(*. (c) by Richard Lang, 2003 .*)

 (* theory collecting all knowledge for LinearEquations

    created by: rlang 

          date: 02.10

    changed by: rlang

    last change by: rlang

              date: 02.10.20

 *)

 theory LinEq imports Poly Equation begin

 consts

    Solve'_lineq'_equation

              :: "[bool,real, 

 		   bool list] => bool list"

                ("((Script Solve'_lineq'_equation (_ _ =))// 

                   (_))" 9)

 axioms

 (*-- normalize --*)

   (*WN0509 compare PolyEq.all_left "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"*)

   all_left          "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)"

   makex1_x          "a^^^1  = a"  

   real_assoc_1      "a+(b+c) = a+b+c"

   real_assoc_2      "a*(b*c) = a*b*c"

 (*-- solve --*)

   lin_isolate_add1  "(a + b*bdv = 0) = (b*bdv = (-1)*a)"

   lin_isolate_add2  "(a +   bdv = 0) = (  bdv = (-1)*a)"

   lin_isolate_div   "[|Not(b=0)|] ==> (b*bdv = c) = (bdv = c / b)"

 ML {*

 val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)

   append_rls "LinEq_prls" e_rls 

 	     [Calc ("op =",eval_equal "#equal_"),

 	      Calc ("Tools.matches",eval_matches ""),

 	      Calc ("Tools.lhs"    ,eval_lhs ""),

 	      Calc ("Tools.rhs"    ,eval_rhs ""),

 	      Calc ("Poly.has'_degree'_in",eval_has_degree_in ""),

  	      Calc ("Poly.is'_polyrat'_in",eval_is_polyrat_in ""),

 	      Calc ("Atools.occurs'_in",eval_occurs_in ""),    

 	      Calc ("Atools.ident",eval_ident "#ident_"),

 	      Thm ("not_true",num_str not_true),

 	      Thm ("not_false",num_str not_false),

 	      Thm ("and_true",num_str and_true),

 	      Thm ("and_false",num_str and_false),

 	      Thm ("or_true",num_str or_true),

 	      Thm ("or_false",num_str or_false)

               ];

 (* ----- erls ----- *)

 val LinEq_crls = 

    append_rls "LinEq_crls" poly_crls

    [Thm  ("real_assoc_1",num_str real_assoc_1)

     (*		

      Don't use

      Calc ("HOL.divide", eval_cancel "#divide_"),

      Calc ("Atools.pow" ,eval_binop "#power_"),

      *)

     ];

 (* ----- crls ----- *)

 val LinEq_erls = 

    append_rls "LinEq_erls" Poly_erls

    [Thm  ("real_assoc_1",num_str real_assoc_1)

     (*		

      Don't use

      Calc ("HOL.divide", eval_cancel "#divide_"),

      Calc ("Atools.pow" ,eval_binop "#power_"),

      *)

     ];

 ruleset' := overwritelthy thy (!ruleset',

 			[("LinEq_erls",LinEq_erls)(*FIXXXME:del with rls.rls'*)

 			 ]);

 val LinPoly_simplify = prep_rls(

   Rls {id = "LinPoly_simplify", preconds = [], 

        rew_ord = ("termlessI",termlessI), 

        erls = LinEq_erls, 

        srls = Erls, 

        calc = [], 

        (*asm_thm = [],*)

        rules = [

 		Thm  ("real_assoc_1",num_str real_assoc_1),

 		Calc ("op +",eval_binop "#add_"),

 		Calc ("op -",eval_binop "#sub_"),

 		Calc ("op *",eval_binop "#mult_"),

 		(*  Dont use  

 		 Calc ("HOL.divide", eval_cancel "#divide_"),		

 		 Calc ("Root.sqrt",eval_sqrt "#sqrt_"),

 		 *)

 		Calc ("Atools.pow" ,eval_binop "#power_")

 		],

        scr = Script ((term_of o the o (parse thy)) "empty_script")

        }:rls);

 ruleset' := overwritelthy thy (!ruleset',

 			  [("LinPoly_simplify",LinPoly_simplify)]);

