
neuper@37906: (* equational systems, minimal -- for use in Biegelinie
neuper@37906:    author: Walther Neuper
neuper@37906:    050826,
neuper@37906:    (c) due to copyright terms
neuper@37906: *)
neuper@37906: 
neuper@37997: theory EqSystem imports Integrate Rational Root begin
neuper@37906: 
neuper@37906: consts
neuper@37906: 
walther@60278:   occur_exactly_in :: 
neuper@37998:    "[real list, real list, 'a] => bool" ("_ from _ occur'_exactly'_in _")
neuper@37906: 
neuper@37906:   (*descriptions in the related problems*)
neuper@37997:   solveForVars       :: "real list => toreall"
neuper@37997:   solution           :: "bool list => toreall"
neuper@37906: 
neuper@37906:   (*the CAS-command, eg. "solveSystem [x+y=1,y=2] [x,y]"*)
neuper@37906:   solveSystem        :: "[bool list, real list] => bool list"
neuper@37906: 
walther@60377: lemma commute_0_equality : \<open>(0 = a) = (a = 0)\<close>
walther@60377:   by auto
walther@60377: 
neuper@52148: axiomatization where
neuper@37906:   (*WN0510 see simliar rules 'isolate_' 'separate_' (by RL)
neuper@37906:     [bdv_1,bdv_2,bdv_3,bdv_4] work also for 2 and 3 bdvs, ugly !*)
walther@60377:   (* these require lemmas about occur_exactly_in* )
walther@60377:   lemma xxx : 
walther@60377:     \<open>[| [] from [bdv_1, bdv_2, bdv_3, bdv_4] occur_exactly_in a |] ==> (a + b = c) = (b = c + -1 * a)\<close>
walther@60377:     by auto
walther@60377:   ( **)
neuper@37983:   separate_bdvs_add:   
neuper@37998:     "[| [] from [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a |] 
neuper@52148: 		      			     ==> (a + b = c) = (b = c + -1*a)" and
neuper@37983:   separate_bdvs0:
neuper@37954:     "[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in b; Not (b=!=0)  |] 
neuper@52148: 		      			     ==> (a = b) = (a + -1*b = 0)" and
neuper@37983:   separate_bdvs_add1:  
neuper@37954:     "[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in c |] 
neuper@52148: 		      			     ==> (a = b + c) = (a + -1*c = b)" and
neuper@37983:   separate_bdvs_add2:
neuper@37954:     "[| Not (some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in a) |] 
neuper@52148: 		      			     ==> (a + b = c) = (b = -1*a + c)" and
neuper@37983:   separate_bdvs_mult:  
neuper@37998:     "[| [] from [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a; Not (a=!=0) |] 
t@42197: 		      			     ==>(a * b = c) = (b = c / a)" 
neuper@55276: axiomatization where (*..if replaced by "and" we get an error in 
wneuper@59370:   ---  rewrite in [EqSystem,normalise,2x2] --- step "--- 3---";*)
t@42197:   order_system_NxN:     "[a,b] = [b,a]"
neuper@37906:   (*requires rew_ord for termination, eg. ord_simplify_Integral;
walther@60377:     works for lists of any length, interestingly !?!
walther@60377:     CONTRADICTS PROPERTIES OF LIST: take set instead*)
neuper@37906: 
wneuper@59472: ML \<open>
neuper@37954: (** eval functions **)
neuper@37954: 
neuper@37954: (*certain variables of a given list occur _all_ in a term
neuper@37954:   args: all: ..variables, which are under consideration (eg. the bound vars)
neuper@37954:         vs:  variables which must be in t, 
neuper@37954:              and none of the others in all must be in t
neuper@37954:         t: the term under consideration
neuper@37954:  *)
neuper@37954: fun occur_exactly_in vs all t =
walther@59603:     let fun occurs_in' a b = Prog_Expr.occurs_in b a
neuper@37954:     in foldl and_ (true, map (occurs_in' t) vs)
neuper@37954:        andalso not (foldl or_ (false, map (occurs_in' t) 
neuper@37954:                                           (subtract op = vs all)))
neuper@37954:     end;
neuper@37954: 
walther@60278: (*("occur_exactly_in", ("EqSystem.occur_exactly_in", 
walther@60330:                         eval_occur_exactly_in "#eval_occur_exactly_in_") )*)
walther@60278: fun eval_occur_exactly_in _ "EqSystem.occur_exactly_in"
walther@60335: 			  (p as (Const (\<^const_name>\<open>EqSystem.occur_exactly_in\<close>,_) 
neuper@37954: 				       $ vs $ all $ t)) _ =
wneuper@59389:     if occur_exactly_in (TermC.isalist2list vs) (TermC.isalist2list all) t
walther@59868:     then SOME ((UnparseC.term p) ^ " = True",
wneuper@59390: 	       HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
walther@59868:     else SOME ((UnparseC.term p) ^ " = False",
wneuper@59390: 	       HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
neuper@37954:   | eval_occur_exactly_in _ _ _ _ = NONE;
wneuper@59472: \<close>
wenzelm@60313: calculation occur_exactly_in = \<open>eval_occur_exactly_in "#eval_occur_exactly_in_"\<close>
wenzelm@60313: 
wneuper@59472: ML \<open>
neuper@37954: (** rewrite order 'ord_simplify_System' **)
neuper@37954: 
walther@59997: (* order wrt. several linear (i.e. without exponents) variables "c", "c_2",..
