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Test quantified formulas

This commit is contained in:
Patrick Lühne 2020-04-06 15:07:53 +02:00
parent cc3265fc72
commit c11156b2ce
Signed by: patrick
GPG Key ID: 05F3611E97A70ABF
1 changed files with 675 additions and 51 deletions
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726
src/format/formulas.rs
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@ -587,6 +587,11 @@ mod tests
#[test]
fn format_combination_boolean_and_lower()
{
// Boolean + not
assert_eq!(format(not(true_())), "not true");
assert_eq!(format(not(false_())), "not false");
// Boolean + quantified formula
assert_eq!(format(exists(vec![variable_declaration("X")], true_())), "exists X true");
assert_eq!(format(exists(vec![variable_declaration("X")], false_())), "exists X false");
assert_eq!(format(
@ -608,19 +613,19 @@ mod tests
variable_declaration("Z")], false_())),
"forall X, Y, Z false");
assert_eq!(format(not(true_())), "not true");
assert_eq!(format(not(false_())), "not false");
// Boolean + and
assert_eq!(format(and(vec![true_()])), "true");
assert_eq!(format(and(vec![true_(), true_(), true_()])), "true and true and true");
assert_eq!(format(and(vec![false_()])), "false");
assert_eq!(format(and(vec![false_(), false_(), false_()])), "false and false and false");
// Boolean + or
assert_eq!(format(or(vec![true_()])), "true");
assert_eq!(format(or(vec![true_(), true_(), true_()])), "true or true or true");
assert_eq!(format(or(vec![false_()])), "false");
assert_eq!(format(or(vec![false_(), false_(), false_()])), "false or false or false");
// Boolean + implies
assert_eq!(format(
implies(ImplicationDirection::LeftToRight, true_(), true_())),
"true -> true");
@ -634,6 +639,7 @@ mod tests
implies(ImplicationDirection::RightToLeft, false_(), false_())),
"false <- false");
// Boolean + if and only if
assert_eq!(format(if_and_only_if(vec![true_()])), "true");
assert_eq!(format(
if_and_only_if(vec![true_(), true_(), true_()])),
@ -652,6 +658,7 @@ mod tests
let term_3 = || exponentiate(constant("a"), exponentiate(constant("b"), constant("c")));
let term_4 = || negative(function("f", vec![integer(5), add(variable("X"), integer(3))]));
// Compare + not
assert_eq!(format(not(greater(term_1(), term_2()))), "not (a + b) * c > |d - e|");
assert_eq!(format(not(less(term_1(), term_2()))), "not (a + b) * c < |d - e|");
assert_eq!(format(not(less_or_equal(term_1(), term_2()))), "not (a + b) * c <= |d - e|");
@ -659,6 +666,7 @@ mod tests
assert_eq!(format(not(equal(term_1(), term_2()))), "not (a + b) * c = |d - e|");
assert_eq!(format(not(not_equal(term_1(), term_2()))), "not (a + b) * c != |d - e|");
// Compare + quantified formula
assert_eq!(format(
exists(vec![variable_declaration("X")], greater(term_1(), term_2()))),
"exists X (a + b) * c > |d - e|");
@ -696,6 +704,7 @@ mod tests
for_all(vec![variable_declaration("X")], not_equal(term_1(), term_2()))),
"forall X (a + b) * c != |d - e|");
// Compare + and
assert_eq!(format(
and(vec![greater(term_1(), term_2()), greater(term_3(), term_4()),
greater(term_2(), term_4())])),
@ -721,6 +730,7 @@ mod tests
not_equal(term_2(), term_4())])),
"(a + b) * c != |d - e| and a ** b ** c != -f(5, X + 3) and |d - e| != -f(5, X + 3)");
// Compare + or
assert_eq!(format(
or(vec![greater(term_1(), term_2()), greater(term_3(), term_4()),
greater(term_2(), term_4())])),
@ -746,6 +756,7 @@ mod tests
not_equal(term_2(), term_4())])),
"(a + b) * c != |d - e| or a ** b ** c != -f(5, X + 3) or |d - e| != -f(5, X + 3)");
// Compare + implies
assert_eq!(format(
implies(ImplicationDirection::LeftToRight, greater(term_1(), term_2()),
greater(term_3(), term_4()))),
@ -795,6 +806,7 @@ mod tests
not_equal(term_3(), term_4()))),
"a ** b ** c != -f(5, X + 3) <- (a + b) * c != |d - e|");
// Compare + if and only if
assert_eq!(format(
if_and_only_if(vec![greater(term_1(), term_2()), greater(term_3(), term_4()),
greater(term_2(), term_4())])),
@ -894,18 +906,6 @@ mod tests
"forall X, Y, Z not p");
// Not + and
assert_eq!(format(
not(and(vec![predicate("p", vec![])]))),
"not p");
assert_eq!(format(
not(and(vec![and(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(or(vec![and(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(if_and_only_if(vec![and(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(and(vec![predicate("p", vec![]), predicate("q", vec![]), predicate("r", vec![])]))),
"not (p and q and r)");
@ -952,18 +952,6 @@ mod tests
"not p and not q and not r");
// Not + or
assert_eq!(format(
not(or(vec![predicate("p", vec![])]))),
"not p");
assert_eq!(format(
not(and(vec![or(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(or(vec![or(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(if_and_only_if(vec![or(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(or(vec![predicate("p", vec![]), predicate("q", vec![]), predicate("r", vec![])]))),
"not (p or q or r)");
@ -1078,18 +1066,6 @@ mod tests
"not q <- not p");
// Not + if and only if
assert_eq!(format(
not(if_and_only_if(vec![predicate("p", vec![])]))),
"not p");
assert_eq!(format(
not(and(vec![if_and_only_if(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(or(vec![if_and_only_if(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(if_and_only_if(vec![if_and_only_if(vec![predicate("p", vec![])])]))),
"not p");
assert_eq!(format(
not(if_and_only_if(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])]))),
@ -1138,31 +1114,679 @@ mod tests
}
#[test]
fn format_combination_quantifiers_and_lower()
fn format_combination_quantified_formula_and_lower()
{
// Quantified formula + quantified formula
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")], exists(vec![variable_declaration("A"),
variable_declaration("B"), variable_declaration("C")],
