src/HOL/Tools/int_arith.ML
 author haftmann Thu Jan 28 11:48:49 2010 +0100 (2010-01-28) changeset 34974 18b41bba42b5 parent 33296 a3924d1069e5 child 35028 108662d50512 permissions -rw-r--r--
new theory Algebras.thy for generic algebraic structures
```     1 (* Author: Tobias Nipkow
```
```     2
```
```     3 Instantiation of the generic linear arithmetic package for int.
```
```     4 *)
```
```     5
```
```     6 signature INT_ARITH =
```
```     7 sig
```
```     8   val setup: Context.generic -> Context.generic
```
```     9   val global_setup: theory -> theory
```
```    10 end
```
```    11
```
```    12 structure Int_Arith : INT_ARITH =
```
```    13 struct
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```    14
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```    15 (* Update parameters of arithmetic prover *)
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```    16
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```    17 (* reduce contradictory =/</<= to False *)
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```    18
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```    19 (* Evaluation of terms of the form "m R n" where R is one of "=", "<=" or "<",
```
```    20    and m and n are ground terms over rings (roughly speaking).
```
```    21    That is, m and n consist only of 1s combined with "+", "-" and "*".
```
```    22 *)
```
```    23
```
```    24 val zeroth = (symmetric o mk_meta_eq) @{thm of_int_0};
```
```    25
```
```    26 val lhss0 = [@{cpat "0::?'a::ring"}];
```
```    27
```
```    28 fun proc0 phi ss ct =
```
```    29   let val T = ctyp_of_term ct
```
```    30   in if typ_of T = @{typ int} then NONE else
```
```    31      SOME (instantiate' [SOME T] [] zeroth)
```
```    32   end;
```
```    33
```
```    34 val zero_to_of_int_zero_simproc =
```
```    35   make_simproc {lhss = lhss0, name = "zero_to_of_int_zero_simproc",
```
```    36   proc = proc0, identifier = []};
```
```    37
```
```    38 val oneth = (symmetric o mk_meta_eq) @{thm of_int_1};
```
```    39
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```    40 val lhss1 = [@{cpat "1::?'a::ring_1"}];
```
```    41
```
```    42 fun proc1 phi ss ct =
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```    43   let val T = ctyp_of_term ct
```
```    44   in if typ_of T = @{typ int} then NONE else
```
```    45      SOME (instantiate' [SOME T] [] oneth)
```
```    46   end;
```
```    47
```
```    48 val one_to_of_int_one_simproc =
```
```    49   make_simproc {lhss = lhss1, name = "one_to_of_int_one_simproc",
```
```    50   proc = proc1, identifier = []};
```
```    51
```
```    52 fun check (Const (@{const_name Algebras.one}, @{typ int})) = false
```
```    53   | check (Const (@{const_name Algebras.one}, _)) = true
```
```    54   | check (Const (s, _)) = member (op =) [@{const_name "op ="},
```
```    55       @{const_name Algebras.times}, @{const_name Algebras.uminus},
```
```    56       @{const_name Algebras.minus}, @{const_name Algebras.plus},
```
```    57       @{const_name Algebras.zero},
```
```    58       @{const_name Algebras.less}, @{const_name Algebras.less_eq}] s
```
```    59   | check (a \$ b) = check a andalso check b
```
```    60   | check _ = false;
```
```    61
```
```    62 val conv =
```
```    63   Simplifier.rewrite
```
```    64    (HOL_basic_ss addsimps
```
```    65      ((map (fn th => th RS sym) [@{thm of_int_add}, @{thm of_int_mult},
```
```    66              @{thm of_int_diff},  @{thm of_int_minus}])@
```
```    67       [@{thm of_int_less_iff}, @{thm of_int_le_iff}, @{thm of_int_eq_iff}])
```
```    68      addsimprocs [zero_to_of_int_zero_simproc,one_to_of_int_one_simproc]);
```
```    69
```
```    70 fun sproc phi ss ct = if check (term_of ct) then SOME (conv ct) else NONE
```
```    71
```
```    72 val lhss' =
```
```    73   [@{cpat "(?x::?'a::ring_char_0) = (?y::?'a)"},
```
```    74    @{cpat "(?x::?'a::ordered_idom) < (?y::?'a)"},
```
```    75    @{cpat "(?x::?'a::ordered_idom) <= (?y::?'a)"}]
```
```    76
```
```    77 val zero_one_idom_simproc =
```
```    78   make_simproc {lhss = lhss' , name = "zero_one_idom_simproc",
```
```    79   proc = sproc, identifier = []}
```
```    80
```
```    81 val fast_int_arith_simproc =
```
```    82   Simplifier.simproc @{theory} "fast_int_arith"
```
```    83      ["(m::'a::{ordered_idom,number_ring}) < n",
```
```    84       "(m::'a::{ordered_idom,number_ring}) <= n",
```
```    85       "(m::'a::{ordered_idom,number_ring}) = n"] (K Lin_Arith.simproc);
```
```    86
```
```    87 val global_setup = Simplifier.map_simpset
```
```    88   (fn simpset => simpset addsimprocs [fast_int_arith_simproc]);
```
```    89
```
```    90
```
```    91 fun number_of thy T n =
```
```    92   if not (Sign.of_sort thy (T, @{sort number}))
```
```    93   then raise CTERM ("number_of", [])
```
```    94   else Numeral.mk_cnumber (Thm.ctyp_of thy T) n
```
```    95
```
```    96 val setup =
```
```    97   Lin_Arith.add_inj_thms [@{thm zle_int} RS iffD2, @{thm int_int_eq} RS iffD2]
```
```    98   #> Lin_Arith.add_lessD @{thm zless_imp_add1_zle}
```
```    99   #> Lin_Arith.add_simps (@{thms simp_thms} @ @{thms arith_simps} @ @{thms rel_simps}
```
```   100       @ @{thms arith_special} @ @{thms int_arith_rules})
```
```   101   #> Lin_Arith.add_simprocs [zero_one_idom_simproc]
```
```   102   #> Lin_Arith.set_number_of number_of
```
```   103   #> Lin_Arith.add_inj_const (@{const_name of_nat}, HOLogic.natT --> HOLogic.intT)
```
```   104   #> Lin_Arith.add_discrete_type @{type_name Int.int}
```
```   105
```
```   106 end;
```