1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/Tools/isac/Knowledge/Integrate.ML Wed Aug 25 16:20:07 2010 +0200
1.3 @@ -0,0 +1,357 @@
1.4 +(* tools for integration over the reals
1.5 + author: Walther Neuper 050905, 08:51
1.6 + (c) due to copyright terms
1.7 +
1.8 +use"Knowledge/Integrate.ML";
1.9 +use"Integrate.ML";
1.10 +
1.11 +remove_thy"Integrate";
1.12 +use_thy"Knowledge/Isac";
1.13 +*)
1.14 +
1.15 +(** interface isabelle -- isac **)
1.16 +
1.17 +theory' := overwritel (!theory', [("Integrate.thy",Integrate.thy)]);
1.18 +
1.19 +(** eval functions **)
1.20 +
1.21 +val c = Free ("c", HOLogic.realT);
1.22 +(*.create a new unique variable 'c..' in a term; for use by Calc in a rls;
1.23 + an alternative to do this would be '(Try (Calculate new_c_) (new_c es__))'
1.24 + in the script; this will be possible if currying doesnt take the value
1.25 + from a variable, but the value '(new_c es__)' itself.*)
1.26 +fun new_c term =
1.27 + let fun selc var =
1.28 + case (explode o id_of) var of
1.29 + "c"::[] => true
1.30 + | "c"::"_"::is => (case (int_of_str o implode) is of
1.31 + SOME _ => true
1.32 + | NONE => false)
1.33 + | _ => false;
1.34 + fun get_coeff c = case (explode o id_of) c of
1.35 + "c"::"_"::is => (the o int_of_str o implode) is
1.36 + | _ => 0;
1.37 + val cs = filter selc (vars term);
1.38 + in
1.39 + case cs of
1.40 + [] => c
1.41 + | [c] => Free ("c_2", HOLogic.realT)
1.42 + | cs =>
1.43 + let val max_coeff = maxl (map get_coeff cs)
1.44 + in Free ("c_"^string_of_int (max_coeff + 1), HOLogic.realT) end
1.45 + end;
1.46 +
1.47 +(*WN080222
1.48 +(*("new_c", ("Integrate.new'_c", eval_new_c "#new_c_"))*)
1.49 +fun eval_new_c _ _ (p as (Const ("Integrate.new'_c",_) $ t)) _ =
1.50 + SOME ((term2str p) ^ " = " ^ term2str (new_c p),
1.51 + Trueprop $ (mk_equality (p, new_c p)))
1.52 + | eval_new_c _ _ _ _ = NONE;
1.53 +*)
1.54 +
1.55 +(*WN080222:*)
1.56 +(*("add_new_c", ("Integrate.add'_new'_c", eval_add_new_c "#add_new_c_"))
1.57 + add a new c to a term or a fun-equation;
1.58 + this is _not in_ the term, because only applied to _whole_ term*)
1.59 +fun eval_add_new_c (_:string) "Integrate.add'_new'_c" p (_:theory) =
1.60 + let val p' = case p of
1.61 + Const ("op =", T) $ lh $ rh =>
1.62 + Const ("op =", T) $ lh $ mk_add rh (new_c rh)
1.63 + | p => mk_add p (new_c p)
1.64 + in SOME ((term2str p) ^ " = " ^ term2str p',
1.65 + Trueprop $ (mk_equality (p, p')))
1.66 + end
1.67 + | eval_add_new_c _ _ _ _ = NONE;
1.68 +
1.69 +
1.70 +(*("is_f_x", ("Integrate.is'_f'_x", eval_is_f_x "is_f_x_"))*)
1.71 +fun eval_is_f_x _ _(p as (Const ("Integrate.is'_f'_x", _)