predicate("p", vec![])))),
variable_declaration("Z")],
exists(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![])))),
"exists X, Y, Z exists A, B, C p");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")], for_all(vec![variable_declaration("A"),
variable_declaration("Z")],
and(vec![exists(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"exists X, Y, Z exists A, B, C p");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![exists(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"exists X, Y, Z exists A, B, C p");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![exists(vec![variable_declaration("A"),
variable_declaration("B"), variable_declaration("C")],
predicate("p", vec![])))),
predicate("p", vec![]))]))),
"exists X, Y, Z exists A, B, C p");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
for_all(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![])))),
"exists X, Y, Z forall A, B, C p");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![for_all(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"exists X, Y, Z forall A, B, C p");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![for_all(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"exists X, Y, Z forall A, B, C p");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![for_all(vec![variable_declaration("A"),
variable_declaration("B"), variable_declaration("C")],
predicate("p", vec![]))]))),
"exists X, Y, Z forall A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")], exists(vec![variable_declaration("A"),
variable_declaration("B"), variable_declaration("C")],
predicate("p", vec![])))),
variable_declaration("Z")],
exists(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![])))),
"forall X, Y, Z exists A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")], for_all(vec![variable_declaration("A"),
variable_declaration("B"), variable_declaration("C")],
predicate("p", vec![])))),
variable_declaration("Z")],
and(vec![exists(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"forall X, Y, Z exists A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![exists(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"forall X, Y, Z exists A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![exists(vec![variable_declaration("A"),
variable_declaration("B"), variable_declaration("C")], predicate("p", vec![]))]))),
"forall X, Y, Z exists A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
for_all(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![])))),
"forall X, Y, Z forall A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![for_all(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"forall X, Y, Z forall A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![for_all(vec![variable_declaration("A"), variable_declaration("B"),
variable_declaration("C")], predicate("p", vec![]))]))),
"forall X, Y, Z forall A, B, C p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![for_all(vec![variable_declaration("A"),
variable_declaration("B"), variable_declaration("C")],
predicate("p", vec![]))]))),
"forall X, Y, Z forall A, B, C p");
// Quantified formula + and
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![predicate("p", vec![]), predicate("q", vec![]), predicate("r", vec![])]))),
"exists X, Y, Z (p and q and r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![and(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p and q and r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![and(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p and q and r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![and(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p and q and r)");
assert_eq!(format(
and(vec![
exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])),
exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])),
"exists X, Y p and exists A, B q and exists C, D r");
assert_eq!(format(
and(vec![
and(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
and(vec![exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"exists X, Y p and exists A, B q and exists C, D r");
assert_eq!(format(
and(vec![
or(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
or(vec![exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"exists X, Y p and exists A, B q and exists C, D r");
assert_eq!(format(
and(vec![
if_and_only_if(vec![exists(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("C"),
variable_declaration("D")], predicate("r", vec![]))])])),
"exists X, Y p and exists A, B q and exists C, D r");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![predicate("p", vec![]), predicate("q", vec![]), predicate("r", vec![])]))),
"forall X, Y, Z (p and q and r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![and(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p and q and r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![and(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p and q and r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![and(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p and q and r)");
assert_eq!(format(
and(vec![
for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])),
for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])),
"forall X, Y p and forall A, B q and forall C, D r");
assert_eq!(format(
and(vec![
and(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
and(vec![for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"forall X, Y p and forall A, B q and forall C, D r");
assert_eq!(format(
and(vec![
or(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
or(vec![for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"forall X, Y p and forall A, B q and forall C, D r");
assert_eq!(format(
and(vec![
if_and_only_if(vec![for_all(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("C"),
