refactor(library/algebra): construct simplifier sets incrementally
This commit is contained in:
Daniel Selsam
Leonardo de Moura
parent
2682fe9525
commit
a04c28d4c9
15 changed files with 152 additions and 183 deletions
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@ -580,3 +580,30 @@ definition group_of_add_group (A : Type) [G : add_group A] : group A :=
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mul_left_inv := add.left_inv⦄
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end algebra
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namespace simplifier
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namespace unit
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attribute algebra.zero_add [simp]
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attribute algebra.add_zero [simp]
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attribute algebra.one_mul [simp]
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attribute algebra.mul_one [simp]
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end unit
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namespace neg
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attribute algebra.neg_neg [simp]
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attribute algebra.sub_eq_add_neg [simp]
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end neg
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namespace ac
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attribute algebra.add.assoc [simp]
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attribute algebra.add.comm [simp]
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attribute algebra.add.left_comm [simp]
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attribute algebra.mul.left_comm [simp]
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attribute algebra.mul.comm [simp]
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attribute algebra.mul.assoc [simp]
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end ac
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end simplifier
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@ -195,6 +195,9 @@ section
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rewrite [-left_distrib, add.right_inv, mul_zero]
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end
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theorem neg_mul_eq_neg_mul_symm : - a * b = - (a * b) := eq.symm !algebra.neg_mul_eq_neg_mul
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theorem neg_mul_eq_mul_neg_symm : a * - b = - (a * b) := eq.symm !algebra.neg_mul_eq_mul_neg
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theorem neg_mul_neg : -a * -b = a * b :=
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calc
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-a * -b = -(a * -b) : by rewrite -neg_mul_eq_neg_mul
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@ -402,3 +405,22 @@ section
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end
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end algebra
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namespace simplifier
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namespace unit
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attribute algebra.zero_mul [simp]
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attribute algebra.mul_zero [simp]
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end unit
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namespace neg
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attribute algebra.neg_mul_eq_neg_mul_symm [simp]
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attribute algebra.neg_mul_eq_mul_neg_symm [simp]
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end neg
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namespace distrib
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attribute algebra.left_distrib [simp]
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attribute algebra.right_distrib [simp]
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end distrib
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end simplifier
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@ -1,123 +0,0 @@
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/-
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Copyright (c) 2015 Daniel Selsam. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Daniel Selsam
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-/
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import algebra.ring algebra.numeral
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namespace simplifier
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namespace empty
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end empty
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namespace iff
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attribute eq_self_iff_true [simp]
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end iff
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-- TODO(dhs): make these [simp] rules in the global namespace
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namespace neg_helper
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open algebra
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variables {A : Type} [s : ring A] (a b : A)
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include s
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lemma neg_mul1 : (- a) * b = - (a * b) := eq.symm !algebra.neg_mul_eq_neg_mul
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lemma neg_mul2 : a * (- b) = - (a * b) := eq.symm !algebra.neg_mul_eq_mul_neg