1.72 + $ arg)) _ =
1.73 + if is_f_x arg
1.74 + then SOME ((term2str p) ^ " = True",
1.75 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.76 + else SOME ((term2str p) ^ " = False",
1.77 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.78 + | eval_is_f_x _ _ _ _ = NONE;
1.79 +
1.80 +calclist':= overwritel (!calclist',
1.81 + [(*("new_c", ("Integrate.new'_c", eval_new_c "new_c_")),*)
1.82 + ("add_new_c", ("Integrate.add'_new'_c", eval_add_new_c "add_new_c_")),
1.83 + ("is_f_x", ("Integrate.is'_f'_x", eval_is_f_x "is_f_idextifier_"))
1.84 + ]);
1.85 +
1.86 +
1.87 +(** rulesets **)
1.88 +
1.89 +(*.rulesets for integration.*)
1.90 +val integration_rules =
1.91 + Rls {id="integration_rules", preconds = [],
1.92 + rew_ord = ("termlessI",termlessI),
1.93 + erls = Rls {id="conditions_in_integration_rules",
1.94 + preconds = [],
1.95 + rew_ord = ("termlessI",termlessI),
1.96 + erls = Erls,
1.97 + srls = Erls, calc = [],
1.98 + rules = [(*for rewriting conditions in Thm's*)
1.99 + Calc ("Atools.occurs'_in",
1.100 + eval_occurs_in "#occurs_in_"),
1.101 + Thm ("not_true",num_str not_true),
1.102 + Thm ("not_false",not_false)
1.103 + ],
1.104 + scr = EmptyScr},
1.105 + srls = Erls, calc = [],
1.106 + rules = [
1.107 + Thm ("integral_const",num_str integral_const),
1.108 + Thm ("integral_var",num_str integral_var),
1.109 + Thm ("integral_add",num_str integral_add),
1.110 + Thm ("integral_mult",num_str integral_mult),
1.111 + Thm ("integral_pow",num_str integral_pow),
1.112 + Calc ("op +", eval_binop "#add_")(*for n+1*)
1.113 + ],
1.114 + scr = EmptyScr};
1.115 +val add_new_c =
1.116 + Seq {id="add_new_c", preconds = [],
1.117 + rew_ord = ("termlessI",termlessI),
1.118 + erls = Rls {id="conditions_in_add_new_c",
1.119 + preconds = [],
1.120 + rew_ord = ("termlessI",termlessI),
1.121 + erls = Erls,
1.122 + srls = Erls, calc = [],
1.123 + rules = [Calc ("Tools.matches", eval_matches""),
1.124 + Calc ("Integrate.is'_f'_x",
1.125 + eval_is_f_x "is_f_x_"),
1.126 + Thm ("not_true",num_str not_true),
1.127 + Thm ("not_false",num_str not_false)
1.128 + ],
1.129 + scr = EmptyScr},
1.130 + srls = Erls, calc = [],
1.131 + rules = [ (*Thm ("call_for_new_c", num_str call_for_new_c),*)
1.132 + Cal1 ("Integrate.add'_new'_c", eval_add_new_c "new_c_")
1.133 + ],
1.134 + scr = EmptyScr};
1.135 +
1.136 +(*.rulesets for simplifying Integrals.*)
1.137 +
1.138 +(*.for simplify_Integral adapted from 'norm_Rational_rls'.*)
1.139 +val norm_Rational_rls_noadd_fractions =
1.140 +Rls {id = "norm_Rational_rls_noadd_fractions", preconds = [],
