Finish testing biconditionals
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GPG Key ID:
05F3611E97A70ABF
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@ -107,17 +107,7 @@ impl<'formula> FormulaDisplay<'formula>
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},
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_ => false,
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},
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Formula::IfAndOnlyIf(_) => match *parent_formula
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{
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Formula::Not(_)
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| Formula::Exists(_)
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| Formula::ForAll(_)
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| Formula::And(_)
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| Formula::Or(_)
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| Formula::Implies(_)
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=> true,
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_ => false,
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},
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Formula::IfAndOnlyIf(_) => true,
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}
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}
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}
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@ -870,43 +860,41 @@ mod tests
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}
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#[test]
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fn format_combination_not_and_lower()
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fn format_combinations_not()
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{
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// Not + not
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assert!(not(not(p())), "not not p");
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// Not + quantified formulas
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assert_all!(i, not(exists(xyz(), i(p()))), "not exists X, Y, Z p");
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assert_all!(i, not(for_all(xyz(), i(p()))), "not forall X, Y, Z p");
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// Quantified formulas + not
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assert_all!(i, exists(xyz(), i(not(p()))), "exists X, Y, Z not p");
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assert_all!(i, for_all(xyz(), i(not(p()))), "forall X, Y, Z not p");
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// Not + and
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assert_all!(i, and(vec![not(i(p()))]), "not p");
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assert_all!(i, not(i(and(pqr()))), "not (p and q and r)");
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// And + not
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assert_all!(i, and(vec![i(not(p()))]), "not p");
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assert_all!(i, and(vec![i(not(p())), i(not(q())), i(not(r()))]),
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"not p and not q and not r");
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// Not + or
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// Or + not
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assert_all!(i, or(vec![i(not(p()))]), "not p");
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assert_all!(i, not(i(or(pqr()))), "not (p or q or r)");
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assert_all!(i, or(vec![i(not(p())), i(not(q())), i(not(r()))]), "not p or not q or not r");
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// Not + implies
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assert_all!(i, not(i(implies_right(p(), q()))), "not (p -> q)");
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assert_all!(i, not(i(implies_left(p(), q()))), "not (q <- p)");
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// Implies + not
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assert_all!(i, implies_right(i(not(p())), i(not(q()))), "not p -> not q");
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assert_all!(i, implies_left(i(not(p())), i(not(q()))), "not q <- not p");
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// Not + if and only if
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// If and only if + not
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assert_all!(i, if_and_only_if(vec![i(not(p()))]), "not p");
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assert_all!(i, not(i(if_and_only_if(pqr()))), "not (p <-> q <-> r)");
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assert_all!(i, if_and_only_if(vec![i(not(p())), i(not(q())), i(not(r()))]),
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"not p <-> not q <-> not r");
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}
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#[test]
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fn format_combination_quantified_formula_and_lower()
