author | haftmann |
Sat, 02 Dec 2017 16:50:53 +0000 | |
changeset 67116 | 7397a6df81d8 |
parent 62913 | 13252110a6fe |
child 67149 | e61557884799 |
permissions | -rw-r--r-- |
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modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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(* Author: Tobias Nipkow |
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Instantiation of the generic linear arithmetic package for int. |
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*) |
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modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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signature INT_ARITH = |
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modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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sig |
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modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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val setup: Context.generic -> Context.generic |
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modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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end |
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modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure Int_Arith : INT_ARITH = |
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struct |
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(* Update parameters of arithmetic prover *) |
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(* reduce contradictory =/</<= to False *) |
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(* Evaluation of terms of the form "m R n" where R is one of "=", "<=" or "<", |
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and m and n are ground terms over rings (roughly speaking). |
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That is, m and n consist only of 1s combined with "+", "-" and "*". |
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*) |
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val zeroth = Thm.symmetric (mk_meta_eq @{thm of_int_0}); |
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val zero_to_of_int_zero_simproc = |
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Simplifier.make_simproc @{context} "zero_to_of_int_zero_simproc" |
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{lhss = [@{term "0::'a::ring"}], |
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proc = fn _ => fn ctxt => fn ct => |
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let val T = Thm.ctyp_of_cterm ct in |
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if Thm.typ_of T = @{typ int} then NONE |
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else SOME (Thm.instantiate' [SOME T] [] zeroth) |
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end}; |
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val oneth = Thm.symmetric (mk_meta_eq @{thm of_int_1}); |
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val one_to_of_int_one_simproc = |
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Simplifier.make_simproc @{context} "one_to_of_int_one_simproc" |
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{lhss = [@{term "1::'a::ring_1"}], |
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proc = fn _ => fn ctxt => fn ct => |
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let val T = Thm.ctyp_of_cterm ct in |
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if Thm.typ_of T = @{typ int} then NONE |
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else SOME (Thm.instantiate' [SOME T] [] oneth) |
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end}; |
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fun check (Const (@{const_name Groups.one}, @{typ int})) = false |
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| check (Const (@{const_name Groups.one}, _)) = true |
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| check (Const (s, _)) = member (op =) [@{const_name HOL.eq}, |
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@{const_name Groups.times}, @{const_name Groups.uminus}, |
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@{const_name Groups.minus}, @{const_name Groups.plus}, |
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@{const_name Groups.zero}, |
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@{const_name Orderings.less}, @{const_name Orderings.less_eq}] s |
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| check (a $ b) = check a andalso check b |
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| check _ = false; |
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val conv_ss = |
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simpset_of (put_simpset HOL_basic_ss @{context} |
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addsimps |
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((map (fn th => th RS sym) [@{thm of_int_add}, @{thm of_int_mult}, |
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@{thm of_int_diff}, @{thm of_int_minus}])@ |
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[@{thm of_int_less_iff}, @{thm of_int_le_iff}, @{thm of_int_eq_iff}]) |
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addsimprocs [zero_to_of_int_zero_simproc,one_to_of_int_one_simproc]); |
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val zero_one_idom_simproc = |
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Simplifier.make_simproc @{context} "zero_one_idom_simproc" |
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{lhss = |
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[@{term "(x::'a::ring_char_0) = y"}, |
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@{term "(x::'a::linordered_idom) < y"}, |
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@{term "(x::'a::linordered_idom) \<le> y"}], |
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proc = fn _ => fn ctxt => fn ct => |
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if check (Thm.term_of ct) |
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then SOME (Simplifier.rewrite (put_simpset conv_ss ctxt) ct) |
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else NONE}; |
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fun number_of ctxt T n = |
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if not (Sign.of_sort (Proof_Context.theory_of ctxt) (T, @{sort numeral})) |
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then raise CTERM ("number_of", []) |
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else Numeral.mk_cnumber (Thm.ctyp_of ctxt T) n; |
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val setup = |
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Lin_Arith.add_inj_thms [@{thm of_nat_le_iff} RS iffD2, @{thm of_nat_eq_iff} RS iffD2] |
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#> Lin_Arith.add_lessD @{thm zless_imp_add1_zle} |
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#> Lin_Arith.add_simps @{thms of_nat_simps of_int_simps} |
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#> Lin_Arith.add_simps |
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[@{thm of_int_numeral}, @{thm nat_0}, @{thm nat_1}, @{thm diff_nat_numeral}, @{thm nat_numeral}] |
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#> Lin_Arith.add_simprocs [zero_one_idom_simproc] |
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#> Lin_Arith.set_number_of number_of |
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#> Lin_Arith.add_inj_const (@{const_name of_nat}, HOLogic.natT --> HOLogic.intT) |
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#> Lin_Arith.add_discrete_type @{type_name Int.int} |
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end; |