neuper@37906
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(* equational systems, minimal -- for use in Biegelinie
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neuper@37906
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author: Walther Neuper
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neuper@37906
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050826,
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neuper@37906
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(c) due to copyright terms
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neuper@37906
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*)
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neuper@37906
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neuper@37997
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theory EqSystem imports Integrate Rational Root begin
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neuper@37906
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neuper@37906
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consts
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neuper@37906
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walther@60278
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occur_exactly_in ::
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neuper@37998
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"[real list, real list, 'a] => bool" ("_ from _ occur'_exactly'_in _")
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neuper@37906
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neuper@37906
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(*descriptions in the related problems*)
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neuper@37997
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solveForVars :: "real list => toreall"
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neuper@37997
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solution :: "bool list => toreall"
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neuper@37906
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neuper@37906
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(*the CAS-command, eg. "solveSystem [x+y=1,y=2] [x,y]"*)
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neuper@37906
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solveSystem :: "[bool list, real list] => bool list"
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neuper@37906
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neuper@52148
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axiomatization where
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neuper@37906
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(*stated as axioms, todo: prove as theorems
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neuper@37906
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'bdv' is a constant handled on the meta-level
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neuper@37906
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specifically as a 'bound variable' *)
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neuper@37906
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neuper@52148
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commute_0_equality: "(0 = a) = (a = 0)" and
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neuper@37906
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neuper@37906
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(*WN0510 see simliar rules 'isolate_' 'separate_' (by RL)
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neuper@37906
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[bdv_1,bdv_2,bdv_3,bdv_4] work also for 2 and 3 bdvs, ugly !*)
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neuper@37983
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separate_bdvs_add:
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neuper@37998
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"[| [] from [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a |]
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neuper@52148
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==> (a + b = c) = (b = c + -1*a)" and
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neuper@37983
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separate_bdvs0:
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neuper@37954
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"[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in b; Not (b=!=0) |]
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neuper@52148
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==> (a = b) = (a + -1*b = 0)" and
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neuper@37983
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separate_bdvs_add1:
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neuper@37954
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"[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in c |]
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neuper@52148
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==> (a = b + c) = (a + -1*c = b)" and
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neuper@37983
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separate_bdvs_add2:
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neuper@37954
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"[| Not (some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in a) |]
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neuper@52148
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==> (a + b = c) = (b = -1*a + c)" and
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neuper@37983
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separate_bdvs_mult:
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neuper@37998
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"[| [] from [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a; Not (a=!=0) |]
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t@42197
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==>(a * b = c) = (b = c / a)"
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neuper@55276
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axiomatization where (*..if replaced by "and" we get an error in
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wneuper@59370
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--- rewrite in [EqSystem,normalise,2x2] --- step "--- 3---";*)
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t@42197
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order_system_NxN: "[a,b] = [b,a]"
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neuper@37906
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(*requires rew_ord for termination, eg. ord_simplify_Integral;
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neuper@37906
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works for lists of any length, interestingly !?!*)
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neuper@37906
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wneuper@59472
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ML \<open>
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neuper@37954
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(** eval functions **)
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neuper@37954
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neuper@37954
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(*certain variables of a given list occur _all_ in a term
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neuper@37954
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args: all: ..variables, which are under consideration (eg. the bound vars)
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neuper@37954
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vs: variables which must be in t,
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neuper@37954
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and none of the others in all must be in t
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neuper@37954
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t: the term under consideration
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neuper@37954
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*)
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neuper@37954
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fun occur_exactly_in vs all t =
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walther@59603
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let fun occurs_in' a b = Prog_Expr.occurs_in b a
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neuper@37954
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in foldl and_ (true, map (occurs_in' t) vs)
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neuper@37954
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andalso not (foldl or_ (false, map (occurs_in' t)
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neuper@37954
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(subtract op = vs all)))
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neuper@37954
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end;
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neuper@37954
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walther@60278
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(*("occur_exactly_in", ("EqSystem.occur_exactly_in",
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neuper@37954
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eval_occur_exactly_in "#eval_occur_exactly_in_"))*)
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walther@60278
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fun eval_occur_exactly_in _ "EqSystem.occur_exactly_in"
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walther@60278
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(p as (Const ("EqSystem.occur_exactly_in",_)
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neuper@37954
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$ vs $ all $ t)) _ =
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wneuper@59389
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if occur_exactly_in (TermC.isalist2list vs) (TermC.isalist2list all) t
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walther@59868
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then SOME ((UnparseC.term p) ^ " = True",
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wneuper@59390
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HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
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walther@59868
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else SOME ((UnparseC.term p) ^ " = False",
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wneuper@59390
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HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
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neuper@37954
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| eval_occur_exactly_in _ _ _ _ = NONE;
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wneuper@59472
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\<close>
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wneuper@59472
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setup \<open>KEStore_Elems.add_calcs
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s1210629013@52145
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[("occur_exactly_in",
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walther@60278
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("EqSystem.occur_exactly_in",
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wneuper@59472
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eval_occur_exactly_in "#eval_occur_exactly_in_"))]\<close>
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wneuper@59472
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ML \<open>
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neuper@37954
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(** rewrite order 'ord_simplify_System' **)
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neuper@37954
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walther@59997
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(* order wrt. several linear (i.e. without exponents) variables "c", "c_2",..
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neuper@37954
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which leaves the monomials containing c, c_2,... at the end of an Integral
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neuper@37954
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and puts the c, c_2,... rightmost within a monomial.