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lemma sub_def : a - b = a + (- b) := rfl
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end neg_helper
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namespace neg
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attribute neg_helper.neg_mul1 [simp]
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attribute neg_helper.neg_mul2 [simp]
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attribute neg_helper.sub_def [simp]
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attribute algebra.neg_neg [simp]
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end neg
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namespace unit
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attribute algebra.zero_add [simp]
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attribute algebra.add_zero [simp]
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attribute algebra.zero_mul [simp]
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attribute algebra.mul_zero [simp]
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attribute algebra.one_mul [simp]
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attribute algebra.mul_one [simp]
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end unit
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namespace ac
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export simplifier.iff simplifier.neg simplifier.unit
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attribute algebra.add.assoc [simp]
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attribute algebra.add.comm [simp]
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attribute algebra.add.left_comm [simp]
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attribute algebra.mul.left_comm [simp]
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attribute algebra.mul.comm [simp]
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attribute algebra.mul.assoc [simp]
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end ac
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namespace distrib
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attribute algebra.left_distrib [simp]
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attribute algebra.right_distrib [simp]
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end distrib
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namespace som
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export simplifier.ac simplifier.distrib
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end som
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namespace numeral
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-- TODO(dhs): remove `add1` from the original lemmas and delete this
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namespace numeral_helper
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open algebra
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theorem bit1_add_bit1 {A : Type} [s : add_comm_semigroup A]
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[s' : has_one A] (a b : A) : bit1 a + bit1 b = bit0 ((a + b) + 1)
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:= norm_num.bit1_add_bit1 a b
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theorem bit1_add_one {A : Type} [s : add_comm_semigroup A] [s' : has_one A] (a : A)
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: bit1 a + one = bit0 (a + 1) := norm_num.add1_bit1 a
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theorem one_add_bit1 {A : Type} [s : add_comm_semigroup A] [s' : has_one A] (a : A)
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: one + bit1 a = bit0 (a + 1) := by rewrite [!add.comm, bit1_add_one]
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lemma one_add_bit0 [simp] {A : Type} [s : add_comm_semigroup A] [s' : has_one A] (a : A)
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: 1 + bit0 a = bit1 a := norm_num.one_add_bit0 a
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lemma bit0_add_one [simp] {A : Type} [s : add_comm_semigroup A] [s' : has_one A] (a : A)
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: bit0 a + 1 = bit1 a := norm_num.bit0_add_one a
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lemma mul_bit0_helper0 [simp] {A : Type} [s : comm_ring A] (a b : A)
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: bit0 a * bit0 b = bit0 (bit0 a * b) := norm_num.mul_bit0_helper (bit0 a) b (bit0 a * b) rfl
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lemma mul_bit0_helper1 [simp] {A : Type} [s : comm_ring A] (a b : A)
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: bit1 a * bit0 b = bit0 (bit1 a * b) := norm_num.mul_bit0_helper (bit1 a) b (bit1 a * b) rfl
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lemma mul_bit1_helper0 [simp] {A : Type} [s : comm_ring A] (a b : A)
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: bit0 a * bit1 b = bit0 (bit0 a * b) + bit0 a := norm_num.mul_bit1_helper (bit0 a) b (bit0 a * b) (bit0 (bit0 a * b) + bit0 a) rfl rfl
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lemma mul_bit1_helper1 [simp] {A : Type} [s : comm_ring A] (a b : A)
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: bit1 a * bit1 b = bit0 (bit1 a * b) + bit1 a := norm_num.mul_bit1_helper (bit1 a) b (bit1 a * b) (bit0 (bit1 a * b) + bit1 a) rfl rfl
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end numeral_helper
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export simplifier.ac
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attribute norm_num.bit0_add_bit0 [simp]
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attribute numeral_helper.bit1_add_one [simp]
