feat(library/norm_num): fix numeral normalization to work on new numeral structure; add support for multiplication
This commit is contained in:
Rob Lewis
Leonardo de Moura
parent
f4ce2bcbfe
commit
958add9ef8
6 changed files with 663 additions and 27 deletions
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@ -1,8 +1,138 @@
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import algebra.ring -- has_add, has_one, ... will be moved to init in the future
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/-
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Copyright (c) 2015 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Robert Y. Lewis
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-/
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import algebra.ring
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open algebra
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variable {A : Type}
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-- variables [s : ring A]
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-- set_option pp.all true
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-- check bit1 (bit0 (one : A))
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definition add1 [s : has_add A] [s' : has_one A] (a : A) : A := add a one
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theorem add_comm_four [s : add_comm_semigroup A] (a b : A) : a + a + (b + b) = (a + b) + (a + b) :=
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by rewrite [-add.assoc at {1}, add.comm, {a + b}add.comm at {1}, *add.assoc]
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theorem add_comm_middle [s : add_comm_semigroup A] (a b c : A) : a + b + c = a + c + b :=
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by rewrite [add.assoc, add.comm b, -add.assoc]
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theorem bit0_add_bit0 [s : add_comm_semigroup A] (a b : A) : bit0 a + bit0 b = bit0 (a + b) :=
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!add_comm_four
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theorem bit0_add_bit0_helper [s : add_comm_semigroup A] (a b t : A) (H : a + b = t) :
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bit0 a + bit0 b = bit0 t :=
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by rewrite -H; apply bit0_add_bit0
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theorem bit1_add_bit0 [s : add_comm_semigroup A] [s' : has_one A] (a b : A) :
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bit1 a + bit0 b = bit1 (a + b) :=
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begin
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rewrite [↑bit0, ↑bit1, add_comm_middle], congruence, apply add_comm_four
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end
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theorem bit1_add_bit0_helper [s : add_comm_semigroup A] [s' : has_one A] (a b t : A) (H : a + b = t) :
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bit1 a + bit0 b = bit1 t :=
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by rewrite -H; apply bit1_add_bit0
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theorem bit0_add_bit1 [s : add_comm_semigroup A] [s' : has_one A] (a b : A) :
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bit0 a + bit1 b = bit1 (a + b) :=
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by rewrite [{bit0 a + _}add.comm, {a + _}add.comm]; apply bit1_add_bit0
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theorem bit0_add_bit1_helper [s : add_comm_semigroup A] [s' : has_one A] (a b t : A) (H : a + b = t) :
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bit0 a + bit1 b = bit1 t :=
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by rewrite -H; apply bit0_add_bit1
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theorem bit1_add_bit1 [s : add_comm_semigroup A] [s' : has_one A] (a b : A) : bit1 a + bit1 b = bit0 (add1 (a + b)) :=
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begin
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rewrite ↑[bit0, bit1, add1],
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apply sorry
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end
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theorem bit1_add_bit1_helper [s : add_comm_semigroup A] [s' : has_one A] (a b t s: A)
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(H : (a + b) = t) (H2 : add1 t = s) : bit1 a + bit1 b = bit0 s :=
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begin rewrite [-H2, -H], apply bit1_add_bit1 end
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theorem bin_add_zero [s : add_monoid A] (a : A) : a + zero = a := !add_zero
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theorem bin_zero_add [s : add_monoid A] (a : A) : zero + a = a := !zero_add
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theorem one_add_bit0 [s : add_comm_semigroup A] [s' : has_one A] (a : A) : one + bit0 a = bit1 a :=
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begin rewrite ↑[bit0, bit1], rewrite add.comm end
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theorem bit0_add_one [s : has_add A] [s' : has_one A] (a : A) : bit0 a + one = bit1 a := rfl
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theorem bit1_add_one [s : has_add A] [s' : has_one A] (a : A) : bit1 a + one = add1 (bit1 a) := rfl
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theorem bit1_add_one_helper [s : has_add A] [s' : has_one A] (a t : A) (H : add1 (bit1 a) = t) :
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bit1 a + one = t :=
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by rewrite -H
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theorem one_add_bit1 [s : add_comm_semigroup A] [s' : has_one A] (a : A) :
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one + bit1 a = add1 (bit1 a) := !add.comm
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theorem one_add_bit1_helper [s : add_comm_semigroup A] [s' : has_one A] (a t : A)
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(H : add1 (bit1 a) = t) : one + bit1 a = t :=
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by rewrite -H; apply one_add_bit1
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theorem add1_bit0 [s : has_add A] [s' : has_one A] (a : A) : add1 (bit0 a) = bit1 a :=
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rfl
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theorem add1_bit1 [s : add_comm_semigroup A] [s' : has_one A] (a : A) :
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add1 (bit1 a) = bit0 (add1 a) :=
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begin
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rewrite ↑[add1, bit1, bit0],
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rewrite [add.assoc, add_comm_four]
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end
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theorem add1_bit1_helper [s : add_comm_semigroup A] [s' : has_one A] (a t : A) (H : add1 a = t) :
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add1 (bit1 a) = bit0 t :=
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by rewrite -H; apply add1_bit1
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theorem add1_one [s : has_add A] [s' : has_one A] : add1 (one : A) = bit0 one :=
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rfl
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theorem add1_zero [s : add_monoid A] [s' : has_one A] : add1 (zero : A) = one :=
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begin
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rewrite [↑add1, zero_add]
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end
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theorem one_add_one [s : has_add A] [s' : has_one A] : (one : A) + one = bit0 one :=
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rfl
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theorem subst_into_sum [s : has_add A] (l r tl tr t : A) (prl : l = tl) (prr : r = tr) (prt : tl + tr = t) :
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l + r = t :=
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by rewrite [prl, prr, prt]
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-- multiplication
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theorem mul_zero [s : mul_zero_class A] (a : A) : a * zero = zero :=
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by rewrite [↑zero, mul_zero]
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theorem zero_mul [s : mul_zero_class A] (a : A) : zero * a = zero :=
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by rewrite [↑zero, zero_mul]
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theorem mul_one [s : monoid A] (a : A) : a * one = a :=