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neuper@37954
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neuper@37954
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WN050906 this is a quick and dirty adaption of ord_make_polynomial_in,
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neuper@37954
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which was most adequate, because it uses size_of_term*)
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neuper@37954
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(**)
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neuper@37954
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local (*. for simplify_System .*)
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neuper@37954
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(**)
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neuper@37954
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open Term; (* for type order = EQUAL | LESS | GREATER *)
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neuper@37954
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neuper@37954
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fun pr_ord EQUAL = "EQUAL"
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neuper@37954
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| pr_ord LESS = "LESS"
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neuper@37954
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| pr_ord GREATER = "GREATER";
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neuper@37954
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neuper@37954
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fun dest_hd' (Const (a, T)) = (((a, 0), T), 0)
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neuper@37954
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| dest_hd' (Free (ccc, T)) =
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neuper@40836
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(case Symbol.explode ccc of
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neuper@37954
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"c"::[] => ((("|||||||||||||||||||||", 0), T), 1)(*greatest string WN*)
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neuper@37954
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| "c"::"_"::_ => ((("|||||||||||||||||||||", 0), T), 1)
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neuper@37954
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| _ => (((ccc, 0), T), 1))
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neuper@37954
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| dest_hd' (Var v) = (v, 2)
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neuper@37954
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| dest_hd' (Bound i) = ((("", i), dummyT), 3)
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walther@60269
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| dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4)
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walther@60269
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| dest_hd' _ = raise ERROR "dest_hd': uncovered case in fun.def.";
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neuper@37954
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neuper@37954
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fun size_of_term' (Free (ccc, _)) =
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neuper@40836
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(case Symbol.explode ccc of (*WN0510 hack for the bound variables*)
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neuper@37954
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"c"::[] => 1000
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wneuper@59390
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| "c"::"_"::is => 1000 * ((TermC.int_of_str o implode) is)
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neuper@37954
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| _ => 1)
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neuper@37954
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| size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
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neuper@37954
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| size_of_term' (f$t) = size_of_term' f + size_of_term' t
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neuper@37954
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| size_of_term' _ = 1;
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neuper@37954
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neuper@37997
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fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
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neuper@52070
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(case term_ord' pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord)
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neuper@37997
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| term_ord' pr thy (t, u) =
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neuper@52070
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(if pr
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neuper@52070
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then
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neuper@52070
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let
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neuper@52070
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val (f, ts) = strip_comb t and (g, us) = strip_comb u;
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walther@59870
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val _ = tracing ("t= f@ts= \"" ^ UnparseC.term_in_thy thy f ^ "\" @ \"[" ^
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walther@59870
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commas (map (UnparseC.term_in_thy thy) ts) ^ "]\"");
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walther@59870
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val _ = tracing ("u= g@us= \"" ^ UnparseC.term_in_thy thy g ^ "\" @ \"[" ^
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walther@59870
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commas (map (UnparseC.term_in_thy thy) us) ^ "]\"");
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neuper@52070
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val _ = tracing ("size_of_term(t,u)= (" ^ string_of_int (size_of_term' t) ^ ", " ^
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neuper@52070
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string_of_int (size_of_term' u) ^ ")");
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neuper@52070
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val _ = tracing ("hd_ord(f,g) = " ^ ((pr_ord o hd_ord) (f,g)));
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neuper@52070
