(* equations and functions; functions NOT as lambda-terms

    author: Walther Neuper 2005, 2006

    (c) due to copyright terms

 *)

 theory Equation imports Base_Tools begin

 text \<open>univariate equations over terms :

   In 2003 Richard Lang prototyped ISAC's equation solver while also alpha-testing

   the Lucas-Interpreter's Subproblem mechanism.

   This prototype suffers from the drop-out of Matthias Goldgruber for a year,

   who had started to work on simplification in parallel. So this implementation

   replaced simplifiers by many specific theorems for specific terms in specific

   phases of equation solving; these specific solutions wait for generalisation

   in future improvements of ISAC's equation solver.

 \<close>

 consts

   (*descriptions in the related problems TODOshift here from Descriptions.thy*)

   substitution      :: "bool => una"

   (*the CAS-commands*)

   solve             :: "[bool * 'a] => bool list" (* solve (x+1=2, x) *)

   solveTest         :: "[bool * 'a] => bool list" (* for test collection *)

 text \<open>defines equation and univariate-equation

         created by: rlang 

               date: 02.09

         changed by: rlang

         last change by: rlang

                   date: 02.11.29

         (c) by Richard Lang, 2003\<close>

 ML \<open>

 val thy = @{theory};

 val ctxt = Rule.thy2ctxt thy;

 val univariate_equation_prls = 

     Rule.append_rls "univariate_equation_prls" Rule.e_rls 

 	       [Rule.Num_Calc ("Prog_Expr.matches", Prog_Expr.eval_matches "")];

 \<close>

 setup \<open>KEStore_Elems.add_rlss [("univariate_equation_prls",

   (Context.theory_name @{theory}, Auto_Prog.prep_rls @{theory} univariate_equation_prls))]\<close>

 setup \<open>KEStore_Elems.add_pbts

   [(Specify.prep_pbt thy "pbl_equ" [] Celem.e_pblID

       (["equation"],

         [("#Given" ,["equality e_e","solveFor v_v"]),

           ("#Where" ,["matches (?a = ?b) e_e"]),

           ("#Find"  ,["solutions v_v'i'"])],

         Rule.append_rls "equation_prls" Rule.e_rls  [Rule.Num_Calc ("Prog_Expr.matches", Prog_Expr.eval_matches "")],

         SOME "solve (e_e::bool, v_v)", [])),

     (Specify.prep_pbt thy "pbl_equ_univ" [] Celem.e_pblID

       (["univariate","equation"],

         [("#Given" ,["equality e_e","solveFor v_v"]),

           ("#Where" ,["matches (?a = ?b) e_e"]),

           ("#Find"  ,["solutions v_v'i'"])],

         univariate_equation_prls, SOME "solve (e_e::bool, v_v)", []))]\<close>

 ML\<open>

 (*.function for handling the cas-input "solve (x+1=2, x)":

    make a model which is already in ctree-internal format.*)

 (* val (h,argl) = strip_comb (str2term "solve (x+1=2, x)");

    val (h,argl) = strip_comb ((Thm.term_of o the o (parse thy)) 

 				  "solveTest (x+1=2, x)");

    *)

 fun argl2dtss [Const ("Product_Type.Pair", _) $ eq $ bdv] =

     [((the o (TermC.parseNEW ctxt)) "equality", [eq]),

      ((the o (TermC.parseNEW ctxt)) "solveFor", [bdv]),

      ((the o (TermC.parseNEW ctxt)) "solutions", 

       [(the o (TermC.parseNEW ctxt)) "L"])

      ]

   | argl2dtss _ = error "Equation.ML: wrong argument for argl2dtss";

 \<close>

 setup \<open>KEStore_Elems.add_cas

   [((Thm.term_of o the o (TermC.parse thy)) "solveTest", 

       (("Test", ["univariate","equation","test"], ["no_met"]), argl2dtss)),

     ((Thm.term_of o the o (TermC.parse thy)) "solve",

       (("Isac_Knowledge", ["univariate","equation"], ["no_met"]), argl2dtss))]\<close>

 setup \<open>KEStore_Elems.add_mets

     [Specify.prep_met thy "met_equ" [] Celem.e_metID

 	    (["Equation"], [],

 	      {rew_ord'="tless_true", rls'=Rule.Erls, calc = [], srls = Rule.e_rls, prls=Rule.e_rls, crls = Atools_erls,

           errpats = [], nrls = Rule.e_rls},

         @{thm refl})]

 \<close>

 end