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by rewrite [↑one, mul_one]
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theorem mul_bit0 [s : distrib A] (a b : A) : a * (bit0 b) = bit0 (a * b) :=
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by rewrite [↑bit0, left_distrib]
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theorem mul_bit0_helper [s : distrib A] (a b t : A) (H : a * b = t) : a * (bit0 b) = bit0 t :=
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by rewrite -H; apply mul_bit0
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theorem mul_bit1 [s : semiring A] (a b : A) : a * (bit1 b) = bit0 (a * b) + a :=
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by rewrite [↑bit1, ↑bit0, +left_distrib, ↑one, mul_one]
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theorem mul_bit1_helper [s : semiring A] (a b s t : A) (Hs : a * b = s) (Ht : bit0 s + a = t) :
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a * (bit1 b) = t :=
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begin rewrite [-Ht, -Hs, mul_bit1] end
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theorem subst_into_prod [s : has_mul A] (l r tl tr t : A) (prl : l = tl) (prr : r = tr)
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(prt : tl * tr = t) :
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l * r = t :=
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by rewrite [prl, prr, prt]
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theorem mk_cong (op : A → A) (a b : A) (H : a = b) : op a = op b :=
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by congruence; exact H
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theorem mk_eq (a : A) : a = a := rfl
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@ -43,6 +43,7 @@ Author: Leonardo de Moura
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#include "library/aux_recursors.h"
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#include "library/decl_stats.h"
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#include "library/meng_paulson.h"
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#include "library/norm_num.h"
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namespace lean {
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void initialize_library_module() {
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@ -85,6 +86,7 @@ void initialize_library_module() {
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initialize_aux_recursors();
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initialize_decl_stats();
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initialize_meng_paulson();
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initialize_norm_num();
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}
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void finalize_library_module() {
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@ -127,5 +129,6 @@ void finalize_library_module() {
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finalize_print();
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finalize_fingerprint();
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finalize_constants();
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finalize_norm_num();
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}
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}
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@ -1,18 +1,447 @@
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/*
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Copyright (c) 2015 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Rob Lewis
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Author: Robert Y. Lewis
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*/
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#include "library/norm_num.h"
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#include "library/constants.cpp"
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namespace lean {
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bool norm_num_context::is_numeral(expr const &) const {
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// TODO(Rob)
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static name * g_add = nullptr,
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* g_add1 = nullptr,
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* g_mul = nullptr,
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* g_sub = nullptr,
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* g_bit0_add_bit0 = nullptr,
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* g_bit1_add_bit0 = nullptr,
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* g_bit0_add_bit1 = nullptr,
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* g_bit1_add_bit1 = nullptr,
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* g_bin_add_0 = nullptr,
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* g_bin_0_add = nullptr,
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* g_bin_add_1 = nullptr,
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* g_1_add_bit0 = nullptr,
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* g_bit0_add_1 = nullptr,
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* g_bit1_add_1 = nullptr,
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* g_1_add_bit1 = nullptr,
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* g_one_add_one = nullptr,
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* g_add1_bit0 = nullptr,
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* g_add1_bit1 = nullptr,
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* g_add1_zero = nullptr,
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* g_add1_one = nullptr,
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* g_subst_sum = nullptr,
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* g_subst_prod = nullptr,
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* g_mk_cong = nullptr,
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* g_mk_eq = nullptr,
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* g_mul_zero = nullptr,
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* g_zero_mul = nullptr,
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* g_mul_one = nullptr,
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* g_mul_bit0 = nullptr,
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* g_mul_bit1 = nullptr,
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* g_has_mul = nullptr,
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* g_add_monoid = nullptr,
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* g_monoid = nullptr,
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* g_add_comm = nullptr,
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* g_mul_zero_class= nullptr,
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* g_distrib = nullptr,
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* g_semiring = nullptr;
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static bool is_numeral_aux(expr const & e, bool is_first) {
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buffer<expr> args;
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expr const & f = get_app_args(e, args);
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if (!is_constant(f)) {
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return false;
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}
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if (const_name(f) == *g_one) {
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return args.size() == 2;
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} else if (const_name(f) == *g_zero) {
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return is_first && args.size() == 2;
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} else if (const_name(f) == *g_bit1 || const_name(f) == *g_bit0) {
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return args.size() == 3 && is_numeral_aux(args[2], false);
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}
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return false;
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}
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pair<expr, expr> norm_num_context::mk_norm(expr const &) {
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bool norm_num_context::is_numeral(expr const & e) const {
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return is_numeral_aux(e, true);
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}
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/*
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Takes e : instance A, and tries to synthesize has_add A.