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val _ = tracing ("terms_ord (ts,us) = " ^(pr_ord o terms_ord str false) (ts,us));
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neuper@52070
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val _=tracing("-------");
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neuper@52070
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in () end
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neuper@52070
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else ();
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neuper@52070
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case int_ord (size_of_term' t, size_of_term' u) of
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neuper@52070
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EQUAL =>
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neuper@52070
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let val (f, ts) = strip_comb t and (g, us) = strip_comb u
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neuper@52070
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in (case hd_ord (f, g) of
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neuper@52070
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EQUAL => (terms_ord str pr) (ts, us)
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neuper@52070
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| ord => ord)
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neuper@52070
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end
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neuper@37954
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| ord => ord)
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neuper@37954
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and hd_ord (f, g) = (* ~ term.ML *)
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neuper@52070
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prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord (dest_hd' f, dest_hd' g)
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walther@60269
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and terms_ord _ pr (ts, us) = list_ord (term_ord' pr (ThyC.get_theory "Isac_Knowledge"))(ts, us);
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neuper@37954
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(**)
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neuper@37954
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in
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neuper@37954
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(**)
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neuper@37954
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(*WN0510 for preliminary use in eval_order_system, see case-study mat-eng.tex
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neuper@37954
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fun ord_simplify_System_rev (pr:bool) thy subst tu =
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neuper@37954
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(term_ord' pr thy (Library.swap tu) = LESS);*)
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neuper@37954
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neuper@37954
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(*for the rls's*)
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walther@60269
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fun ord_simplify_System (pr:bool) thy _(*subst*) tu =
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neuper@37954
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(term_ord' pr thy tu = LESS);
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neuper@37954
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(**)
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neuper@37954
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end;
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neuper@37954
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(**)
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walther@59857
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Rewrite_Ord.rew_ord' := overwritel (! Rewrite_Ord.rew_ord',
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wenzelm@60291
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[("ord_simplify_System", ord_simplify_System false \<^theory>)
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neuper@37954
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]);
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wneuper@59472
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\<close>
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wneuper@59472
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ML \<open>
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neuper@37954
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(** rulesets **)
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neuper@37954
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neuper@37954
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(*.adapted from 'order_add_mult_in' by just replacing the rew_ord.*)
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neuper@37954
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val order_add_mult_System =
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walther@59851
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Rule_Def.Repeat{id = "order_add_mult_System", preconds = [],
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neuper@37954
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rew_ord = ("ord_simplify_System",
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bonzai@41919
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ord_simplify_System false @{theory "Integrate"}),
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walther@59852
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erls = Rule_Set.empty,srls = Rule_Set.Empty, calc = [], errpatts = [],
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wenzelm@60297
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rules = [\<^rule_thm>\<open>mult.commute\<close>,
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neuper@37954
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(* z * w = w * z *)
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wenzelm@60297
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\<^rule_thm>\<open>real_mult_left_commute\<close>,
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neuper@37954
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(*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
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wenzelm@60297
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\<^rule_thm>\<open>mult.assoc\<close>,
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neuper@37954
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(*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
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wenzelm@60297
