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/* See LICENSE file for copyright and license details. */
#ifndef TEST
#include "common.h"
/**
* Check if two clauses have a term in common or
* a term in common but mutually inverse
*
* Both clauses must be clauses of binary connectives
*
* @param a One of the clauses
* @param b The other clause
* @param common_inv_out Output parameter for whether the common term is mutually inverted
* @param a_common_out Output parameter for `a`'s copy of the common term
* @param a_unique_out Output parameter for `a`'s uncommon term
* @param b_common_out Output parameter for `b`'s copy of the common term
* @param b_unique_out Output parameter for `b`'s uncommon term
* @return Whether the the clauses have a common or inversely common term
*/
static int
has_common(LIBNORMALFORM_SENTENCE *a, LIBNORMALFORM_SENTENCE *b, int *common_inv_out,
LIBNORMALFORM_SENTENCE **a_common_out, LIBNORMALFORM_SENTENCE **a_unique_out,
LIBNORMALFORM_SENTENCE **b_common_out, LIBNORMALFORM_SENTENCE **b_unique_out)
{
LIBNORMALFORM_SENTENCE *al = LEFT(a);
LIBNORMALFORM_SENTENCE *ar = RIGHT(a);
LIBNORMALFORM_SENTENCE *bl = LEFT(b);
LIBNORMALFORM_SENTENCE *br = RIGHT(b);
if (al->equals(al, bl, common_inv_out)) {
*a_common_out = al;
*b_common_out = bl;
*a_unique_out = ar;
*b_unique_out = br;
return 1;
} else if (ar->equals(ar, br, common_inv_out)) {
*a_common_out = ar;
*b_common_out = br;
*a_unique_out = al;
*b_unique_out = bl;
return 1;
} else if (al->equals(al, br, common_inv_out)) {
*a_common_out = al;
*b_common_out = br;
*a_unique_out = ar;
*b_unique_out = bl;
return 1;
} else if (ar->equals(ar, bl, common_inv_out)) {
*a_common_out = ar;
*b_common_out = bl;
*a_unique_out = al;
*b_unique_out = br;
return 1;
}
return 0;
}
LIBNORMALFORM_SENTENCE *
(libnormalform_xor2)(LIBNORMALFORM_SENTENCE *l, LIBNORMALFORM_SENTENCE *r)
{
int inv;
LIBNORMALFORM_SENTENCE *t, *not_a, *a, *b, *c;
if (!l || !r) {
libnormalform_free(l);
libnormalform_free(r);
return NULL;
}
if (l->equals(l, r, &inv)) {
libnormalform_free(l);
libnormalform_free(r);
if (!inv) {
/* x ⊕ x = 0 */
return libnormalform_false();
} else {
/* x ⊕ ¬x = 1 */
return libnormalform_true();
}
} else if (l->type == TYPE_TRUE) {
/* 1 ⊕ x = (1 ∨ x) ∧ ¬(1 ∧ x) = 1 ∧ ¬x = ¬x */
r = libnormalform_not(r);
return_r:
libnormalform_free(l);
return r;
} else if (l->type == TYPE_FALSE) {
/* 0 ⊕ x = (0 ∨ x) ∧ ¬(0 ∧ x) = x ∧ ¬0 = x ∧ 1 = x */
