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(* equational systems, minimal -- for use in Biegelinie
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author: Walther Neuper
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050826,
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(c) due to copyright terms
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*)
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theory EqSystem imports Rational Root begin
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consts
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occur'_exactly'_in ::
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"[real list, real list, 'a] => bool" ("_ from'_ _ occur'_exactly'_in _")
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(*descriptions in the related problems*)
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solveForVars :: real list => toreall
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solution :: bool list => toreall
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(*the CAS-command, eg. "solveSystem [x+y=1,y=2] [x,y]"*)
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solveSystem :: "[bool list, real list] => bool list"
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(*Script-names*)
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SolveSystemScript :: "[bool list, real list, bool list]
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=> bool list"
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("((Script SolveSystemScript (_ _ =))// (_))" 9)
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axioms
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(*stated as axioms, todo: prove as theorems
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'bdv' is a constant handled on the meta-level
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specifically as a 'bound variable' *)
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commute_0_equality "(0 = a) = (a = 0)"
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(*WN0510 see simliar rules 'isolate_' 'separate_' (by RL)
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[bdv_1,bdv_2,bdv_3,bdv_4] work also for 2 and 3 bdvs, ugly !*)
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separate_bdvs_add
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"[| [] from_ [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a |]
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==> (a + b = c) = (b = c + -1*a)"
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separate_bdvs0
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"[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in b; Not (b=!=0) |]
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==> (a = b) = (a + -1*b = 0)"
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separate_bdvs_add1
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"[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in c |]
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==> (a = b + c) = (a + -1*c = b)"
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separate_bdvs_add2
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"[| Not (some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in a) |]
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==> (a + b = c) = (b = -1*a + c)"
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separate_bdvs_mult
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"[| [] from_ [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a; Not (a=!=0) |]
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==>(a * b = c) = (b = c / a)"
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(*requires rew_ord for termination, eg. ord_simplify_Integral;
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works for lists of any length, interestingly !?!*)
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order_system_NxN "[a,b] = [b,a]"
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ML {*
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(** eval functions **)
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(*certain variables of a given list occur _all_ in a term
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args: all: ..variables, which are under consideration (eg. the bound vars)
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vs: variables which must be in t,
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and none of the others in all must be in t
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t: the term under consideration
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*)
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fun occur_exactly_in vs all t =
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let fun occurs_in' a b = occurs_in b a
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in foldl and_ (true, map (occurs_in' t) vs)
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andalso not (foldl or_ (false, map (occurs_in' t)
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(subtract op = vs all)))
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end;
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(*("occur_exactly_in", ("EqSystem.occur'_exactly'_in",
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eval_occur_exactly_in "#eval_occur_exactly_in_"))*)
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fun eval_occur_exactly_in _ "EqSystem.occur'_exactly'_in"
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(p as (Const ("EqSystem.occur'_exactly'_in",_)
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$ vs $ all $ t)) _ =
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if occur_exactly_in (isalist2list vs) (isalist2list all) t
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then SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = False",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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| eval_occur_exactly_in _ _ _ _ = NONE;
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calclist':=
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overwritel (!calclist',
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[("occur_exactly_in",
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("EqSystem.occur'_exactly'_in",
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eval_occur_exactly_in "#eval_occur_exactly_in_"))
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]);
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(** rewrite order 'ord_simplify_System' **)
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(* order wrt. several linear (i.e. without exponents) variables "c","c_2",..
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which leaves the monomials containing c, c_2,... at the end of an Integral
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and puts the c, c_2,... rightmost within a monomial.
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WN050906 this is a quick and dirty adaption of ord_make_polynomial_in,
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which was most adequate, because it uses size_of_term*)
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(**)
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local (*. for simplify_System .*)
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(**)
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open Term; (* for type order = EQUAL | LESS | GREATER *)
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fun pr_ord EQUAL = "EQUAL"
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| pr_ord LESS = "LESS"
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| pr_ord GREATER = "GREATER";
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fun dest_hd' (Const (a, T)) = (((a, 0), T), 0)
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| dest_hd' (Free (ccc, T)) =
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(case explode ccc of
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"c"::[] => ((("|||||||||||||||||||||", 0), T), 1)(*greatest string WN*)
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| "c"::"_"::_ => ((("|||||||||||||||||||||", 0), T), 1)
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| _ => (((ccc, 0), T), 1))
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| dest_hd' (Var v) = (v, 2)
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| dest_hd' (Bound i) = ((("", i), dummyT), 3)
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| dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4);
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fun size_of_term' (Free (ccc, _)) =
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(case explode ccc of (*WN0510 hack for the bound variables*)
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"c"::[] => 1000
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| "c"::"_"::is => 1000 * ((str2int o implode) is)
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| _ => 1)
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| size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
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| size_of_term' (f$t) = size_of_term' f + size_of_term' t
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| size_of_term' _ = 1;
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fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
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(case term_ord' pr thy (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
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| term_ord' pr thy (t, u) =
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(if pr then
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let
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val (f, ts) = strip_comb t and (g, us) = strip_comb u;