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\<^rule_thm>\<open>add.commute\<close>,
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neuper@37954
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(*z + w = w + z*)
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wenzelm@60297
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\<^rule_thm>\<open>add.left_commute\<close>,
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neuper@37954
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(*x + (y + z) = y + (x + z)*)
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wenzelm@60297
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\<^rule_thm>\<open>add.assoc\<close>
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neuper@37954
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(*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
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neuper@37954
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],
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walther@59878
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scr = Rule.Empty_Prog};
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wneuper@59472
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\<close>
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wneuper@59472
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ML \<open>
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neuper@37954
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(*.adapted from 'norm_Rational' by
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neuper@37954
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#1 using 'ord_simplify_System' in 'order_add_mult_System'
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neuper@37954
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#2 NOT using common_nominator_p .*)
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neuper@37954
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val norm_System_noadd_fractions =
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walther@59851
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Rule_Def.Repeat {id = "norm_System_noadd_fractions", preconds = [],
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walther@59857
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rew_ord = ("dummy_ord",Rewrite_Ord.dummy_ord),
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walther@59851
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erls = norm_rat_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
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neuper@37954
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rules = [(*sequence given by operator precedence*)
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wneuper@59416
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Rule.Rls_ discard_minus,
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wneuper@59416
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Rule.Rls_ powers,
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wneuper@59416
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Rule.Rls_ rat_mult_divide,
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wneuper@59416
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Rule.Rls_ expand,
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wneuper@59416
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Rule.Rls_ reduce_0_1_2,
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wneuper@59416
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Rule.Rls_ (*order_add_mult #1*) order_add_mult_System,
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wneuper@59416
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Rule.Rls_ collect_numerals,
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wneuper@59416
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(*Rule.Rls_ add_fractions_p, #2*)
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wneuper@59416
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Rule.Rls_ cancel_p
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neuper@37954
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],
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walther@59878
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scr = Rule.Empty_Prog
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wneuper@59406
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};
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wneuper@59472
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\<close>
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wneuper@59472
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ML \<open>
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neuper@37954
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214 |
(*.adapted from 'norm_Rational' by
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neuper@37954
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*1* using 'ord_simplify_System' in 'order_add_mult_System'.*)
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neuper@37954
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val norm_System =
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walther@59851
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217 |
Rule_Def.Repeat {id = "norm_System", preconds = [],
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walther@59857
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rew_ord = ("dummy_ord",Rewrite_Ord.dummy_ord),
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walther@59851
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219 |
erls = norm_rat_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
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neuper@37954
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rules = [(*sequence given by operator precedence*)
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wneuper@59416
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Rule.Rls_ discard_minus,
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wneuper@59416
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Rule.Rls_ powers,
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wneuper@59416
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223 |
Rule.Rls_ rat_mult_divide,
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wneuper@59416
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Rule.Rls_ expand,
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wneuper@59416
|
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Rule.Rls_ reduce_0_1_2,
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wneuper@59416
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226 |
Rule.Rls_ (*order_add_mult *1*) order_add_mult_System,
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wneuper@59416
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227 |
Rule.Rls_ collect_numerals,
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wneuper@59416
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228 |