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attribute norm_num.bit1_add_bit0 [simp]
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attribute numeral_helper.bit1_add_bit1 [simp]
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attribute norm_num.bit0_add_bit1 [simp]
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attribute numeral_helper.one_add_bit1 [simp]
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attribute norm_num.one_add_one [simp]
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attribute numeral_helper.one_add_bit0 [simp]
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attribute numeral_helper.bit0_add_one [simp]
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attribute numeral_helper.mul_bit0_helper0 [simp]
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attribute numeral_helper.mul_bit0_helper1 [simp]
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attribute numeral_helper.mul_bit1_helper0 [simp]
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attribute numeral_helper.mul_bit1_helper1 [simp]
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end numeral
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end simplifier
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@ -8,6 +8,13 @@ import init.logic
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namespace simplifier
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namespace empty
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end empty
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namespace prove
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attribute eq_self_iff_true [simp]
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end prove
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namespace unit_simp
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open eq.ops
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@ -556,6 +556,20 @@ simp_rule_sets get_simp_rule_sets(environment const & env, io_state const & ios,
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return set;
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}
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simp_rule_sets get_simp_rule_sets(environment const & env, io_state const & ios, std::initializer_list<name> const & nss) {
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simp_rule_sets set;
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for (name const & ns : nss) {
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list<rrs_entry> const * entries = rrs_ext::get_entries(env, ns);
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if (entries) {
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for (auto const & e : *entries) {
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tmp_type_context tctx(env, ios);
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set = add_core(tctx, set, e.m_name, e.m_priority);
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}
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}
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}
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return set;
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}
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io_state_stream const & operator<<(io_state_stream const & out, simp_rule_sets const & s) {
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options const & opts = out.get_options();
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out.get_stream() << mk_pair(s.pp(out.get_formatter()), opts);
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@ -8,7 +8,6 @@ Author: Leonardo de Moura
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#include "library/tmp_type_context.h"
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#include "library/head_map.h"
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#include "library/io_state_stream.h"
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#include <vector>
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#ifndef LEAN_SIMP_DEFAULT_PRIORITY
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#define LEAN_SIMP_DEFAULT_PRIORITY 1000
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@ -146,6 +145,8 @@ bool is_congr_rule(environment const & env, name const & n);
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simp_rule_sets get_simp_rule_sets(environment const & env);
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/** \brief Get simplification rule sets in the given namespace. */
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simp_rule_sets get_simp_rule_sets(environment const & env, io_state const & ios, name const & ns);
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/** \brief Get simplification rule sets in the given namespaces. */
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simp_rule_sets get_simp_rule_sets(environment const & env, io_state const & ios, std::initializer_list<name> const & nss);
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io_state_stream const & operator<<(io_state_stream const & out, simp_rule_sets const & s);
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@ -1,7 +1,7 @@
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/*
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Copyright (c) 2015 Daniel Selsam. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Daniel Selsam
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Copyright (c) 2015 Daniel Selsam. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Daniel Selsam
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*/
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#include "kernel/abstract.h"
