Test term formatting

2020-03-30 04:28:36 +02:00 · 2020-03-30 04:28:36 +02:00 · 23e1854346
commit 23e1854346
parent a3da369346
1 changed files with 735 additions and 0 deletions
--- a/src/format/terms.rs
+++ b/src/format/terms.rs
@ -263,3 +263,738 @@ impl std::fmt::Display for crate::Term
 		write!(format, "{}", display_term(&self, None))
 	}
 }
+
+#[cfg(test)]
+mod tests
+{
+	use crate::*;
+
+	fn format(term: Box<ast::Term>) -> String
+	{
+		format!("{}", term)
+	}
+
+	fn absolute_value(argument: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::absolute_value(argument))
+	}
+
+	fn add(left: Box<Term>, right: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::add(left, right))
+	}
+
+	fn constant(name: &str) -> Box<Term>
+	{
+		Box::new(Term::function(function_declaration(name, 0), vec![]))
+	}
+
+	fn divide(left: Box<Term>, right: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::divide(left, right))
+	}
+
+	fn exponentiate(left: Box<Term>, right: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::exponentiate(left, right))
+	}
+
+	fn false_() -> Box<Term>
+	{
+		Box::new(Term::false_())
+	}
+
+	fn function(name: &str, arguments: Vec<Box<Term>>) -> Box<Term>
+	{
+		Box::new(Term::function(function_declaration(name, arguments.len()), arguments))
+	}
+
+	fn function_declaration(name: &str, arity: usize) -> std::rc::Rc<FunctionDeclaration>
+	{
+		std::rc::Rc::new(FunctionDeclaration::new(name.to_string(), arity))
+	}
+
+	fn infimum() -> Box<Term>
+	{
+		Box::new(Term::infimum())
+	}
+
+	fn integer(value: i32) -> Box<Term>
+	{
+		Box::new(Term::integer(value))
+	}
+
+	fn modulo(left: Box<Term>, right: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::modulo(left, right))
+	}
+
+	fn multiply(left: Box<Term>, right: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::multiply(left, right))
+	}
+
+	fn negative(argument: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::negative(argument))
+	}
+
+	fn subtract(left: Box<Term>, right: Box<Term>) -> Box<Term>
+	{
+		Box::new(Term::subtract(left, right))
+	}
+
+	fn supremum() -> Box<Term>
+	{
+		Box::new(Term::supremum())
+	}
+
+	fn string(value: &str) -> Box<Term>
+	{
+		Box::new(Term::string(value.to_string()))
+	}
+
+	fn true_() -> Box<Term>
+	{
+		Box::new(Term::true_())
+	}
+
+	fn variable(name: &str) -> Box<Term>
+	{
+		Box::new(Term::variable(variable_declaration(name)))
+	}
+
+	fn variable_declaration(name: &str) -> std::rc::Rc<VariableDeclaration>
+	{
+		std::rc::Rc::new(VariableDeclaration::new(name.to_string()))
+	}
+
+	#[test]
+	fn format_binary_operation()
+	{
+		assert_eq!(format(add(constant("a"), constant("b"))), "a + b");
+		assert_eq!(format(subtract(constant("a"), constant("b"))), "a - b");
+		assert_eq!(format(multiply(constant("a"), constant("b"))), "a * b");
+		assert_eq!(format(divide(constant("a"), constant("b"))), "a / b");
+		assert_eq!(format(modulo(constant("a"), constant("b"))), "a % b");
+		assert_eq!(format(exponentiate(constant("a"), constant("b"))), "a ** b");
+	}
+
+	#[test]
+	fn format_boolean()
+	{
+		assert_eq!(format(true_()), "true");
+		assert_eq!(format(false_()), "false");
+	}
+
+	#[test]
+	fn format_special_integer()
+	{