Rule.Rls_ add_fractions_p,
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wneuper@59416
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Rule.Rls_ cancel_p
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neuper@37954
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],
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walther@59878
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231 |
scr = Rule.Empty_Prog
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wneuper@59406
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};
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wneuper@59472
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\<close>
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wneuper@59472
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234 |
ML \<open>
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neuper@37954
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235 |
(*.simplify an equational system BEFORE solving it such that parentheses are
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neuper@37954
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236 |
( ((u0*v0)*w0) + ( ((u1*v1)*w1) * c + ... +((u4*v4)*w4) * c_4 ) )
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neuper@37954
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237 |
ATTENTION: works ONLY for bound variables c, c_1, c_2, c_3, c_4 :ATTENTION
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neuper@37954
|
238 |
This is a copy from 'make_ratpoly_in' with respective reductions:
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neuper@37954
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239 |
*0* expand the term, ie. distribute * and / over +
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neuper@37954
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240 |
*1* ord_simplify_System instead of termlessI
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neuper@37954
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*2* no add_fractions_p (= common_nominator_p_rls !)
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neuper@37954
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*3* discard_parentheses only for (.*(.*.))
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neuper@37954
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243 |
analoguous to simplify_Integral .*)
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neuper@37954
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244 |
val simplify_System_parenthesized =
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walther@59878
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245 |
Rule_Set.Sequence {id = "simplify_System_parenthesized", preconds = []:term list,
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walther@59857
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246 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
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walther@59851
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247 |
erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
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wenzelm@60297
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248 |
rules = [\<^rule_thm>\<open>distrib_right\<close>,
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neuper@37954
|
249 |
(*"(?z1.0 + ?z2.0) * ?w = ?z1.0 * ?w + ?z2.0 * ?w"*)
|
wenzelm@60297
|
250 |
\<^rule_thm>\<open>add_divide_distrib\<close>,
|
neuper@37954
|
251 |
(*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)
|
neuper@37954
|
252 |
(*^^^^^ *0* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*)
|
wneuper@59416
|
253 |
Rule.Rls_ norm_Rational_noadd_fractions(**2**),
|
wneuper@59416
|
254 |
Rule.Rls_ (*order_add_mult_in*) norm_System_noadd_fractions (**1**),
|
wenzelm@60296
|
255 |
\<^rule_thm_sym>\<open>mult.assoc\<close>
|
wneuper@59416
|
256 |
(*Rule.Rls_ discard_parentheses *3**),
|
wneuper@59416
|
257 |
Rule.Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
|
wneuper@59416
|
258 |
Rule.Rls_ separate_bdv2,
|
wenzelm@60294
|
259 |
\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e")
|
neuper@37954
|
260 |
],
|
walther@59878
|
261 |
scr = Rule.Empty_Prog};
|
wneuper@59472
|
262 |
\<close>
|
wneuper@59472
|
263 |
ML \<open>
|
neuper@37954
|
264 |
(*.simplify an equational system AFTER solving it;
|
neuper@37954
|
265 |
This is a copy of 'make_ratpoly_in' with the differences
|
neuper@37954
|
266 |
*1* ord_simplify_System instead of termlessI .*)
|
neuper@37954
|
267 |
(*TODO.WN051031 ^^^^^^^^^^ should be in EACH rls contained *)
|
neuper@37954
|
268 |
val simplify_System =
|
walther@59878
|
269 |
Rule_Set.Sequence {id = "simplify_System", preconds = []:term list,
|
walther@59857
|
270 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@59851
|
271 |
erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wneuper@59416
|
272 |
rules = [Rule.Rls_ norm_Rational,
|
wneuper@59416
|
273 |
Rule.Rls_ (*order_add_mult_in*) norm_System (**1**),
|
wneuper@59416
|
274 |
Rule.Rls_ discard_parentheses,
|
wneuper@59416
|
275 |
Rule.Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
|
wneuper@59416
|
276 |
Rule.Rls_ separate_bdv2,
|
wenzelm@60294
|
277 |
\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e")
|
neuper@37954
|
278 |
],
|
walther@59878
|
279 |
scr = Rule.Empty_Prog};
|
neuper@37906
|
280 |
(*
|
neuper@37954
|
281 |
val simplify_System =
|
walther@59852
|
282 |
Rule_Set.append_rules "simplify_System" simplify_System_parenthesized
|
wenzelm@60296
|
283 |
[\<^rule_thm_sym>\<open>add.assoc\<close>];
|
neuper@37954
|
284 |
*)
|
wneuper@59472
|
285 |
\<close>
|
wneuper@59472
|
286 |
ML \<open>
|
neuper@37954
|
287 |
val isolate_bdvs =
|
walther@59851
|
288 |
Rule_Def.Repeat {id="isolate_bdvs", preconds = [],
|
walther@59857
|
289 |
rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
|
walther@59852
|
290 |
erls = Rule_Set.append_rules "erls_isolate_bdvs" Rule_Set.empty
|
wenzelm@60294
|
291 |
[(\<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_"))],
|
walther@59851
|
292 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
neuper@37997
|
293 |
rules =
|
wenzelm@60297
|
294 |
[\<^rule_thm>\<open>commute_0_equality\<close>,
|
wenzelm@60297
|
295 |
\<^rule_thm>\<open>separate_bdvs_add\<close>,
|
wenzelm@60297
|
296 |
\<^rule_thm>\<open>separate_bdvs_mult\<close>],
|
walther@59878
|
297 |
scr = Rule.Empty_Prog};
|
wneuper@59472
|
298 |
\<close>
|
wneuper@59472
|
299 |
ML \<open>
|
neuper@37954
|
300 |
val isolate_bdvs_4x4 =
|
walther@59851
|
301 |
Rule_Def.Repeat {id="isolate_bdvs_4x4", preconds = [],
|
walther@59857
|
302 |
rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
|
walther@59852
|
303 |
erls = Rule_Set.append_rules
|
walther@59852
|
304 |
"erls_isolate_bdvs_4x4" Rule_Set.empty
|
wenzelm@60294
|
305 |
[\<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_"),
|
wenzelm@60294
|
306 |
\<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
|
wenzelm@60294
|
307 |