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val _=writeln("t= f@ts= \""^
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((Syntax.string_of_term (thy2ctxt thy)) f)^"\" @ \"["^
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(commas(map(string_of_cterm o cterm_of(sign_of thy)) ts))^"]\"");
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val _=writeln("u= g@us= \""^
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((Syntax.string_of_term (thy2ctxt thy)) g)^"\" @ \"["^
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(commas(map(string_of_cterm o cterm_of(sign_of thy)) us))^"]\"");
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val _=writeln("size_of_term(t,u)= ("^
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(string_of_int(size_of_term' t))^", "^
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(string_of_int(size_of_term' u))^")");
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val _=writeln("hd_ord(f,g) = "^((pr_ord o hd_ord)(f,g)));
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val _=writeln("terms_ord(ts,us) = "^
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((pr_ord o terms_ord str false)(ts,us)));
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val _=writeln("-------");
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in () end
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else ();
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case int_ord (size_of_term' t, size_of_term' u) of
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EQUAL =>
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let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
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(case hd_ord (f, g) of EQUAL => (terms_ord str pr) (ts, us)
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| ord => ord)
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end
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| ord => ord)
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and hd_ord (f, g) = (* ~ term.ML *)
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prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd' f,
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dest_hd' g)
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and terms_ord str pr (ts, us) =
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list_ord (term_ord' pr (assoc_thy "Isac.thy"))(ts, us);
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(**)
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in
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(**)
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(*WN0510 for preliminary use in eval_order_system, see case-study mat-eng.tex
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fun ord_simplify_System_rev (pr:bool) thy subst tu =
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(term_ord' pr thy (Library.swap tu) = LESS);*)
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(*for the rls's*)
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fun ord_simplify_System (pr:bool) thy subst tu =
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(term_ord' pr thy tu = LESS);
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(**)
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end;
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(**)
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rew_ord' := overwritel (!rew_ord',
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[("ord_simplify_System", ord_simplify_System false thy)
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]);
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(** rulesets **)
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(*.adapted from 'order_add_mult_in' by just replacing the rew_ord.*)
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val order_add_mult_System =
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Rls{id = "order_add_mult_System", preconds = [],
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rew_ord = ("ord_simplify_System",
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ord_simplify_System false (theory "Integrate")),
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erls = e_rls,srls = Erls, calc = [],
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rules = [Thm ("real_mult_commute",num_str real_mult_commute),
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(* z * w = w * z *)
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Thm ("real_mult_left_commute",num_str real_mult_left_commute),
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(*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
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Thm ("real_mult_assoc",num_str real_mult_assoc),
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(*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
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Thm ("real_add_commute",num_str real_add_commute),
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(*z + w = w + z*)
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Thm ("real_add_left_commute",num_str real_add_left_commute),
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(*x + (y + z) = y + (x + z)*)
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Thm ("real_add_assoc",num_str real_add_assoc)
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(*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
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],
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scr = EmptyScr}:rls;
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(*.adapted from 'norm_Rational' by
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#1 using 'ord_simplify_System' in 'order_add_mult_System'
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#2 NOT using common_nominator_p .*)
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val norm_System_noadd_fractions =
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Rls {id = "norm_System_noadd_fractions", preconds = [],
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rew_ord = ("dummy_ord",dummy_ord),
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erls = norm_rat_erls, srls = Erls, calc = [],
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rules = [(*sequence given by operator precedence*)
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Rls_ discard_minus,
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Rls_ powers,
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Rls_ rat_mult_divide,
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Rls_ expand,
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Rls_ reduce_0_1_2,
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Rls_ (*order_add_mult #1*) order_add_mult_System,
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Rls_ collect_numerals,
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(*Rls_ add_fractions_p, #2*)
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Rls_ cancel_p
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],
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scr = Script ((term_of o the o (parse thy))
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"empty_script")
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}:rls;
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(*.adapted from 'norm_Rational' by
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*1* using 'ord_simplify_System' in 'order_add_mult_System'.*)
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val norm_System =
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Rls {id = "norm_System", preconds = [],
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rew_ord = ("dummy_ord",dummy_ord),
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erls = norm_rat_erls, srls = Erls, calc = [],
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rules = [(*sequence given by operator precedence*)
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Rls_ discard_minus,
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Rls_ powers,
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Rls_ rat_mult_divide,
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Rls_ expand,
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Rls_ reduce_0_1_2,
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Rls_ (*order_add_mult *1*) order_add_mult_System,
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Rls_ collect_numerals,
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Rls_ add_fractions_p,
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Rls_ cancel_p
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],
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scr = Script ((term_of o the o (parse thy))
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"empty_script")
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}:rls;
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(*.simplify an equational system BEFORE solving it such that parentheses are
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( ((u0*v0)*w0) + ( ((u1*v1)*w1) * c + ... +((u4*v4)*w4) * c_4 ) )
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ATTENTION: works ONLY for bound variables c, c_1, c_2, c_3, c_4 :ATTENTION
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This is a copy from 'make_ratpoly_in' with respective reductions:
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*0* expand the term, ie. distribute * and / over +
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*1* ord_simplify_System instead of termlessI
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*2* no add_fractions_p (= common_nominator_p_rls !)
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*3* discard_parentheses only for (.*(.*.))