neuper@37954:    which leaves the monomials containing c, c_2,... at the end of an Integral
neuper@37954:    and puts the c, c_2,... rightmost within a monomial.
neuper@37954: 
neuper@37954:    WN050906 this is a quick and dirty adaption of ord_make_polynomial_in,
neuper@37954:    which was most adequate, because it uses size_of_term*)
neuper@37954: (**)
neuper@37954: local (*. for simplify_System .*)
neuper@37954: (**)
neuper@37954: open Term;  (* for type order = EQUAL | LESS | GREATER *)
neuper@37954: 
neuper@37954: fun pr_ord EQUAL = "EQUAL"
neuper@37954:   | pr_ord LESS  = "LESS"
neuper@37954:   | pr_ord GREATER = "GREATER";
neuper@37954: 
neuper@37954: fun dest_hd' (Const (a, T)) = (((a, 0), T), 0)
neuper@37954:   | dest_hd' (Free (ccc, T)) =
neuper@40836:     (case Symbol.explode ccc of
neuper@37954: 	"c"::[] => ((("|||||||||||||||||||||", 0), T), 1)(*greatest string WN*)
neuper@37954:       | "c"::"_"::_ => ((("|||||||||||||||||||||", 0), T), 1)
neuper@37954:       | _ => (((ccc, 0), T), 1))
neuper@37954:   | dest_hd' (Var v) = (v, 2)
neuper@37954:   | dest_hd' (Bound i) = ((("", i), dummyT), 3)
walther@60269:   | dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4)
walther@60269:   | dest_hd' _ = raise ERROR "dest_hd': uncovered case in fun.def.";
neuper@37954: 
neuper@37954: fun size_of_term' (Free (ccc, _)) =
neuper@40836:     (case Symbol.explode ccc of (*WN0510 hack for the bound variables*)
neuper@37954: 	"c"::[] => 1000
wneuper@59390:       | "c"::"_"::is => 1000 * ((TermC.int_of_str o implode) is)
neuper@37954:       | _ => 1)
neuper@37954:   | size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
neuper@37954:   | size_of_term' (f$t) = size_of_term' f  +  size_of_term' t
neuper@37954:   | size_of_term' _ = 1;
neuper@37954: 
neuper@37997: fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) =       (* ~ term.ML *)
neuper@52070:     (case term_ord' pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord)
neuper@37997:   | term_ord' pr thy (t, u) =
neuper@52070:     (if pr
neuper@52070:      then 
neuper@52070:        let
neuper@52070:          val (f, ts) = strip_comb t and (g, us) = strip_comb u;
walther@60375:          val _ = tracing ("t= f @ ts= \"" ^ UnparseC.term_in_thy thy f ^ "\" @ \"[" ^
walther@59870:            commas (map (UnparseC.term_in_thy thy) ts) ^ "]\"");
walther@60375:          val _ = tracing ("u= g @ us= \"" ^ UnparseC.term_in_thy thy g ^ "\" @ \"[" ^
walther@59870:            commas (map (UnparseC.term_in_thy thy) us) ^ "]\"");
walther@60375:          val _ = tracing ("size_of_term (t, u) = (" ^ string_of_int (size_of_term' t) ^ ", " ^
neuper@52070:            string_of_int (size_of_term' u) ^ ")");
walther@60375:          val _ = tracing ("hd_ord (f, g)      = " ^ ((pr_ord o hd_ord) (f, g)) );
walther@60375:     (** )val _ = @{print tracing}{a = "hd_ord (f, g)      = ", z = hd_ord (f, g)}( **)
walther@60375:          val _ = tracing ("terms_ord (ts, us) = " ^(pr_ord o terms_ord str false) (ts,us));
walther@60375:          val _= tracing ("-------");
neuper@52070:        in () end
neuper@52070:      else ();
neuper@52070:     case int_ord (size_of_term' t, size_of_term' u) of
neuper@52070:       EQUAL =>
neuper@52070:         let val (f, ts) = strip_comb t and (g, us) = strip_comb u 
neuper@52070:         in (case hd_ord (f, g) of 
neuper@52070:               EQUAL => (terms_ord str pr) (ts, us) 
neuper@52070:             | ord => ord)
neuper@52070:         end
neuper@37954: 	 | ord => ord)
neuper@37954: and hd_ord (f, g) =                                        (* ~ term.ML *)
neuper@52070:   prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord (dest_hd' f, dest_hd' g)
walther@60269: and terms_ord _ pr (ts, us) = list_ord (term_ord' pr (ThyC.get_theory "Isac_Knowledge"))(ts, us);
neuper@37954: (**)
neuper@37954: in
neuper@37954: (**)
neuper@37954: (*WN0510 for preliminary use in eval_order_system, see case-study mat-eng.tex
neuper@37954: fun ord_simplify_System_rev (pr:bool) thy subst tu = 
neuper@37954:     (term_ord' pr thy (Library.swap tu) = LESS);*)
neuper@37954: 
neuper@37954: (*for the rls's*)