\<^rule_eval>\<open>Prog_Expr.some_occur_in\<close> (Prog_Expr.eval_some_occur_in "#some_occur_in_"),
|
wenzelm@60297
|
308 |
\<^rule_thm>\<open>not_true\<close>,
|
wenzelm@60297
|
309 |
\<^rule_thm>\<open>not_false\<close>
|
neuper@37954
|
310 |
],
|
walther@59851
|
311 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
312 |
rules = [\<^rule_thm>\<open>commute_0_equality\<close>,
|
wenzelm@60297
|
313 |
\<^rule_thm>\<open>separate_bdvs0\<close>,
|
wenzelm@60297
|
314 |
\<^rule_thm>\<open>separate_bdvs_add1\<close>,
|
wenzelm@60297
|
315 |
\<^rule_thm>\<open>separate_bdvs_add2\<close>,
|
wenzelm@60297
|
316 |
\<^rule_thm>\<open>separate_bdvs_mult\<close>
|
walther@59878
|
317 |
], scr = Rule.Empty_Prog};
|
neuper@37954
|
318 |
|
wneuper@59472
|
319 |
\<close>
|
wneuper@59472
|
320 |
ML \<open>
|
neuper@37997
|
321 |
|
neuper@37954
|
322 |
(*.order the equations in a system such, that a triangular system (if any)
|
neuper@37954
|
323 |
appears as [..c_4 = .., ..., ..., ..c_1 + ..c_2 + ..c_3 ..c_4 = ..].*)
|
neuper@37954
|
324 |
val order_system =
|
walther@59851
|
325 |
Rule_Def.Repeat {id="order_system", preconds = [],
|
neuper@37954
|
326 |
rew_ord = ("ord_simplify_System",
|
wenzelm@60291
|
327 |
ord_simplify_System false \<^theory>),
|
walther@59851
|
328 |
erls = Rule_Set.Empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
329 |
rules = [\<^rule_thm>\<open>order_system_NxN\<close>
|
neuper@37954
|
330 |
],
|
walther@59878
|
331 |
scr = Rule.Empty_Prog};
|
neuper@37954
|
332 |
|
neuper@37954
|
333 |
val prls_triangular =
|
walther@59851
|
334 |
Rule_Def.Repeat {id="prls_triangular", preconds = [],
|
walther@59857
|
335 |
rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
|
walther@59851
|
336 |
erls = Rule_Def.Repeat {id="erls_prls_triangular", preconds = [],
|
walther@59857
|
337 |
rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
|
walther@59851
|
338 |
erls = Rule_Set.Empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
neuper@37997
|
339 |
rules = [(*for precond NTH_CONS ...*)
|
wenzelm@60294
|
340 |
\<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
|
wenzelm@60294
|
341 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_")
|
neuper@37954
|
342 |
(*immediately repeated rewrite pushes
|
neuper@37954
|
343 |
'+' into precondition !*)
|
neuper@37954
|
344 |
],
|
walther@59878
|
345 |
scr = Rule.Empty_Prog},
|
walther@59851
|
346 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
347 |
rules = [\<^rule_thm>\<open>NTH_CONS\<close>,
|
wenzelm@60294
|
348 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
|
wenzelm@60297
|
349 |
\<^rule_thm>\<open>NTH_NIL\<close>,
|
wenzelm@60297
|
350 |
\<^rule_thm>\<open>tl_Cons\<close>,
|
wenzelm@60297
|
351 |
\<^rule_thm>\<open>tl_Nil\<close>,
|
wenzelm@60294
|
352 |
\<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_")
|
neuper@37954
|
353 |
],
|
walther@59878
|
354 |
scr = Rule.Empty_Prog};
|
wneuper@59472
|
355 |
\<close>
|
wneuper@59472
|
356 |
ML \<open>
|
neuper@37954
|
357 |
|
neuper@37954
|
358 |
(*WN060914 quickly created for 4x4;
|
neuper@37954
|
359 |
more similarity to prls_triangular desirable*)
|
neuper@37954
|
360 |
val prls_triangular4 =
|
walther@59851
|
361 |
Rule_Def.Repeat {id="prls_triangular4", preconds = [],
|
walther@59857
|
362 |
rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
|
walther@59851
|
363 |
erls = Rule_Def.Repeat {id="erls_prls_triangular4", preconds = [],
|
walther@59857
|
364 |
rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord),
|
walther@59851
|
365 |
erls = Rule_Set.Empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
neuper@37997
|
366 |
rules = [(*for precond NTH_CONS ...*)
|
wenzelm@60294
|
367 |
\<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
|
wenzelm@60294
|
368 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_")
|
neuper@37954
|
369 |
(*immediately repeated rewrite pushes
|
neuper@37954
|
370 |
'+' into precondition !*)
|
neuper@37954
|
371 |
],
|
walther@59878
|
372 |
scr = Rule.Empty_Prog},
|
walther@59851
|
373 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
374 |
rules = [\<^rule_thm>\<open>NTH_CONS\<close>,
|
wenzelm@60294
|
375 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
|
wenzelm@60297
|
376 |
\<^rule_thm>\<open>NTH_NIL\<close>,
|
wenzelm@60297
|
377 |
\<^rule_thm>\<open>tl_Cons\<close>,
|
wenzelm@60297
|
378 |
\<^rule_thm>\<open>tl_Nil\<close>,
|
wenzelm@60294
|
379 |
\<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_")
|
neuper@37954
|
380 |
],
|
walther@59878
|
381 |
scr = Rule.Empty_Prog};
|
wneuper@59472
|
382 |
\<close>
|
t@42197
|
383 |
|
wenzelm@60289
|
384 |
rule_set_knowledge
|
wenzelm@60286
|
385 |
simplify_System_parenthesized = \<open>prep_rls' simplify_System_parenthesized\<close> and
|
wenzelm@60286
|
386 |
simplify_System = \<open>prep_rls' simplify_System\<close> and
|
wenzelm@60286
|
387 |
isolate_bdvs = \<open>prep_rls' isolate_bdvs\<close> and
|
wenzelm@60286
|
388 |
isolate_bdvs_4x4 = \<open>prep_rls' isolate_bdvs_4x4\<close> and
|
wenzelm@60286
|
389 |
order_system = \<open>prep_rls' order_system\<close> and
|
wenzelm@60286
|
390 |
order_add_mult_System = \<open>prep_rls' order_add_mult_System\<close> and
|
wenzelm@60286
|
391 |
norm_System_noadd_fractions = \<open>prep_rls' norm_System_noadd_fractions\<close> and
|
wenzelm@60286
|
392 |
norm_System = \<open>prep_rls' norm_System\<close>
|
t@42197
|
393 |
|
walther@60023
|
394 |
|
walther@60023
|
395 |
section \<open>Problems\<close>
|
walther@60023
|
396 |
|
wenzelm@60306
|
397 |
problem pbl_equsys : "system" =
|
wenzelm@60306
|
398 |
\<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
|
wenzelm@60306
|
399 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
400 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
401 |
Find: "solution ss'''" (*''' is copy-named*)
|
wenzelm@60306
|
402 |
|
wenzelm@60306
|
403 |
problem pbl_equsys_lin : "LINEAR/system" =
|
wenzelm@60306
|
404 |
\<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
|
wenzelm@60306
|
405 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
406 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
407 |
(*TODO.WN050929 check linearity*)
|
wenzelm@60306
|
408 |
Find: "solution ss'''"
|
wenzelm@60306
|
409 |
|
wenzelm@60306
|
410 |
problem pbl_equsys_lin_2x2: "2x2/LINEAR/system" =
|
wenzelm@60306
|
411 |
\<open>Rule_Set.append_rules "prls_2x2_linear_system" Rule_Set.empty
|
wenzelm@60306
|
412 |
[\<^rule_thm>\<open>LENGTH_CONS\<close>,
|
wenzelm@60306
|
413 |
\<^rule_thm>\<open>LENGTH_NIL\<close>,
|
wenzelm@60306
|
414 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
|
wenzelm@60306
|
415 |
\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_")]\<close>
|
wenzelm@60306
|
416 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
417 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
418 |
Where: "Length (e_s:: bool list) = 2" "Length v_s = 2"
|
wenzelm@60306
|
419 |
Find: "solution ss'''"
|
wenzelm@60306
|
420 |
|
wenzelm@60306
|
421 |
problem pbl_equsys_lin_2x2_tri : "triangular/2x2/LINEAR/system" =
|
wenzelm@60306
|
422 |
\<open>prls_triangular\<close>