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analoguous to simplify_Integral .*)
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val simplify_System_parenthesized =
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Seq {id = "simplify_System_parenthesized", preconds = []:term list,
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rew_ord = ("dummy_ord", dummy_ord),
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erls = Atools_erls, srls = Erls, calc = [],
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rules = [Thm ("real_add_mult_distrib",num_str real_add_mult_distrib),
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(*"(?z1.0 + ?z2.0) * ?w = ?z1.0 * ?w + ?z2.0 * ?w"*)
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neuper@37954
|
261 |
Thm ("real_add_divide_distrib",num_str real_add_divide_distrib),
|
neuper@37954
|
262 |
(*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)
|
neuper@37954
|
263 |
(*^^^^^ *0* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*)
|
neuper@37954
|
264 |
Rls_ norm_Rational_noadd_fractions(**2**),
|
neuper@37954
|
265 |
Rls_ (*order_add_mult_in*) norm_System_noadd_fractions (**1**),
|
neuper@37954
|
266 |
Thm ("sym_real_mult_assoc", num_str (real_mult_assoc RS sym))
|
neuper@37954
|
267 |
(*Rls_ discard_parentheses *3**),
|
neuper@37954
|
268 |
Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
|
neuper@37954
|
269 |
Rls_ separate_bdv2,
|
neuper@37954
|
270 |
Calc ("HOL.divide" ,eval_cancel "#divide_")
|
neuper@37954
|
271 |
],
|
neuper@37954
|
272 |
scr = EmptyScr}:rls;
|
neuper@37954
|
273 |
|
neuper@37954
|
274 |
(*.simplify an equational system AFTER solving it;
|
neuper@37954
|
275 |
This is a copy of 'make_ratpoly_in' with the differences
|
neuper@37954
|
276 |
*1* ord_simplify_System instead of termlessI .*)
|
neuper@37954
|
277 |
(*TODO.WN051031 ^^^^^^^^^^ should be in EACH rls contained *)
|
neuper@37954
|
278 |
val simplify_System =
|
neuper@37954
|
279 |
Seq {id = "simplify_System", preconds = []:term list,
|
neuper@37954
|
280 |
rew_ord = ("dummy_ord", dummy_ord),
|
neuper@37954
|
281 |
erls = Atools_erls, srls = Erls, calc = [],
|
neuper@37954
|
282 |
rules = [Rls_ norm_Rational,
|
neuper@37954
|
283 |
Rls_ (*order_add_mult_in*) norm_System (**1**),
|
neuper@37954
|
284 |
Rls_ discard_parentheses,
|
neuper@37954
|
285 |
Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
|
neuper@37954
|
286 |
Rls_ separate_bdv2,
|
neuper@37954
|
287 |
Calc ("HOL.divide" ,eval_cancel "#divide_")
|
neuper@37954
|
288 |
],
|
neuper@37954
|
289 |
scr = EmptyScr}:rls;
|
neuper@37906
|
290 |
(*
|
neuper@37954
|
291 |
val simplify_System =
|
neuper@37954
|
292 |
append_rls "simplify_System" simplify_System_parenthesized
|
neuper@37954
|
293 |
[Thm ("sym_real_add_assoc", num_str (real_add_assoc RS sym))];
|
neuper@37954
|
294 |
*)
|
neuper@37954
|
295 |
|
neuper@37954
|
296 |
val isolate_bdvs =
|
neuper@37954
|
297 |
Rls {id="isolate_bdvs", preconds = [],
|
neuper@37954
|
298 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
299 |
erls = append_rls "erls_isolate_bdvs" e_rls
|
neuper@37954
|
300 |
[(Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
301 |
eval_occur_exactly_in
|
neuper@37954
|
302 |
"#eval_occur_exactly_in_"))
|
neuper@37954
|
303 |
],
|
neuper@37954
|
304 |
srls = Erls, calc = [],
|
neuper@37954
|
305 |
rules = [Thm ("commute_0_equality",
|
neuper@37954
|
306 |
num_str commute_0_equality),
|
neuper@37954
|
307 |
Thm ("separate_bdvs_add", num_str separate_bdvs_add),
|
neuper@37954
|
308 |
Thm ("separate_bdvs_mult", num_str separate_bdvs_mult)],
|
neuper@37954
|
309 |
scr = EmptyScr};
|
neuper@37954
|
310 |
val isolate_bdvs_4x4 =
|
neuper@37954
|
311 |
Rls {id="isolate_bdvs_4x4", preconds = [],
|
neuper@37954
|
312 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
313 |
erls = append_rls
|
neuper@37954
|
314 |
"erls_isolate_bdvs_4x4" e_rls
|
neuper@37954
|
315 |
[Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
316 |
eval_occur_exactly_in "#eval_occur_exactly_in_"),
|
neuper@37954
|
317 |
Calc ("Atools.ident",eval_ident "#ident_"),
|
neuper@37954
|
318 |
Calc ("Atools.some'_occur'_in",
|
neuper@37954
|
319 |
eval_some_occur_in "#some_occur_in_"),
|
neuper@37954
|
320 |
Thm ("not_true",num_str not_true),
|
neuper@37954
|
321 |
Thm ("not_false",num_str not_false)
|
neuper@37954
|
322 |
],
|
neuper@37954
|
323 |
srls = Erls, calc = [],
|
neuper@37954
|
324 |
rules = [Thm ("commute_0_equality",
|