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fn format_combinations_quantified_formula()
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{
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// Not + quantified formula
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assert_all!(i, not(exists(xyz(), i(p()))), "not exists X, Y, Z p");
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assert_all!(i, not(for_all(xyz(), i(p()))), "not forall X, Y, Z p");
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// Quantified formula + quantified formula
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assert_all!(i, exists(x1y1z1(), i(exists(x2y2z2(), p()))),
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"exists X1, Y1, Z1 exists X2, Y2, Z2 p");
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@ -917,91 +905,87 @@ mod tests
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assert_all!(i, for_all(x1y1z1(), i(for_all(x2y2z2(), p()))),
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"forall X1, Y1, Z1 forall X2, Y2, Z2 p");
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// Quantified formula + and
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assert_all!(i, exists(xyz(), i(and(pqr()))), "exists X, Y, Z (p and q and r)");
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// And + quantified formula
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assert_all!(i, and(vec![i(exists(xyz(), p()))]), "exists X, Y, Z p");
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assert_all!(i, and(vec![i(for_all(xyz(), p()))]), "forall X, Y, Z p");
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assert_all!(i, and(vec![i(exists(x1y1z1(), p())), i(exists(x2y2z2(), q())),
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i(exists(x3y3z3(), r()))]),
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"exists X1, Y1, Z1 p and exists X2, Y2, Z2 q and exists X3, Y3, Z3 r");
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assert_all!(i, for_all(xyz(), i(and(pqr()))), "forall X, Y, Z (p and q and r)");
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assert_all!(i, and(vec![i(for_all(x1y1z1(), p())), i(for_all(x2y2z2(), q())),
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i(for_all(x3y3z3(), r()))]),
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"forall X1, Y1, Z1 p and forall X2, Y2, Z2 q and forall X3, Y3, Z3 r");
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// Quantified formula + or
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assert_all!(i, exists(xyz(), i(or(pqr()))), "exists X, Y, Z (p or q or r)");
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// Or + quantified formula
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assert_all!(i, or(vec![i(exists(xyz(), p()))]), "exists X, Y, Z p");
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assert_all!(i, or(vec![i(for_all(xyz(), p()))]), "forall X, Y, Z p");
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assert_all!(i, or(vec![i(exists(x1y1z1(), p())), i(exists(x2y2z2(), q())),
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i(exists(x3y3z3(), r()))]),
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"exists X1, Y1, Z1 p or exists X2, Y2, Z2 q or exists X3, Y3, Z3 r");
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assert_all!(i, for_all(xyz(), i(or(pqr()))), "forall X, Y, Z (p or q or r)");
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assert_all!(i, or(vec![i(for_all(x1y1z1(), p())), i(for_all(x2y2z2(), q())),
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i(for_all(x3y3z3(), r()))]),
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"forall X1, Y1, Z1 p or forall X2, Y2, Z2 q or forall X3, Y3, Z3 r");
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// Quantified formula + implies
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assert_all!(i, exists(xyz(), i(implies_right(p(), q()))), "exists X, Y, Z (p -> q)");
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assert_all!(i, exists(xyz(), i(implies_left(p(), q()))), "exists X, Y, Z (q <- p)");
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// Implies + quantified formula
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assert_all!(i, implies_right(i(exists(x1y1z1(), p())), i(exists(x2y2z2(), q()))),
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"exists X1, Y1, Z1 p -> exists X2, Y2, Z2 q");
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assert_all!(i, implies_left(i(exists(x1y1z1(), p())), i(exists(x2y2z2(), q()))),
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"exists X2, Y2, Z2 q <- exists X1, Y1, Z1 p");
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assert_all!(i, for_all(xyz(), i(implies_right(p(), q()))), "forall X, Y, Z (p -> q)");
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assert_all!(i, for_all(xyz(), i(implies_left(p(), q()))), "forall X, Y, Z (q <- p)");
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assert_all!(i, implies_right(i(for_all(x1y1z1(), p())), i(for_all(x2y2z2(), q()))),
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"forall X1, Y1, Z1 p -> forall X2, Y2, Z2 q");