+		assert_eq!(format(infimum()), "#inf");
+		assert_eq!(format(supremum()), "#sup");
+	}
+
+	#[test]
+	fn format_integer()
+	{
+		assert_eq!(format(integer(0)), "0");
+		assert_eq!(format(integer(1)), "1");
+		assert_eq!(format(integer(10000)), "10000");
+		assert_eq!(format(integer(-1)), "-1");
+		assert_eq!(format(integer(-10000)), "-10000");
+	}
+
+	#[test]
+	fn format_string()
+	{
+		assert_eq!(format(string("")), "\"\"");
+		assert_eq!(format(string(" ")), "\" \"");
+		assert_eq!(format(string("     ")), "\"     \"");
+		assert_eq!(format(string("a")), "\"a\"");
+		assert_eq!(format(string("test test")), "\"test test\"");
+		assert_eq!(format(string("123 123")), "\"123 123\"");
+		assert_eq!(format(string("\ntest\n123\n")), "\"\\ntest\\n123\\n\"");
+		assert_eq!(format(string("\ttest\t123\t")), "\"\\ttest\\t123\\t\"");
+		assert_eq!(format(string("\\test\\123\\")), "\"\\\\test\\\\123\\\\\"");
+		assert_eq!(format(string("🙂test🙂123🙂")), "\"🙂test🙂123🙂\"");
+	}
+
+	#[test]
+	fn format_function()
+	{
+		assert_eq!(format(constant("a")), "a");
+		assert_eq!(format(constant("constant")), "constant");
+		assert_eq!(format(function("f", vec![constant("a")])), "f(a)");
+		assert_eq!(format(
+			function("f", vec![constant("a"), constant("b"), constant("c")])),
+			"f(a, b, c)");
+		assert_eq!(format(
+			function("function", vec![constant("a"), constant("b"), constant("c")])),
+			"function(a, b, c)");
+
+		// TODO: escape functions that start with capital letters or that conflict with keywords
+	}
+
+	#[test]
+	fn format_variable()
+	{
+		assert_eq!(format(variable("X")), "X");
+		assert_eq!(format(variable("Variable")), "Variable");
+	}
+
+	#[test]
+	fn format_combination_boolean_and_lower()
+	{
+		assert_eq!(format(function("f", vec![true_(), true_(), true_()])), "f(true, true, true)");
+		assert_eq!(format(
+			function("f", vec![false_(), false_(), false_()])),
+			"f(false, false, false)");
+
+		assert_eq!(format(absolute_value(true_())), "|true|");
+		assert_eq!(format(absolute_value(false_())), "|false|");
+
+		assert_eq!(format(negative(true_())), "-true");
+		assert_eq!(format(negative(false_())), "-false");
+
+		assert_eq!(format(exponentiate(true_(), true_())), "true ** true");
+		assert_eq!(format(exponentiate(false_(), false_())), "false ** false");
+
+		assert_eq!(format(multiply(true_(), true_())), "true * true");
+		assert_eq!(format(multiply(false_(), false_())), "false * false");
+
+		assert_eq!(format(divide(true_(), true_())), "true / true");
+		assert_eq!(format(divide(false_(), false_())), "false / false");
+
+		assert_eq!(format(modulo(true_(), true_())), "true % true");
+		assert_eq!(format(modulo(false_(), false_())), "false % false");
+
+		assert_eq!(format(add(true_(), true_())), "true + true");
+		assert_eq!(format(add(false_(), false_())), "false + false");
+
+		assert_eq!(format(subtract(true_(), true_())), "true - true");
+		assert_eq!(format(subtract(false_(), false_())), "false - false");
+	}
+
+	#[test]
+	fn format_combination_special_integer_and_lower()
+	{
+		assert_eq!(format(
+			function("f", vec![infimum(), infimum(), infimum()])),
+			"f(#inf, #inf, #inf)");
+		assert_eq!(format(