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*/
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expr norm_num_context::mk_has_add(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_has_add, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize has_add instance");
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}
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}
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expr norm_num_context::mk_has_mul(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_has_mul, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize has_mul instance");
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}
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}
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expr norm_num_context::mk_has_one(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_has_one, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize has_one instance");
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}
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}
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expr norm_num_context::mk_add_monoid(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_add_monoid, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize add_monoid instance");
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}
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}
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expr norm_num_context::mk_monoid(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_monoid, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize monoid instance");
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}
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}
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expr norm_num_context::mk_add_comm(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_add_comm, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize add_comm_semigroup instance");
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}
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}
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expr norm_num_context::mk_has_distrib(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_distrib, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize has_distrib instance");
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}
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}
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expr norm_num_context::mk_mul_zero_class(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_mul_zero_class, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize mul_zero instance");
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}
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}
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expr norm_num_context::mk_semiring(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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expr t = mk_app(mk_constant(*g_semiring, const_levels(f)), args[0]);
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optional<expr> inst = mk_class_instance(m_env, m_ctx, t);
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if (inst) {
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return *inst;
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} else {
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throw exception("failed to synthesize semiring instance");
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}
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}
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expr norm_num_context::mk_const(name const & n) {
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return mk_constant(n, m_lvls);
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}
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expr norm_num_context::mk_cong(expr const & op, expr const & type, expr const & a, expr const & b, expr const & eq) {
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return mk_app({mk_const(*g_mk_cong), type, op, a, b, eq});
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}
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pair<expr, expr> norm_num_context::mk_norm(expr const & e) {
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buffer<expr> args;
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expr f = get_app_args(e, args);
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if (!is_constant(f)) {
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throw exception("cannot take norm of nonconstant");
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}
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m_lvls = const_levels(f);
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if (const_name(f) == *g_add && args.size() == 4) {
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auto lhs_p = mk_norm(args[2]);
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auto rhs_p = mk_norm(args[3]);
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auto add_p = mk_norm_add(lhs_p.first, rhs_p.first);
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expr prf = mk_app({mk_const(*g_subst_sum), args[0], mk_has_add(args[1]), args[2], args[3],
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lhs_p.first, rhs_p.first, add_p.first, lhs_p.second, rhs_p.second, add_p.second});
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return pair<expr, expr>(add_p.first, prf);
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} else if (const_name(f) == *g_mul && args.size() == 4) {
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auto lhs_p = mk_norm(args[2]);
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auto rhs_p = mk_norm(args[3]);
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auto mul_p = mk_norm_mul(lhs_p.first, rhs_p.first);
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expr prf = mk_app({mk_const(*g_subst_prod), args[0], mk_has_mul(args[1]), args[2], args[3],
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lhs_p.first, rhs_p.first, mul_p.first, lhs_p.second, rhs_p.second, mul_p.second});
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return pair<expr, expr>(mul_p.first, prf);
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} else if (const_name(f) == *g_bit0 && args.size() == 3) {
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auto arg = mk_norm(args[2]);
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expr rv = mk_app({f, args[0], args[1], arg.first});
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expr prf = mk_cong(mk_app({f, args[0], args[1]}), args[0], args[2], arg.first, arg.second);
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return pair<expr, expr>(rv, prf);
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} else if (const_name(f) == *g_bit1 && args.size() == 4) {
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auto arg = mk_norm(args[3]);
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expr rv = mk_app({f, args[0], args[1], args[2], arg.first});
|
||||
expr prf = mk_cong(mk_app({f, args[0], args[1], args[2]}), args[0], args[3], arg.first, arg.second);
|
||||
return pair<expr, expr>(rv, prf);
|
||||
} else if ((const_name(f) == *g_zero || const_name(f) == *g_one) && args.size() == 2) {
|
||||
return pair<expr, expr>(e, mk_app({mk_const(*g_mk_eq), args[0], e}));
|
||||
} else {
|
||||
std::cout << "error with name " << const_name(f) << " and size " << args.size() << ".\n";
|
||||
throw exception("mk_norm found unrecognized combo ");
|
||||
}
|
||||
// TODO(Rob): cases for sub, div
|
||||
}
|
||||
|
||||
// returns <t, p> such that p is a proof that lhs + rhs = t.