neuper@37954
|
325 |
num_str commute_0_equality),
|
neuper@37954
|
326 |
Thm ("separate_bdvs0", num_str separate_bdvs0),
|
neuper@37954
|
327 |
Thm ("separate_bdvs_add1", num_str separate_bdvs_add1),
|
neuper@37954
|
328 |
Thm ("separate_bdvs_add1", num_str separate_bdvs_add2),
|
neuper@37954
|
329 |
Thm ("separate_bdvs_mult", num_str separate_bdvs_mult)],
|
neuper@37954
|
330 |
scr = EmptyScr};
|
neuper@37954
|
331 |
|
neuper@37954
|
332 |
(*.order the equations in a system such, that a triangular system (if any)
|
neuper@37954
|
333 |
appears as [..c_4 = .., ..., ..., ..c_1 + ..c_2 + ..c_3 ..c_4 = ..].*)
|
neuper@37954
|
334 |
val order_system =
|
neuper@37954
|
335 |
Rls {id="order_system", preconds = [],
|
neuper@37954
|
336 |
rew_ord = ("ord_simplify_System",
|
neuper@37954
|
337 |
ord_simplify_System false thy),
|
neuper@37954
|
338 |
erls = Erls, srls = Erls, calc = [],
|
neuper@37954
|
339 |
rules = [Thm ("order_system_NxN", num_str order_system_NxN)
|
neuper@37954
|
340 |
],
|
neuper@37954
|
341 |
scr = EmptyScr};
|
neuper@37954
|
342 |
|
neuper@37954
|
343 |
val prls_triangular =
|
neuper@37954
|
344 |
Rls {id="prls_triangular", preconds = [],
|
neuper@37954
|
345 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
346 |
erls = Rls {id="erls_prls_triangular", preconds = [],
|
neuper@37954
|
347 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
348 |
erls = Erls, srls = Erls, calc = [],
|
neuper@37954
|
349 |
rules = [(*for precond nth_Cons_ ...*)
|
neuper@37954
|
350 |
Calc ("op <",eval_equ "#less_"),
|
neuper@37954
|
351 |
Calc ("op +", eval_binop "#add_")
|
neuper@37954
|
352 |
(*immediately repeated rewrite pushes
|
neuper@37954
|
353 |
'+' into precondition !*)
|
neuper@37954
|
354 |
],
|
neuper@37954
|
355 |
scr = EmptyScr},
|
neuper@37954
|
356 |
srls = Erls, calc = [],
|
neuper@37954
|
357 |
rules = [Thm ("nth_Cons_",num_str nth_Cons_),
|
neuper@37954
|
358 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
359 |
Thm ("nth_Nil_",num_str nth_Nil_),
|
neuper@37954
|
360 |
Thm ("tl_Cons",num_str tl_Cons),
|
neuper@37954
|
361 |
Thm ("tl_Nil",num_str tl_Nil),
|
neuper@37954
|
362 |
Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
363 |
eval_occur_exactly_in
|
neuper@37954
|
364 |
"#eval_occur_exactly_in_")
|
neuper@37954
|
365 |
],
|
neuper@37954
|
366 |
scr = EmptyScr};
|
neuper@37954
|
367 |
|
neuper@37954
|
368 |
(*WN060914 quickly created for 4x4;
|
neuper@37954
|
369 |
more similarity to prls_triangular desirable*)
|
neuper@37954
|
370 |
val prls_triangular4 =
|
neuper@37954
|
371 |
Rls {id="prls_triangular4", preconds = [],
|
neuper@37954
|
372 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
373 |
erls = Rls {id="erls_prls_triangular4", preconds = [],
|
neuper@37954
|
374 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
375 |
erls = Erls, srls = Erls, calc = [],
|
neuper@37954
|
376 |
rules = [(*for precond nth_Cons_ ...*)
|
neuper@37954
|
377 |
Calc ("op <",eval_equ "#less_"),
|
neuper@37954
|
378 |
Calc ("op +", eval_binop "#add_")
|
neuper@37954
|
379 |
(*immediately repeated rewrite pushes
|
neuper@37954
|
380 |
'+' into precondition !*)
|
neuper@37954
|
381 |
],
|
neuper@37954
|
382 |
scr = EmptyScr},
|
neuper@37954
|
383 |
srls = Erls, calc = [],
|
neuper@37954
|
384 |
rules = [Thm ("nth_Cons_",num_str nth_Cons_),
|
neuper@37954
|
385 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
386 |
Thm ("nth_Nil_",num_str nth_Nil_),
|
neuper@37954
|
387 |
Thm ("tl_Cons",num_str tl_Cons),
|
neuper@37954
|
388 |
Thm ("tl_Nil",num_str tl_Nil),
|
neuper@37954
|
389 |
Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
390 |
eval_occur_exactly_in
|
neuper@37954
|
391 |
"#eval_occur_exactly_in_")
|
neuper@37954
|
392 |
],
|
neuper@37954
|
393 |
scr = EmptyScr};
|
neuper@37954
|
394 |
|
neuper@37954
|
395 |
ruleset' :=
|
neuper@37954
|
396 |
overwritelthy thy
|
neuper@37954
|
397 |
(!ruleset',
|
neuper@37954
|
398 |
[("simplify_System_parenthesized", prep_rls simplify_System_parenthesized),
|
neuper@37954
|
399 |
("simplify_System", prep_rls simplify_System),
|
neuper@37954
|
400 |
("isolate_bdvs", prep_rls isolate_bdvs),
|
neuper@37954
|
401 |
("isolate_bdvs_4x4", prep_rls isolate_bdvs_4x4),
|
neuper@37954
|
402 |
("order_system", prep_rls order_system),
|
neuper@37954
|
403 |
("order_add_mult_System", prep_rls order_add_mult_System),
|
neuper@37954
|
404 |
("norm_System_noadd_fractions", prep_rls norm_System_noadd_fractions),
|
neuper@37954
|
405 |
