src/HOL/Groebner_Basis.thy
author haftmann
Fri Oct 10 19:55:32 2014 +0200 (2014-10-10)
changeset 58646 cd63a4b12a33
parent 57951 7896762b638b
child 58777 6ba2f1fa243b
permissions -rw-r--r--
specialized specification: avoid trivial instances
     1 (*  Title:      HOL/Groebner_Basis.thy
     2     Author:     Amine Chaieb, TU Muenchen
     3 *)
     4 
     5 header {* Groebner bases *}
     6 
     7 theory Groebner_Basis
     8 imports Semiring_Normalization
     9 keywords "try0" :: diag
    10 begin
    11 
    12 subsection {* Groebner Bases *}
    13 
    14 lemmas bool_simps = simp_thms(1-34) -- {* FIXME move to @{theory HOL} *}
    15 
    16 lemma nnf_simps: -- {* FIXME shadows fact binding in @{theory HOL} *}
    17   "(\<not>(P \<and> Q)) = (\<not>P \<or> \<not>Q)" "(\<not>(P \<or> Q)) = (\<not>P \<and> \<not>Q)"
    18   "(P \<longrightarrow> Q) = (\<not>P \<or> Q)"
    19   "(P = Q) = ((P \<and> Q) \<or> (\<not>P \<and> \<not> Q))" "(\<not> \<not>(P)) = P"
    20   by blast+
    21 
    22 lemma dnf:
    23   "(P & (Q | R)) = ((P&Q) | (P&R))"
    24   "((Q | R) & P) = ((Q&P) | (R&P))"
    25   "(P \<and> Q) = (Q \<and> P)"
    26   "(P \<or> Q) = (Q \<or> P)"
    27   by blast+
    28 
    29 lemmas weak_dnf_simps = dnf bool_simps
    30 
    31 lemma PFalse:
    32     "P \<equiv> False \<Longrightarrow> \<not> P"
    33     "\<not> P \<Longrightarrow> (P \<equiv> False)"
    34   by auto
    35 
    36 named_theorems algebra "pre-simplification rules for algebraic methods"
    37 ML_file "Tools/groebner.ML"
    38 
    39 method_setup algebra = {*
    40   let
    41     fun keyword k = Scan.lift (Args.$$$ k -- Args.colon) >> K ()
    42     val addN = "add"
    43     val delN = "del"
    44     val any_keyword = keyword addN || keyword delN
    45     val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
    46   in
    47     Scan.optional (keyword addN |-- thms) [] --
    48      Scan.optional (keyword delN |-- thms) [] >>
    49     (fn (add_ths, del_ths) => fn ctxt =>
    50       SIMPLE_METHOD' (Groebner.algebra_tac add_ths del_ths ctxt))
    51   end
    52 *} "solve polynomial equations over (semi)rings and ideal membership problems using Groebner bases"
    53 
    54 declare dvd_def[algebra]
    55 declare dvd_eq_mod_eq_0[symmetric, algebra]
    56 declare mod_div_trivial[algebra]
    57 declare mod_mod_trivial[algebra]
    58 declare div_by_0[algebra]
    59 declare mod_by_0[algebra]
    60 declare zmod_zdiv_equality[symmetric,algebra]
    61 declare div_mod_equality2[symmetric, algebra]
    62 declare div_minus_minus[algebra]
    63 declare mod_minus_minus[algebra]
    64 declare div_minus_right[algebra]
    65 declare mod_minus_right[algebra]
    66 declare div_0[algebra]
    67 declare mod_0[algebra]
    68 declare mod_by_1[algebra]
    69 declare div_by_1[algebra]
    70 declare mod_minus1_right[algebra]
    71 declare div_minus1_right[algebra]
    72 declare mod_mult_self2_is_0[algebra]
    73 declare mod_mult_self1_is_0[algebra]
    74 declare zmod_eq_0_iff[algebra]
    75 declare dvd_0_left_iff[algebra]
    76 declare zdvd1_eq[algebra]
    77 declare zmod_eq_dvd_iff[algebra]
    78 declare nat_mod_eq_iff[algebra]
    79 
    80 end