1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/Tools/isac/Knowledge/RatEq.ML Wed Aug 25 16:20:07 2010 +0200
1.3 @@ -0,0 +1,203 @@
1.4 +(*.(c) by Richard Lang, 2003 .*)
1.5 +(* collecting all knowledge for RationalEquations
1.6 + created by: rlang
1.7 + date: 02.09
1.8 + changed by: rlang
1.9 + last change by: rlang
1.10 + date: 02.11.29
1.11 +*)
1.12 +
1.13 +(* use"Knowledge/RatEq.ML";
1.14 + use"RatEq.ML";
1.15 + remove_thy"RatEq";
1.16 + use_thy"Isac";
1.17 +
1.18 + use"ROOT.ML";
1.19 + cd"IsacKnowledge";
1.20 + *)
1.21 +"******* RatEq.ML begin *******";
1.22 +
1.23 +theory' := overwritel (!theory', [("RatEq.thy",RatEq.thy)]);
1.24 +
1.25 +(*-------------------------functions-----------------------*)
1.26 +(* is_rateqation_in becomes true, if a bdv is in the denominator of a fraction*)
1.27 +fun is_rateqation_in t v =
1.28 + let
1.29 + fun coeff_in c v = member op = (vars c) v;
1.30 + fun finddivide (_ $ _ $ _ $ _) v = raise error("is_rateqation_in:")
1.31 + (* at the moment there is no term like this, but ....*)
1.32 + | finddivide (t as (Const ("HOL.divide",_) $ _ $ b)) v = coeff_in b v
1.33 + | finddivide (_ $ t1 $ t2) v = (finddivide t1 v)
1.34 + orelse (finddivide t2 v)
1.35 + | finddivide (_ $ t1) v = (finddivide t1 v)
1.36 + | finddivide _ _ = false;
1.37 + in
1.38 + finddivide t v
1.39 + end;
1.40 +
1.41 +fun eval_is_ratequation_in _ _ (p as (Const ("RatEq.is'_ratequation'_in",_) $ t $ v)) _ =
1.42 + if is_rateqation_in t v then
1.43 + SOME ((term2str p) ^ " = True",
1.44 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.45 + else SOME ((term2str p) ^ " = True",
1.46 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.47 + | eval_is_ratequation_in _ _ _ _ = ((*writeln"### nichts matcht";*) NONE);
1.48 +
1.49 +(*-------------------------rulse-----------------------*)
1.50 +val RatEq_prls = (*15.10.02:just the following order due to subterm evaluation*)
1.51 + append_rls "RatEq_prls" e_rls
1.52 + [Calc ("Atools.ident",eval_ident "#ident_"),
1.53 + Calc ("Tools.matches",eval_matches ""),
1.54 + Calc ("Tools.lhs" ,eval_lhs ""),
1.55 + Calc ("Tools.rhs" ,eval_rhs ""),
1.56 + Calc ("RatEq.is'_ratequation'_in",eval_is_ratequation_in ""),
1.57 + Calc ("op =",eval_equal "#equal_"),
1.58 + Thm ("not_true",num_str not_true),
1.59 + Thm ("not_false",num_str not_false),
1.60 + Thm ("and_true",num_str and_true),
1.61 + Thm ("and_false",num_str and_false),
1.62 + Thm ("or_true",num_str or_true),
1.63 + Thm ("or_false",num_str or_false)
1.64 + ];
1.65 +
1.66 +
1.67 +(*rls = merge_rls erls Poly_erls *)
1.68 +val rateq_erls =
1.69 + remove_rls "rateq_erls" (*WN: ein Hack*)
1.70 + (merge_rls "is_ratequation_in" calculate_Rational
1.71 + (append_rls "is_ratequation_in"
1.72 + Poly_erls
1.73 + [(*Calc ("HOL.divide", eval_cancel "#divide_"),*)
1.74 + Calc ("RatEq.is'_ratequation'_in",
1.75 + eval_is_ratequation_in "")
1.76 +
1.77 + ]))
1.78 + [Thm ("and_commute",num_str and_commute), (*WN: ein Hack*)
1.79 + Thm ("or_commute",num_str or_commute) (*WN: ein Hack*)
1.80 + ];
1.81 +ruleset' := overwritelthy thy (!ruleset',
1.82 + [("rateq_erls",rateq_erls)(*FIXXXME:del with rls.rls'*)
1.83 + ]);
1.84 +
1.85 +
1.86 +val RatEq_crls =
1.87 + remove_rls "RatEq_crls" (*WN: ein Hack*)
1.88 + (merge_rls "is_ratequation_in" calculate_Rational
1.89 + (append_rls "is_ratequation_in"
1.90 + Poly_erls
1.91 + [(*Calc ("HOL.divide", eval_cancel "#divide_"),*)
1.92 + Calc ("RatEq.is'_ratequation'_in",
1.93 + eval_is_ratequation_in "")
1.94 + ]))
1.95 + [Thm ("and_commute",num_str and_commute), (*WN: ein Hack*)
1.96 + Thm ("or_commute",num_str or_commute) (*WN: ein Hack*)
1.97 + ];
1.98 +
1.99 +val RatEq_eliminate = prep_rls(
1.100 + Rls {id = "RatEq_eliminate", preconds = [], rew_ord = ("termlessI",termlessI),
1.101 + erls = rateq_erls, srls = Erls, calc = [],
1.102 + (*asm_thm = [("rat_mult_denominator_both",""),("rat_mult_denominator_left",""),
1.103 + ("rat_mult_denominator_right","")],*)
1.104 + rules = [
1.105 + Thm("rat_mult_denominator_both",num_str rat_mult_denominator_both),