("norm_System", prep_rls norm_System)
|
neuper@37954
|
406 |
]);
|
neuper@37954
|
407 |
|
neuper@37954
|
408 |
|
neuper@37954
|
409 |
(** problems **)
|
neuper@37954
|
410 |
|
neuper@37954
|
411 |
store_pbt
|
neuper@37954
|
412 |
(prep_pbt (theory "EqSystem") "pbl_equsys" [] e_pblID
|
neuper@37954
|
413 |
(["system"],
|
neuper@37954
|
414 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
415 |
("#Find" ,["solution ss___"](*___ is copy-named*))
|
neuper@37954
|
416 |
],
|
neuper@37954
|
417 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37954
|
418 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
419 |
[]));
|
neuper@37954
|
420 |
store_pbt
|
neuper@37954
|
421 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin" [] e_pblID
|
neuper@37954
|
422 |
(["linear", "system"],
|
neuper@37954
|
423 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
424 |
(*TODO.WN050929 check linearity*)
|
neuper@37954
|
425 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
426 |
],
|
neuper@37954
|
427 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37954
|
428 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
429 |
[]));
|
neuper@37954
|
430 |
store_pbt
|
neuper@37954
|
431 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin_2x2" [] e_pblID
|
neuper@37954
|
432 |
(["2x2", "linear", "system"],
|
neuper@37954
|
433 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37954
|
434 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
435 |
("#Where" ,["length_ (es_:: bool list) = 2", "length_ vs_ = 2"]),
|
neuper@37954
|
436 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
437 |
],
|
neuper@37954
|
438 |
append_rls "prls_2x2_linear_system" e_rls
|
neuper@37954
|
439 |
[Thm ("length_Cons_",num_str length_Cons_),
|
neuper@37954
|
440 |
Thm ("length_Nil_",num_str length_Nil_),
|
neuper@37954
|
441 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
442 |
Calc ("op =",eval_equal "#equal_")
|
neuper@37954
|
443 |
],
|
neuper@37954
|
444 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
445 |
[]));
|
neuper@37954
|
446 |
store_pbt
|
neuper@37954
|
447 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin_2x2_tri" [] e_pblID
|
neuper@37954
|
448 |
(["triangular", "2x2", "linear", "system"],
|
neuper@37954
|
449 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
450 |
("#Where" ,
|
neuper@37954
|
451 |
["(tl vs_) from_ vs_ occur_exactly_in (nth_ 1 (es_::bool list))",
|
neuper@37954
|
452 |
" vs_ from_ vs_ occur_exactly_in (nth_ 2 (es_::bool list))"]),
|
neuper@37954
|
453 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
454 |
],
|
neuper@37954
|
455 |
prls_triangular,
|
neuper@37954
|
456 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
457 |
[["EqSystem","top_down_substitution","2x2"]]));
|
neuper@37954
|
458 |
store_pbt
|
neuper@37954
|
459 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin_2x2_norm" [] e_pblID
|
neuper@37954
|
460 |
(["normalize", "2x2", "linear", "system"],
|
neuper@37954
|
461 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
462 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
463 |
],
|
neuper@37954
|
464 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37954
|
465 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
466 |
[["EqSystem","normalize","2x2"]]));
|
neuper@37954
|
467 |
store_pbt
|
neuper@37954
|
468 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin_3x3" [] e_pblID
|
neuper@37954
|
469 |
(["3x3", "linear", "system"],
|
neuper@37954
|
470 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37954
|
471 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
472 |
("#Where" ,["length_ (es_:: bool list) = 3", "length_ vs_ = 3"]),
|
neuper@37954
|
473 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
474 |
],
|
neuper@37954
|
475 |
append_rls "prls_3x3_linear_system" e_rls
|
neuper@37954
|
476 |
[Thm ("length_Cons_",num_str length_Cons_),
|
neuper@37954
|
477 |
Thm ("length_Nil_",num_str length_Nil_),
|
neuper@37954
|
478 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
479 |
Calc ("op =",eval_equal "#equal_")
|
neuper@37954
|
480 |
],
|
neuper@37954
|
481 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
482 |
[]));
|
neuper@37954
|
483 |
store_pbt
|
neuper@37954
|
484 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin_4x4" [] e_pblID
|
neuper@37954
|
485 |
(["4x4", "linear", "system"],
|
neuper@37954
|
486 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37954
|
487 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