1.141 + rew_ord = ("dummy_ord",dummy_ord),
1.142 + erls = norm_rat_erls, srls = Erls, calc = [],
1.143 + rules = [(*Rls_ common_nominator_p_rls,!!!*)
1.144 + Rls_ (*rat_mult_div_pow original corrected WN051028*)
1.145 + (Rls {id = "rat_mult_div_pow", preconds = [],
1.146 + rew_ord = ("dummy_ord",dummy_ord),
1.147 + erls = (*FIXME.WN051028 e_rls,*)
1.148 + append_rls "e_rls-is_polyexp" e_rls
1.149 + [Calc ("Poly.is'_polyexp",
1.150 + eval_is_polyexp "")],
1.151 + srls = Erls, calc = [],
1.152 + rules = [Thm ("rat_mult",num_str rat_mult),
1.153 + (*"?a / ?b * (?c / ?d) = ?a * ?c / (?b * ?d)"*)
1.154 + Thm ("rat_mult_poly_l",num_str rat_mult_poly_l),
1.155 + (*"?c is_polyexp ==> ?c * (?a / ?b) = ?c * ?a / ?b"*)
1.156 + Thm ("rat_mult_poly_r",num_str rat_mult_poly_r),
1.157 + (*"?c is_polyexp ==> ?a / ?b * ?c = ?a * ?c / ?b"*)
1.158 +
1.159 + Thm ("real_divide_divide1_mg", real_divide_divide1_mg),
1.160 + (*"y ~= 0 ==> (u / v) / (y / z) = (u * z) / (y * v)"*)
1.161 + Thm ("real_divide_divide1_eq", real_divide_divide1_eq),
1.162 + (*"?x / (?y / ?z) = ?x * ?z / ?y"*)
1.163 + Thm ("real_divide_divide2_eq", real_divide_divide2_eq),
1.164 + (*"?x / ?y / ?z = ?x / (?y * ?z)"*)
1.165 + Calc ("HOL.divide" ,eval_cancel "#divide_"),
1.166 +
1.167 + Thm ("rat_power", num_str rat_power)
1.168 + (*"(?a / ?b) ^^^ ?n = ?a ^^^ ?n / ?b ^^^ ?n"*)
1.169 + ],
1.170 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.171 + }),
1.172 + Rls_ make_rat_poly_with_parentheses,
1.173 + Rls_ cancel_p_rls,(*FIXME:cancel_p does NOT order sometimes*)
1.174 + Rls_ rat_reduce_1
1.175 + ],
1.176 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.177 + }:rls;
1.178 +
1.179 +(*.for simplify_Integral adapted from 'norm_Rational'.*)
1.180 +val norm_Rational_noadd_fractions =
1.181 + Seq {id = "norm_Rational_noadd_fractions", preconds = [],
1.182 + rew_ord = ("dummy_ord",dummy_ord),
1.183 + erls = norm_rat_erls, srls = Erls, calc = [],
1.184 + rules = [Rls_ discard_minus_,
1.185 + Rls_ rat_mult_poly,(* removes double fractions like a/b/c *)
1.186 + Rls_ make_rat_poly_with_parentheses, (*WN0510 also in(#)below*)
1.187 + Rls_ cancel_p_rls, (*FIXME.MG:cancel_p does NOT order sometim*)
1.188 + Rls_ norm_Rational_rls_noadd_fractions,(* the main rls (#) *)
1.189 + Rls_ discard_parentheses_ (* mult only *)
1.190 + ],
1.191 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.192 + }:rls;
1.193 +
1.194 +(*.simplify terms before and after Integration such that
1.195 + ..a.x^2/2 + b.x^3/3.. is made to ..a/2.x^2 + b/3.x^3.. (and NO
1.196 + common denominator as done by norm_Rational or make_ratpoly_in.