 (*isolate the bound variable in an linear equation; 'bdv' is a meta-constant*)

 val LinEq_simplify = prep_rls(

 Rls {id = "LinEq_simplify", preconds = [],

      rew_ord = ("e_rew_ord",e_rew_ord),

      erls = LinEq_erls,

      srls = Erls,

      calc = [],

      (*asm_thm = [("lin_isolate_div","")],*)

      rules = [

 	      Thm("lin_isolate_add1",num_str lin_isolate_add1), 

 	      (* a+bx=0 -> bx=-a *)

 	      Thm("lin_isolate_add2",num_str lin_isolate_add2), 

 	      (* a+ x=0 ->  x=-a *)

 	      Thm("lin_isolate_div",num_str lin_isolate_div)    

 	      (*   bx=c -> x=c/b *)  

 	      ],

      scr = Script ((term_of o the o (parse thy)) "empty_script")

      }:rls);

 ruleset' := overwritelthy thy (!ruleset',

 			[("LinEq_simplify",LinEq_simplify)]);

 (*----------------------------- problem types --------------------------------*)

 (* 

 show_ptyps(); 

 (get_pbt ["linear","univariate","equation"]);

 *)

 (* ---------linear----------- *)

 store_pbt

  (prep_pbt LinEq.thy "pbl_equ_univ_lin" [] e_pblID

  (["linear","univariate","equation"],

   [("#Given" ,["equality e_","solveFor v_"]),

    ("#Where" ,["False", (*WN0509 just detected: this pbl can never be used?!?*)

                "Not( (lhs e_) is_polyrat_in v_)",

                "Not( (rhs e_) is_polyrat_in v_)",

                "((lhs e_) has_degree_in v_)=1",

 	       "((rhs e_) has_degree_in v_)=1"]),

    ("#Find"  ,["solutions v_i_"]) 

   ],

   LinEq_prls, SOME "solve (e_::bool, v_)",

   [["LinEq","solve_lineq_equation"]]));

 (*-------------- methods------------------------------------------------------*)

 store_met

  (prep_met LinEq.thy "met_eqlin" [] e_metID

  (["LinEq"],

    [],

    {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,

     crls=LinEq_crls, nrls=norm_Poly

     (*, asm_rls=[],asm_thm=[]*)}, "empty_script"));

 (* ansprechen mit ["LinEq","solve_univar_equation"] *)

 store_met

 (prep_met LinEq.thy "met_eq_lin" [] e_metID

  (["LinEq","solve_lineq_equation"],

    [("#Given" ,["equality e_","solveFor v_"]),

     ("#Where" ,["Not( (lhs e_) is_polyrat_in v_)",

                 "( (lhs e_)  has_degree_in v_)=1"]),

     ("#Find"  ,["solutions v_i_"])

    ],

    {rew_ord'="termlessI",

     rls'=LinEq_erls,

     srls=e_rls,

     prls=LinEq_prls,

     calc=[],

     crls=LinEq_crls, nrls=norm_Poly(*,

     asm_rls=[],

     asm_thm=[("lin_isolate_div","")]*)},

     "Script Solve_lineq_equation (e_::bool) (v_::real) =                 " ^

     "(let e_ =((Try         (Rewrite     all_left            False)) @@  " ^ 

     "          (Try (Repeat (Rewrite     makex1_x           False))) @@  " ^ 

     "          (Try         (Rewrite_Set expand_binoms       False)) @@  " ^ 

     "          (Try (Repeat (Rewrite_Set_Inst [(bdv,v_::real)]           " ^

     "                                 make_ratpoly_in    False)))    @@  " ^

     "          (Try (Repeat (Rewrite_Set LinPoly_simplify      False)))) e_;" ^

     "     e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]                  " ^

     "                                          LinEq_simplify True)) @@  " ^

     "            (Repeat(Try (Rewrite_Set LinPoly_simplify     False)))) e_ " ^

     " in ((Or_to_List e_)::bool list))"

  ));

 "******* LinEq.ML end *******";

 get_met ["LinEq","solve_lineq_equation"];

 *}

 end