+			function("f", vec![supremum(), supremum(), supremum()])),
+			"f(#sup, #sup, #sup)");
+
+		assert_eq!(format(absolute_value(infimum())), "|#inf|");
+		assert_eq!(format(absolute_value(supremum())), "|#sup|");
+
+		assert_eq!(format(negative(infimum())), "-#inf");
+		assert_eq!(format(negative(supremum())), "-#sup");
+
+		assert_eq!(format(exponentiate(infimum(), infimum())), "#inf ** #inf");
+		assert_eq!(format(exponentiate(supremum(), supremum())), "#sup ** #sup");
+
+		assert_eq!(format(multiply(infimum(), infimum())), "#inf * #inf");
+		assert_eq!(format(multiply(supremum(), supremum())), "#sup * #sup");
+
+		assert_eq!(format(divide(infimum(), infimum())), "#inf / #inf");
+		assert_eq!(format(divide(supremum(), supremum())), "#sup / #sup");
+
+		assert_eq!(format(modulo(infimum(), infimum())), "#inf % #inf");
+		assert_eq!(format(modulo(supremum(), supremum())), "#sup % #sup");
+
+		assert_eq!(format(add(infimum(), infimum())), "#inf + #inf");
+		assert_eq!(format(add(supremum(), supremum())), "#sup + #sup");
+
+		assert_eq!(format(subtract(infimum(), infimum())), "#inf - #inf");
+		assert_eq!(format(subtract(supremum(), supremum())), "#sup - #sup");
+	}
+
+	#[test]
+	fn format_combination_integer_and_lower()
+	{
+		assert_eq!(format(function("f", vec![integer(0), integer(0), integer(0)])),
+			"f(0, 0, 0)");
+		assert_eq!(format(function("f", vec![integer(10000), integer(10000), integer(10000)])),
+			"f(10000, 10000, 10000)");
+		assert_eq!(format(function("f", vec![integer(-10000), integer(-10000), integer(-10000)])),
+			"f(-10000, -10000, -10000)");
+
+		assert_eq!(format(absolute_value(integer(0))), "|0|");
+		assert_eq!(format(absolute_value(integer(10000))), "|10000|");
+		assert_eq!(format(absolute_value(integer(-10000))), "|-10000|");
+
+		assert_eq!(format(negative(integer(0))), "-0");
+		assert_eq!(format(negative(integer(10000))), "-10000");
+		assert_eq!(format(negative(integer(-10000))), "--10000");
+
+		assert_eq!(format(exponentiate(integer(0), integer(0))), "0 ** 0");
+		assert_eq!(format(exponentiate(integer(10000), integer(10000))), "10000 ** 10000");
+		assert_eq!(format(exponentiate(integer(-10000), integer(-10000))), "-10000 ** -10000");
+
+		assert_eq!(format(multiply(integer(0), integer(0))), "0 * 0");
+		assert_eq!(format(multiply(integer(10000), integer(10000))), "10000 * 10000");
+		assert_eq!(format(multiply(integer(-10000), integer(-10000))), "-10000 * -10000");
+
+		assert_eq!(format(divide(integer(0), integer(0))), "0 / 0");
+		assert_eq!(format(divide(integer(10000), integer(10000))), "10000 / 10000");
+		assert_eq!(format(divide(integer(-10000), integer(-10000))), "-10000 / -10000");
+
+		assert_eq!(format(modulo(integer(0), integer(0))), "0 % 0");
+		assert_eq!(format(modulo(integer(10000), integer(10000))), "10000 % 10000");
+		assert_eq!(format(modulo(integer(-10000), integer(-10000))), "-10000 % -10000");
+
+		assert_eq!(format(add(integer(0), integer(0))), "0 + 0");
+		assert_eq!(format(add(integer(10000), integer(10000))), "10000 + 10000");
+		assert_eq!(format(add(integer(-10000), integer(-10000))), "-10000 + -10000");
+
+		assert_eq!(format(subtract(integer(0), integer(0))), "0 - 0");