walther@60324: fun ord_simplify_System (pr:bool) thy _(*subst*) (ts, us) = 
walther@60324:     (term_ord' pr thy (TermC.numerals_to_Free ts, TermC.numerals_to_Free us) = LESS);
Walther@60506: 
Walther@60506: (**)end;(**)
Walther@60506: \<close> ML \<open>
wneuper@59472: \<close>
Walther@60506: setup \<open>KEStore_Elems.add_rew_ord [
Walther@60506:   ("ord_simplify_System", ord_simplify_System false \<^theory>)]\<close>
Walther@60506: 
wneuper@59472: ML \<open>
neuper@37954: (** rulesets **)
neuper@37954: 
neuper@37954: (*.adapted from 'order_add_mult_in' by just replacing the rew_ord.*)
neuper@37954: val order_add_mult_System = 
walther@60358:   Rule_Def.Repeat{
walther@60358:     id = "order_add_mult_System", preconds = [], 
walther@60358:     rew_ord = ("ord_simplify_System", ord_simplify_System false @{theory "Integrate"}),
walther@60358:     erls = Rule_Set.empty,srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [
walther@60358:       \<^rule_thm>\<open>mult.commute\<close>, (* z * w = w * z *)
walther@60358:       \<^rule_thm>\<open>real_mult_left_commute\<close>, (*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
walther@60358:       \<^rule_thm>\<open>mult.assoc\<close>,	 (*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
walther@60358:       \<^rule_thm>\<open>add.commute\<close>, (*z + w = w + z*)
walther@60358:       \<^rule_thm>\<open>add.left_commute\<close>, (*x + (y + z) = y + (x + z)*)
walther@60358:       \<^rule_thm>\<open>add.assoc\<close>	],  (*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
walther@60358:     scr = Rule.Empty_Prog};
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37954: (*.adapted from 'norm_Rational' by
neuper@37954:   #1 using 'ord_simplify_System' in 'order_add_mult_System'
neuper@37954:   #2 NOT using common_nominator_p                          .*)
neuper@37954: val norm_System_noadd_fractions = 
walther@59851:   Rule_Def.Repeat {id = "norm_System_noadd_fractions", preconds = [], 
walther@60358:     rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), 
walther@60358:     erls = norm_rat_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [(*sequence given by operator precedence*)
walther@60358:   		Rule.Rls_ discard_minus,
walther@60358:   		Rule.Rls_ powers,
walther@60358:   		Rule.Rls_ rat_mult_divide,
walther@60358:   		Rule.Rls_ expand,
walther@60358:   		Rule.Rls_ reduce_0_1_2,
walther@60358:   		Rule.Rls_ (*order_add_mult #1*) order_add_mult_System,
walther@60358:   		Rule.Rls_ collect_numerals,
walther@60358:   		(*Rule.Rls_ add_fractions_p, #2*)
walther@60358:   		Rule.Rls_ cancel_p],
walther@60358:     scr = Rule.Empty_Prog};
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37954: (*.adapted from 'norm_Rational' by
neuper@37954:   *1* using 'ord_simplify_System' in 'order_add_mult_System'.*)
neuper@37954: val norm_System = 
walther@59851:   Rule_Def.Repeat {id = "norm_System", preconds = [], 
walther@60358:     rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord), 
walther@60358:     erls = norm_rat_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [(*sequence given by operator precedence*)
walther@60358:   		Rule.Rls_ discard_minus,
walther@60358:   		Rule.Rls_ powers,
walther@60358:   		Rule.Rls_ rat_mult_divide,
walther@60358:   		Rule.Rls_ expand,
walther@60358:   		Rule.Rls_ reduce_0_1_2,
walther@60358:   		Rule.Rls_ (*order_add_mult *1*) order_add_mult_System,
walther@60358:   		Rule.Rls_ collect_numerals,
walther@60358:   		Rule.Rls_ add_fractions_p,
walther@60358:   		Rule.Rls_ cancel_p],
walther@60358:     scr = Rule.Empty_Prog};
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37954: (*.simplify an equational system BEFORE solving it such that parentheses are
neuper@37954:    ( ((u0*v0)*w0) + ( ((u1*v1)*w1) * c + ... +((u4*v4)*w4) * c_4 ) )
neuper@37954: ATTENTION: works ONLY for bound variables c, c_1, c_2, c_3, c_4 :ATTENTION
neuper@37954:    This is a copy from 'make_ratpoly_in' with respective reductions:
neuper@37954:    *0* expand the term, ie. distribute * and / over +
neuper@37954:    *1* ord_simplify_System instead of termlessI
neuper@37954:    *2* no add_fractions_p (= common_nominator_p_rls !)
