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tune axioms for derivatives

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2020-05-25 12:41:30 -07:00
parent 97b480ded3
commit 4e01d5b5c1
8 changed files with 207 additions and 65 deletions
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56
src/ast/rewriter/arith_rewriter.cpp
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@ -239,6 +239,60 @@ bool arith_rewriter::is_bound(expr * arg1, expr * arg2, op_kind kind, expr_ref &
return false;
}
bool arith_rewriter::is_non_negative(expr* e) {
seq_util seq(m());
if (seq.str.is_length(e))
return true;
// TBD: check for even power
return false;
}
/**
* perform static analysis on arg1 to determine a non-negative lower bound.
* a + b + r1 <= r2 -> false if r1 > r2 and a >= 0, b >= 0
* a + b + r1 >= r2 -> false if r1 < r2 and a <= 0, b <= 0
*/
bool arith_rewriter::is_separated(expr* arg1, expr* arg2, op_kind kind, expr_ref& result) {
if (kind != LE && kind != GE)
return false;
rational bound(0), r1, r2;
expr_ref narg(m());
bool has_bound = true;
if (!m_util.is_numeral(arg2, r2))
return false;
auto update_bound = [&](expr* arg) {
if (m_util.is_numeral(arg, r1)) {
bound += r1;
return;
}
if (kind == LE && is_non_negative(arg))
return;
if (kind == GE && is_neg_poly(arg, narg) && is_non_negative(narg))
return;
has_bound = false;
};
if (m_util.is_add(arg1)) {
for (expr* arg : *to_app(arg1)) {
update_bound(arg);
}
}
else {
update_bound(arg1);
}
if (!has_bound)
return false;
if (kind == LE && r1 > r2) {
result = m().mk_false();
return true;
}
if (kind == GE && r1 < r2) {
result = m().mk_false();
return true;
}
return false;
}
bool arith_rewriter::elim_to_real_var(expr * var, expr_ref & new_var) {
numeral val;
if (m_util.is_numeral(var, val)) {
@ -427,6 +481,8 @@ br_status arith_rewriter::mk_le_ge_eq_core(expr * arg1, expr * arg2, op_kind kin
ANUM_LE_GE_EQ();
}
}
if (is_separated(arg1, arg2, kind, result))
return BR_DONE;
if (is_bound(arg1, arg2, kind, result))
return BR_DONE;
if (is_bound(arg2, arg1, inv(kind), result))