+		assert_eq!(format(subtract(integer(10000), integer(10000))), "10000 - 10000");
+		assert_eq!(format(subtract(integer(-10000), integer(-10000))), "-10000 - -10000");
+	}
+
+	#[test]
+	fn format_combination_string_and_lower()
+	{
+		assert_eq!(format(function("f", vec![string(""), string(""), string("")])),
+			"f(\"\", \"\", \"\")");
+		assert_eq!(format(function("f", vec![string("test 123"), string("test 123"),
+				string("test 123")])),
+			"f(\"test 123\", \"test 123\", \"test 123\")");
+		assert_eq!(format(function("f", vec![string("\\a\nb🙂c\t"), string("\\a\nb🙂c\t"),
+				string("\\a\nb🙂c\t")])),
+			"f(\"\\\\a\\nb🙂c\\t\", \"\\\\a\\nb🙂c\\t\", \"\\\\a\\nb🙂c\\t\")");
+
+		assert_eq!(format(absolute_value(string(""))), "|\"\"|");
+		assert_eq!(format(absolute_value(string("test 123"))), "|\"test 123\"|");
+		assert_eq!(format(absolute_value(string("\\a\nb🙂c\t"))), "|\"\\\\a\\nb🙂c\\t\"|");
+
+		assert_eq!(format(negative(string(""))), "-\"\"");
+		assert_eq!(format(negative(string("test 123"))), "-\"test 123\"");
+		assert_eq!(format(negative(string("\\a\nb🙂c\t"))), "-\"\\\\a\\nb🙂c\\t\"");
+
+		assert_eq!(format(exponentiate(string(""), string(""))), "\"\" ** \"\"");
+		assert_eq!(format(
+			exponentiate(string("test 123"), string("test 123"))),
+			"\"test 123\" ** \"test 123\"");
+		assert_eq!(format(
+			exponentiate(string("\\a\nb🙂c\t"), string("\\a\nb🙂c\t"))),
+			"\"\\\\a\\nb🙂c\\t\" ** \"\\\\a\\nb🙂c\\t\"");
+
+		assert_eq!(format(multiply(string(""), string(""))), "\"\" * \"\"");
+		assert_eq!(format(
+			multiply(string("test 123"), string("test 123"))),
+			"\"test 123\" * \"test 123\"");
+		assert_eq!(format(
+			multiply(string("\\a\nb🙂c\t"), string("\\a\nb🙂c\t"))),
+			"\"\\\\a\\nb🙂c\\t\" * \"\\\\a\\nb🙂c\\t\"");
+
+		assert_eq!(format(divide(string(""), string(""))), "\"\" / \"\"");
+		assert_eq!(format(
+			divide(string("test 123"), string("test 123"))),
+			"\"test 123\" / \"test 123\"");
+		assert_eq!(format(
+			divide(string("\\a\nb🙂c\t"), string("\\a\nb🙂c\t"))),
+			"\"\\\\a\\nb🙂c\\t\" / \"\\\\a\\nb🙂c\\t\"");
+
+		assert_eq!(format(modulo(string(""), string(""))), "\"\" % \"\"");
+		assert_eq!(format(
+			modulo(string("test 123"), string("test 123"))),
+			"\"test 123\" % \"test 123\"");
+		assert_eq!(format(
+			modulo(string("\\a\nb🙂c\t"), string("\\a\nb🙂c\t"))),
+			"\"\\\\a\\nb🙂c\\t\" % \"\\\\a\\nb🙂c\\t\"");
+
+		assert_eq!(format(add(string(""), string(""))), "\"\" + \"\"");
+		assert_eq!(format(
+			add(string("test 123"), string("test 123"))),
+			"\"test 123\" + \"test 123\"");
+		assert_eq!(format(
+			add(string("\\a\nb🙂c\t"), string("\\a\nb🙂c\t"))),
+			"\"\\\\a\\nb🙂c\\t\" + \"\\\\a\\nb🙂c\\t\"");
+
+		assert_eq!(format(subtract(string(""), string(""))), "\"\" - \"\"");
+		assert_eq!(format(
+			subtract(string("test 123"), string("test 123"))),
+			"\"test 123\" - \"test 123\"");
+		assert_eq!(format(
+			subtract(string("\\a\nb🙂c\t"), string("\\a\nb🙂c\t"))),
+			"\"\\\\a\\nb🙂c\\t\" - \"\\\\a\\nb🙂c\\t\"");
+	}
+
+	#[test]
+	fn format_combination_variable_and_lower()
+	{
+		assert_eq!(format(variable("X")), "X");
+		assert_eq!(format(variable("Variable")), "Variable");
+
+		assert_eq!(format(absolute_value(variable("X"))), "|X|");