neuper@37954:    *3* discard_parentheses only for (.*(.*.))
neuper@37954:    analoguous to simplify_Integral                                       .*)
neuper@37954: val simplify_System_parenthesized = 
walther@59878:   Rule_Set.Sequence {id = "simplify_System_parenthesized", preconds = []:term list, 
walther@60358:     rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@60358:     erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [
walther@60358:        \<^rule_thm>\<open>distrib_right\<close>, (*"(?z1.0 + ?z2.0) * ?w = ?z1.0 * ?w + ?z2.0 * ?w"*)
walther@60358: 	     \<^rule_thm>\<open>add_divide_distrib\<close>, (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)
walther@60358: 	     Rule.Rls_ norm_Rational_noadd_fractions,
walther@60358: 	     Rule.Rls_ (*order_add_mult_in*) norm_System_noadd_fractions,
walther@60358: 	     \<^rule_thm_sym>\<open>mult.assoc\<close>,
walther@60358: 	     Rule.Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
walther@60358: 	     Rule.Rls_ separate_bdv2,
walther@60358: 	     \<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e")],
walther@60358:     scr = Rule.Empty_Prog};      
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37954: (*.simplify an equational system AFTER solving it;
neuper@37954:    This is a copy of 'make_ratpoly_in' with the differences
neuper@37954:    *1* ord_simplify_System instead of termlessI           .*)
neuper@37954: (*TODO.WN051031 ^^^^^^^^^^ should be in EACH rls contained *)
neuper@37954: val simplify_System = 
walther@59878:   Rule_Set.Sequence {id = "simplify_System", preconds = []:term list, 
walther@60358:     rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@60358:     erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [
walther@60358:       Rule.Rls_ norm_Rational,
walther@60358: 	    Rule.Rls_ (*order_add_mult_in*) norm_System (**1**),
walther@60358: 	    Rule.Rls_ discard_parentheses,
walther@60358: 	    Rule.Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
walther@60358: 	    Rule.Rls_ separate_bdv2,
walther@60358: 	    \<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e")],
walther@60358:     scr = Rule.Empty_Prog};      
neuper@37906: (*
neuper@37954: val simplify_System = 
walther@59852:     Rule_Set.append_rules "simplify_System" simplify_System_parenthesized
wenzelm@60296: 	       [\<^rule_thm_sym>\<open>add.assoc\<close>];
neuper@37954: *)
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37954: val isolate_bdvs = 
walther@60358:   Rule_Def.Repeat {
walther@60358:     id="isolate_bdvs", preconds = [], rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord), 
walther@60358:     erls = Rule_Set.append_rules "erls_isolate_bdvs" Rule_Set.empty [
walther@60358:       (\<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_"))], 
walther@60358:     srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [
walther@60358:       \<^rule_thm>\<open>commute_0_equality\<close>,
walther@60358:       \<^rule_thm>\<open>separate_bdvs_add\<close>,
walther@60358:       \<^rule_thm>\<open>separate_bdvs_mult\<close>],
walther@60358:     scr = Rule.Empty_Prog};
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37954: val isolate_bdvs_4x4 = 
walther@60358:   Rule_Def.Repeat {id="isolate_bdvs_4x4", preconds = [], 
walther@60358:     rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord), 
walther@60358:     erls = Rule_Set.append_rules "erls_isolate_bdvs_4x4" Rule_Set.empty [
walther@60358:       \<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_"),
walther@60358:       \<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
walther@60358:       \<^rule_eval>\<open>Prog_Expr.some_occur_in\<close> (Prog_Expr.eval_some_occur_in "#some_occur_in_"),
walther@60358:       \<^rule_thm>\<open>not_true\<close>,
walther@60358:       \<^rule_thm>\<open>not_false\<close>], 
walther@60358:     srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [
walther@60358:       \<^rule_thm>\<open>commute_0_equality\<close>,
walther@60358:       \<^rule_thm>\<open>separate_bdvs0\<close>,
walther@60358:       \<^rule_thm>\<open>separate_bdvs_add1\<close>,
walther@60358:       \<^rule_thm>\<open>separate_bdvs_add2\<close>,
walther@60358:       \<^rule_thm>\<open>separate_bdvs_mult\<close>],
walther@60358:     scr = Rule.Empty_Prog};
neuper@37954: 
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37997: 
neuper@37954: (*.order the equations in a system such, that a triangular system (if any)
neuper@37954:    appears as [..c_4 = .., ..., ..., ..c_1 + ..c_2 + ..c_3 ..c_4 = ..].*)