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#include "kernel/expr_maps.h"
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@ -60,10 +60,11 @@ using simp::result;
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/* Names */
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static name * g_simplify_empty_namespace = nullptr;
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static name * g_simplify_prove_namespace = nullptr;
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static name * g_simplify_neg_namespace = nullptr;
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static name * g_simplify_unit_namespace = nullptr;
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static name * g_simplify_ac_namespace = nullptr;
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static name * g_simplify_som_namespace = nullptr;
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static name * g_simplify_distrib_namespace = nullptr;
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static name * g_simplify_numeral_namespace = nullptr;
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/* Options */
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@ -980,7 +981,9 @@ result simplifier::fuse(expr const & e) {
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/* Prove (1) == (3) using simplify with [ac] */
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flet<bool> no_simplify_numerals(m_numerals, false);
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auto pf_1_3 = prove(get_app_builder().mk_eq(e, e_grp),
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get_simp_rule_sets(env(), ios(), *g_simplify_ac_namespace));
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get_simp_rule_sets(env(), ios(),
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{*g_simplify_prove_namespace, *g_simplify_unit_namespace,
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*g_simplify_neg_namespace, *g_simplify_ac_namespace}));
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if (!pf_1_3) {
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diagnostic(env(), ios()) << e << "\n\n =?=\n\n" << e_grp << "\n";
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throw blast_exception("Failed to prove (1) == (3) during fusion", e);
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@ -988,7 +991,10 @@ result simplifier::fuse(expr const & e) {
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/* Prove (4) == (5) using simplify with [som] */
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auto pf_4_5 = prove(get_app_builder().mk_eq(e_grp_ls, e_fused_ls),
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get_simp_rule_sets(env(), ios(), *g_simplify_som_namespace));
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get_simp_rule_sets(env(), ios(),
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{*g_simplify_prove_namespace, *g_simplify_unit_namespace,
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*g_simplify_neg_namespace, *g_simplify_ac_namespace,
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*g_simplify_distrib_namespace}));
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if (!pf_4_5) {
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diagnostic(env(), ios()) << e_grp_ls << "\n\n =?=\n\n" << e_fused_ls << "\n";
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throw blast_exception("Failed to prove (4) == (5) during fusion", e);
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@ -996,7 +1002,9 @@ result simplifier::fuse(expr const & e) {
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/* Prove (5) == (6) using simplify with [numeral] */
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flet<bool> simplify_numerals(m_numerals, true);
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result r_simp_ls = simplify(e_fused_ls, get_simp_rule_sets(env(), ios(), *g_simplify_ac_namespace));
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result r_simp_ls = simplify(e_fused_ls, get_simp_rule_sets(env(), ios(),
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{*g_simplify_unit_namespace, *g_simplify_neg_namespace,
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*g_simplify_ac_namespace}));
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/* Prove (4) == (6) by transitivity of proofs (2) and (3) */
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expr pf_4_6;
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@ -1049,10 +1057,11 @@ expr_pair simplifier::split_summand(expr const & e, expr const & f_mul, expr con
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/* Setup and teardown */
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void initialize_simplifier() {
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g_simplify_empty_namespace = new name{"simplifier", "empty"};
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g_simplify_prove_namespace = new name{"simplifier", "prove"};
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g_simplify_neg_namespace = new name{"simplifier", "neg"};
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g_simplify_unit_namespace = new name{"simplifier", "unit"};
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g_simplify_ac_namespace = new name{"simplifier", "ac"};
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g_simplify_som_namespace = new name{"simplifier", "som"};
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g_simplify_distrib_namespace = new name{"simplifier", "distrib"};
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g_simplify_numeral_namespace = new name{"simplifier", "numeral"};
