wneuper/isa: src/Tools/isac/Knowledge/LinEq.thy@28b67cae58c3

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

     2 (* theory collecting all knowledge for LinearEquations

     3    created by: rlang

     4          date: 02.10

     5    changed by: rlang

     6    last change by: rlang

     7              date: 02.10.20

     8 *)

    10 theory LinEq imports Poly Equation begin

    12 consts

    13    Solve'_lineq'_equation

    14              :: "[bool,real,

    15 		   bool list] => bool list"

    16                ("((Script Solve'_lineq'_equation (_ _ =))// (_))" 9)

    18 axiomatization where

    19 (*-- normalise --*)

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

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

    22   makex1_x:          "a^^^1  = a" and

    23   real_assoc_1:      "a+(b+c) = a+b+c" and

    24   real_assoc_2:      "a*(b*c) = a*b*c" and

    26 (*-- solve --*)

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

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

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

    31 ML \<open>

    32 val thy = @{theory};

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

    35   Rule.append_rls "LinEq_prls" Rule.e_rls

    36 	     [Rule.Calc ("HOL.eq",eval_equal "#equal_"),

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

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

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

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

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

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

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

    44 	      Rule.Thm ("not_true",TermC.num_str @{thm not_true}),

    45 	      Rule.Thm ("not_false",TermC.num_str @{thm not_false}),

    46 	      Rule.Thm ("and_true",TermC.num_str @{thm and_true}),

    47 	      Rule.Thm ("and_false",TermC.num_str @{thm and_false}),

    48 	      Rule.Thm ("or_true",TermC.num_str @{thm or_true}),

    49 	      Rule.Thm ("or_false",TermC.num_str @{thm or_false})

    50               ];

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

    52 val LinEq_crls =

    53    Rule.append_rls "LinEq_crls" poly_crls

    54    [Rule.Thm  ("real_assoc_1",TermC.num_str @{thm real_assoc_1})

    55     (*

    56      Don't use

    57      Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),

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

    59      *)

    60     ];

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

    63 val LinEq_erls =

    64    Rule.append_rls "LinEq_erls" Poly_erls

    65    [Rule.Thm  ("real_assoc_1",TermC.num_str @{thm real_assoc_1})

    66     (*

    67      Don't use

    68      Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),

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

    70      *)

    71     ];

    72 \<close>

    73 setup \<open>KEStore_Elems.add_rlss

    74   [("LinEq_erls", (Context.theory_name @{theory}, LinEq_erls))]\<close>

    75 ML \<open>

    77 val LinPoly_simplify = prep_rls'(

    78   Rule.Rls {id = "LinPoly_simplify", preconds = [],

    79        rew_ord = ("termlessI",termlessI),

    80        erls = LinEq_erls,

    81        srls = Rule.Erls,

    82        calc = [], errpatts = [],

    83        rules = [

    84 		Rule.Thm  ("real_assoc_1",TermC.num_str @{thm real_assoc_1}),

    85 		Rule.Calc ("Groups.plus_class.plus",eval_binop "#add_"),

    86 		Rule.Calc ("Groups.minus_class.minus",eval_binop "#sub_"),

    87 		Rule.Calc ("Groups.times_class.times",eval_binop "#mult_"),

    88 		(*  Dont use

    89 		 Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),

    90 		 Rule.Calc ("NthRoot.sqrt",eval_sqrt "#sqrt_"),

    91 		 *)

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

    93 		],

    94        scr = Rule.EmptyScr});

    95 \<close>

    96 setup \<open>KEStore_Elems.add_rlss

    97   [("LinPoly_simplify", (Context.theory_name @{theory}, LinPoly_simplify))]\<close>

    98 ML \<open>

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

   101 val LinEq_simplify = prep_rls'(

   102 Rule.Rls {id = "LinEq_simplify", preconds = [],

   103      rew_ord = ("e_rew_ord", Rule.e_rew_ord),

   104      erls = LinEq_erls,

   105      srls = Rule.Erls,

   106      calc = [], errpatts = [],

   107      rules = [

   108 	      Rule.Thm("lin_isolate_add1",TermC.num_str @{thm lin_isolate_add1}),

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

   110 	      Rule.Thm("lin_isolate_add2",TermC.num_str @{thm lin_isolate_add2}),

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

   112 	      Rule.Thm("lin_isolate_div",TermC.num_str @{thm lin_isolate_div})

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

   114 	      ],

   115      scr = Rule.EmptyScr});

   116 \<close>

   117 setup \<open>KEStore_Elems.add_rlss

   118   [("LinEq_simplify", (Context.theory_name @{theory}, LinEq_simplify))]\<close>

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

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

   122 setup \<open>KEStore_Elems.add_pbts

   123   [(Specify.prep_pbt thy "pbl_equ_univ_lin" [] Celem.e_pblID

   124       (["LINEAR", "univariate", "equation"],

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

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

   127               "Not( (lhs e_e) is_polyrat_in v_v)",

   128               "Not( (rhs e_e) is_polyrat_in v_v)",

   129               "((lhs e_e) has_degree_in v_v)=1",

   130 	            "((rhs e_e) has_degree_in v_v)=1"]),

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

   132         LinEq_prls, SOME "solve (e_e::bool, v_v)", [["LinEq", "solve_lineq_equation"]]))]\<close>

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

   135 setup \<open>KEStore_Elems.add_mets

   136     [Specify.prep_met thy "met_eqlin" [] Celem.e_metID

   137       (["LinEq"], [],

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

   139           crls = LinEq_crls, errpats = [], nrls = norm_Poly},

   140         "empty_script")]

   141 \<close>

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

   143 setup \<open>KEStore_Elems.add_mets

   144     [Specify.prep_met thy "met_eq_lin" [] Celem.e_metID

   145       (["LinEq","solve_lineq_equation"],

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

   147           ("#Where", ["Not ((lhs e_e) is_polyrat_in v_v)", "((lhs e_e)  has_degree_in v_v) = 1"]),

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

   149         {rew_ord' = "termlessI", rls' = LinEq_erls, srls = Rule.e_rls, prls = LinEq_prls, calc = [],

   150           crls = LinEq_crls, errpats = [], nrls = norm_Poly},

   151         "Script Solve_lineq_equation (e_e::bool) (v_v::real) =                 " ^

   152           "(let e_e =((Try         (Rewrite      all_left           False)) @@   " ^

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

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

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

   156           "                                 make_ratpoly_in    False)))    @@    " ^

   157           "           (Try (Repeat (Rewrite_Set LinPoly_simplify      False))))e_e;" ^

   158           "     e_e = ((Try (Rewrite_Set_Inst [(bdv, v_v::real)]                  " ^

   159           "                                     LinEq_simplify True)) @@  " ^

   160           "            (Repeat(Try (Rewrite_Set LinPoly_simplify     False)))) e_e " ^

   161           " in ((Or_to_List e_e)::bool list))")]

   162 \<close>

   163 ML \<open>Specify.get_met' @{theory} ["LinEq","solve_lineq_equation"];\<close>

   165 end

author	Walther Neuper <wneuper@ist.tugraz.at>
	Wed, 28 Nov 2018 11:46:00 +0100
changeset 59473	28b67cae58c3
parent 59472	3e904f8ec16c
child 59489	cfcbcac0bae8
permissions	-rw-r--r--