1.197 + This is a copy from 'make_ratpoly_in' with respective reduction of rules and
1.198 + *1* expand the term, ie. distribute * and / over +
1.199 +.*)
1.200 +val separate_bdv2 =
1.201 + append_rls "separate_bdv2"
1.202 + collect_bdv
1.203 + [Thm ("separate_bdv", num_str separate_bdv),
1.204 + (*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
1.205 + Thm ("separate_bdv_n", num_str separate_bdv_n),
1.206 + Thm ("separate_1_bdv", num_str separate_1_bdv),
1.207 + (*"?bdv / ?b = (1 / ?b) * ?bdv"*)
1.208 + Thm ("separate_1_bdv_n", num_str separate_1_bdv_n)(*,
1.209 + (*"?bdv ^^^ ?n / ?b = 1 / ?b * ?bdv ^^^ ?n"*)
1.210 + *****Thm ("real_add_divide_distrib",
1.211 + *****num_str real_add_divide_distrib)
1.212 + (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)----------*)
1.213 + ];
1.214 +val simplify_Integral =
1.215 + Seq {id = "simplify_Integral", preconds = []:term list,
1.216 + rew_ord = ("dummy_ord", dummy_ord),
1.217 + erls = Atools_erls, srls = Erls,
1.218 + calc = [], (*asm_thm = [],*)
1.219 + rules = [Thm ("real_add_mult_distrib",num_str real_add_mult_distrib),
1.220 + (*"(?z1.0 + ?z2.0) * ?w = ?z1.0 * ?w + ?z2.0 * ?w"*)
1.221 + Thm ("real_add_divide_distrib",num_str real_add_divide_distrib),
1.222 + (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)
1.223 + (*^^^^^ *1* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*)
1.224 + Rls_ norm_Rational_noadd_fractions,
1.225 + Rls_ order_add_mult_in,
1.226 + Rls_ discard_parentheses,
1.227 + (*Rls_ collect_bdv, from make_polynomial_in*)
1.228 + Rls_ separate_bdv2,
1.229 + Calc ("HOL.divide" ,eval_cancel "#divide_")
1.230 + ],
1.231 + scr = EmptyScr}:rls;
1.232 +
1.233 +
1.234 +(*simplify terms before and after Integration such that
1.235 + ..a.x^2/2 + b.x^3/3.. is made to ..a/2.x^2 + b/3.x^3.. (and NO
1.236 + common denominator as done by norm_Rational or make_ratpoly_in.
1.237 + This is a copy from 'make_polynomial_in' with insertions from
1.238 + 'make_ratpoly_in'
1.239 +THIS IS KEPT FOR COMPARISON ............................................
1.240 +* val simplify_Integral = prep_rls(
1.241 +* Seq {id = "", preconds = []:term list,
1.242 +* rew_ord = ("dummy_ord", dummy_ord),
1.243 +* erls = Atools_erls, srls = Erls,
1.244 +* calc = [], (*asm_thm = [],*)
1.245 +* rules = [Rls_ expand_poly,
1.246 +* Rls_ order_add_mult_in,
1.247 +* Rls_ simplify_power,
1.248 +* Rls_ collect_numerals,
1.249 +* Rls_ reduce_012,
1.250 +* Thm ("realpow_oneI",num_str realpow_oneI),
1.251 +* Rls_ discard_parentheses,
1.252 +* Rls_ collect_bdv,
1.253 +* (*below inserted from 'make_ratpoly_in'*)
1.254 +* Rls_ (append_rls "separate_bdv"
1.255 +* collect_bdv
1.256 +* [Thm ("separate_bdv", num_str separate_bdv),
1.257 +* (*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
1.258 +* Thm ("separate_bdv_n", num_str separate_bdv_n),
1.259 +* Thm ("separate_1_bdv", num_str separate_1_bdv),
1.260 +* (*"?bdv / ?b = (1 / ?b) * ?bdv"*)
1.261 +* Thm ("separate_1_bdv_n", num_str separate_1_bdv_n)(*,
1.262 +* (*"?bdv ^^^ ?n / ?b = 1 / ?b * ?bdv ^^^ ?n"*)
1.263 +* Thm ("real_add_divide_distrib",
1.264 +* num_str real_add_divide_distrib)
1.265 +* (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)*)
1.266 +* ]),
1.267 +* Calc ("HOL.divide" ,eval_cancel "#divide_")
1.268 +* ],
1.269 +* scr = EmptyScr
1.270 +* }:rls);
1.271 +.......................................................................*)