488 |
("#Where" ,["length_ (es_:: bool list) = 4", "length_ vs_ = 4"]),
|
neuper@37954
|
489 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
490 |
],
|
neuper@37954
|
491 |
append_rls "prls_4x4_linear_system" e_rls
|
neuper@37954
|
492 |
[Thm ("length_Cons_",num_str length_Cons_),
|
neuper@37954
|
493 |
Thm ("length_Nil_",num_str length_Nil_),
|
neuper@37954
|
494 |
Calc ("op +", eval_binop "#add_"),
|
neuper@37954
|
495 |
Calc ("op =",eval_equal "#equal_")
|
neuper@37954
|
496 |
],
|
neuper@37954
|
497 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
498 |
[]));
|
neuper@37954
|
499 |
store_pbt
|
neuper@37954
|
500 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin_4x4_tri" [] e_pblID
|
neuper@37954
|
501 |
(["triangular", "4x4", "linear", "system"],
|
neuper@37954
|
502 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
503 |
("#Where" , (*accepts missing variables up to diagional form*)
|
neuper@37954
|
504 |
["(nth_ 1 (vs_::real list)) occurs_in (nth_ 1 (es_::bool list))",
|
neuper@37954
|
505 |
"(nth_ 2 (vs_::real list)) occurs_in (nth_ 2 (es_::bool list))",
|
neuper@37954
|
506 |
"(nth_ 3 (vs_::real list)) occurs_in (nth_ 3 (es_::bool list))",
|
neuper@37954
|
507 |
"(nth_ 4 (vs_::real list)) occurs_in (nth_ 4 (es_::bool list))"
|
neuper@37954
|
508 |
]),
|
neuper@37954
|
509 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
510 |
],
|
neuper@37954
|
511 |
append_rls "prls_tri_4x4_lin_sys" prls_triangular
|
neuper@37954
|
512 |
[Calc ("Atools.occurs'_in",eval_occurs_in "")],
|
neuper@37954
|
513 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
514 |
[["EqSystem","top_down_substitution","4x4"]]));
|
neuper@37954
|
515 |
|
neuper@37954
|
516 |
store_pbt
|
neuper@37954
|
517 |
(prep_pbt (theory "EqSystem") "pbl_equsys_lin_4x4_norm" [] e_pblID
|
neuper@37954
|
518 |
(["normalize", "4x4", "linear", "system"],
|
neuper@37954
|
519 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
520 |
(*length_ is checked 1 level above*)
|
neuper@37954
|
521 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
522 |
],
|
neuper@37954
|
523 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37954
|
524 |
SOME "solveSystem es_ vs_",
|
neuper@37954
|
525 |
[["EqSystem","normalize","4x4"]]));
|
neuper@37954
|
526 |
|
neuper@37954
|
527 |
|
neuper@37954
|
528 |
(* show_ptyps();
|
neuper@37954
|
529 |
*)
|
neuper@37954
|
530 |
|
neuper@37954
|
531 |
(** methods **)
|
neuper@37954
|
532 |
|
neuper@37954
|
533 |
store_met
|
neuper@37954
|
534 |
(prep_met (theory "EqSystem") "met_eqsys" [] e_metID
|
neuper@37954
|
535 |
(["EqSystem"],
|
neuper@37954
|
536 |
[],
|
neuper@37954
|
537 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
538 |
srls = Erls, prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
539 |
"empty_script"
|
neuper@37954
|
540 |
));
|
neuper@37954
|
541 |
store_met
|
neuper@37954
|
542 |
(prep_met (theory "EqSystem") "met_eqsys_topdown" [] e_metID
|
neuper@37954
|
543 |
(["EqSystem","top_down_substitution"],
|
neuper@37954
|
544 |
[],
|
neuper@37954
|
545 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
546 |
srls = Erls, prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
547 |
"empty_script"
|
neuper@37954
|
548 |
));
|
neuper@37954
|
549 |
store_met
|
neuper@37954
|
550 |
(prep_met (theory "EqSystem") "met_eqsys_topdown_2x2" [] e_metID
|
neuper@37954
|
551 |
(["EqSystem","top_down_substitution","2x2"],
|
neuper@37954
|
552 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
553 |
("#Where" ,
|
neuper@37954
|
554 |
["(tl vs_) from_ vs_ occur_exactly_in (nth_ 1 (es_::bool list))",
|
neuper@37954
|
555 |
" vs_ from_ vs_ occur_exactly_in (nth_ 2 (es_::bool list))"]),
|
neuper@37954
|
556 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
557 |
],
|
neuper@37954
|
558 |
{rew_ord'="ord_simplify_System", rls' = Erls, calc = [],
|
neuper@37954
|
559 |
srls = append_rls "srls_top_down_2x2" e_rls
|
neuper@37954
|
560 |
[Thm ("hd_thm",num_str hd_thm),
|
neuper@37954
|
561 |
Thm ("tl_Cons",num_str tl_Cons),
|
neuper@37954
|
562 |
Thm ("tl_Nil",num_str tl_Nil)
|
neuper@37954
|
563 |
],
|
neuper@37954
|
564 |
prls = prls_triangular, crls = Erls, nrls = Erls},
|
neuper@37954
|
565 |
"Script SolveSystemScript (es_::bool list) (vs_::real list) = " ^
|
neuper@37954
|
566 |
" (let e1__ = Take (hd es_); " ^
|
neuper@37954
|
567 |
" e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
568 |
" isolate_bdvs False)) @@ " ^
|
neuper@37954
|
