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^^^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)"
28 val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
29 Rule.append_rls "LinEq_prls" Rule.e_rls
30 [Rule.Calc ("HOL.eq", Prog_Expr.eval_equal "#equal_"),
31 Rule.Calc ("Prog_Expr.matches", Prog_Expr.eval_matches ""),
32 Rule.Calc ("Prog_Expr.lhs" , Prog_Expr.eval_lhs ""),
33 Rule.Calc ("Prog_Expr.rhs" , Prog_Expr.eval_rhs ""),
34 Rule.Calc ("Poly.has'_degree'_in", eval_has_degree_in ""),
35 Rule.Calc ("Poly.is'_polyrat'_in", eval_is_polyrat_in ""),
36 Rule.Calc ("Prog_Expr.occurs'_in", Prog_Expr.eval_occurs_in ""),
37 Rule.Calc ("Prog_Expr.ident", Prog_Expr.eval_ident "#ident_"),
38 Rule.Thm ("not_true",TermC.num_str @{thm not_true}),
39 Rule.Thm ("not_false",TermC.num_str @{thm not_false}),
40 Rule.Thm ("and_true",TermC.num_str @{thm and_true}),
41 Rule.Thm ("and_false",TermC.num_str @{thm and_false}),
42 Rule.Thm ("or_true",TermC.num_str @{thm or_true}),
43 Rule.Thm ("or_false",TermC.num_str @{thm or_false})
45 (* ----- erls ----- *)
47 Rule.append_rls "LinEq_crls" poly_crls
48 [Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1})
51 Rule.Calc ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e"),
52 Rule.Calc ("Prog_Expr.pow" , (**)eval_binop "#power_"),
56 (* ----- crls ----- *)
58 Rule.append_rls "LinEq_erls" Poly_erls
59 [Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1})
62 Rule.Calc ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e"),
63 Rule.Calc ("Prog_Expr.pow" , (**)eval_binop "#power_"),
67 setup \<open>KEStore_Elems.add_rlss
68 [("LinEq_erls", (Context.theory_name @{theory}, LinEq_erls))]\<close>
71 val LinPoly_simplify = prep_rls'(
72 Rule.Rls {id = "LinPoly_simplify", preconds = [],
73 rew_ord = ("termlessI",termlessI),
76 calc = [], errpatts = [],
78 Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1}),
79 Rule.Calc ("Groups.plus_class.plus", (**)eval_binop "#add_"),
80 Rule.Calc ("Groups.minus_class.minus", (**)eval_binop "#sub_"),
81 Rule.Calc ("Groups.times_class.times", (**)eval_binop "#mult_"),
83 Rule.Calc ("Rings.divide_class.divide", Prog_Expr.eval_cancel "#divide_e"),
84 Rule.Calc ("NthRoot.sqrt", eval_sqrt "#sqrt_"),
86 Rule.Calc ("Prog_Expr.pow" , (**)eval_binop "#power_")
88 scr = Rule.EmptyScr});
90 setup \<open>KEStore_Elems.add_rlss
91 [("LinPoly_simplify", (Context.theory_name @{theory}, LinPoly_simplify))]\<close>
94 (*isolate the bound variable in an linear equation; 'bdv' is a meta-constant*)
95 val LinEq_simplify = prep_rls'(
96 Rule.Rls {id = "LinEq_simplify", preconds = [],
97 rew_ord = ("e_rew_ord", Rule.e_rew_ord),
100 calc = [], errpatts = [],
102 Rule.Thm("lin_isolate_add1",TermC.num_str @{thm lin_isolate_add1}),
103 (* a+bx=0 -> bx=-a *)
104 Rule.Thm("lin_isolate_add2",TermC.num_str @{thm lin_isolate_add2}),
106 Rule.Thm("lin_isolate_div",TermC.num_str @{thm lin_isolate_div})
109 scr = Rule.EmptyScr});
111 setup \<open>KEStore_Elems.add_rlss
112 [("LinEq_simplify", (Context.theory_name @{theory}, LinEq_simplify))]\<close>
114 (*----------------------------- problem types --------------------------------*)
115 (* ---------linear----------- *)
116 setup \<open>KEStore_Elems.add_pbts
117 [(Specify.prep_pbt thy "pbl_equ_univ_lin" [] Celem.e_pblID
118 (["LINEAR", "univariate", "equation"],
119 [("#Given" ,["equality e_e", "solveFor v_v"]),
120 ("#Where" ,["HOL.False", (*WN0509 just detected: this pbl can never be used?!?*)
121 "Not( (lhs e_e) is_polyrat_in v_v)",
122 "Not( (rhs e_e) is_polyrat_in v_v)",
123 "((lhs e_e) has_degree_in v_v)=1",
124 "((rhs e_e) has_degree_in v_v)=1"]),
125 ("#Find" ,["solutions v_v'i'"])],
126 LinEq_prls, SOME "solve (e_e::bool, v_v)", [["LinEq", "solve_lineq_equation"]]))]\<close>
128 (*-------------- methods------------------------------------------------------*)
129 setup \<open>KEStore_Elems.add_mets
130 [Specify.prep_met thy "met_eqlin" [] Celem.e_metID
132 {rew_ord' = "tless_true",rls' = Atools_erls,calc = [], srls = Rule.e_rls, prls = Rule.e_rls,
133 crls = LinEq_crls, errpats = [], nrls = norm_Poly},
136 (* ansprechen mit ["LinEq","solve_univar_equation"] *)
138 partial_function (tailrec) solve_linear_equation :: "bool \<Rightarrow> real \<Rightarrow> bool list"
140 "solve_linear_equation e_e v_v = (
143 (Try (Rewrite ''all_left'')) #>
144 (Try (Repeat (Rewrite ''makex1_x''))) #>
145 (Try (Rewrite_Set ''expand_binoms'')) #>
146 (Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)] ''make_ratpoly_in''))) #>
147 (Try (Repeat (Rewrite_Set ''LinPoly_simplify''))) ) e_e;
149 (Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''LinEq_simplify'')) #>
150 (Repeat (Try (Rewrite_Set ''LinPoly_simplify''))) ) e_e
153 setup \<open>KEStore_Elems.add_mets
154 [Specify.prep_met thy "met_eq_lin" [] Celem.e_metID
155 (["LinEq","solve_lineq_equation"],
156 [("#Given", ["equality e_e", "solveFor v_v"]),
157 ("#Where", ["Not ((lhs e_e) is_polyrat_in v_v)", "((lhs e_e) has_degree_in v_v) = 1"]),
158 ("#Find", ["solutions v_v'i'"])],
159 {rew_ord' = "termlessI", rls' = LinEq_erls, srls = Rule.e_rls, prls = LinEq_prls, calc = [],
160 crls = LinEq_crls, errpats = [], nrls = norm_Poly},
161 @{thm solve_linear_equation.simps})]
163 ML \<open>Specify.get_met' @{theory} ["LinEq","solve_lineq_equation"];\<close>