neuper@37954: val order_system = 
walther@60358:   Rule_Def.Repeat {id="order_system", preconds = [], 
walther@60358: 	  rew_ord = ("ord_simplify_System", ord_simplify_System false \<^theory>), 
walther@60358: 	  erls = Rule_Set.Empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358: 	  rules = [
walther@60358:       \<^rule_thm>\<open>order_system_NxN\<close>],
walther@60358: 	  scr = Rule.Empty_Prog};
neuper@37954: 
neuper@37954: val prls_triangular = 
walther@60358:   Rule_Def.Repeat {
walther@60358:     id="prls_triangular", preconds = [], rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord), 
walther@60358:     erls = Rule_Def.Repeat {
walther@60358:       id="erls_prls_triangular", preconds = [], rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord), 
walther@60358:       erls = Rule_Set.Empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:       rules = [(*for precond NTH_CONS ...*)
walther@60358:          \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
walther@60358:          \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
walther@60358:          \<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_")],
walther@60358:          (*immediately repeated rewrite pushes '+' into precondition !*)
walther@60358:       scr = Rule.Empty_Prog}, 
walther@60358:     srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [
walther@60358:       \<^rule_thm>\<open>NTH_CONS\<close>,
walther@60358:       \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
walther@60358:       \<^rule_thm>\<open>NTH_NIL\<close>,
walther@60358:       \<^rule_thm>\<open>tl_Cons\<close>,
walther@60358:       \<^rule_thm>\<open>tl_Nil\<close>,
walther@60358:       \<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_")],
walther@60358:     scr = Rule.Empty_Prog};
wneuper@59472: \<close>
wneuper@59472: ML \<open>
neuper@37954: 
neuper@37954: (*WN060914 quickly created for 4x4; 
neuper@37954:  more similarity to prls_triangular desirable*)
neuper@37954: val prls_triangular4 = 
walther@60358:   Rule_Def.Repeat {
walther@60358:   id="prls_triangular4", preconds = [], rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord), 
walther@60358:   erls = Rule_Def.Repeat {
walther@60358:     id="erls_prls_triangular4", preconds = [], rew_ord = ("e_rew_ord", Rewrite_Ord.e_rew_ord), 
walther@60358:     erls = Rule_Set.Empty, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:     rules = [(*for precond NTH_CONS ...*)
walther@60358:   	   \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
walther@60358:   	   \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_")],
walther@60358:   	   (*immediately repeated rewrite pushes '+' into precondition !*)
walther@60358:     scr = Rule.Empty_Prog}, 
walther@60358:   srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358:   rules = [
walther@60358:     \<^rule_thm>\<open>NTH_CONS\<close>,
walther@60358:     \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
walther@60358:     \<^rule_thm>\<open>NTH_NIL\<close>,
walther@60358:     \<^rule_thm>\<open>tl_Cons\<close>,
walther@60358:     \<^rule_thm>\<open>tl_Nil\<close>,
walther@60358:     \<^rule_eval>\<open>occur_exactly_in\<close> (eval_occur_exactly_in "#eval_occur_exactly_in_")],
walther@60358:   scr = Rule.Empty_Prog};
wneuper@59472: \<close>
t@42197: 
wenzelm@60289: rule_set_knowledge
wenzelm@60286:   simplify_System_parenthesized = \<open>prep_rls' simplify_System_parenthesized\<close> and
wenzelm@60286:   simplify_System = \<open>prep_rls' simplify_System\<close> and
wenzelm@60286:   isolate_bdvs = \<open>prep_rls' isolate_bdvs\<close> and
wenzelm@60286:   isolate_bdvs_4x4 = \<open>prep_rls' isolate_bdvs_4x4\<close> and 
wenzelm@60286:   order_system = \<open>prep_rls' order_system\<close> and 
wenzelm@60286:   order_add_mult_System = \<open>prep_rls' order_add_mult_System\<close> and
wenzelm@60286:   norm_System_noadd_fractions = \<open>prep_rls' norm_System_noadd_fractions\<close> and
wenzelm@60286:   norm_System = \<open>prep_rls' norm_System\<close>
t@42197: 
walther@60023: 
walther@60023: section \<open>Problems\<close>
walther@60023: 
wenzelm@60306: problem pbl_equsys : "system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   Find: "solution ss'''" (*''' is copy-named*)
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin : "LINEAR/system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   (*TODO.WN050929 check linearity*)
wenzelm@60306:   Find: "solution ss'''"