|
wenzelm@60306
|
423 |
Method: "EqSystem/top_down_substitution/2x2"
|
wenzelm@60306
|
424 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
425 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
426 |
Where:
|
wenzelm@60306
|
427 |
"(tl v_s) from v_s occur_exactly_in (NTH 1 (e_s::bool list))"
|
wenzelm@60306
|
428 |
" v_s from v_s occur_exactly_in (NTH 2 (e_s::bool list))"
|
wenzelm@60306
|
429 |
Find: "solution ss'''"
|
wenzelm@60306
|
430 |
|
wenzelm@60306
|
431 |
problem pbl_equsys_lin_2x2_norm : "normalise/2x2/LINEAR/system" =
|
wenzelm@60306
|
432 |
\<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
|
wenzelm@60306
|
433 |
Method: "EqSystem/normalise/2x2"
|
wenzelm@60306
|
434 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
435 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
436 |
Find: "solution ss'''"
|
wenzelm@60306
|
437 |
|
wenzelm@60306
|
438 |
problem pbl_equsys_lin_3x3 : "3x3/LINEAR/system" =
|
wenzelm@60306
|
439 |
\<open>Rule_Set.append_rules "prls_3x3_linear_system" Rule_Set.empty
|
wenzelm@60306
|
440 |
[\<^rule_thm>\<open>LENGTH_CONS\<close>,
|
wenzelm@60306
|
441 |
\<^rule_thm>\<open>LENGTH_NIL\<close>,
|
wenzelm@60306
|
442 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
|
wenzelm@60306
|
443 |
\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_")]\<close>
|
wenzelm@60306
|
444 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
445 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
446 |
Where: "Length (e_s:: bool list) = 3" "Length v_s = 3"
|
wenzelm@60306
|
447 |
Find: "solution ss'''"
|
wenzelm@60306
|
448 |
|
wenzelm@60306
|
449 |
problem pbl_equsys_lin_4x4 : "4x4/LINEAR/system" =
|
wenzelm@60306
|
450 |
\<open>Rule_Set.append_rules "prls_4x4_linear_system" Rule_Set.empty
|
wenzelm@60306
|
451 |
[\<^rule_thm>\<open>LENGTH_CONS\<close>,
|
wenzelm@60306
|
452 |
\<^rule_thm>\<open>LENGTH_NIL\<close>,
|
wenzelm@60306
|
453 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
|
wenzelm@60306
|
454 |
\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_")]\<close>
|
wenzelm@60306
|
455 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
456 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
457 |
Where: "Length (e_s:: bool list) = 4" "Length v_s = 4"
|
wenzelm@60306
|
458 |
Find: "solution ss'''"
|
wenzelm@60306
|
459 |
|
wenzelm@60306
|
460 |
problem pbl_equsys_lin_4x4_tri : "triangular/4x4/LINEAR/system" =
|
wenzelm@60306
|
461 |
\<open>Rule_Set.append_rules "prls_tri_4x4_lin_sys" prls_triangular
|
wenzelm@60306
|
462 |
[\<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in "")]\<close>
|
wenzelm@60306
|
463 |
Method: "EqSystem/top_down_substitution/4x4"
|
wenzelm@60306
|
464 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
465 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
466 |
Where: (*accepts missing variables up to diagional form*)
|
wenzelm@60306
|
467 |
"(NTH 1 (v_s::real list)) occurs_in (NTH 1 (e_s::bool list))"
|
wenzelm@60306
|
468 |
"(NTH 2 (v_s::real list)) occurs_in (NTH 2 (e_s::bool list))"
|
wenzelm@60306
|
469 |
"(NTH 3 (v_s::real list)) occurs_in (NTH 3 (e_s::bool list))"
|
wenzelm@60306
|
470 |
"(NTH 4 (v_s::real list)) occurs_in (NTH 4 (e_s::bool list))"
|
wenzelm@60306
|
471 |
Find: "solution ss'''"
|
wenzelm@60306
|
472 |
|
wenzelm@60306
|
473 |
problem pbl_equsys_lin_4x4_norm : "normalise/4x4/LINEAR/system" =
|
wenzelm@60306
|
474 |
\<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
|
wenzelm@60306
|
475 |
Method: "EqSystem/normalise/4x4"
|
wenzelm@60306
|
476 |
CAS: "solveSystem e_s v_s"
|
wenzelm@60306
|
477 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60306
|
478 |
(*Length is checked 1 level above*)
|
wenzelm@60306
|
479 |
Find: "solution ss'''"
|
neuper@37954
|
480 |
|
wneuper@59472
|
481 |
ML \<open>
|
neuper@37997
|
482 |
(*this is for NTH only*)
|
walther@59851
|
483 |
val srls = Rule_Def.Repeat {id="srls_normalise_4x4",
|
neuper@37954
|
484 |
preconds = [],
|
neuper@37954
|
485 |
rew_ord = ("termlessI",termlessI),
|
walther@59852
|
486 |
erls = Rule_Set.append_rules "erls_in_srls_IntegrierenUnd.." Rule_Set.empty
|
neuper@37997
|
487 |
[(*for asm in NTH_CONS ...*)
|
wenzelm@60294
|
488 |
\<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
|
neuper@37997
|
489 |
(*2nd NTH_CONS pushes n+-1 into asms*)
|
wenzelm@60294
|
490 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_")
|
neuper@37954
|
491 |
],
|
walther@59851
|
492 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
wenzelm@60297
|
493 |
rules = [\<^rule_thm>\<open>NTH_CONS\<close>,
|
wenzelm@60294
|
494 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
|
wenzelm@60297
|
495 |
\<^rule_thm>\<open>NTH_NIL\<close>],
|
walther@59878
|
496 |
scr = Rule.Empty_Prog};
|
wneuper@59472
|
497 |
\<close>
|
neuper@37954
|
498 |
|
walther@60023
|
499 |
section \<open>Methods\<close>
|
walther@60023
|
500 |
|
wenzelm@60303
|
501 |
method met_eqsys : "EqSystem" =
|
wenzelm@60303
|
502 |
\<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [], srls = Rule_Set.Empty, prls = Rule_Set.Empty, crls = Rule_Set.Empty,
|
wenzelm@60303
|
503 |
errpats = [], nrls = Rule_Set.Empty}\<close>
|
wenzelm@60303
|
504 |
|
wenzelm@60303
|
505 |
method met_eqsys_topdown : "EqSystem/top_down_substitution" =
|
wenzelm@60303
|
506 |
\<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [], srls = Rule_Set.Empty, prls = Rule_Set.Empty, crls = Rule_Set.Empty,
|
wenzelm@60303
|
507 |
errpats = [], nrls = Rule_Set.Empty}\<close>
|
wneuper@59545
|
508 |
|
wneuper@59504
|
509 |
partial_function (tailrec) solve_system :: "bool list => real list => bool list"
|
wneuper@59504
|
510 |
where
|
walther@59635
|
511 |
"solve_system e_s v_s = (
|
walther@59635
|
512 |
let
|
walther@59635
|
513 |
e_1 = Take (hd e_s);
|
walther@59635
|
514 |
e_1 = (
|
walther@59637
|
515 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''isolate_bdvs'')) #>
|
walther@59635
|
516 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System''))
|
walther@59635
|
517 |
) e_1;
|
walther@59635
|
518 |
e_2 = Take (hd (tl e_s));
|
walther@59635
|
519 |
e_2 = (
|
walther@59637
|
520 |
(Substitute [e_1]) #>
|
walther@59637
|
521 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System_parenthesized'' )) #>
|
walther@59637
|
522 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''isolate_bdvs'' )) #>
|
walther@59635
|
523 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System'' ))
|
walther@59635
|
524 |
) e_2;
|
walther@59635
|
525 |
e__s = Take [e_1, e_2]
|
walther@59635
|
526 |
in
|
walther@59635
|
527 |
Try (Rewrite_Set ''order_system'' ) e__s) "
|
wenzelm@60303
|
528 |
|
wenzelm@60303
|
529 |
method met_eqsys_topdown_2x2 : "EqSystem/top_down_substitution/2x2" =
|
wenzelm@60303
|
530 |
\<open>{rew_ord'="ord_simplify_System", rls' = Rule_Set.Empty, calc = [],
|
wenzelm@60303
|
531 |
srls = Rule_Set.append_rules "srls_top_down_2x2" Rule_Set.empty
|
wenzelm@60303
|
532 |
[\<^rule_thm>\<open>hd_thm\<close>,
|
wenzelm@60303
|
533 |
\<^rule_thm>\<open>tl_Cons\<close>,
|
wenzelm@60303
|
534 |
\<^rule_thm>\<open>tl_Nil\<close>],