|
||||
pair<expr, expr> norm_num_context::mk_norm_add(expr const & lhs, expr const & rhs) {
|
||||
buffer<expr> args_lhs;
|
||||
buffer<expr> args_rhs;
|
||||
expr lhs_head = get_app_args (lhs, args_lhs);
|
||||
expr rhs_head = get_app_args (rhs, args_rhs);
|
||||
if (!is_constant(lhs_head) || !is_constant(rhs_head)) {
|
||||
throw exception("cannot take norm_add of nonconstant");
|
||||
}
|
||||
auto type = args_lhs[0];
|
||||
auto typec = args_lhs[1];
|
||||
expr rv;
|
||||
expr prf;
|
||||
if (is_bit0(lhs) && is_bit0(rhs)) { // typec is has_add
|
||||
auto p = mk_norm_add(args_lhs[2], args_rhs[2]);
|
||||
rv = mk_app(lhs_head, type, typec, p.first);
|
||||
prf = mk_app({mk_const(*g_bit0_add_bit0), type, mk_add_comm(typec), args_lhs[2], args_rhs[2], p.first, p.second});
|
||||
} else if (is_bit0(lhs) && is_bit1(rhs)) {
|
||||
auto p = mk_norm_add(args_lhs[2], args_rhs[3]);
|
||||
rv = mk_app({rhs_head, type, args_rhs[1], args_rhs[2], p.first});
|
||||
prf = mk_app({mk_const(*g_bit0_add_bit1), type, mk_add_comm(typec), args_rhs[1], args_lhs[2], args_rhs[3], p.first, p.second});
|
||||
} else if (is_bit0(lhs) && is_one(rhs)) {
|
||||
rv = mk_app({mk_const(*g_bit1), type, args_rhs[1], args_lhs[1], args_lhs[2]});
|
||||
prf = mk_app({mk_const(*g_bit0_add_1), type, typec, args_rhs[1], args_lhs[2]});
|
||||
} else if (is_bit1(lhs) && is_bit0(rhs)) { // typec is has_one
|
||||
auto p = mk_norm_add(args_lhs[3], args_rhs[2]);
|
||||
rv = mk_app(lhs_head, type, typec, args_lhs[2], p.first);
|
||||
prf = mk_app({mk_const(*g_bit1_add_bit0), type, mk_add_comm(typec), typec, args_lhs[3], args_rhs[2], p.first, p.second});
|
||||
} else if (is_bit1(lhs) && is_bit1(rhs)) { // typec is has_one
|
||||
auto add_ts = mk_norm_add(args_lhs[3], args_rhs[3]);
|
||||
expr add1 = mk_app({mk_const(*g_add1), type, args_lhs[2], typec, add_ts.first});
|
||||
auto p = mk_norm_add1(add1);
|
||||
rv = mk_app({mk_const(*g_bit0), type, args_lhs[2], p.first});
|
||||
prf = mk_app({mk_const(*g_bit1_add_bit1), type, mk_add_comm(typec), typec, args_lhs[3], args_rhs[3], add_ts.first, p.first, add_ts.second, p.second});
|
||||
} else if (is_bit1(lhs) && is_one(rhs)) { // typec is has_one
|
||||
expr add1 = mk_app({mk_const(*g_add1), type, args_lhs[2], typec, lhs});
|
||||
auto p = mk_norm_add1(add1);
|
||||
rv = p.first;
|
||||
prf = mk_app({mk_const(*g_bit1_add_1), type, args_lhs[2], typec, args_lhs[3], p.first, p.second});
|
||||
} else if (is_one(lhs) && is_bit0(rhs)) { // typec is has_one
|
||||
rv = mk_app({mk_const(*g_bit1), type, typec, args_rhs[1], args_rhs[2]});
|
||||
prf = mk_app({mk_const(*g_1_add_bit0), type, mk_add_comm(typec), typec, args_rhs[2]});
|
||||
} else if (is_one(lhs) && is_bit1(rhs)) { // typec is has_one
|
||||
expr add1 = mk_app({mk_const(*g_add1), type, args_rhs[2], args_rhs[1], rhs});
|
||||
auto p = mk_norm_add1(add1);
|
||||
rv = p.first;
|
||||
prf = mk_app({mk_const(*g_1_add_bit1), type, mk_add_comm(typec), typec, args_rhs[3], p.first, p.second});
|
||||
} else if (is_one(lhs) && is_one(rhs)) {
|
||||
rv = mk_app({mk_const(*g_bit0), type, mk_has_add(typec), lhs});
|
||||
prf = mk_app({mk_const(*g_one_add_one), type, mk_has_add(typec), typec});
|
||||
} else if (is_zero(lhs)) {
|
||||
rv = rhs;
|
||||
prf = mk_app({mk_const(*g_bin_0_add), type, mk_add_monoid(typec), rhs});
|
||||
} else if (is_zero(rhs)) {
|
||||
rv = lhs;
|
||||
prf = mk_app({mk_const(*g_bin_add_0), type, mk_add_monoid(typec), lhs});
