Isar command 'problem' as combination of KEStore_Elems.add_pbts + Problem.prep_import, without change of semantics;
1 (*. (c) by Richard Lang, 2003 .*)
2 (* theory collecting all knowledge for LinearEquations
10 theory LinEq imports Poly Equation begin
14 (*WN0509 compare PolyEq.all_left "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"*)
15 all_left: "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)" and
16 makex1_x: "a \<up> 1 = a" and
17 real_assoc_1: "a+(b+c) = a+b+c" and
18 real_assoc_2: "a*(b*c) = a*b*c" and
21 lin_isolate_add1: "(a + b*bdv = 0) = (b*bdv = (-1)*a)" and
22 lin_isolate_add2: "(a + bdv = 0) = ( bdv = (-1)*a)" and
23 lin_isolate_div: "[|Not(b=0)|] ==> (b*bdv = c) = (bdv = c / b)"
26 val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
27 Rule_Set.append_rules "LinEq_prls" Rule_Set.empty
28 [\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
29 \<^rule_eval>\<open>Prog_Expr.matches\<close> (Prog_Expr.eval_matches ""),
30 \<^rule_eval>\<open>Prog_Expr.lhs\<close> (Prog_Expr.eval_lhs ""),
31 \<^rule_eval>\<open>Prog_Expr.rhs\<close> (Prog_Expr.eval_rhs ""),
32 \<^rule_eval>\<open>has_degree_in\<close> (eval_has_degree_in ""),
33 \<^rule_eval>\<open>is_polyrat_in\<close> (eval_is_polyrat_in ""),
34 \<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in ""),
35 \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
36 \<^rule_thm>\<open>not_true\<close>,
37 \<^rule_thm>\<open>not_false\<close>,
38 \<^rule_thm>\<open>and_true\<close>,
39 \<^rule_thm>\<open>and_false\<close>,
40 \<^rule_thm>\<open>or_true\<close>,
41 \<^rule_thm>\<open>or_false\<close>
43 (* ----- erls ----- *)
45 Rule_Set.append_rules "LinEq_crls" poly_crls
46 [\<^rule_thm>\<open>real_assoc_1\<close>
49 \<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
50 \<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_"),
54 (* ----- crls ----- *)
56 Rule_Set.append_rules "LinEq_erls" Poly_erls
57 [\<^rule_thm>\<open>real_assoc_1\<close>
60 \<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
61 \<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_"),
65 rule_set_knowledge LinEq_erls = LinEq_erls
68 val LinPoly_simplify = prep_rls'(
69 Rule_Def.Repeat {id = "LinPoly_simplify", preconds = [],
70 rew_ord = ("termlessI",termlessI),
72 srls = Rule_Set.Empty,
73 calc = [], errpatts = [],
75 \<^rule_thm>\<open>real_assoc_1\<close>,
76 \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
77 \<^rule_eval>\<open>minus\<close> (**)(eval_binop "#sub_"),
78 \<^rule_eval>\<open>times\<close> (**)(eval_binop "#mult_"),
80 \<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
81 \<^rule_eval>\<open>sqrt\<close> (eval_sqrt "#sqrt_"),
83 \<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_")
85 scr = Rule.Empty_Prog});
87 rule_set_knowledge LinPoly_simplify = LinPoly_simplify
90 (*isolate the bound variable in an linear equation; 'bdv' is a meta-constant*)
91 val LinEq_simplify = prep_rls'(
92 Rule_Def.Repeat {id = "LinEq_simplify", preconds = [],
93 rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
95 srls = Rule_Set.Empty,
96 calc = [], errpatts = [],
98 \<^rule_thm>\<open>lin_isolate_add1\<close>,
100 \<^rule_thm>\<open>lin_isolate_add2\<close>,
102 \<^rule_thm>\<open>lin_isolate_div\<close>
105 scr = Rule.Empty_Prog});
107 rule_set_knowledge LinEq_simplify = LinEq_simplify
109 (*----------------------------- problems --------------------------------*)
110 (* ---------linear----------- *)
112 problem pbl_equ_univ_lin : "LINEAR/univariate/equation" =
113 \<open>LinEq_prls\<close>
114 Method: "LinEq/solve_lineq_equation"
115 CAS: "solve (e_e::bool, v_v)"
116 Given: "equality e_e" "solveFor v_v"
117 Where: "HOL.False" (*WN0509 just detected: this pbl can never be used?!?*)
118 "Not( (lhs e_e) is_polyrat_in v_v)"
119 "Not( (rhs e_e) is_polyrat_in v_v)"
120 "((lhs e_e) has_degree_in v_v)=1"
121 "((rhs e_e) has_degree_in v_v)=1"
122 Find: "solutions v_v'i'"
124 (*-------------- methods------------------------------------------------------*)
125 method met_eqlin : "LinEq" =
126 \<open>{rew_ord' = "tless_true",rls' = Atools_erls,calc = [], srls = Rule_Set.empty, prls = Rule_Set.empty,
127 crls = LinEq_crls, errpats = [], nrls = norm_Poly}\<close>
128 (* ansprechen mit ["LinEq", "solve_univar_equation"] *)
130 partial_function (tailrec) solve_linear_equation :: "bool \<Rightarrow> real \<Rightarrow> bool list"
132 "solve_linear_equation e_e v_v = (
135 (Try (Rewrite ''all_left'')) #>
136 (Try (Repeat (Rewrite ''makex1_x''))) #>
137 (Try (Rewrite_Set ''expand_binoms'')) #>
138 (Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)] ''make_ratpoly_in''))) #>
139 (Try (Repeat (Rewrite_Set ''LinPoly_simplify''))) ) e_e;
141 (Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''LinEq_simplify'')) #>
142 (Repeat (Try (Rewrite_Set ''LinPoly_simplify''))) ) e_e
146 method met_eq_lin : "LinEq/solve_lineq_equation" =
147 \<open>{rew_ord' = "termlessI", rls' = LinEq_erls, srls = Rule_Set.empty, prls = LinEq_prls, calc = [],
148 crls = LinEq_crls, errpats = [], nrls = norm_Poly}\<close>
149 Program: solve_linear_equation.simps
150 Given: "equality e_e" "solveFor v_v"
151 Where: "Not ((lhs e_e) is_polyrat_in v_v)" "((lhs e_e) has_degree_in v_v) = 1"
152 Find: "solutions v_v'i'"
155 MethodC.from_store' @{theory} ["LinEq", "solve_lineq_equation"];