|
wenzelm@60303
|
535 |
prls = prls_triangular, crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
|
wenzelm@60303
|
536 |
Program: solve_system.simps
|
wenzelm@60303
|
537 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60303
|
538 |
Where:
|
wenzelm@60303
|
539 |
"(tl v_s) from v_s occur_exactly_in (NTH 1 (e_s::bool list))"
|
wenzelm@60303
|
540 |
" v_s from v_s occur_exactly_in (NTH 2 (e_s::bool list))"
|
wenzelm@60303
|
541 |
Find: "solution ss'''"
|
wenzelm@60303
|
542 |
|
wenzelm@60303
|
543 |
method met_eqsys_norm : "EqSystem/normalise" =
|
wenzelm@60303
|
544 |
\<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [], srls = Rule_Set.Empty, prls = Rule_Set.Empty, crls = Rule_Set.Empty,
|
wenzelm@60303
|
545 |
errpats = [], nrls = Rule_Set.Empty}\<close>
|
wneuper@59545
|
546 |
|
wneuper@59504
|
547 |
partial_function (tailrec) solve_system2 :: "bool list => real list => bool list"
|
wneuper@59504
|
548 |
where
|
walther@59635
|
549 |
"solve_system2 e_s v_s = (
|
walther@59635
|
550 |
let
|
walther@59635
|
551 |
e__s = (
|
walther@59637
|
552 |
(Try (Rewrite_Set ''norm_Rational'' )) #>
|
walther@59637
|
553 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System_parenthesized'' )) #>
|
walther@59637
|
554 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''isolate_bdvs'' )) #>
|
walther@59637
|
555 |
(Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System_parenthesized'' )) #>
|
walther@59635
|
556 |
(Try (Rewrite_Set ''order_system'' ))
|
walther@59635
|
557 |
) e_s
|
walther@59635
|
558 |
in
|
walther@59635
|
559 |
SubProblem (''EqSystem'', [''LINEAR'', ''system''], [''no_met''])
|
walther@59635
|
560 |
[BOOL_LIST e__s, REAL_LIST v_s])"
|
wenzelm@60303
|
561 |
|
wenzelm@60303
|
562 |
method met_eqsys_norm_2x2 : "EqSystem/normalise/2x2" =
|
wenzelm@60303
|
563 |
\<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [],
|
wenzelm@60303
|
564 |
srls = Rule_Set.append_rules "srls_normalise_2x2" Rule_Set.empty
|
wenzelm@60303
|
565 |
[\<^rule_thm>\<open>hd_thm\<close>,
|
wenzelm@60303
|
566 |
\<^rule_thm>\<open>tl_Cons\<close>,
|
wenzelm@60303
|
567 |
\<^rule_thm>\<open>tl_Nil\<close>],
|
wenzelm@60303
|
568 |
prls = Rule_Set.Empty, crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
|
wenzelm@60303
|
569 |
Program: solve_system2.simps
|
wenzelm@60303
|
570 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60303
|
571 |
Find: "solution ss'''"
|
wneuper@59545
|
572 |
|
wneuper@59504
|
573 |
partial_function (tailrec) solve_system3 :: "bool list => real list => bool list"
|
wneuper@59504
|
574 |
where
|
walther@59635
|
575 |
"solve_system3 e_s v_s = (
|
walther@59635
|
576 |
let
|
walther@59635
|
577 |
e__s = (
|
walther@59637
|
578 |
(Try (Rewrite_Set ''norm_Rational'' )) #>
|
walther@59637
|
579 |
(Repeat (Rewrite ''commute_0_equality'' )) #>
|
walther@59635
|
580 |
(Try (Rewrite_Set_Inst [(''bdv_1'', NTH 1 v_s), (''bdv_2'', NTH 2 v_s ),
|
walther@59637
|
581 |
(''bdv_3'', NTH 3 v_s), (''bdv_3'', NTH 4 v_s )] ''simplify_System_parenthesized'' )) #>
|
walther@59635
|
582 |
(Try (Rewrite_Set_Inst [(''bdv_1'', NTH 1 v_s), (''bdv_2'', NTH 2 v_s ),
|
walther@59637
|
583 |
(''bdv_3'', NTH 3 v_s), (''bdv_3'', NTH 4 v_s )] ''isolate_bdvs_4x4'' )) #>
|
walther@59635
|
584 |
(Try (Rewrite_Set_Inst [(''bdv_1'', NTH 1 v_s), (''bdv_2'', NTH 2 v_s ),
|
walther@59637
|
585 |
(''bdv_3'', NTH 3 v_s), (''bdv_3'', NTH 4 v_s )] ''simplify_System_parenthesized'' )) #>
|
walther@59635
|
586 |
(Try (Rewrite_Set ''order_system''))
|
walther@59635
|
587 |
) e_s
|
walther@59635
|
588 |
in
|
walther@59635
|
589 |
SubProblem (''EqSystem'', [''LINEAR'', ''system''], [''no_met''])
|
walther@59635
|
590 |
[BOOL_LIST e__s, REAL_LIST v_s])"
|
wenzelm@60303
|
591 |
|
wenzelm@60303
|
592 |
method met_eqsys_norm_4x4 : "EqSystem/normalise/4x4" =
|
wenzelm@60303
|
593 |
\<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [],
|
wenzelm@60303
|
594 |
srls =
|
wenzelm@60303
|
595 |
Rule_Set.append_rules "srls_normalise_4x4" srls
|
wenzelm@60303
|
596 |
[\<^rule_thm>\<open>hd_thm\<close>, \<^rule_thm>\<open>tl_Cons\<close>, \<^rule_thm>\<open>tl_Nil\<close>],
|
wenzelm@60303
|
597 |
prls = Rule_Set.Empty, crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
|
wenzelm@60303
|
598 |
Program: solve_system3.simps
|
wenzelm@60303
|
599 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60303
|
600 |
Find: "solution ss'''"
|
wenzelm@60303
|
601 |
(*STOPPED.WN06? met ["EqSystem", "normalise", "4x4"] #>#>#>#>#>#>#>#>#>#>#>#>#>@*)
|
wneuper@59545
|
602 |
|
wneuper@59504
|
603 |
partial_function (tailrec) solve_system4 :: "bool list => real list => bool list"
|
wneuper@59504
|
604 |
where
|
walther@59635
|
605 |
"solve_system4 e_s v_s = (
|
walther@59635
|
606 |
let
|
walther@59635
|
607 |
e_1 = NTH 1 e_s;
|
walther@59635
|
608 |
e_2 = Take (NTH 2 e_s);
|
walther@59635
|
609 |
e_2 = (
|
walther@59637
|
610 |
(Substitute [e_1]) #>
|
walther@59635
|
611 |
(Try (Rewrite_Set_Inst [(''bdv_1'',NTH 1 v_s), (''bdv_2'',NTH 2 v_s),
|
walther@59637
|
612 |
(''bdv_3'',NTH 3 v_s), (''bdv_4'',NTH 4 v_s)] ''simplify_System_parenthesized'' )) #>
|
walther@59635
|
613 |
(Try (Rewrite_Set_Inst [(''bdv_1'',NTH 1 v_s), (''bdv_2'',NTH 2 v_s),
|
walther@59637
|
614 |
(''bdv_3'',NTH 3 v_s), (''bdv_4'',NTH 4 v_s)] ''isolate_bdvs'' )) #>
|
walther@59635
|
615 |
(Try (Rewrite_Set_Inst [(''bdv_1'',NTH 1 v_s), (''bdv_2'',NTH 2 v_s),
|
walther@59635
|
616 |
(''bdv_3'',NTH 3 v_s), (''bdv_4'',NTH 4 v_s)] ''norm_Rational'' ))
|
walther@59635
|
617 |
) e_2
|
walther@59635
|
618 |
in
|
walther@59635
|
619 |
[e_1, e_2, NTH 3 e_s, NTH 4 e_s])"
|
wenzelm@60303
|
620 |
|
wenzelm@60303
|
621 |
method met_eqsys_topdown_4x4 : "EqSystem/top_down_substitution/4x4" =
|
wenzelm@60303
|
622 |
\<open>{rew_ord'="ord_simplify_System", rls' = Rule_Set.Empty, calc = [],
|
wenzelm@60303
|
623 |
srls = Rule_Set.append_rules "srls_top_down_4x4" srls [],
|
wenzelm@60303
|
624 |
prls = Rule_Set.append_rules "prls_tri_4x4_lin_sys" prls_triangular
|
wenzelm@60303
|
625 |
[\<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in "")],
|
wenzelm@60303
|
626 |
crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
|
wenzelm@60303
|
627 |
(*FIXXXXME.WN060916: this script works ONLY for exp 7.79 #>#>#>#>#>#>#>#>#>#>*)
|
wenzelm@60303
|
628 |
Program: solve_system4.simps
|
wenzelm@60303
|
629 |
Given: "equalities e_s" "solveForVars v_s"
|
wenzelm@60303
|
630 |
Where: (*accepts missing variables up to diagonal form*)
|
wenzelm@60303
|
631 |
"(NTH 1 (v_s::real list)) occurs_in (NTH 1 (e_s::bool list))"
|
wenzelm@60303
|
632 |
"(NTH 2 (v_s::real list)) occurs_in (NTH 2 (e_s::bool list))"
|
wenzelm@60303
|
633 |
"(NTH 3 (v_s::real list)) occurs_in (NTH 3 (e_s::bool list))"
|
wenzelm@60303
|
634 |
"(NTH 4 (v_s::real list)) occurs_in (NTH 4 (e_s::bool list))"
|
wenzelm@60303
|
635 |
Find: "solution ss'''"
|
wenzelm@60303
|
636 |
|
wenzelm@60303
|
637 |
ML \<open>
|
walther@60278
|
638 |
\<close> ML \<open>
|
walther@60278
|
639 |
\<close> ML \<open>
|
wneuper@59472
|
640 |
\<close>
|
walther@60278
|
641 |
end
|