|
||||
}
|
||||
else {
|
||||
std::cout << "\n\n bad args: " << lhs_head << ", " << rhs_head << "\n";
|
||||
throw exception("mk_norm_add got malformed args");
|
||||
}
|
||||
return pair<expr, expr>(rv, prf);
|
||||
}
|
||||
|
||||
pair<expr, expr> norm_num_context::mk_norm_add1(expr const & e) {
|
||||
buffer<expr> args;
|
||||
expr f = get_app_args(e, args);
|
||||
expr p = args[3];
|
||||
buffer<expr> ne_args;
|
||||
expr ne = get_app_args(p, ne_args);
|
||||
expr rv;
|
||||
expr prf;
|
||||
// args[1] = has_add, args[2] = has_one
|
||||
if (is_bit0(p)) {
|
||||
auto has_one = args[2];
|
||||
rv = mk_app({mk_const(*g_bit1), args[0], args[2], args[1], ne_args[2]});
|
||||
prf = mk_app({mk_const(*g_add1_bit0), args[0], args[1], args[2], ne_args[2]});
|
||||
} else if (is_bit1(p)) { // ne_args : has_one, has_add
|
||||
auto np = mk_norm_add1(mk_app({mk_const(*g_add1), args[0], args[1], args[2], ne_args[3]}));
|
||||
rv = mk_app({mk_const(*g_bit0), args[0], args[1], np.first});
|
||||
prf = mk_app({mk_const(*g_add1_bit1), args[0], mk_add_comm(args[1]), args[2], ne_args[3], np.first, np.second});
|
||||
} else if (is_zero(p)) {
|
||||
rv = mk_app({mk_const(*g_one), args[0], args[2]});
|
||||
prf = mk_app({mk_const(*g_add1_zero), args[0], mk_add_monoid(args[1]), args[2]});
|
||||
} else if (is_one(p)) {
|
||||
rv = mk_app({mk_const(*g_bit0), args[0], args[1], mk_app({mk_const(*g_one), args[0], args[2]})});
|
||||
prf = mk_app({mk_const(*g_add1_one), args[0], args[1], args[2]});
|
||||
} else {
|
||||
std::cout << "malformed add1: " << ne << "\n";
|
||||
throw exception("malformed add1");
|
||||
}
|
||||
return pair<expr, expr>(rv, prf);
|
||||
}
|
||||
|
||||
pair<expr, expr> norm_num_context::mk_norm_mul(expr const & lhs, expr const & rhs) {
|
||||
buffer<expr> args_lhs;
|
||||
buffer<expr> args_rhs;
|
||||
expr lhs_head = get_app_args (lhs, args_lhs);
|
||||
expr rhs_head = get_app_args (rhs, args_rhs);
|
||||
if (!is_constant(lhs_head) || !is_constant(rhs_head)) {
|
||||
throw exception("cannot take norm_add of nonconstant");
|
||||
}
|
||||
auto type = args_rhs[0];
|
||||
auto typec = args_rhs[1];
|
||||
expr rv;
|
||||
expr prf;
|
||||
if (is_zero(rhs)) {
|
||||
rv = rhs;
|
||||
prf = mk_app({mk_const(*g_mul_zero), type, mk_mul_zero_class(typec), lhs});
|
||||
} else if (is_zero(lhs)) {
|
||||
rv = lhs;
|
||||
prf = mk_app({mk_const(*g_zero_mul), type, mk_mul_zero_class(typec), rhs});
|
||||
} else if (is_one(rhs)) {
|
||||
rv = lhs;
|
||||
prf = mk_app({mk_const(*g_mul_one), type, mk_monoid(typec), lhs});
|
||||
} else if (is_bit0(rhs)) {
|
||||
auto mtp = mk_norm_mul(lhs, args_rhs[2]);
|
||||
rv = mk_app({rhs_head, type, typec, mtp.first});
|
||||
prf = mk_app({mk_const(*g_mul_bit0), type, mk_has_distrib(typec), lhs, args_rhs[2], mtp.first, mtp.second});
|
||||
} else if (is_bit1(rhs)) {
|
||||
std::cout << "is_bit1 " << rhs << "\n";
|
||||
auto mtp = mk_norm_mul(lhs, args_rhs[3]);
|
||||
auto atp = mk_norm_add(mk_app({mk_const(*g_bit0), type, args_rhs[2], mtp.first}), lhs);
|
||||
rv = atp.first;
|
||||
prf = mk_app({mk_const(*g_mul_bit1), type, mk_semiring(typec), lhs, args_rhs[3],
|
||||
mtp.first, atp.first, mtp.second, atp.second});
|
||||
} else {
|
||||
std::cout << "bad args to mk_norm_mul: " << rhs << "\n";
|
||||
throw exception("mk_norm_mul got malformed args");
|
||||
}
|
||||
return pair<expr, expr>(rv, prf);