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin_2x2: "2x2/LINEAR/system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "prls_2x2_linear_system" Rule_Set.empty 
wenzelm@60306:     [\<^rule_thm>\<open>LENGTH_CONS\<close>,
wenzelm@60306:       \<^rule_thm>\<open>LENGTH_NIL\<close>,
wenzelm@60306:       \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
wenzelm@60306:       \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_")]\<close>
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   Where: "Length (e_s:: bool list) = 2" "Length v_s = 2"
wenzelm@60306:   Find: "solution ss'''"
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin_2x2_tri : "triangular/2x2/LINEAR/system" =
wenzelm@60306:   \<open>prls_triangular\<close>
Walther@60449:   Method_Ref: "EqSystem/top_down_substitution/2x2"
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   Where:
wenzelm@60306:     "(tl v_s) from v_s occur_exactly_in (NTH 1 (e_s::bool list))"
wenzelm@60306:     "    v_s  from v_s occur_exactly_in (NTH 2 (e_s::bool list))"
wenzelm@60306:   Find: "solution ss'''"
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin_2x2_norm : "normalise/2x2/LINEAR/system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
Walther@60449:   Method_Ref: "EqSystem/normalise/2x2"
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   Find: "solution ss'''"
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin_3x3 : "3x3/LINEAR/system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "prls_3x3_linear_system" Rule_Set.empty 
wenzelm@60306:     [\<^rule_thm>\<open>LENGTH_CONS\<close>,
wenzelm@60306:       \<^rule_thm>\<open>LENGTH_NIL\<close>,
wenzelm@60306:       \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
wenzelm@60306:       \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_")]\<close>
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   Where: "Length (e_s:: bool list) = 3" "Length v_s = 3"
wenzelm@60306:   Find: "solution ss'''"
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin_4x4 : "4x4/LINEAR/system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "prls_4x4_linear_system" Rule_Set.empty 
wenzelm@60306:     [\<^rule_thm>\<open>LENGTH_CONS\<close>,
wenzelm@60306:       \<^rule_thm>\<open>LENGTH_NIL\<close>,
wenzelm@60306:       \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
wenzelm@60306:       \<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_")]\<close>
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   Where: "Length (e_s:: bool list) = 4" "Length v_s = 4"
wenzelm@60306:   Find: "solution ss'''"
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin_4x4_tri : "triangular/4x4/LINEAR/system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "prls_tri_4x4_lin_sys" prls_triangular
wenzelm@60306:     [\<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in "")]\<close>
Walther@60449:   Method_Ref: "EqSystem/top_down_substitution/4x4"
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   Where: (*accepts missing variables up to diagional form*)
wenzelm@60306:     "(NTH 1 (v_s::real list)) occurs_in (NTH 1 (e_s::bool list))"
wenzelm@60306:     "(NTH 2 (v_s::real list)) occurs_in (NTH 2 (e_s::bool list))"
wenzelm@60306:     "(NTH 3 (v_s::real list)) occurs_in (NTH 3 (e_s::bool list))"
wenzelm@60306:     "(NTH 4 (v_s::real list)) occurs_in (NTH 4 (e_s::bool list))"
wenzelm@60306:   Find: "solution ss'''"
wenzelm@60306: 
wenzelm@60306: problem pbl_equsys_lin_4x4_norm : "normalise/4x4/LINEAR/system" =
wenzelm@60306:   \<open>Rule_Set.append_rules "empty" Rule_Set.empty [(*for preds in where_*)]\<close>
Walther@60449:   Method_Ref: "EqSystem/normalise/4x4"
wenzelm@60306:   CAS: "solveSystem e_s v_s"
wenzelm@60306:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60306:   (*Length is checked 1 level above*)
wenzelm@60306:   Find: "solution ss'''"
neuper@37954: 
wneuper@59472: ML \<open>
neuper@37997: (*this is for NTH only*)
walther@59851: val srls = Rule_Def.Repeat {id="srls_normalise_4x4", 
neuper@37954: 		preconds = [], 
neuper@37954: 		rew_ord = ("termlessI",termlessI), 
walther@59852: 		erls = Rule_Set.append_rules "erls_in_srls_IntegrierenUnd.." Rule_Set.empty
neuper@37997: 				  [(*for asm in NTH_CONS ...*)
wenzelm@60294: 				   \<^rule_eval>\<open>less\<close> (Prog_Expr.eval_equ "#less_"),
neuper@37997: 				   (*2nd NTH_CONS pushes n+-1 into asms*)
wenzelm@60294: 				   \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_")
neuper@37954: 				   ], 
walther@59851: 		srls = Rule_Set.Empty, calc = [], errpatts = [],
wenzelm@60297: 		rules = [\<^rule_thm>\<open>NTH_CONS\<close>,
