(* 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

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_Set.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'' )) #>

    (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_Set.e_rls, prls = Rule_Set.e_rls, calc = [],

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

        @{thm diophant_equation.simps})]

\<close>

end