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assert_all!(i, implies_left(i(for_all(x1y1z1(), p())), i(for_all(x2y2z2(), q()))),
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"forall X2, Y2, Z2 q <- forall X1, Y1, Z1 p");
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// Quantified formula + if and only if
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assert_all!(i, exists(xyz(), i(if_and_only_if(pqr()))), "exists X, Y, Z (p <-> q <-> r)");
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// If and only if + quantified formula
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assert_all!(i, if_and_only_if(vec![i(exists(x1y1z1(), p()))]), "exists X1, Y1, Z1 p");
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assert_all!(i, if_and_only_if(vec![i(for_all(x1y1z1(), p()))]), "forall X1, Y1, Z1 p");
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assert_all!(i, if_and_only_if(vec![i(exists(x1y1z1(), p())), i(exists(x2y2z2(), q())),
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i(exists(x3y3z3(), r()))]),
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"exists X1, Y1, Z1 p <-> exists X2, Y2, Z2 q <-> exists X3, Y3, Z3 r");
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assert_all!(i, for_all(xyz(), i(if_and_only_if(pqr()))), "forall X, Y, Z (p <-> q <-> r)");
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assert_all!(i, if_and_only_if(vec![i(for_all(x1y1z1(), p())), i(for_all(x2y2z2(), q())),
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i(for_all(x3y3z3(), r()))]),
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"forall X1, Y1, Z1 p <-> forall X2, Y2, Z2 q <-> forall X3, Y3, Z3 r");
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}
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#[test]
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fn format_combination_and_and_lower()
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fn format_combinations_and()
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{
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// Not + and
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assert_all!(i, not(i(and(vec![p()]))), "not p");
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assert_all!(i, not(i(and(pqr()))), "not (p and q and r)");
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// Quantified formula + and
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assert_all!(i, exists(xyz(), i(and(vec![p()]))), "exists X, Y, Z p");
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assert_all!(i, for_all(xyz(), i(and(vec![p()]))), "forall X, Y, Z p");
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assert_all!(i, exists(xyz(), i(and(pqr()))), "exists X, Y, Z (p and q and r)");
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assert_all!(i, for_all(xyz(), i(and(pqr()))), "forall X, Y, Z (p and q and r)");
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// And + and
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assert_all!(i, and(vec![i(and(vec![p()]))]), "p");
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assert_all!(i, and(vec![i(and(pqr()))]), "p and q and r");
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assert_all!(i, and(vec![i(and(vec![p()])), i(and(vec![q()])), i(and(vec![r()]))]),
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"p and q and r");
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assert_all!(i, and(vec![i(and(p1q1r1())), i(and(p2q2r2())), i(and(p3q3r3()))]),
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"p1 and q1 and r1 and p2 and q2 and r2 and p3 and q3 and r3");
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// And + or
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assert_all!(i, and(vec![i(or(vec![p()])), i(or(vec![q()])), i(or(vec![r()]))]),
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"p and q and r");
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assert_all!(i, and(vec![i(or(p1q1r1())), i(or(p2q2r2())), i(or(p3q3r3()))]),
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"(p1 or q1 or r1) and (p2 or q2 or r2) and (p3 or q3 or r3)");
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// Or + and
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assert_all!(i, or(vec![i(and(vec![p()]))]), "p");
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assert_all!(i, or(vec![i(and(pqr()))]), "p and q and r");
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assert_all!(i, or(vec![i(and(vec![p()])), i(and(vec![q()])), i(and(vec![r()]))]),
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"p or q or r");
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assert_all!(i, or(vec![i(and(p1q1r1())), i(and(p2q2r2())), i(and(p3q3r3()))]),
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"p1 and q1 and r1 or p2 and q2 and r2 or p3 and q3 and r3");
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// And + implies
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assert_all!(i, and(vec![i(implies_right(p1(), q1())), i(implies_right(p2(), q2())),
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i(implies_right(p3(), q3()))]),