wenzelm@60294: 			 \<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
wenzelm@60297: 			 \<^rule_thm>\<open>NTH_NIL\<close>],
walther@59878: 		scr = Rule.Empty_Prog};
wneuper@59472: \<close>
neuper@37954: 
walther@60023: section \<open>Methods\<close>
walther@60023: 
wenzelm@60303: method met_eqsys : "EqSystem" =
wenzelm@60303:   \<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [], srls = Rule_Set.Empty, prls = Rule_Set.Empty, crls = Rule_Set.Empty,
wenzelm@60303:     errpats = [], nrls = Rule_Set.Empty}\<close>
wenzelm@60303: 
wenzelm@60303: method met_eqsys_topdown : "EqSystem/top_down_substitution" =
wenzelm@60303:   \<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [], srls = Rule_Set.Empty, prls = Rule_Set.Empty, crls = Rule_Set.Empty,
wenzelm@60303:     errpats = [], nrls = Rule_Set.Empty}\<close>
wneuper@59545: 
wneuper@59504: partial_function (tailrec) solve_system :: "bool list => real list => bool list"
wneuper@59504:   where
walther@59635: "solve_system e_s v_s = (
walther@59635:   let
walther@59635:     e_1 = Take (hd e_s);                                                         
walther@59635:     e_1 = (
walther@59637:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''isolate_bdvs'')) #>                   
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System''))
walther@59635:       ) e_1;                 
walther@59635:     e_2 = Take (hd (tl e_s));                                                    
walther@59635:     e_2 = (
walther@59637:       (Substitute [e_1]) #>                                                 
walther@59637:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System_parenthesized'' )) #>      
walther@59637:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''isolate_bdvs'' )) #>                   
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System'' ))
walther@59635:       ) e_2;                 
walther@59635:     e__s = Take [e_1, e_2]                                                       
walther@59635:   in
walther@59635:     Try (Rewrite_Set ''order_system'' ) e__s)                              "
wenzelm@60303: 
wenzelm@60303: method met_eqsys_topdown_2x2 : "EqSystem/top_down_substitution/2x2" =
wenzelm@60303:   \<open>{rew_ord'="ord_simplify_System", rls' = Rule_Set.Empty, calc = [], 
wenzelm@60303:     srls = Rule_Set.append_rules "srls_top_down_2x2" Rule_Set.empty
wenzelm@60303:         [\<^rule_thm>\<open>hd_thm\<close>,
wenzelm@60303:           \<^rule_thm>\<open>tl_Cons\<close>,
wenzelm@60303:           \<^rule_thm>\<open>tl_Nil\<close>], 
wenzelm@60303:     prls = prls_triangular, crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
wenzelm@60303:   Program: solve_system.simps
wenzelm@60303:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60303:   Where:
wenzelm@60303:     "(tl v_s) from v_s occur_exactly_in (NTH 1 (e_s::bool list))"
wenzelm@60303:     "    v_s  from v_s occur_exactly_in (NTH 2 (e_s::bool list))"
wenzelm@60303:   Find: "solution ss'''"
wenzelm@60303: 
wenzelm@60303: method met_eqsys_norm : "EqSystem/normalise" =
wenzelm@60303:   \<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [], srls = Rule_Set.Empty, prls = Rule_Set.Empty, crls = Rule_Set.Empty,
wenzelm@60303:     errpats = [], nrls = Rule_Set.Empty}\<close>
wneuper@59545: 
wneuper@59504: partial_function (tailrec) solve_system2 :: "bool list => real list => bool list"
wneuper@59504:   where
walther@59635: "solve_system2 e_s v_s = (
walther@59635:   let
walther@59635:     e__s = (
walther@59637:       (Try (Rewrite_Set ''norm_Rational'' )) #>
walther@59637:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System_parenthesized'' )) #>
walther@59637:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''isolate_bdvs'' )) #>
walther@59637:       (Try (Rewrite_Set_Inst [(''bdv_1'', hd v_s), (''bdv_2'', hd (tl v_s))] ''simplify_System_parenthesized'' )) #>
walther@59635:       (Try (Rewrite_Set ''order_system'' ))
walther@59635:       ) e_s
walther@59635:   in
walther@59635:     SubProblem (''EqSystem'', [''LINEAR'', ''system''], [''no_met''])
walther@59635:       [BOOL_LIST e__s, REAL_LIST v_s])"
wenzelm@60303: 
wenzelm@60303: method met_eqsys_norm_2x2 : "EqSystem/normalise/2x2" =
wenzelm@60303:   \<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [], 
wenzelm@60303:     srls = Rule_Set.append_rules "srls_normalise_2x2" Rule_Set.empty
wenzelm@60303:         [\<^rule_thm>\<open>hd_thm\<close>,
wenzelm@60303:           \<^rule_thm>\<open>tl_Cons\<close>,
wenzelm@60303:           \<^rule_thm>\<open>tl_Nil\<close>], 
