src/HOL/Groebner_Basis.thy
 author blanchet Thu Jan 30 13:38:28 2014 +0100 (2014-01-30) changeset 55178 318cd8ac1817 parent 54251 adea9f6986b2 child 55509 bd67ebe275e0 permissions -rw-r--r--
added 'algebra' and 'meson' to 'try0'
```     1 (*  Title:      HOL/Groebner_Basis.thy
```
```     2     Author:     Amine Chaieb, TU Muenchen
```
```     3 *)
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```     4
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```     5 header {* Groebner bases *}
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```     6
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```     7 theory Groebner_Basis
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```     8 imports Semiring_Normalization
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```     9 begin
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```    10
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```    11 subsection {* Groebner Bases *}
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```    12
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```    13 lemmas bool_simps = simp_thms(1-34) -- {* FIXME move to @{theory HOL} *}
```
```    14
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```    15 lemma nnf_simps: -- {* FIXME shadows fact binding in @{theory HOL} *}
```
```    16   "(\<not>(P \<and> Q)) = (\<not>P \<or> \<not>Q)" "(\<not>(P \<or> Q)) = (\<not>P \<and> \<not>Q)"
```
```    17   "(P \<longrightarrow> Q) = (\<not>P \<or> Q)"
```
```    18   "(P = Q) = ((P \<and> Q) \<or> (\<not>P \<and> \<not> Q))" "(\<not> \<not>(P)) = P"
```
```    19   by blast+
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```    20
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```    21 lemma dnf:
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```    22   "(P & (Q | R)) = ((P&Q) | (P&R))"
```
```    23   "((Q | R) & P) = ((Q&P) | (R&P))"
```
```    24   "(P \<and> Q) = (Q \<and> P)"
```
```    25   "(P \<or> Q) = (Q \<or> P)"
```
```    26   by blast+
```
```    27
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```    28 lemmas weak_dnf_simps = dnf bool_simps
```
```    29
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```    30 lemma PFalse:
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```    31     "P \<equiv> False \<Longrightarrow> \<not> P"
```
```    32     "\<not> P \<Longrightarrow> (P \<equiv> False)"
```
```    33   by auto
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```    34
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```    35 ML {*
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```    36 structure Algebra_Simplification = Named_Thms
```
```    37 (
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```    38   val name = @{binding algebra}
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```    39   val description = "pre-simplification rules for algebraic methods"
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```    40 )
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```    41 *}
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```    42
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```    43 setup Algebra_Simplification.setup
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```    44
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```    45 ML_file "Tools/groebner.ML"
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```    46
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```    47 method_setup algebra = {*
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```    48   let
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```    49     fun keyword k = Scan.lift (Args.\$\$\$ k -- Args.colon) >> K ()
```
```    50     val addN = "add"
```
```    51     val delN = "del"
```
```    52     val any_keyword = keyword addN || keyword delN
```
```    53     val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat;
```
```    54   in
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```    55     Scan.optional (keyword addN |-- thms) [] --
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```    56      Scan.optional (keyword delN |-- thms) [] >>
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```    57     (fn (add_ths, del_ths) => fn ctxt =>
```
```    58       SIMPLE_METHOD' (Groebner.algebra_tac add_ths del_ths ctxt))
```
```    59   end
```
```    60 *} "solve polynomial equations over (semi)rings and ideal membership problems using Groebner bases"
```
```    61
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```    62 declare dvd_def[algebra]
```
```    63 declare dvd_eq_mod_eq_0[symmetric, algebra]
```
```    64 declare mod_div_trivial[algebra]
```
```    65 declare mod_mod_trivial[algebra]
```
```    66 declare div_by_0[algebra]
```
```    67 declare mod_by_0[algebra]
```
```    68 declare zmod_zdiv_equality[symmetric,algebra]
```
```    69 declare div_mod_equality2[symmetric, algebra]
```
```    70 declare div_minus_minus[algebra]
```
```    71 declare mod_minus_minus[algebra]
```
```    72 declare div_minus_right[algebra]
```
```    73 declare mod_minus_right[algebra]
```
```    74 declare div_0[algebra]
```
```    75 declare mod_0[algebra]
```
```    76 declare mod_by_1[algebra]
```
```    77 declare div_by_1[algebra]
```
```    78 declare mod_minus1_right[algebra]
```
```    79 declare div_minus1_right[algebra]
```
```    80 declare mod_mult_self2_is_0[algebra]
```
```    81 declare mod_mult_self1_is_0[algebra]
```
```    82 declare zmod_eq_0_iff[algebra]
```
```    83 declare dvd_0_left_iff[algebra]
```
```    84 declare zdvd1_eq[algebra]
```
```    85 declare zmod_eq_dvd_iff[algebra]
```
```    86 declare nat_mod_eq_iff[algebra]
```
```    87
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```    88
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```    89 subsection {* Try0 *}
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```    90
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```    91 ML_file "Tools/try0.ML"
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```    92
```
```    93 end
```