variable_declaration("D")], predicate("r", vec![]))])])),
"forall X, Y p and forall A, B q and forall C, D r");
// Quantified formula + or
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![predicate("p", vec![]), predicate("q", vec![]), predicate("r", vec![])]))),
"exists X, Y, Z (p or q or r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![or(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p or q or r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![or(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p or q or r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![or(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p or q or r)");
assert_eq!(format(
or(vec![
exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])),
exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])),
"exists X, Y p or exists A, B q or exists C, D r");
assert_eq!(format(
or(vec![
and(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
and(vec![exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"exists X, Y p or exists A, B q or exists C, D r");
assert_eq!(format(
or(vec![
or(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
or(vec![exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"exists X, Y p or exists A, B q or exists C, D r");
assert_eq!(format(
or(vec![
if_and_only_if(vec![exists(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("C"),
variable_declaration("D")], predicate("r", vec![]))])])),
"exists X, Y p or exists A, B q or exists C, D r");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![predicate("p", vec![]), predicate("q", vec![]), predicate("r", vec![])]))),
"forall X, Y, Z (p or q or r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![or(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p or q or r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![or(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p or q or r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![or(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p or q or r)");
assert_eq!(format(
or(vec![
for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])),
for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])),
"forall X, Y p or forall A, B q or forall C, D r");
assert_eq!(format(
or(vec![
and(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
and(vec![for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"forall X, Y p or forall A, B q or forall C, D r");
assert_eq!(format(
or(vec![
or(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
or(vec![for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"forall X, Y p or forall A, B q or forall C, D r");
assert_eq!(format(
or(vec![
if_and_only_if(vec![for_all(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("C"),
variable_declaration("D")], predicate("r", vec![]))])])),
"forall X, Y p or forall A, B q or forall C, D r");
// Quantified formula + implies
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
implies(ImplicationDirection::LeftToRight, predicate("p", vec![]),
predicate("q", vec![])))),
"exists X, Y, Z (p -> q)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![implies(ImplicationDirection::LeftToRight, predicate("p", vec![]),
predicate("q", vec![]))]))),
"exists X, Y, Z (p -> q)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![implies(ImplicationDirection::LeftToRight, predicate("p", vec![]),
predicate("q", vec![]))]))),
"exists X, Y, Z (p -> q)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![implies(ImplicationDirection::LeftToRight,
predicate("p", vec![]), predicate("q", vec![]))]))),
"exists X, Y, Z (p -> q)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
implies(ImplicationDirection::RightToLeft, predicate("p", vec![]),
predicate("q", vec![])))),
"exists X, Y, Z (q <- p)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![implies(ImplicationDirection::RightToLeft, predicate("p", vec![]),
predicate("q", vec![]))]))),
"exists X, Y, Z (q <- p)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![implies(ImplicationDirection::RightToLeft, predicate("p", vec![]),
predicate("q", vec![]))]))),
"exists X, Y, Z (q <- p)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![implies(ImplicationDirection::RightToLeft,
predicate("p", vec![]), predicate("q", vec![]))]))),
"exists X, Y, Z (q <- p)");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])))),
"exists X, Y p -> exists A, B q");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
and(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"exists X, Y p -> exists A, B q");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
or(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"exists X, Y p -> exists A, B q");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
if_and_only_if(vec![exists(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]))),
"exists X, Y p -> exists A, B q");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])))),
"exists A, B q <- exists X, Y p");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
and(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"exists A, B q <- exists X, Y p");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
or(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"exists A, B q <- exists X, Y p");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
if_and_only_if(vec![exists(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]))),
"exists A, B q <- exists X, Y p");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
implies(ImplicationDirection::LeftToRight, predicate("p", vec![]),
predicate("q", vec![])))),
"forall X, Y, Z (p -> q)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![implies(ImplicationDirection::LeftToRight, predicate("p", vec![]),
predicate("q", vec![]))]))),