|
||||
}
|
||||
|
||||
pair<expr, expr> norm_num_context::mk_norm_div(expr const &, expr const &) {
|
||||
// TODO(Rob)
|
||||
throw exception("not implemented yet - norm_num`");
|
||||
throw exception("not implemented yet -- mk_norm_div");
|
||||
}
|
||||
|
||||
pair<expr, expr> norm_num_context::mk_norm_sub(expr const &, expr const &) {
|
||||
// TODO(Rob)
|
||||
throw exception("not implemented yet -- mk_norm_sub");
|
||||
}
|
||||
|
||||
void initialize_norm_num() {
|
||||
g_add = new name("add");
|
||||
g_add1 = new name("add1");
|
||||
g_mul = new name("mul");
|
||||
g_sub = new name("sub");
|
||||
g_bit0_add_bit0 = new name("bit0_add_bit0_helper");
|
||||
g_bit1_add_bit0 = new name("bit1_add_bit0_helper");
|
||||
g_bit0_add_bit1 = new name("bit0_add_bit1_helper");
|
||||
g_bit1_add_bit1 = new name("bit1_add_bit1_helper");
|
||||
g_bin_add_0 = new name("bin_add_zero");
|
||||
g_bin_0_add = new name("bin_zero_add");
|
||||
g_bin_add_1 = new name("bin_add_one");
|
||||
g_1_add_bit0 = new name("one_add_bit0");
|
||||
g_bit0_add_1 = new name("bit0_add_one");
|
||||
g_bit1_add_1 = new name("bit1_add_one_helper");
|
||||
g_1_add_bit1 = new name("one_add_bit1_helper");
|
||||
g_one_add_one = new name("one_add_one");
|
||||
g_add1_bit0 = new name("add1_bit0");
|
||||
g_add1_bit1 = new name("add1_bit1_helper");
|
||||
g_add1_zero = new name("add1_zero");
|
||||
g_add1_one = new name("add1_one");
|
||||
g_subst_sum = new name("subst_into_sum");
|
||||
g_subst_prod = new name("subst_into_prod");
|
||||
g_mk_cong = new name("mk_cong");
|
||||
g_mk_eq = new name("mk_eq");
|
||||
g_zero_mul = new name("zero_mul");
|
||||
g_mul_zero = new name("mul_zero");
|
||||
g_mul_one = new name("mul_one");
|
||||
g_mul_bit0 = new name("mul_bit0_helper");
|
||||
g_mul_bit1 = new name("mul_bit1_helper");
|
||||
g_has_mul = new name("has_mul");
|
||||
g_add_monoid = new name("algebra", "add_monoid");
|
||||
g_monoid = new name("algebra", "monoid");
|
||||
g_add_comm = new name("algebra", "add_comm_semigroup");
|
||||
g_mul_zero_class = new name("algebra", "mul_zero_class");
|
||||
g_distrib = new name("algebra", "distrib");
|
||||
g_semiring = new name("algebra", "semiring");
|
||||
}
|
||||
|
||||
void finalize_norm_num() {
|
||||
delete g_add;
|
||||
delete g_add1;
|
||||
delete g_mul;
|
||||
delete g_sub;
|
||||
delete g_bit0_add_bit0;
|
||||
delete g_bit1_add_bit0;
|
||||
delete g_bit0_add_bit1;
|
||||
delete g_bit1_add_bit1;
|
||||
delete g_bin_add_0;
|
||||
delete g_bin_0_add;
|
||||
delete g_bin_add_1;
|
||||
delete g_1_add_bit0;
|
||||
delete g_bit0_add_1;
|
||||
delete g_bit1_add_1;
|
||||
delete g_1_add_bit1;
|
||||
delete g_one_add_one;
|
||||
delete g_add1_bit0;
|
||||
delete g_add1_bit1;
|
||||
delete g_add1_zero;
|
||||
delete g_add1_one;
|
||||
delete g_subst_sum;
|
||||
delete g_subst_prod;
|
||||
delete g_mk_cong;
|
||||
delete g_mk_eq;
|
||||
delete g_mul_zero;
|
||||
delete g_zero_mul;
|
||||
delete g_mul_one;
|
||||
delete g_mul_bit0;
|
||||
delete g_mul_bit1;
|
||||
delete g_has_mul;
|
||||
delete g_add_monoid;
|
||||
delete g_monoid;
|
||||
delete g_add_comm;
|
||||
delete g_mul_zero_class;
|
||||
delete g_distrib;
|
||||
delete g_semiring;
|
||||
}
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,17 +1,36 @@
|
|||
/*
|
||||
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
|
||||
Released under Apache 2.0 license as described in the file LICENSE.