1.106 + (* a/b=c/d -> ad=cb *)
1.107 + Thm("rat_mult_denominator_left",num_str rat_mult_denominator_left),
1.108 + (* a =c/d -> ad=c *)
1.109 + Thm("rat_mult_denominator_right",num_str rat_mult_denominator_right)
1.110 + (* a/b=c -> a=cb *)
1.111 + ],
1.112 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.113 + }:rls);
1.114 +ruleset' := overwritelthy thy (!ruleset',
1.115 + [("RatEq_eliminate",RatEq_eliminate)
1.116 + ]);
1.117 +
1.118 +
1.119 +
1.120 +
1.121 +val RatEq_simplify = prep_rls(
1.122 + Rls {id = "RatEq_simplify", preconds = [], rew_ord = ("termlessI",termlessI),
1.123 + erls = rateq_erls, srls = Erls, calc = [],
1.124 + (*asm_thm = [("rat_double_rat_1",""),("rat_double_rat_2",""),
1.125 + ("rat_double_rat_3","")],*)
1.126 + rules = [
1.127 + Thm("real_rat_mult_1",num_str real_rat_mult_1),
1.128 + (*a*(b/c) = (a*b)/c*)
1.129 + Thm("real_rat_mult_2",num_str real_rat_mult_2),
1.130 + (*(a/b)*(c/d) = (a*c)/(b*d)*)
1.131 + Thm("real_rat_mult_3",num_str real_rat_mult_3),
1.132 + (* (a/b)*c = (a*c)/b*)
1.133 + Thm("real_rat_pow",num_str real_rat_pow),
1.134 + (*(a/b)^^^2 = a^^^2/b^^^2*)
1.135 + Thm("real_diff_minus",num_str real_diff_minus),
1.136 + (* a - b = a + (-1) * b *)
1.137 + Thm("rat_double_rat_1",num_str rat_double_rat_1),
1.138 + (* (a / (c/d) = (a*d) / c) *)
1.139 + Thm("rat_double_rat_2",num_str rat_double_rat_2),
1.140 + (* ((a/b) / (c/d) = (a*d) / (b*c)) *)
1.141 + Thm("rat_double_rat_3",num_str rat_double_rat_3)
1.142 + (* ((a/b) / c = a / (b*c) ) *)
1.143 + ],
1.144 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.145 + }:rls);
1.146 +ruleset' := overwritelthy thy (!ruleset',
1.147 + [("RatEq_simplify",RatEq_simplify)
1.148 + ]);
1.149 +
1.150 +(*-------------------------Problem-----------------------*)
1.151 +(*
1.152 +(get_pbt ["rational","univariate","equation"]);
1.153 +show_ptyps();
1.154 +*)
1.155 +store_pbt
1.156 + (prep_pbt RatEq.thy "pbl_equ_univ_rat" [] e_pblID
1.157 + (["rational","univariate","equation"],
1.158 + [("#Given" ,["equality e_","solveFor v_"]),
1.159 + ("#Where" ,["(e_::bool) is_ratequation_in (v_::real)"]),
1.160 + ("#Find" ,["solutions v_i_"])
1.161 + ],
1.162 +
1.163 + RatEq_prls, SOME "solve (e_::bool, v_)",
1.164 + [["RatEq","solve_rat_equation"]]));
1.165 +
1.166 +
1.167 +(*-------------------------methods-----------------------*)
1.168 +store_met
1.169 + (prep_met RatEq.thy "met_rateq" [] e_metID
1.170 + (["RatEq"],
1.171 + [],
1.172 + {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
1.173 + crls=RatEq_crls, nrls=norm_Rational
1.174 + (*, asm_rls=[],asm_thm=[]*)}, "empty_script"));
1.175 +store_met
1.176 + (prep_met RatEq.thy "met_rat_eq" [] e_metID
1.177 + (["RatEq","solve_rat_equation"],
1.178 + [("#Given" ,["equality e_","solveFor v_"]),
1.179 + ("#Where" ,["(e_::bool) is_ratequation_in (v_::real)"]),
1.180 + ("#Find" ,["solutions v_i_"])
1.181 + ],
1.182 + {rew_ord'="termlessI",
1.183 + rls'=rateq_erls,
1.184 + srls=e_rls,
1.185 + prls=RatEq_prls,
1.186 + calc=[],
1.187 + crls=RatEq_crls, nrls=norm_Rational(*,
1.188 + asm_rls=[],
1.189 + asm_thm=[("rat_double_rat_1",""),("rat_double_rat_2",""),("rat_double_rat_3",""),
1.190 + ("rat_mult_denominator_both",""),("rat_mult_denominator_left",""),
1.191 + ("rat_mult_denominator_right","")]*)},
1.192 + "Script Solve_rat_equation (e_::bool) (v_::real) = \
1.193 + \(let e_ = ((Repeat(Try (Rewrite_Set RatEq_simplify True))) @@ \
1.194 + \ (Repeat(Try (Rewrite_Set norm_Rational False))) @@ \
1.195 + \ (Repeat(Try (Rewrite_Set common_nominator_p False))) @@ \
1.196 + \ (Repeat(Try (Rewrite_Set RatEq_eliminate True)))) e_;\
1.197 + \ (L_::bool list) = (SubProblem (RatEq_,[univariate,equation], \
1.198 + \ [no_met]) [bool_ e_, real_ v_]) \
1.199 + \ in Check_elementwise L_ {(v_::real). Assumptions})"
1.200 + ));
1.201 +
1.202 +calclist':= overwritel (!calclist',
1.203 + [("is_ratequation_in", ("RatEq.is_ratequation_in",
1.204 + eval_is_ratequation_in ""))
1.205 + ]);
1.206 +"******* RatEq.ML end *******";