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

   author: Walther Neuper 2005, 2006

   (c) due to copyright terms

*)

theory Equation imports Atools begin

text {* 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.

*}

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 *)

  (*Script-names*)

  Function2Equality :: "[bool, bool,       bool] 

					 => bool"

                  ("((Script Function2Equality (_ _ =))// (_))" 9)

text {* 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 *}

ML {*

val thy = @{theory};

val ctxt = thy2ctxt thy;

val univariate_equation_prls = 

    append_rls "univariate_equation_prls" e_rls 

	       [Calc ("Tools.matches",eval_matches "")];

ruleset' := 

overwritelthy @{theory} (!ruleset',

		   [("univariate_equation_prls",

		     prep_rls univariate_equation_prls)]);

store_pbt 

 (prep_pbt thy "pbl_equ" [] e_pblID

 (["equation"],

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

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

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

  ],

  append_rls "equation_prls" e_rls 

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

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

  []));

store_pbt

 (prep_pbt thy "pbl_equ_univ" [] 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)",[]));

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

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

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

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

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

   *)

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

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

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

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

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

     ]

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

castab := 

overwritel (!castab, 

	    [((term_of o the o (parse thy)) "solveTest", 

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

	       argl2dtss)),

	     ((term_of o the o (parse thy)) "solve",  

	      (("Isac", ["univariate","equation"], ["no_met"]), 

	       argl2dtss))

	     ]);

store_met

    (prep_met thy "met_equ" [] e_metID

	      (["Equation"],

	       [],

	       {rew_ord'="tless_true", rls'=Erls, calc = [], 

		srls = e_rls, 

		prls=e_rls,

	     crls = Atools_erls, errpats = [], nrls = e_rls},

"empty_script"

));

*}

end