|
||||
|
||||
Author: Rob Lewis
|
||||
Author: Robert Y. Lewis
|
||||
*/
|
||||
#pragma once
|
||||
#include "kernel/environment.h"
|
||||
#include "library/local_context.h"
|
||||
#include "library/num.h"
|
||||
#include "library/class_instance_synth.h"
|
||||
|
||||
namespace lean {
|
||||
class norm_num_context {
|
||||
environment m_env;
|
||||
local_context m_ctx;
|
||||
levels m_lvls;
|
||||
pair<expr, expr> mk_norm_add(expr const &, expr const &);
|
||||
pair<expr, expr> mk_norm_add1(expr const &);
|
||||
pair<expr, expr> mk_norm_mul(expr const &, expr const &);
|
||||
pair<expr, expr> mk_norm_div(expr const &, expr const &);
|
||||
pair<expr, expr> mk_norm_sub(expr const &, expr const &);
|
||||
expr mk_const(name const & n);
|
||||
expr mk_cong(expr const &, expr const &, expr const &, expr const &, expr const &);
|
||||
expr mk_has_add(expr const &);
|
||||
expr mk_has_mul(expr const &);
|
||||
expr mk_has_one(expr const &);
|
||||
expr mk_add_monoid(expr const &);
|
||||
expr mk_monoid(expr const &);
|
||||
expr mk_has_distrib(expr const &);
|
||||
expr mk_add_comm(expr const &);
|
||||
expr mk_mul_zero_class(expr const &);
|
||||
expr mk_semiring(expr const &);
|
||||
|
||||
public:
|
||||
norm_num_context(environment const & env, local_context const & ctx):m_env(env), m_ctx(ctx) {}
|
||||
|
||||
|
|
@ -26,4 +45,6 @@ inline bool is_numeral(environment const & env, expr const & e) {
|
|||
inline pair<expr, expr> mk_norm_num(environment const & env, local_context const & ctx, expr const & e) {
|
||||
return norm_num_context(env, ctx).mk_norm(e);
|
||||
}
|
||||
void initialize_norm_num();
|
||||
void finalize_norm_num();
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,10 +1,12 @@
|
|||
/*
|
||||
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
|
||||
Released under Apache 2.0 license as described in the file LICENSE.
|
||||
|
||||
Author: Rob Lewis
|
||||
Author: Robert Y. Lewis
|
||||
*/
|
||||
#include "kernel/type_checker.h"
|
||||
#include "library/util.h"
|
||||
#include "library/reducible.h"
|
||||
#include "library/normalize.h"
|
||||
#include "library/norm_num.h"
|
||||
#include "library/tactic/expr_to_tactic.h"
|
||||
|
||||
|
|
@ -23,19 +25,30 @@ tactic norm_num_tactic() {
|
|||
throw_tactic_exception_if_enabled(s, "norm_num tactic failed, conclusion is not an equality");
|
||||
return none_proof_state();
|
||||
}
|
||||
type_checker_ptr rtc = mk_type_checker(env, UnfoldReducible);
|
||||
lhs = normalize(*rtc, lhs);
|
||||
rhs = normalize(*rtc, rhs);
|
||||
|
||||
buffer<expr> hyps;
|
||||
g.get_hyps(hyps);
|
||||
local_context ctx(to_list(hyps));
|
||||
try {
|
||||
//bool bs = is_numeral(env, lhs);
|
||||
pair<expr, expr> p = mk_norm_num(env, ctx, lhs);
|
||||
expr new_lhs = p.first;
|
||||
expr new_pr = p.second;
|
||||
if (new_lhs != rhs) {
|
||||
throw_tactic_exception_if_enabled(s, "norm_num tactic failed, lhs normal form doesn't match rhs");
|
||||
return none_proof_state();
|
||||
}
|
||||
expr new_lhs_pr = p.second;
|
||||
pair<expr, expr> p2 = mk_norm_num(env, ctx, rhs);
|
||||
expr new_rhs = p2.first;
|
||||
expr new_rhs_pr = p2.second;
