(* Title:  Knowledge/DiophantEq.thy

    Author: Mathias Lehnfeld 2011

    (c) due to copyright terms

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 *)

 theory DiophantEq imports Base_Tools Equation Test

 begin

 consts

   Diophant'_equation :: "[bool, int, bool ] 

                                        => bool "

                     ("((Script Diophant'_equation (_ _ =))//(_))" 9)

 axiomatization where

   int_isolate_add: "(bdv + a = b) = (bdv = b + (-1)*(a::int))"

 ML \<open>val thy = @{theory}\<close>

 text \<open>problemclass for the usecase\<close>

 setup \<open>KEStore_Elems.add_pbts

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

       (["diophantine","equation"],

         [("#Given" ,["boolTestGiven e_e","intTestGiven (v_v::int)"]),

           (*                                      TODO: drop ^^^^^*)

           ("#Where" ,[]),

           ("#Find"  ,["boolTestFind s_s"])],

         Rule.e_rls, SOME "solve (e_e::bool, v_v::int)", [["LinEq","solve_lineq_equation"]]))]\<close>

 text \<open>method solving the usecase\<close>

 partial_function (tailrec) diophant_equation :: "bool => int => bool"

   where

 "diophant_equation e_e v_v =

   (Repeat

       ((Try (Rewrite_Inst [(''bdv'', v_v)] ''int_isolate_add'' False)) @@

        (Try (Calculate ''PLUS'')) @@

        (Try (Calculate ''TIMES''))) e_e)"

 setup \<open>KEStore_Elems.add_mets

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

       (["Test","solve_diophant"],

         [("#Given" ,["boolTestGiven e_e","intTestGiven (v_v::int)"]),

           (*                                      TODO: drop ^^^^^*)

           ("#Where" ,[]),

           ("#Find"  ,["boolTestFind s_s"])],

         {rew_ord' = "e_rew_ord", rls' = tval_rls, srls = Rule.e_rls, prls = Rule.e_rls, calc = [],

           crls = tval_rls, errpats = [], nrls = Test_simplify},

         "Script Diophant_equation (e_e::bool) (v_v::int)=                  " ^

           "(Repeat                                                          " ^

           "    ((Try (Rewrite_Inst [(''bdv'',v_v::int)] ''int_isolate_add'' False)) @@" ^

           "     (Try (Calculate ''PLUS'')) @@  " ^

           "     (Try (Calculate ''TIMES''))) e_e::bool)")]

 \<close>

 end