1.272 +
1.273 +val integration =
1.274 + Seq {id="integration", preconds = [],
1.275 + rew_ord = ("termlessI",termlessI),
1.276 + erls = Rls {id="conditions_in_integration",
1.277 + preconds = [],
1.278 + rew_ord = ("termlessI",termlessI),
1.279 + erls = Erls,
1.280 + srls = Erls, calc = [],
1.281 + rules = [],
1.282 + scr = EmptyScr},
1.283 + srls = Erls, calc = [],
1.284 + rules = [ Rls_ integration_rules,
1.285 + Rls_ add_new_c,
1.286 + Rls_ simplify_Integral
1.287 + ],
1.288 + scr = EmptyScr};
1.289 +ruleset' :=
1.290 +overwritelthy thy (!ruleset',
1.291 + [("integration_rules", prep_rls integration_rules),
1.292 + ("add_new_c", prep_rls add_new_c),
1.293 + ("simplify_Integral", prep_rls simplify_Integral),
1.294 + ("integration", prep_rls integration),
1.295 + ("separate_bdv2", separate_bdv2),
1.296 + ("norm_Rational_noadd_fractions", norm_Rational_noadd_fractions),
1.297 + ("norm_Rational_rls_noadd_fractions",
1.298 + norm_Rational_rls_noadd_fractions)
1.299 + ]);
1.300 +
1.301 +(** problems **)
1.302 +
1.303 +store_pbt
1.304 + (prep_pbt Integrate.thy "pbl_fun_integ" [] e_pblID
1.305 + (["integrate","function"],
1.306 + [("#Given" ,["functionTerm f_", "integrateBy v_"]),
1.307 + ("#Find" ,["antiDerivative F_"])
1.308 + ],
1.309 + append_rls "e_rls" e_rls [(*for preds in where_*)],
1.310 + SOME "Integrate (f_, v_)",
1.311 + [["diff","integration"]]));
1.312 +
1.313 +(*here "named" is used differently from Differentiation"*)
1.314 +store_pbt
1.315 + (prep_pbt Integrate.thy "pbl_fun_integ_nam" [] e_pblID
1.316 + (["named","integrate","function"],
1.317 + [("#Given" ,["functionTerm f_", "integrateBy v_"]),
1.318 + ("#Find" ,["antiDerivativeName F_"])
1.319 + ],
1.320 + append_rls "e_rls" e_rls [(*for preds in where_*)],
1.321 + SOME "Integrate (f_, v_)",
1.322 + [["diff","integration","named"]]));
1.323 +
1.324 +(** methods **)
1.325 +
1.326 +store_met
1.327 + (prep_met Integrate.thy "met_diffint" [] e_metID
1.328 + (["diff","integration"],
1.329 + [("#Given" ,["functionTerm f_", "integrateBy v_"]),
1.330 + ("#Find" ,["antiDerivative F_"])
1.331 + ],
1.332 + {rew_ord'="tless_true", rls'=Atools_erls, calc = [],
1.333 + srls = e_rls,
1.334 + prls=e_rls,
1.335 + crls = Atools_erls, nrls = e_rls},
1.336 +"Script IntegrationScript (f_::real) (v_::real) = \
1.337 +\ (let t_ = Take (Integral f_ D v_) \
1.338 +\ in (Rewrite_Set_Inst [(bdv,v_)] integration False) (t_::real))"
1.339 +));
1.340 +
1.341 +store_met
1.342 + (prep_met Integrate.thy "met_diffint_named" [] e_metID
1.343 + (["diff","integration","named"],
1.344 + [("#Given" ,["functionTerm f_", "integrateBy v_"]),
1.345 + ("#Find" ,["antiDerivativeName F_"])
1.346 + ],
1.347 + {rew_ord'="tless_true", rls'=Atools_erls, calc = [],
1.348 + srls = e_rls,
1.349 + prls=e_rls,
1.350 + crls = Atools_erls, nrls = e_rls},
1.351 +"Script NamedIntegrationScript (f_::real) (v_::real) (F_::real=>real) = \
1.352 +\ (let t_ = Take (F_ v_ = Integral f_ D v_) \
1.353 +\ in ((Try (Rewrite_Set_Inst [(bdv,v_)] simplify_Integral False)) @@\
1.354 +\ (Rewrite_Set_Inst [(bdv,v_)] integration False)) t_)"
1.355 +(*
1.356 +"Script NamedIntegrationScript (f_::real) (v_::real) (F_::real=>real) = \
1.357 +\ (let t_ = Take (F_ v_ = Integral f_ D v_) \
1.358 +\ in (Rewrite_Set_Inst [(bdv,v_)] integration False) t_)"
1.359 +*)
1.360 + ));