"forall X, Y, Z (p -> q)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![implies(ImplicationDirection::LeftToRight, predicate("p", vec![]),
predicate("q", vec![]))]))),
"forall X, Y, Z (p -> q)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![implies(ImplicationDirection::LeftToRight,
predicate("p", vec![]), predicate("q", vec![]))]))),
"forall X, Y, Z (p -> q)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
implies(ImplicationDirection::RightToLeft, predicate("p", vec![]),
predicate("q", vec![])))),
"forall X, Y, Z (q <- p)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![implies(ImplicationDirection::RightToLeft, predicate("p", vec![]),
predicate("q", vec![]))]))),
"forall X, Y, Z (q <- p)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![implies(ImplicationDirection::RightToLeft, predicate("p", vec![]),
predicate("q", vec![]))]))),
"forall X, Y, Z (q <- p)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![implies(ImplicationDirection::RightToLeft,
predicate("p", vec![]), predicate("q", vec![]))]))),
"forall X, Y, Z (q <- p)");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])))),
"forall X, Y p -> forall A, B q");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
and(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"forall X, Y p -> forall A, B q");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
or(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"forall X, Y p -> forall A, B q");
assert_eq!(format(
implies(ImplicationDirection::LeftToRight,
if_and_only_if(vec![for_all(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]))),
"forall X, Y p -> forall A, B q");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])))),
"forall A, B q <- forall X, Y p");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
and(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"forall A, B q <- forall X, Y p");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
or(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]))),
"forall A, B q <- forall X, Y p");
assert_eq!(format(
implies(ImplicationDirection::RightToLeft,
if_and_only_if(vec![for_all(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]))),
"forall A, B q <- forall X, Y p");
// Quantified formula + if and only if
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])]))),
"exists X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![if_and_only_if(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![if_and_only_if(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"exists X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
exists(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![if_and_only_if(vec![predicate("p", vec![]),
predicate("q", vec![]), predicate("r", vec![])])]))),
"exists X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
if_and_only_if(vec![
exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])),
exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])),
"exists X, Y p <-> exists A, B q <-> exists C, D r");
assert_eq!(format(
if_and_only_if(vec![
and(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
and(vec![exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"exists X, Y p <-> exists A, B q <-> exists C, D r");
assert_eq!(format(
if_and_only_if(vec![
or(vec![exists(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![exists(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
or(vec![exists(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"exists X, Y p <-> exists A, B q <-> exists C, D r");
assert_eq!(format(
if_and_only_if(vec![
if_and_only_if(vec![exists(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]),
if_and_only_if(vec![exists(vec![variable_declaration("C"),
variable_declaration("D")], predicate("r", vec![]))])])),
"exists X, Y p <-> exists A, B q <-> exists C, D r");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])]))),
"forall X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
and(vec![if_and_only_if(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
or(vec![if_and_only_if(vec![predicate("p", vec![]), predicate("q", vec![]),
predicate("r", vec![])])]))),
"forall X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
for_all(vec![variable_declaration("X"), variable_declaration("Y"),
variable_declaration("Z")],
if_and_only_if(vec![if_and_only_if(vec![predicate("p", vec![]),
predicate("q", vec![]), predicate("r", vec![])])]))),
"forall X, Y, Z (p <-> q <-> r)");
assert_eq!(format(
if_and_only_if(vec![
for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![])),
for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![])),
for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])),
"forall X, Y p <-> forall A, B q <-> forall C, D r");
assert_eq!(format(
if_and_only_if(vec![
and(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
and(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
and(vec![for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"forall X, Y p <-> forall A, B q <-> forall C, D r");
assert_eq!(format(
if_and_only_if(vec![
or(vec![for_all(vec![variable_declaration("X"), variable_declaration("Y")],
predicate("p", vec![]))]),
or(vec![for_all(vec![variable_declaration("A"), variable_declaration("B")],
predicate("q", vec![]))]),
or(vec![for_all(vec![variable_declaration("C"), variable_declaration("D")],
predicate("r", vec![]))])])),
"forall X, Y p <-> forall A, B q <-> forall C, D r");
assert_eq!(format(
if_and_only_if(vec![
if_and_only_if(vec![for_all(vec![variable_declaration("X"),
variable_declaration("Y")], predicate("p", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("A"),
variable_declaration("B")], predicate("q", vec![]))]),
if_and_only_if(vec![for_all(vec![variable_declaration("C"),
variable_declaration("D")], predicate("r", vec![]))])])),
"forall X, Y p <-> forall A, B q <-> forall C, D r");
}
}