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"(p1 -> q1) and (p2 -> q2) and (p3 -> q3)");
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assert_all!(i, and(vec![i(implies_left(p1(), q1())), i(implies_left(p2(), q2())),
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i(implies_left(p3(), q3()))]),
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"(q1 <- p1) and (q2 <- p2) and (q3 <- p3)");
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// Implies + and
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assert_all!(i, implies_right(i(and(vec![p()])), i(and(vec![q()]))), "p -> q");
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assert_all!(i, implies_left(i(and(vec![p()])), i(and(vec![q()]))), "q <- p");
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assert_all!(i, implies_right(i(and(p1q1r1())), i(and(p2q2r2()))),
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"p1 and q1 and r1 -> p2 and q2 and r2");
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assert_all!(i, implies_left(i(and(p1q1r1())), i(and(p2q2r2()))),
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"p2 and q2 and r2 <- p1 and q1 and r1");
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// And + if and only if
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assert_all!(i, and(vec![i(if_and_only_if(vec![p()])), i(if_and_only_if(vec![q()])),
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i(if_and_only_if(vec![r()]))]),
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"p and q and r");
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assert_all!(i, and(vec![i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2())),
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i(if_and_only_if(p3q3r3()))]),
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"(p1 <-> q1 <-> r1) and (p2 <-> q2 <-> r2) and (p3 <-> q3 <-> r3)");
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// If and only if + and
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assert_all!(i, if_and_only_if(vec![i(and(vec![p()]))]), "p");
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assert_all!(i, if_and_only_if(vec![i(and(pqr()))]), "p and q and r");
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assert_all!(i, if_and_only_if(vec![i(and(vec![p()])), i(and(vec![q()])),
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i(and(vec![r()]))]),
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"p <-> q <-> r");
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@ -1010,37 +994,45 @@ mod tests
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}
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#[test]
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fn format_combination_or_and_lower()
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fn format_combinations_or()
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{
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// Not + or
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assert_all!(i, not(i(or(vec![p()]))), "not p");
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assert_all!(i, not(i(or(pqr()))), "not (p or q or r)");
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// Quantified formula + or
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assert_all!(i, exists(xyz(), i(or(vec![p()]))), "exists X, Y, Z p");
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assert_all!(i, for_all(xyz(), i(or(vec![p()]))), "forall X, Y, Z p");
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assert_all!(i, exists(xyz(), i(or(pqr()))), "exists X, Y, Z (p or q or r)");
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assert_all!(i, for_all(xyz(), i(or(pqr()))), "forall X, Y, Z (p or q or r)");
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// And + or
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assert_all!(i, and(vec![i(or(vec![p()]))]), "p");
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assert_all!(i, and(vec![i(or(pqr()))]), "p or q or r");
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assert_all!(i, and(vec![i(or(vec![p()])), i(or(vec![q()])), i(or(vec![r()]))]),
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"p and q and r");
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assert_all!(i, and(vec![i(or(p1q1r1())), i(or(p2q2r2())), i(or(p3q3r3()))]),
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"(p1 or q1 or r1) and (p2 or q2 or r2) and (p3 or q3 or r3)");
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// Or + or
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assert_all!(i, or(vec![i(or(vec![p()]))]), "p");
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assert_all!(i, or(vec![i(or(pqr()))]), "p or q or r");
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assert_all!(i, or(vec![i(or(vec![p()])), i(or(vec![q()])), i(or(vec![r()]))]),
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"p or q or r");
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assert_all!(i, or(vec![i(or(p1q1r1())), i(or(p2q2r2())), i(or(p3q3r3()))]),
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"p1 or q1 or r1 or p2 or q2 or r2 or p3 or q3 or r3");
