\<close>
40 calculation POWER (realpow) = \<open>(**)eval_binop "#power_"\<close>
41 calculation boollist2sum = \<open>Prog_Expr.eval_boollist2sum ""\<close>
43 subsection \<open>rewrite-order for rule-sets\<close>
49 fun termlessI (_: subst) uv = LibraryC.termless uv;
50 fun term_ordI (_: subst) uv = Term_Ord.term_ord uv;
53 (*TODO.WN0509 reduce ids: tless_true = e_rew_ord' = Rewrite_Ord.function_empty = Rewrite_Ord.function_empty*)
54 val tless_true = Rewrite_Ord.function_empty;
57 setup \<open>KEStore_Elems.add_rew_ord [
58 ("tless_true", tless_true),
59 ("Rewrite_Ord.id_empty", tless_true),
60 ("e_rew_ord'", tless_true),
61 ("dummy_ord", Rewrite_Ord.function_empty)]\<close>
63 subsection \<open>rule-sets\<close>
66 val Atools_erls = Rule_Set.append_rules "Atools_erls" Rule_Set.empty [
67 \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
68 \<^rule_thm>\<open>not_true\<close>, (*"(~ True) = False"*)
69 \<^rule_thm>\<open>not_false\<close>, (*"(~ False) = True"*)
70 \<^rule_thm>\<open>and_true\<close>, (*"(?a & True) = ?a"*)
71 \<^rule_thm>\<open>and_false\<close>, (*"(?a & False) = False"*)
72 \<^rule_thm>\<open>or_true\<close>, (*"(?a | True) = True"*)
73 \<^rule_thm>\<open>or_false\<close>, (*"(?a | False) = ?a"*)
75 \<^rule_thm>\<open>rat_leq1\<close>,
76 \<^rule_thm>\<open>rat_leq2\<close>,
77 \<^rule_thm>\<open>rat_leq3\<close>,
78 \<^rule_thm>\<open>refl\<close>,
79 \<^rule_thm>\<open>order_refl\<close>,
80 \<^rule_thm>\<open>radd_left_cancel_le\<close>,
82 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
83 \<^rule_eval>\<open>less_eq\<close> (Prog_Expr.eval_equ "#less_equal_"),
85 \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
86 \<^rule_eval>\<open>Prog_Expr.is_num\<close> (Prog_Expr.eval_is_num "#is_num_"),
87 \<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in ""),
88 \<^rule_eval>\<open>Prog_Expr.matches\<close> (Prog_Expr.eval_matches "")];
92 val Atools_crls = Rule_Set.append_rules "Atools_crls" Rule_Set.empty [
93 \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
94 \<^rule_thm>\<open>not_true\<close>,
95 \<^rule_thm>\<open>not_false\<close>,
96 \<^rule_thm>\<open>and_true\<close>,
97 \<^rule_thm>\<open>and_false\<close>,
98 \<^rule_thm>\<open>or_true\<close>,
99 \<^rule_thm>\<open>or_false\<close>,
101 \<^rule_thm>\<open>rat_leq1\<close>,
102 \<^rule_thm>\<open>rat_leq2\<close>,
103 \<^rule_thm>\<open>rat_leq3\<close>,
104 \<^rule_thm>\<open>refl\<close>,
105 \<^rule_thm>\<open>order_refl\<close>,
106 \<^rule_thm>\<open>radd_left_cancel_le\<close>,
108 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
109 \<^rule_eval>\<open>less_eq\<close> (Prog_Expr.eval_equ "#less_equal_"),
111 \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
112 \<^rule_eval>\<open>Prog_Expr.is_num\<close> (Prog_Expr.eval_is_num "#is_num_"),
113 \<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in ""),
114 \<^rule_eval>\<open>Prog_Expr.matches\<close> (Prog_Expr.eval_matches "")];
117 subsection \<open>ONCE AGAIN extend rule-set for evaluating pre-conditions and program-expressions\<close>
118 text \<open>requires "eval_binop" from above\<close>
120 val prog_expr = Rule_Set.append_rules "prog_expr" prog_expr [
121 \<^rule_eval>\<open>times\<close> (**)(eval_binop "#mult_"),
122 \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
123 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
124 \<^rule_eval>\<open>less_eq\<close> (Prog_Expr.eval_equ "#less_equal_"),
125 \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
126 \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),(*atom <> atom -> False*)
128 \<^rule_eval>\<open>Prog_Expr.Vars\<close> (Prog_Expr.eval_var "#Vars_"),
130 \<^rule_thm>\<open>if_True\<close>,
131 \<^rule_thm>\<open>if_False\<close>];
133 val prog_expr = Auto_Prog.prep_rls @{theory} (Rule_Set.merge "list_erls"
134 (Rule_Def.Repeat {id = "replaced", preconds = [], rew_ord = ("termlessI", termlessI),
135 erls = Rule_Def.Repeat {id = "list_elrs", preconds = [], rew_ord = ("termlessI", termlessI),
136 erls = Rule_Set.empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
138 \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
139 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_") (*..for nth_Cons_*)],
140 scr = Rule.Empty_Prog},
141 srls = Rule_Set.Empty, calc = [], errpatts = [],
142 rules = [], scr = Rule.Empty_Prog})
146 subsection \<open>setup for extended rule-set\<close>
148 rule_set_knowledge prog_expr = \<open>Auto_Prog.prep_rls @{theory} prog_expr\<close>