569 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
570 |
" simplify_System False))) e1__; " ^
|
neuper@37954
|
571 |
" e2__ = Take (hd (tl es_)); " ^
|
neuper@37954
|
572 |
" e2__ = ((Substitute [e1__]) @@ " ^
|
neuper@37954
|
573 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
574 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37954
|
575 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
576 |
" isolate_bdvs False)) @@ " ^
|
neuper@37954
|
577 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
578 |
" simplify_System False))) e2__; " ^
|
neuper@37954
|
579 |
" es__ = Take [e1__, e2__] " ^
|
neuper@37954
|
580 |
" in (Try (Rewrite_Set order_system False)) es__)"
|
neuper@37954
|
581 |
(*---------------------------------------------------------------------------
|
neuper@37954
|
582 |
this script does NOT separate the equations as abolve,
|
neuper@37954
|
583 |
but it does not yet work due to preliminary script-interpreter,
|
neuper@37954
|
584 |
see eqsystem.sml 'script [EqSystem,top_down_substitution,2x2] Vers.2'
|
neuper@37954
|
585 |
|
neuper@37954
|
586 |
"Script SolveSystemScript (es_::bool list) (vs_::real list) = " ^
|
neuper@37954
|
587 |
" (let es__ = Take es_; " ^
|
neuper@37954
|
588 |
" e1__ = hd es__; " ^
|
neuper@37954
|
589 |
" e2__ = hd (tl es__); " ^
|
neuper@37954
|
590 |
" es__ = [e1__, Substitute [e1__] e2__] " ^
|
neuper@37954
|
591 |
" in ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
592 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37954
|
593 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))] " ^
|
neuper@37954
|
594 |
" isolate_bdvs False)) @@ " ^
|
neuper@37954
|
595 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
596 |
" simplify_System False))) es__)"
|
neuper@37954
|
597 |
---------------------------------------------------------------------------*)
|
neuper@37954
|
598 |
));
|
neuper@37954
|
599 |
store_met
|
neuper@37954
|
600 |
(prep_met (theory "EqSystem") "met_eqsys_norm" [] e_metID
|
neuper@37954
|
601 |
(["EqSystem","normalize"],
|
neuper@37954
|
602 |
[],
|
neuper@37954
|
603 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
604 |
srls = Erls, prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
605 |
"empty_script"
|
neuper@37954
|
606 |
));
|
neuper@37954
|
607 |
store_met
|
neuper@37954
|
608 |
(prep_met (theory "EqSystem") "met_eqsys_norm_2x2" [] e_metID
|
neuper@37954
|
609 |
(["EqSystem","normalize","2x2"],
|
neuper@37954
|
610 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
611 |
("#Find" ,["solution ss___"])],
|
neuper@37954
|
612 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
613 |
srls = append_rls "srls_normalize_2x2" e_rls
|
neuper@37954
|
614 |
[Thm ("hd_thm",num_str hd_thm),
|
neuper@37954
|
615 |
Thm ("tl_Cons",num_str tl_Cons),
|
neuper@37954
|
616 |
Thm ("tl_Nil",num_str tl_Nil)
|
neuper@37954
|
617 |
],
|
neuper@37954
|
618 |
prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
619 |
"Script SolveSystemScript (es_::bool list) (vs_::real list) = " ^
|
neuper@37954
|
620 |
" (let es__ = ((Try (Rewrite_Set norm_Rational False)) @@ " ^
|
neuper@37954
|
621 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
622 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37954
|
623 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
624 |
" isolate_bdvs False)) @@ " ^
|
neuper@37954
|
625 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
|
neuper@37954
|
626 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37954
|
627 |
" (Try (Rewrite_Set order_system False))) es_ " ^
|
neuper@37954
|
628 |
" in (SubProblem (EqSystem_,[linear,system],[no_met]) " ^
|
neuper@37954
|
629 |
" [bool_list_ es__, real_list_ vs_]))"
|
neuper@37954
|
630 |
));
|
neuper@37954
|
631 |
|
neuper@37954
|
632 |
(*this is for nth_ only*)
|
neuper@37954
|
633 |
val srls = Rls {id="srls_normalize_4x4",
|
neuper@37954
|
634 |
preconds = [],
|
neuper@37954
|
635 |
rew_ord = ("termlessI",termlessI),
|
neuper@37954
|
636 |
erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
|
neuper@37954
|
637 |
[(*for asm in nth_Cons_ ...*)
|
neuper@37954
|
638 |
Calc ("op <",eval_equ "#less_"),
|
neuper@37954
|
639 |
(*2nd nth_Cons_ pushes n+-1 into asms*)
|
neuper@37954
|
640 |
Calc("op +", eval_binop "#add_")
|
neuper@37954
|
641 |
],
|
neuper@37954
|
642 |
srls = Erls, calc = [],
|
neuper@37954
|
643 |
rules = [Thm ("nth_Cons_",num_str nth_Cons_),
|
neuper@37954
|
644 |
Calc("op +", eval_binop "#add_"),
|
neuper@37954
|
645 |