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// Or + implies
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assert_all!(i, or(vec![i(implies_right(p1(), q1())), i(implies_right(p2(), q2())),
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i(implies_right(p3(), q3()))]),
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"(p1 -> q1) or (p2 -> q2) or (p3 -> q3)");
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assert_all!(i, or(vec![i(and(vec![implies_right(p1(), q1())])),
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i(and(vec![implies_right(p2(), q2())])), i(and(vec![implies_right(p3(), q3())]))]),
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"(p1 -> q1) or (p2 -> q2) or (p3 -> q3)");
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assert_all!(i, or(vec![i(implies_left(p1(), q1())), i(implies_left(p2(), q2())),
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i(implies_left(p3(), q3()))]),
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"(q1 <- p1) or (q2 <- p2) or (q3 <- p3)");
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// Implies + or
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assert_all!(i, implies_right(i(or(vec![p()])), i(or(vec![q()]))), "p -> q");
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assert_all!(i, implies_left(i(or(vec![p()])), i(or(vec![q()]))), "q <- p");
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assert_all!(i, implies_right(i(or(p1q1r1())), i(or(p2q2r2()))),
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"p1 or q1 or r1 -> p2 or q2 or r2");
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assert_all!(i, implies_left(i(or(p1q1r1())), i(or(p2q2r2()))),
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"p2 or q2 or r2 <- p1 or q1 or r1");
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// Or + if and only if
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assert_all!(i, or(vec![i(if_and_only_if(vec![p()])), i(if_and_only_if(vec![q()])),
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i(if_and_only_if(vec![r()]))]),
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"p or q or r");
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assert_all!(i, or(vec![i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2())),
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i(if_and_only_if(p3q3r3()))]),
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"(p1 <-> q1 <-> r1) or (p2 <-> q2 <-> r2) or (p3 <-> q3 <-> r3)");
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// If and only if + or
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assert_all!(i, if_and_only_if(vec![i(or(vec![p()]))]), "p");
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assert_all!(i, if_and_only_if(vec![i(or(pqr()))]), "p or q or r");
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assert_all!(i, if_and_only_if(vec![i(or(vec![p()])), i(or(vec![q()])), i(or(vec![r()]))]),
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"p <-> q <-> r");
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assert_all!(i, if_and_only_if(vec![i(or(p1q1r1())), i(or(p2q2r2())), i(or(p3q3r3()))]),
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@ -1048,8 +1040,38 @@ mod tests
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}
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#[test]
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fn format_combination_implies_and_lower()
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fn format_combinations_implies()
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{
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// Not + implies
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assert_all!(i, not(i(implies_right(p(), q()))), "not (p -> q)");
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assert_all!(i, not(i(implies_left(p(), q()))), "not (q <- p)");
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// Quantified formula + implies
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assert_all!(i, exists(xyz(), i(implies_right(p(), q()))), "exists X, Y, Z (p -> q)");
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assert_all!(i, exists(xyz(), i(implies_left(p(), q()))), "exists X, Y, Z (q <- p)");
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assert_all!(i, for_all(xyz(), i(implies_right(p(), q()))), "forall X, Y, Z (p -> q)");
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assert_all!(i, for_all(xyz(), i(implies_left(p(), q()))), "forall X, Y, Z (q <- p)");
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// And + implies
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assert_all!(i, and(vec![i(implies_right(p(), q()))]), "p -> q");
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assert_all!(i, and(vec![i(implies_left(p(), q()))]), "q <- p");
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assert_all!(i, and(vec![i(implies_right(p1(), q1())), i(implies_right(p2(), q2())),
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i(implies_right(p3(), q3()))]),
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"(p1 -> q1) and (p2 -> q2) and (p3 -> q3)");