goto return_r;
} else if (r->type == TYPE_TRUE) {
/* x ⊕ 1 = 1 ⊕ x = ¬x */
l = libnormalform_not(l);
return_l:
libnormalform_free(r);
return l;
} else if (r->type == TYPE_FALSE) {
/* x ⊕ 0 = 0 ⊕ x = x */
goto return_l;
} else if (l->type == TYPE_OR && r->type == TYPE_OR) { /* TODO test */
if (!has_common(l, r, &inv, &a, &b, ¬_a, &c) || !inv)
goto asis;
/* (a ∨ b) ⊕ (¬a ∨ c) =
* (a ∨ b ∨ ¬a ∨ c) ∧ ¬((a ∨ b) ∧ (¬a ∨ c)) =
* ¬(a ∨ b) ∨ ¬(¬a ∨ c) */
return libnormalform_or2(libnormalform_not(l), libnormalform_not(r));
} else if (l->type == TYPE_AND && r->type == TYPE_AND) { /* TODO test */
if (!has_common(l, r, &inv, &a, &b, ¬_a, &c))
goto asis;
if (!inv) {
/* (a ∧ b) ⊕ (a ∧ c) =
* ((a ∧ b) ∨ (a ∧ c)) ∧ ¬((a ∧ b) ∧ (a ∧ c)) =
* a ∧ (b ∨ c) ∧ ¬(a ∧ b ∧ c) =
* a ∧ (b ∨ c) ∧ (¬a ∨ ¬b ∨ ¬c) =
* a ∧ (b ∨ c) ∧ (¬b ∨ ¬c) =
* a ∧ (b ⊕ c)
*/
a = libnormalform_ref(a);
b = libnormalform_ref(b);
c = libnormalform_ref(c);
libnormalform_free(l);
libnormalform_free(r);
return libnormalform_and2(a, libnormalform_xor2(c, b));
} else {
/* (a ∧ b) ⊕ (¬a ∧ c) =
* ((a ∧ b) ∨ (¬a ∧ c)) ∧ ¬((a ∧ b) ∧ (¬a ∧ c)) =
* ((a ∧ b) ∨ (¬a ∧ c)) ∧ ¬(a ∧ b ∧ ¬a ∧ c) =
* ((a ∧ b) ∨ (¬a ∧ c)) ∧ ¬⊥ =
* (a ∧ b) ∨ (¬a ∧ c)
*/
return libnormalform_or2__(l, r);
}
} else if (l->type == TYPE_OR && r->type == TYPE_AND) { /* TODO test */
t = l, l = r, r = t;
goto and_xor_or;
} else if (l->type == TYPE_AND && r->type == TYPE_OR) { /* TODO test */
and_xor_or:
if (!has_common(l, r, &inv, &a, &b, ¬_a, &c))
goto asis;
if (!inv) {
/* (a ∧ b) ⊕ (a ∨ c) =
* ((a ∧ b) ∨ (a ∨ c)) ∧ ¬((a ∧ b) ∧ (a ∨ c)) =
* ((a ∧ b) ∨ a ∨ c) ∧ ¬(a ∧ b ∧ (a ∨ c)) =
* (a ∨ c) ∧ ¬(a ∧ b) =
* ¬(a ∧ b) ∧ (a ∨ c)
*/
return libnormalform_and2__(libnormalform_not(l), r);
} else {
/* (a ∧ b) ⊕ (¬a ∨ c) =
* ((a ∧ b) ∨ (¬a ∨ c)) ∧ ¬((a ∧ b) ∧ (¬a ∨ c)) =
* ((a ∧ b) ∨ ¬a ∨ c) ∧ ¬(a ∧ b ∧ (¬a ∨ c)) =
* ((a ∧ b) ∨ ¬a ∨ c) ∧ ¬(a ∧ b ∧ (⊥ ∨ c)) =
* ((a ∧ b) ∨ ¬a ∨ c) ∧ ¬(a ∧ b ∧ c) =
* ((a ∧ b) ∨ ¬a ∨ c) ∧ (¬a ∨ ¬b ∨ ¬c) =
* (b ∨ ¬a ∨ c) ∧ (¬a ∨ ¬b ∨ ¬c) =
* (¬a ∨ b ∨ c) ∧ (¬a ∨ ¬b ∨ ¬c) =
* ¬a ∨ ((b ∨ c) ∧ (¬b ∨ ¬c)) =
* ¬a ∨ (b ⊕ c)
*/
not_a = libnormalform_ref(not_a);
b = libnormalform_ref(b);
c = libnormalform_ref(c);
libnormalform_free(l);
libnormalform_free(r);
return libnormalform_or2(not_a, libnormalform_xor2(c, b));
}
} else {
asis:
return libnormalform_xor2__(l, r);
}
}
#else
#define USE_TWO
#include "libnormalform_xor.c"
#endif
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