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g_simplify_max_steps = new name{"simplify", "max_steps"};
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@ -1097,10 +1106,11 @@ void finalize_simplifier() {
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delete g_simplify_max_steps;
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delete g_simplify_numeral_namespace;
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delete g_simplify_som_namespace;
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delete g_simplify_distrib_namespace;
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delete g_simplify_ac_namespace;
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delete g_simplify_unit_namespace;
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delete g_simplify_empty_namespace;
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delete g_simplify_neg_namespace;
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delete g_simplify_prove_namespace;
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}
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/* Entry points */
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@ -1,5 +1,5 @@
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import algebra.simplifier
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open algebra simplifier.som
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import algebra.ring
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open algebra
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set_option simplify.max_steps 1000
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universe l
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@ -7,4 +7,6 @@ constants (T : Type.{l}) (s : algebra.comm_ring T)
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constants (x1 x2 x3 x4 : T) (f g : T → T)
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attribute s [instance]
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#simplify eq simplifier.som 0 x2 + (1 * g x1 + 0 + (f x3 * 3 * 1 * (x2 + 0 + g x1 * 7) * x2 * 1)) + 5 * (x4 + f x1)
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open simplifier.unit simplifier.ac simplifier.neg simplifier.distrib
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#simplify eq env 0 x2 + (1 * g x1 + 0 + (f x3 * 3 * 1 * (x2 + 0 + g x1 * 7) * x2 * 1)) + 5 * (x4 + f x1)
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@ -1,5 +1,5 @@
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-- Basic fusion
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import algebra.simplifier
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import algebra.ring algebra.numeral
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open algebra
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universe l
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@ -9,19 +9,21 @@ attribute s [instance]
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set_option simplify.max_steps 50000
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set_option simplify.fuse true
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#simplify eq simplifier.som 0 x1
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#simplify eq simplifier.som 0 x1 + x1
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#simplify eq simplifier.som 0 (x1 + x1) + x1
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#simplify eq simplifier.som 0 (x1 + x1) + (x1 + x1)
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#simplify eq simplifier.som 0 x1 + x1 + x1 + x1
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#simplify eq simplifier.som 0 x1 + x1 + (x1 + x1) + x1
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#simplify eq simplifier.som 0 x1 - x1
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#simplify eq simplifier.som 0 (x1 - x1) + x1
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#simplify eq simplifier.som 0 (x1 + x1) - (x1 + x1)
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#simplify eq simplifier.som 0 x1 + x1 - x1 - x1
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#simplify eq simplifier.som 0 x1 + x1 + (x1 + x1) + x1
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#simplify eq simplifier.som 0 (x1 - x2) + x2 - x1
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#simplify eq simplifier.som 0 (x1 + x1 + x2 + x1) - 2* x2 + 1 * x2 - 3 * x1
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#simplify eq simplifier.som 0 x2 + x1 - x2 - - x1
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#simplify eq simplifier.som 0 (x1 - 2 * x3 * x2) + x2 * x3 * 3 - 1 * 0 * x1 * x2
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#simplify eq simplifier.som 0 x2 + x1 - x2 - (- x1)
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open simplifier.unit simplifier.ac simplifier.neg
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#simplify eq env 0 x1
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#simplify eq env 0 x1 + x1
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#simplify eq env 0 (x1 + x1) + x1
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#simplify eq env 0 (x1 + x1) + (x1 + x1)
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#simplify eq env 0 x1 + x1 + x1 + x1
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#simplify eq env 0 x1 + x1 + (x1 + x1) + x1
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#simplify eq env 0 x1 - x1
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#simplify eq env 0 (x1 - x1) + x1
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#simplify eq env 0 (x1 + x1) - (x1 + x1)
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#simplify eq env 0 x1 + x1 - x1 - x1