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assert_all!(i, and(vec![i(implies_left(p1(), q1())), i(implies_left(p2(), q2())),
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i(implies_left(p3(), q3()))]),
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"(q1 <- p1) and (q2 <- p2) and (q3 <- p3)");
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// Or + implies
|
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assert_all!(i, or(vec![i(implies_right(p(), q()))]), "p -> q");
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assert_all!(i, or(vec![i(implies_left(p(), q()))]), "q <- p");
|
||||
assert_all!(i, or(vec![i(implies_right(p1(), q1())), i(implies_right(p2(), q2())),
|
||||
i(implies_right(p3(), q3()))]),
|
||||
"(p1 -> q1) or (p2 -> q2) or (p3 -> q3)");
|
||||
assert_all!(i, or(vec![i(implies_left(p1(), q1())), i(implies_left(p2(), q2())),
|
||||
i(implies_left(p3(), q3()))]),
|
||||
"(q1 <- p1) or (q2 <- p2) or (q3 <- p3)");
|
||||
|
||||
// Implies + implies
|
||||
assert_all!(i, implies_right(i(implies_right(p1(), q1())), i(implies_right(p2(), q2()))),
|
||||
"(p1 -> q1) -> p2 -> q2");
|
||||
|
|
@ -1060,11 +1082,9 @@ mod tests
|
|||
assert_all!(i, implies_left(i(implies_left(p1(), q1())), i(implies_left(p2(), q2()))),
|
||||
"q2 <- p2 <- (q1 <- p1)");
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||||
|
||||
// Implies + if and only if
|
||||
assert_all!(i, implies_right(i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2()))),
|
||||
"(p1 <-> q1 <-> r1) -> (p2 <-> q2 <-> r2)");
|
||||
assert_all!(i, implies_left(i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2()))),
|
||||
"(p2 <-> q2 <-> r2) <- (p1 <-> q1 <-> r1)");
|
||||
// If and only if + implies
|
||||
assert_all!(i, if_and_only_if(vec![i(implies_right(p(), q()))]), "p -> q");
|
||||
assert_all!(i, if_and_only_if(vec![i(implies_left(p(), q()))]), "q <- p");
|
||||
assert_all!(i, if_and_only_if(vec![i(implies_right(p1(), q1())),
|
||||
i(implies_right(p2(), q2())), i(implies_right(p3(), q3()))]),
|
||||
"p1 -> q1 <-> p2 -> q2 <-> p3 -> q3");
|
||||
|
|
@ -1072,4 +1092,58 @@ mod tests
|
|||
i(implies_left(p3(), q3()))]),
|
||||
"q1 <- p1 <-> q2 <- p2 <-> q3 <- p3");
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn format_combinations_if_and_only_if()
|
||||
{
|
||||
// Not + if and only if
|
||||
assert_all!(i, not(i(if_and_only_if(vec![p()]))), "not p");
|
||||
assert_all!(i, not(i(if_and_only_if(pqr()))), "not (p <-> q <-> r)");
|
||||
|
||||
// Quantified formula + if and only if
|
||||
assert_all!(i, exists(xyz(), i(if_and_only_if(vec![p()]))), "exists X, Y, Z p");
|
||||
assert_all!(i, for_all(xyz(), i(if_and_only_if(vec![p()]))), "forall X, Y, Z p");
|
||||
assert_all!(i, exists(xyz(), i(if_and_only_if(pqr()))), "exists X, Y, Z (p <-> q <-> r)");
|
||||
assert_all!(i, for_all(xyz(), i(if_and_only_if(pqr()))), "forall X, Y, Z (p <-> q <-> r)");
|
||||
|
||||
// And + if and only if
|
||||
assert_all!(i, and(vec![i(if_and_only_if(vec![p()]))]), "p");
|
||||
assert_all!(i, and(vec![i(if_and_only_if(pqr()))]), "p <-> q <-> r");
|
||||
assert_all!(i, and(vec![i(if_and_only_if(vec![p()])), i(if_and_only_if(vec![q()])),
|
||||
i(if_and_only_if(vec![r()]))]),
|
||||
"p and q and r");
|
||||
assert_all!(i, and(vec![i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2())),
|
||||
i(if_and_only_if(p3q3r3()))]),
|
||||
"(p1 <-> q1 <-> r1) and (p2 <-> q2 <-> r2) and (p3 <-> q3 <-> r3)");
|
||||
|
||||
// Or + if and only if
|
||||
assert_all!(i, or(vec![i(if_and_only_if(vec![p()]))]), "p");
|
||||
assert_all!(i, or(vec![i(if_and_only_if(pqr()))]), "p <-> q <-> r");
|
||||
assert_all!(i, or(vec![i(if_and_only_if(vec![p()])), i(if_and_only_if(vec![q()])),
|
||||
i(if_and_only_if(vec![r()]))]),
|
||||
"p or q or r");
|
||||
assert_all!(i, or(vec![i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2())),
|
||||
i(if_and_only_if(p3q3r3()))]),
|
||||
"(p1 <-> q1 <-> r1) or (p2 <-> q2 <-> r2) or (p3 <-> q3 <-> r3)");
|
||||
|
||||
// Implies + if and only if
|
||||
assert_all!(i, implies_right(i(if_and_only_if(vec![p()])), i(if_and_only_if(vec![q()]))),
|
||||
"p -> q");
|
||||
assert_all!(i, implies_left(i(if_and_only_if(vec![p()])), i(if_and_only_if(vec![q()]))),
|
||||
"q <- p");
|
||||
assert_all!(i, implies_right(i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2()))),
|
||||
"(p1 <-> q1 <-> r1) -> (p2 <-> q2 <-> r2)");
|
||||
assert_all!(i, implies_left(i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2()))),
|
||||
"(p2 <-> q2 <-> r2) <- (p1 <-> q1 <-> r1)");
|
||||
|
||||
// If and only if + if and only if
|
||||
assert_all!(i, if_and_only_if(vec![i(if_and_only_if(vec![p()]))]), "p");
|
||||
assert_all!(i, if_and_only_if(vec![i(if_and_only_if(pqr()))]), "p <-> q <-> r");
|
||||
assert_all!(i, if_and_only_if(vec![i(if_and_only_if(vec![p()])),
|
||||
i(if_and_only_if(vec![q()])), i(if_and_only_if(vec![r()]))]),
|
||||
"p <-> q <-> r");
|
||||
assert_all!(i, if_and_only_if(vec![i(if_and_only_if(p1q1r1())), i(if_and_only_if(p2q2r2())),
|
||||
i(if_and_only_if(p3q3r3()))]),
|
||||
"(p1 <-> q1 <-> r1) <-> (p2 <-> q2 <-> r2) <-> (p3 <-> q3 <-> r3)");
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue