clarified theory context: avoid global "val thy = ..." hanging around (left-over from Isabelle2005), which is apt to various pitfalls;
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 ("HOL.eq", Prog_Expr.eval_equal "#equal_"),
29 Rule.Eval ("Prog_Expr.matches", Prog_Expr.eval_matches ""),
30 Rule.Eval ("Prog_Expr.lhs" , Prog_Expr.eval_lhs ""),
31 Rule.Eval ("Prog_Expr.rhs" , Prog_Expr.eval_rhs ""),
32 Rule.Eval ("Poly.has_degree_in", eval_has_degree_in ""),
33 Rule.Eval ("Poly.is_polyrat_in", eval_is_polyrat_in ""),
34 Rule.Eval ("Prog_Expr.occurs_in", Prog_Expr.eval_occurs_in ""),
35 Rule.Eval ("Prog_Expr.ident", Prog_Expr.eval_ident "#ident_"),
36 Rule.Thm ("not_true",ThmC.numerals_to_Free @{thm not_true}),
37 Rule.Thm ("not_false",ThmC.numerals_to_Free @{thm not_false}),
38 Rule.Thm ("and_true",ThmC.numerals_to_Free @{thm and_true}),
39 Rule.Thm ("and_false",ThmC.numerals_to_Free @{thm and_false}),
40 Rule.Thm ("or_true",ThmC.numerals_to_Free @{thm or_true}),
41 Rule.Thm ("or_false",ThmC.numerals_to_Free @{thm or_false})
43 (* ----- erls ----- *)
45 Rule_Set.append_rules "LinEq_crls" poly_crls
46 [Rule.Thm ("real_assoc_1",ThmC.numerals_to_Free @{thm real_assoc_1})
49 Rule.Eval ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e"),
50 Rule.Eval ("Transcendental.powr" , (**)eval_binop "#power_"),
54 (* ----- crls ----- *)
56 Rule_Set.append_rules "LinEq_erls" Poly_erls
57 [Rule.Thm ("real_assoc_1",ThmC.numerals_to_Free @{thm real_assoc_1})
60 Rule.Eval ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e"),
61 Rule.Eval ("Transcendental.powr" , (**)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 ("real_assoc_1",ThmC.numerals_to_Free @{thm real_assoc_1}),
76 Rule.Eval ("Groups.plus_class.plus", (**)eval_binop "#add_"),
77 Rule.Eval ("Groups.minus_class.minus", (**)eval_binop "#sub_"),
78 Rule.Eval ("Groups.times_class.times", (**)eval_binop "#mult_"),
80 Rule.Eval ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e"),
81 Rule.Eval ("NthRoot.sqrt", eval_sqrt "#sqrt_"),
83 Rule.Eval ("Transcendental.powr" , (**)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("lin_isolate_add1",ThmC.numerals_to_Free @{thm lin_isolate_add1}),
100 Rule.Thm("lin_isolate_add2",ThmC.numerals_to_Free @{thm lin_isolate_add2}),
102 Rule.Thm("lin_isolate_div",ThmC.numerals_to_Free @{thm lin_isolate_div})
105 scr = Rule.Empty_Prog});
107 rule_set_knowledge LinEq_simplify = LinEq_simplify
109 (*----------------------------- problem types --------------------------------*)
110 (* ---------linear----------- *)
111 setup \<open>KEStore_Elems.add_pbts
112 [(Problem.prep_input @{theory} "pbl_equ_univ_lin" [] Problem.id_empty
113 (["LINEAR", "univariate", "equation"],
114 [("#Given" ,["equality e_e", "solveFor v_v"]),
115 ("#Where" ,["HOL.False", (*WN0509 just detected: this pbl can never be used?!?*)
116 "Not( (lhs e_e) is_polyrat_in v_v)",
117 "Not( (rhs e_e) is_polyrat_in v_v)",
118 "((lhs e_e) has_degree_in v_v)=1",
119 "((rhs e_e) has_degree_in v_v)=1"]),
120 ("#Find" ,["solutions v_v'i'"])],
121 LinEq_prls, SOME "solve (e_e::bool, v_v)", [["LinEq", "solve_lineq_equation"]]))]\<close>
123 (*-------------- methods------------------------------------------------------*)
124 setup \<open>KEStore_Elems.add_mets
125 [MethodC.prep_input @{theory} "met_eqlin" [] MethodC.id_empty
127 {rew_ord' = "tless_true",rls' = Atools_erls,calc = [], srls = Rule_Set.empty, prls = Rule_Set.empty,
128 crls = LinEq_crls, errpats = [], nrls = norm_Poly},
131 (* ansprechen mit ["LinEq", "solve_univar_equation"] *)
133 partial_function (tailrec) solve_linear_equation :: "bool \<Rightarrow> real \<Rightarrow> bool list"
135 "solve_linear_equation e_e v_v = (
138 (Try (Rewrite ''all_left'')) #>
139 (Try (Repeat (Rewrite ''makex1_x''))) #>
140 (Try (Rewrite_Set ''expand_binoms'')) #>
141 (Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)] ''make_ratpoly_in''))) #>
142 (Try (Repeat (Rewrite_Set ''LinPoly_simplify''))) ) e_e;
144 (Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''LinEq_simplify'')) #>
145 (Repeat (Try (Rewrite_Set ''LinPoly_simplify''))) ) e_e
148 setup \<open>KEStore_Elems.add_mets
149 [MethodC.prep_input @{theory} "met_eq_lin" [] MethodC.id_empty
150 (["LinEq", "solve_lineq_equation"],
151 [("#Given", ["equality e_e", "solveFor v_v"]),
152 ("#Where", ["Not ((lhs e_e) is_polyrat_in v_v)", "((lhs e_e) has_degree_in v_v) = 1"]),
153 ("#Find", ["solutions v_v'i'"])],
154 {rew_ord' = "termlessI", rls' = LinEq_erls, srls = Rule_Set.empty, prls = LinEq_prls, calc = [],
155 crls = LinEq_crls, errpats = [], nrls = norm_Poly},
156 @{thm solve_linear_equation.simps})]
159 MethodC.from_store' @{theory} ["LinEq", "solve_lineq_equation"];