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#simplify eq env 0 x1 + x1 + (x1 + x1) + x1
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#simplify eq env 0 (x1 - x2) + x2 - x1
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#simplify eq env 0 (x1 + x1 + x2 + x1) - 2* x2 + 1 * x2 - 3 * x1
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#simplify eq env 0 x2 + x1 - x2 - - x1
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#simplify eq env 0 (x1 - 2 * x3 * x2) + x2 * x3 * 3 - 1 * 0 * x1 * x2
|
||||
#simplify eq env 0 x2 + x1 - x2 - (- x1)
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
-- normalizing reducible non-subsingleton instances
|
||||
import algebra.simplifier
|
||||
import algebra.ring
|
||||
open algebra
|
||||
|
||||
universe l
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
-- Basic fusion
|
||||
import algebra.simplifier
|
||||
import algebra.ring algebra.numeral
|
||||
open algebra
|
||||
|
||||
universe l
|
||||
|
|
@ -9,19 +9,21 @@ attribute s [instance]
|
|||
set_option simplify.max_steps 50000
|
||||
set_option simplify.fuse true
|
||||
|
||||
#simplify eq simplifier.som 0 x1 * x2
|
||||
#simplify eq simplifier.som 0 x1 * 2 * x2
|
||||
#simplify eq simplifier.som 0 x1 * 2 * x2 * 3
|
||||
#simplify eq simplifier.som 0 2 * x2 + x1 * 8 * x2 * 4
|
||||
#simplify eq simplifier.som 0 2 * x2 - x1 * 8 * x2 * 4
|
||||
#simplify eq simplifier.som 0 2 * x2 - 8 * x2 * 4 * x1
|
||||
#simplify eq simplifier.som 0 x2 * x1 + 3 * x1 + (2 * x2 - 8 * x2 * 4 * x1) + x1 * x2
|
||||
#simplify eq simplifier.som 0 (x1 * x3 + x1 * 2 + x2 * 3 * x3 + x1 * x2) - 2* x2 * x1 + 1 * x2 * x1 - 3 * x1 * x3
|
||||
#simplify eq simplifier.som 0 2 * 2 + x1
|
||||
#simplify eq simplifier.som 0 x2 * (2 * 2) + x1
|
||||
#simplify eq simplifier.som 0 2 * 2 * x2 + x1
|
||||
#simplify eq simplifier.som 0 2 * x2 * 2 + x1
|
||||
#simplify eq simplifier.som 0 200 * x2 * 200 + x1
|
||||
#simplify eq simplifier.som 0 x1 * 200 * x2 * 200 + x1
|
||||
#simplify eq simplifier.som 0 x1 * 200 * x2 * x3 * 200 + x1
|
||||
#simplify eq simplifier.som 0 x1 * 200 * x2 * x3 * x4 * 200 + x1
|
||||
open simplifier.unit simplifier.ac simplifier.neg
|
||||
|
||||
#simplify eq env 0 x1 * x2
|
||||
#simplify eq env 0 x1 * 2 * x2
|
||||
#simplify eq env 0 x1 * 2 * x2 * 3
|
||||
#simplify eq env 0 2 * x2 + x1 * 8 * x2 * 4
|
||||
#simplify eq env 0 2 * x2 - x1 * 8 * x2 * 4
|
||||
#simplify eq env 0 2 * x2 - 8 * x2 * 4 * x1
|
||||
#simplify eq env 0 x2 * x1 + 3 * x1 + (2 * x2 - 8 * x2 * 4 * x1) + x1 * x2
|
||||
#simplify eq env 0 (x1 * x3 + x1 * 2 + x2 * 3 * x3 + x1 * x2) - 2* x2 * x1 + 1 * x2 * x1 - 3 * x1 * x3
|
||||
#simplify eq env 0 2 * 2 + x1
|
||||
#simplify eq env 0 x2 * (2 * 2) + x1
|
||||
#simplify eq env 0 2 * 2 * x2 + x1
|
||||
#simplify eq env 0 2 * x2 * 2 + x1
|
||||
#simplify eq env 0 200 * x2 * 200 + x1
|
||||
#simplify eq env 0 x1 * 200 * x2 * 200 + x1
|
||||
#simplify eq env 0 x1 * 200 * x2 * x3 * 200 + x1
|
||||
#simplify eq env 0 x1 * 200 * x2 * x3 * x4 * 200 + x1
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
-- Nested fusion
|
||||
import algebra.simplifier
|
||||
import algebra.ring algebra.numeral
|
||||
open algebra
|
||||
|
||||
universe l
|
||||
|
|
@ -9,4 +9,6 @@ attribute s [instance]
|
|||
set_option simplify.max_steps 50000
|
||||
set_option simplify.fuse true
|
||||
|
||||
#simplify eq simplifier.som 0 f (x1 * x2 * 3 * 4 - 4 * 3 * x1 * x2) + g (x1 * x2 * 3 * 4 - 4 * 3 * x1 * x2)
|
||||
open simplifier.unit simplifier.ac simplifier.neg
|
||||
|
||||
#simplify eq env 0 f (x1 * x2 * 3 * 4 - 4 * 3 * x1 * x2) + g (x1 * x2 * 3 * 4 - 4 * 3 * x1 * x2)
|
||||
|
|
|
|||
|
|
@ -1,8 +1,8 @@
|
|||
-- Test [light] annotation
|
||||
-- Remark: it will take some additional work to get ⁻¹ to rewrite well
|
||||
-- when there is a proof obligation.
|
||||
import algebra.simplifier algebra.field data.set data.finset
|
||||
open algebra simplifier.ac
|
||||
import algebra.ring algebra.field data.set data.finset
|
||||
open algebra
|
||||
attribute neg [light 2]
|
||||
attribute inv [light 2]
|
||||
|
||||
|
|
@ -12,6 +12,8 @@ attribute add_neg_cancel_left [simp]
|
|||
attribute mul.right_inv [simp]
|
||||
attribute mul_inv_cancel_left [simp]
|
||||
|
||||
open simplifier.unit simplifier.ac
|
||||
|
||||
namespace ag
|
||||
universe l
|
||||
constants (A : Type.{l}) (s1 : add_comm_group A) (s2 : has_one A)
|
||||
|
|
|
|||
|
|
@ -1,9 +1,10 @@
|
|||
import algebra.simplifier
|
||||
import algebra.ring algebra.numeral
|
||||
open algebra
|
||||
|
||||
open simplifier.numeral
|
||||
|
||||
set_option simplify.max_steps 5000000
|
||||
-- TODO(dhs): we need to create the simplifier.numeral namespace incrementally.
|
||||
-- Once it exists, we can uncomment the following line to use it simplify.
|
||||
set_option simplify.numerals true
|
||||
universe l
|
||||
constants (A : Type.{l}) (A_comm_ring : comm_ring A)
|
||||
attribute A_comm_ring [instance]
|
||||
|
|
@ -54,5 +55,4 @@ attribute A_comm_ring [instance]
|
|||
|
||||
#simplify eq env 0 (0 + 45343453:A) * (53653343 + 1) * (53453 + 2) + (0 + 1 + 2 + 2200000000034733)
|
||||
|
||||
-- The following test is too slow
|
||||
-- #simplify eq 0 (23000000000343434534345316:A) * (53653343563534534 + 5367536453653573573453) * 53453756475777536 + 2200000000034733531531531534536
|
||||
#simplify eq env 0 (23000000000343434534345316:A) * (53653343563534534 + 5367536453653573573453) * 53453756475777536 + 2200000000034733531531531534536
|
||||
|
|
|
|||
|
|
@ -40,3 +40,4 @@
|
|||
90
|
||||
15241383936
|
||||
130049014430002489296
|
||||
6599110652246543565516387775250463433475607911914556819497064648
|
||||
|
|
|
|||
Loading…
Reference in a new issue