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: "- a = (-1) * (a::real)" by auto
10 (*Semiring_Normalization.comm_ring_1_class.ring_normalization_rules(1)*)
12 (* should be in Rational.thy, but needed for asms in e.g. d2_pqformula1 in PolyEq, RootEq... *)
13 lemma radd_left_cancel_le: "((k::real) + m \<le> k + n) = (m \<le> n)" by auto
14 (*Groups.ordered_ab_semigroup_add_imp_le_class.add_le_cancel_left*)
16 thm "Fields.linordered_field_class.mult_imp_le_div_pos" (*0 < ?y \<Longrightarrow> ?z * ?y \<le> ?x \<Longrightarrow> ?z \<le> ?x / ?y*)
18 axiomatization where (*for evaluating the assumptions of conditional rules*)
19 (* should be in Rational.thy, but needed for asms in e.g. d2_pqformula1 in PolyEq, RootEq... *)
20 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
21 rat_leq2: "0 \<noteq> d \<Longrightarrow> (a \<le> c / d) = (a * d \<le> c)"(*Quickcheck found a counterexample*) and
22 rat_leq3: "0 \<noteq> b \<Longrightarrow> (a / b \<le> c ) = (a \<le> b * c)"(*Quickcheck found a counterexample*)
25 subsection \<open>setup for ML-functions\<close>
26 text \<open>required by "eval_binop" below\<close>
27 setup \<open>KEStore_Elems.add_calcs
28 [ ("occurs_in", (\<^const_name>\<open>occurs_in\<close>, Prog_Expr.eval_occurs_in "#occurs_in_")),
29 ("some_occur_in", (\<^const_name>\<open>some_occur_in\<close>, Prog_Expr.eval_some_occur_in "#some_occur_in_")),
30 ("is_atom", (\<^const_name>\<open>is_atom\<close>, Prog_Expr.eval_is_atom "#is_atom_")),
31 ("is_even", (\<^const_name>\<open>is_even\<close>, Prog_Expr.eval_is_even "#is_even_")),
32 ("is_const", (\<^const_name>\<open>is_const\<close>, Prog_Expr.eval_const "#is_const_")),
33 ("le", (\<^const_name>\<open>less\<close>, Prog_Expr.eval_equ "#less_")),
34 ("leq", (\<^const_name>\<open>less_eq\<close>, Prog_Expr.eval_equ "#less_equal_")),
35 ("ident", (\<^const_name>\<open>ident\<close>, Prog_Expr.eval_ident "#ident_")),
36 ("equal", (\<^const_name>\<open>HOL.eq\<close>, Prog_Expr.eval_equal "#equal_")),
37 ("PLUS", (\<^const_name>\<open>plus\<close>, (**)eval_binop "#add_")),
38 ("MINUS", (\<^const_name>\<open>minus\<close>, (**)eval_binop "#sub_")),
39 ("TIMES", (\<^const_name>\<open>times\<close>, (**)eval_binop "#mult_")),
40 ("DIVIDE", (\<^const_name>\<open>divide\<close>, Prog_Expr.eval_cancel "#divide_e")),
41 ("POWER",(\<^const_name>\<open>powr\<close>, (**)eval_binop "#power_")),
42 ("boollist2sum", (\<^const_name>\<open>boollist2sum\<close>, Prog_Expr.eval_boollist2sum ""))]\<close>
44 subsection \<open>rewrite-order for rule-sets\<close>
50 fun termlessI (_: subst) uv = LibraryC.termless uv;
51 fun term_ordI (_: subst) uv = Term_Ord.term_ord uv;
54 (*TODO.WN0509 reduce ids: tless_true = e_rew_ord' = Rewrite_Ord.e_rew_ord = Rewrite_Ord.dummy_ord*)
55 val tless_true = Rewrite_Ord.dummy_ord;
56 Rewrite_Ord.rew_ord' := overwritel (! Rewrite_Ord.rew_ord', (*<<<---- use Know_Store.xxx here, too*)
57 [("tless_true", tless_true),
58 ("e_rew_ord'", tless_true),
59 ("dummy_ord", Rewrite_Ord.dummy_ord)]);
62 subsection \<open>rule-sets\<close>
65 val Atools_erls = Rule_Set.append_rules "Atools_erls" Rule_Set.empty
66 [ \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
67 \<^rule_thm>\<open>not_true\<close>,
68 (*"(~ True) = False"*)
69 \<^rule_thm>\<open>not_false\<close>,
70 (*"(~ False) = True"*)
71 \<^rule_thm>\<open>and_true\<close>,
72 (*"(?a & True) = ?a"*)
73 \<^rule_thm>\<open>and_false\<close>,