wenzelm@60303:     prls = Rule_Set.Empty, crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
wenzelm@60303:   Program: solve_system2.simps
wenzelm@60303:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60303:   Find: "solution ss'''"
wneuper@59545: 
wneuper@59504: partial_function (tailrec) solve_system3 :: "bool list => real list => bool list"
wneuper@59504:   where
walther@59635: "solve_system3 e_s v_s = (
walther@59635:   let
walther@59635:     e__s = (
walther@59637:       (Try (Rewrite_Set ''norm_Rational'' )) #>
walther@59637:       (Repeat (Rewrite ''commute_0_equality'' )) #>
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'', NTH 1 v_s), (''bdv_2'', NTH 2 v_s ),
walther@59637:         (''bdv_3'', NTH 3 v_s), (''bdv_3'', NTH 4 v_s )] ''simplify_System_parenthesized'' )) #>
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'', NTH 1 v_s), (''bdv_2'', NTH 2 v_s ),
walther@59637:         (''bdv_3'', NTH 3 v_s), (''bdv_3'', NTH 4 v_s )] ''isolate_bdvs_4x4'' )) #>
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'', NTH 1 v_s), (''bdv_2'', NTH 2 v_s ),
walther@59637:         (''bdv_3'', NTH 3 v_s), (''bdv_3'', NTH 4 v_s )] ''simplify_System_parenthesized'' )) #>
walther@59635:       (Try (Rewrite_Set ''order_system''))
walther@59635:       )  e_s
walther@59635:   in
walther@59635:     SubProblem (''EqSystem'', [''LINEAR'', ''system''], [''no_met''])
walther@59635:       [BOOL_LIST e__s, REAL_LIST v_s])"
wenzelm@60303: 
wenzelm@60303: method met_eqsys_norm_4x4 : "EqSystem/normalise/4x4" =
wenzelm@60303:   \<open>{rew_ord'="tless_true", rls' = Rule_Set.Empty, calc = [],
wenzelm@60303:     srls =
wenzelm@60303:       Rule_Set.append_rules "srls_normalise_4x4" srls
wenzelm@60303:         [\<^rule_thm>\<open>hd_thm\<close>, \<^rule_thm>\<open>tl_Cons\<close>, \<^rule_thm>\<open>tl_Nil\<close>],
wenzelm@60303:     prls = Rule_Set.Empty, crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
wenzelm@60303:   Program: solve_system3.simps
wenzelm@60303:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60303:   Find: "solution ss'''"
wenzelm@60303:   (*STOPPED.WN06? met ["EqSystem", "normalise", "4x4"] #>#>#>#>#>#>#>#>#>#>#>#>#>@*)
wneuper@59545: 
wneuper@59504: partial_function (tailrec) solve_system4 :: "bool list => real list => bool list"
wneuper@59504:   where
walther@59635: "solve_system4 e_s v_s = (
walther@59635:   let
walther@59635:     e_1 = NTH 1 e_s;
walther@59635:     e_2 = Take (NTH 2 e_s);
walther@59635:     e_2 = (
walther@59637:       (Substitute [e_1]) #>
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'',NTH 1 v_s), (''bdv_2'',NTH 2 v_s),
walther@59637:         (''bdv_3'',NTH 3 v_s), (''bdv_4'',NTH 4 v_s)] ''simplify_System_parenthesized'' )) #>
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'',NTH 1 v_s), (''bdv_2'',NTH 2 v_s),
walther@59637:         (''bdv_3'',NTH 3 v_s), (''bdv_4'',NTH 4 v_s)] ''isolate_bdvs'' )) #>
walther@59635:       (Try (Rewrite_Set_Inst [(''bdv_1'',NTH 1 v_s), (''bdv_2'',NTH 2 v_s),
walther@59635:         (''bdv_3'',NTH 3 v_s), (''bdv_4'',NTH 4 v_s)] ''norm_Rational'' ))
walther@59635:       ) e_2
walther@59635:   in
walther@59635:     [e_1, e_2, NTH 3 e_s, NTH 4 e_s])"
wenzelm@60303: 
wenzelm@60303: method met_eqsys_topdown_4x4 : "EqSystem/top_down_substitution/4x4" =
wenzelm@60303:   \<open>{rew_ord'="ord_simplify_System", rls' = Rule_Set.Empty, calc = [], 
wenzelm@60303:     srls = Rule_Set.append_rules "srls_top_down_4x4" srls [], 
wenzelm@60303:     prls = Rule_Set.append_rules "prls_tri_4x4_lin_sys" prls_triangular
walther@60358:       [\<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in "")], 
wenzelm@60303:     crls = Rule_Set.Empty, errpats = [], nrls = Rule_Set.Empty}\<close>
wenzelm@60303:   (*FIXXXXME.WN060916: this script works ONLY for exp 7.79 #>#>#>#>#>#>#>#>#>#>*)
wenzelm@60303:   Program: solve_system4.simps
wenzelm@60303:   Given: "equalities e_s" "solveForVars v_s"
wenzelm@60303:   Where: (*accepts missing variables up to diagonal form*)
wenzelm@60303:     "(NTH 1 (v_s::real list)) occurs_in (NTH 1 (e_s::bool list))"
wenzelm@60303:     "(NTH 2 (v_s::real list)) occurs_in (NTH 2 (e_s::bool list))"
wenzelm@60303:     "(NTH 3 (v_s::real list)) occurs_in (NTH 3 (e_s::bool list))"
wenzelm@60303:     "(NTH 4 (v_s::real list)) occurs_in (NTH 4 (e_s::bool list))"
wenzelm@60303:   Find: "solution ss'''"
wenzelm@60303: 
wenzelm@60303: ML \<open>
walther@60278: \<close> ML \<open>
walther@60278: \<close> ML \<open>
wneuper@59472: \<close>
walther@60278: end