|
||||
//if (new_lhs != new_rhs) {
|
||||
// std::cout << "lhs: " << new_lhs << ", rhs: " << new_rhs << "\n";
|
||||
// throw_tactic_exception_if_enabled(s, "norm_num tactic failed, lhs normal form doesn't match rhs");
|
||||
// return none_proof_state();
|
||||
//}
|
||||
type_checker tc(env);
|
||||
expr g_prf = mk_trans(tc, new_lhs_pr, mk_symm(tc, new_rhs_pr));
|
||||
substitution new_subst = s.get_subst();
|
||||
assign(new_subst, g, new_pr);
|
||||
assign(new_subst, g, g_prf);
|
||||
return some_proof_state(proof_state(s, tail(gs), new_subst));
|
||||
} catch (exception & ex) {
|
||||
throw_tactic_exception_if_enabled(s, ex.what());
|
||||
|
|
|
|||
|
|
@ -1,11 +1,51 @@
|
|||
import algebra.numeral algebra.ring
|
||||
import algebra.numeral algebra.field
|
||||
open algebra
|
||||
|
||||
variable {A : Type}
|
||||
variable [s : ring A]
|
||||
variable [s : comm_ring A]
|
||||
include s
|
||||
|
||||
example : add (bit0 (one:A)) one = bit1 one :=
|
||||
begin
|
||||
norm_num
|
||||
end
|
||||
example : (1 : A) = 0 + 1 := by norm_num
|
||||
example : (1 : A) = 1 + 0 := by norm_num
|
||||
example : (2 : A) = 1 + 1 := by norm_num
|
||||
example : (2 : A) = 0 + 2 := by norm_num
|
||||
example : (3 : A) = 1 + 2 := by norm_num
|
||||
example : (3 : A) = 2 + 1 := by norm_num
|
||||
example : (4 : A) = 3 + 1 := by norm_num
|
||||
example : (4 : A) = 2 + 2 := by norm_num
|
||||
example : (5 : A) = 4 + 1 := by norm_num
|
||||
example : (5 : A) = 3 + 2 := by norm_num
|
||||
example : (5 : A) = 2 + 3 := by norm_num
|
||||
example : (6 : A) = 0 + 6 := by norm_num
|
||||
example : (6 : A) = 3 + 3 := by norm_num
|
||||
example : (6 : A) = 4 + 2 := by norm_num
|
||||
example : (6 : A) = 5 + 1 := by norm_num
|
||||
example : (7 : A) = 4 + 3 := by norm_num
|
||||
example : (7 : A) = 1 + 6 := by norm_num
|
||||
example : (7 : A) = 6 + 1 := by norm_num
|
||||
example : 33 = 5 + (28 : A) := by norm_num
|
||||
|
||||
|
||||
example : (12 : A) = 0 + (2 + 3) + 7 := by norm_num
|
||||
example : (105 : A) = 70 + (33 + 2) := by norm_num
|
||||
example : (45000000000 : A) = 23000000000 + 22000000000 := by norm_num
|
||||
|
||||
example : (0 : A) * 0 = 0 := by norm_num
|
||||
example : (0 : A) * 1 = 0 := by norm_num
|
||||
example : (0 : A) * 2 = 0 := by norm_num
|
||||
example : (2 : A) * 0 = 0 := by norm_num
|
||||
example : (1 : A) * 0 = 0 := by norm_num
|
||||
example : (1 : A) * 1 = 1 := by norm_num
|
||||
example : (2 : A) * 1 = 2 := by norm_num
|
||||
example : (1 : A) * 2 = 2 := by norm_num
|
||||
example : (2 : A) * 2 = 4 := by norm_num
|
||||
example : (3 : A) * 2 = 6 := by norm_num
|
||||
example : (2 : A) * 3 = 6 := by norm_num
|
||||
example : (4 : A) * 1 = 4 := by norm_num
|
||||
example : (1 : A) * 4 = 4 := by norm_num
|
||||
example : (3 : A) * 3 = 9 := by norm_num
|
||||
example : (3 : A) * 4 = 12 := by norm_num
|
||||
example : (4 : A) * 4 = 16 := by norm_num
|
||||
example : (11 : A) * 2 = 22 := by norm_num
|
||||
example : (15 : A) * 6 = 90 := by norm_num
|
||||
example : (123456 : A) * 123456 = 15241383936 := by norm_num
|
||||
|
|
|
|||
Loading…
Reference in a new issue