74 (*"(?a & False) = False"*)
75 \<^rule_thm>\<open>or_true\<close>,
76 (*"(?a | True) = True"*)
77 \<^rule_thm>\<open>or_false\<close>,
78 (*"(?a | False) = ?a"*)
80 \<^rule_thm>\<open>rat_leq1\<close>,
81 \<^rule_thm>\<open>rat_leq2\<close>,
82 \<^rule_thm>\<open>rat_leq3\<close>,
83 \<^rule_thm>\<open>refl\<close>,
84 \<^rule_thm>\<open>order_refl\<close>,
85 \<^rule_thm>\<open>radd_left_cancel_le\<close>,
87 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
88 \<^rule_eval>\<open>less_eq\<close> (Prog_Expr.eval_equ "#less_equal_"),
90 \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
91 \<^rule_eval>\<open>Prog_Expr.is_const\<close> (Prog_Expr.eval_const "#is_const_"),
92 \<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in ""),
93 \<^rule_eval>\<open>Prog_Expr.matches\<close> (Prog_Expr.eval_matches "")];
97 val Atools_crls = Rule_Set.append_rules "Atools_crls" Rule_Set.empty
98 [ \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
99 \<^rule_thm>\<open>not_true\<close>,
100 \<^rule_thm>\<open>not_false\<close>,
101 \<^rule_thm>\<open>and_true\<close>,
102 \<^rule_thm>\<open>and_false\<close>,
103 \<^rule_thm>\<open>or_true\<close>,
104 \<^rule_thm>\<open>or_false\<close>,
106 \<^rule_thm>\<open>rat_leq1\<close>,
107 \<^rule_thm>\<open>rat_leq2\<close>,
108 \<^rule_thm>\<open>rat_leq3\<close>,
109 \<^rule_thm>\<open>refl\<close>,
110 \<^rule_thm>\<open>order_refl\<close>,
111 \<^rule_thm>\<open>radd_left_cancel_le\<close>,
113 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
114 \<^rule_eval>\<open>less_eq\<close> (Prog_Expr.eval_equ "#less_equal_"),
116 \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
117 \<^rule_eval>\<open>Prog_Expr.is_const\<close> (Prog_Expr.eval_const "#is_const_"),
118 \<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in ""),
119 \<^rule_eval>\<open>Prog_Expr.matches\<close> (Prog_Expr.eval_matches "")];
122 subsection \<open>ONCE AGAIN extend rule-set for evaluating pre-conditions and program-expressions\<close>
123 text \<open>requires "eval_binop" from above\<close>
125 val prog_expr = Rule_Set.append_rules "prog_expr" prog_expr
126 [ \<^rule_eval>\<open>times\<close> (**)(eval_binop "#mult_"),
127 \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
128 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
129 \<^rule_eval>\<open>less_eq\<close> (Prog_Expr.eval_equ "#less_equal_"),
130 \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
131 \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),(*atom <> atom -> False*)
133 \<^rule_eval>\<open>Prog_Expr.Vars\<close> (Prog_Expr.eval_var "#Vars_"),
135 \<^rule_thm>\<open>if_True\<close>,
136 \<^rule_thm>\<open>if_False\<close>];
138 val prog_expr = Auto_Prog.prep_rls @{theory} (Rule_Set.merge "list_erls"
139 (Rule_Def.Repeat {id = "replaced", preconds = [], rew_ord = ("termlessI", termlessI),
140 erls = Rule_Def.Repeat {id = "list_elrs", preconds = [], rew_ord = ("termlessI", termlessI),
141 erls = Rule_Set.empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
142 rules = [\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
143 \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_")
144 (* ~~~~~~ for nth_Cons_*)],
145 scr = Rule.Empty_Prog},
146 srls = Rule_Set.Empty, calc = [], errpatts = [],
147 rules = [], scr = Rule.Empty_Prog})
151 subsection \<open>setup for extended rule-set\<close>
153 rule_set_knowledge prog_expr = \<open>Auto_Prog.prep_rls @{theory} prog_expr\<close>