Thm ("nth_Nil_",num_str nth_Nil_)],
|
neuper@37954
|
646 |
scr = EmptyScr};
|
neuper@37954
|
647 |
store_met
|
neuper@37954
|
648 |
(prep_met (theory "EqSystem") "met_eqsys_norm_4x4" [] e_metID
|
neuper@37954
|
649 |
(["EqSystem","normalize","4x4"],
|
neuper@37954
|
650 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
651 |
("#Find" ,["solution ss___"])],
|
neuper@37954
|
652 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
653 |
srls = append_rls "srls_normalize_4x4" srls
|
neuper@37954
|
654 |
[Thm ("hd_thm",num_str hd_thm),
|
neuper@37954
|
655 |
Thm ("tl_Cons",num_str tl_Cons),
|
neuper@37954
|
656 |
Thm ("tl_Nil",num_str tl_Nil)
|
neuper@37954
|
657 |
],
|
neuper@37954
|
658 |
prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
659 |
(*GOON met ["EqSystem","normalize","4x4"] @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@*)
|
neuper@37954
|
660 |
"Script SolveSystemScript (es_::bool list) (vs_::real list) = " ^
|
neuper@37954
|
661 |
" (let es__ = " ^
|
neuper@37954
|
662 |
" ((Try (Rewrite_Set norm_Rational False)) @@ " ^
|
neuper@37954
|
663 |
" (Repeat (Rewrite commute_0_equality False)) @@ " ^
|
neuper@37954
|
664 |
" (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 vs_),(bdv_2, nth_ 2 vs_ ), " ^
|
neuper@37954
|
665 |
" (bdv_3, nth_ 3 vs_),(bdv_3, nth_ 4 vs_ )] " ^
|
neuper@37954
|
666 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37954
|
667 |
" (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 vs_),(bdv_2, nth_ 2 vs_ ), " ^
|
neuper@37954
|
668 |
" (bdv_3, nth_ 3 vs_),(bdv_3, nth_ 4 vs_ )] " ^
|
neuper@37954
|
669 |
" isolate_bdvs_4x4 False)) @@ " ^
|
neuper@37954
|
670 |
" (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 vs_),(bdv_2, nth_ 2 vs_ ), " ^
|
neuper@37954
|
671 |
" (bdv_3, nth_ 3 vs_),(bdv_3, nth_ 4 vs_ )] " ^
|
neuper@37954
|
672 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37954
|
673 |
" (Try (Rewrite_Set order_system False))) es_ " ^
|
neuper@37954
|
674 |
" in (SubProblem (EqSystem_,[linear,system],[no_met]) " ^
|
neuper@37954
|
675 |
" [bool_list_ es__, real_list_ vs_]))"
|
neuper@37954
|
676 |
));
|
neuper@37954
|
677 |
store_met
|
neuper@37954
|
678 |
(prep_met (theory "EqSystem") "met_eqsys_topdown_4x4" [] e_metID
|
neuper@37954
|
679 |
(["EqSystem","top_down_substitution","4x4"],
|
neuper@37954
|
680 |
[("#Given" ,["equalities es_", "solveForVars vs_"]),
|
neuper@37954
|
681 |
("#Where" , (*accepts missing variables up to diagonal form*)
|
neuper@37954
|
682 |
["(nth_ 1 (vs_::real list)) occurs_in (nth_ 1 (es_::bool list))",
|
neuper@37954
|
683 |
"(nth_ 2 (vs_::real list)) occurs_in (nth_ 2 (es_::bool list))",
|
neuper@37954
|
684 |
"(nth_ 3 (vs_::real list)) occurs_in (nth_ 3 (es_::bool list))",
|
neuper@37954
|
685 |
"(nth_ 4 (vs_::real list)) occurs_in (nth_ 4 (es_::bool list))"
|
neuper@37954
|
686 |
]),
|
neuper@37954
|
687 |
("#Find" ,["solution ss___"])
|
neuper@37954
|
688 |
],
|
neuper@37954
|
689 |
{rew_ord'="ord_simplify_System", rls' = Erls, calc = [],
|
neuper@37954
|
690 |
srls = append_rls "srls_top_down_4x4" srls [],
|
neuper@37954
|
691 |
prls = append_rls "prls_tri_4x4_lin_sys" prls_triangular
|
neuper@37954
|
692 |
[Calc ("Atools.occurs'_in",eval_occurs_in "")],
|
neuper@37954
|
693 |
crls = Erls, nrls = Erls},
|
neuper@37954
|
694 |
(*FIXXXXME.WN060916: this script works ONLY for exp 7.79 @@@@@@@@@@@@@@@@@@@@*)
|
neuper@37954
|
695 |
"Script SolveSystemScript (es_::bool list) (vs_::real list) = " ^
|
neuper@37954
|
696 |
" (let e1_ = nth_ 1 es_; " ^
|
neuper@37954
|
697 |
" e2_ = Take (nth_ 2 es_); " ^
|
neuper@37954
|
698 |
" e2_ = ((Substitute [e1_]) @@ " ^
|
neuper@37954
|
699 |
" (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_)," ^
|
neuper@37954
|
700 |
" (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]" ^
|
neuper@37954
|
701 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37954
|
702 |
" (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_)," ^
|
neuper@37954
|
703 |
" (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]" ^
|
neuper@37954
|
704 |
" isolate_bdvs False)) @@ " ^
|
neuper@37954
|
705 |
" (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_)," ^
|
neuper@37954
|
706 |
" (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]" ^
|
neuper@37954
|
707 |
" norm_Rational False))) e2_ " ^
|
neuper@37954
|
708 |
" in [e1_, e2_, nth_ 3 es_, nth_ 4 es_])"
|
neuper@37954
|
709 |
));
|
neuper@37954
|
710 |
*}
|
neuper@37954
|
711 |
|
neuper@37906
|
712 |
end |