+		assert_eq!(format(absolute_value(variable("Variable"))), "|Variable|");
+
+		assert_eq!(format(negative(variable("X"))), "-X");
+		assert_eq!(format(negative(variable("Variable"))), "-Variable");
+
+		assert_eq!(format(exponentiate(variable("X"), variable("X"))), "X ** X");
+		assert_eq!(format(
+			exponentiate(variable("Variable"), variable("Variable"))),
+			"Variable ** Variable");
+
+		assert_eq!(format(multiply(variable("X"), variable("X"))), "X * X");
+		assert_eq!(format(
+			multiply(variable("Variable"), variable("Variable"))),
+			"Variable * Variable");
+
+		assert_eq!(format(divide(variable("X"), variable("X"))), "X / X");
+		assert_eq!(format(
+			divide(variable("Variable"), variable("Variable"))), "Variable / Variable");
+
+		assert_eq!(format(modulo(variable("X"), variable("X"))), "X % X");
+		assert_eq!(format(
+			modulo(variable("Variable"), variable("Variable"))), "Variable % Variable");
+
+		assert_eq!(format(add(variable("X"), variable("X"))), "X + X");
+		assert_eq!(format(
+			add(variable("Variable"), variable("Variable"))), "Variable + Variable");
+
+		assert_eq!(format(subtract(variable("X"), variable("X"))), "X - X");
+		assert_eq!(format(
+			subtract(variable("Variable"), variable("Variable"))), "Variable - Variable");
+	}
+
+	#[test]
+	fn format_combination_function_and_lower()
+	{
+		let f1 = || constant("a");
+		let f2 = || constant("constant");
+		let f3 = || function("f", vec![constant("a")]);
+		let f4 = || function("function", vec![constant("a"), constant("b"), constant("c")]);
+
+		assert_eq!(format(absolute_value(f1())), "|a|");
+		assert_eq!(format(absolute_value(f2())), "|constant|");
+		assert_eq!(format(absolute_value(f3())), "|f(a)|");
+		assert_eq!(format(absolute_value(f4())), "|function(a, b, c)|");
+		assert_eq!(format(function("f", vec![absolute_value(constant("a"))])), "f(|a|)");
+		assert_eq!(format(
+			function("f", vec![absolute_value(constant("a")), absolute_value(constant("b")),
+				absolute_value(constant("c"))])),
+			"f(|a|, |b|, |c|)");
+
+		assert_eq!(format(negative(f1())), "-a");
+		assert_eq!(format(negative(f2())), "-constant");
+		assert_eq!(format(negative(f3())), "-f(a)");
+		assert_eq!(format(negative(f4())), "-function(a, b, c)");
+		assert_eq!(format(function("f", vec![negative(constant("a"))])), "f(-a)");
+		assert_eq!(format(
+			function("f", vec![negative(constant("a")), negative(constant("b")),
+				negative(constant("c"))])),
+			"f(-a, -b, -c)");
+
+		assert_eq!(format(exponentiate(f1(), f1())), "a ** a");
+		assert_eq!(format(exponentiate(f2(), f2())), "constant ** constant");
+		assert_eq!(format(exponentiate(f3(), f3())), "f(a) ** f(a)");
+		assert_eq!(format(exponentiate(f4(), f4())), "function(a, b, c) ** function(a, b, c)");
+		assert_eq!(format(
+			function("f", vec![exponentiate(constant("a"), constant("b"))])),
+			"f(a ** b)");
+		assert_eq!(format(
+			function("f", vec![exponentiate(constant("a"), constant("b")),
+				exponentiate(constant("c"), constant("d")),
+				exponentiate(constant("e"), constant("f"))])),
+			"f(a ** b, c ** d, e ** f)");
+
+		assert_eq!(format(multiply(f1(), f1())), "a * a");
+		assert_eq!(format(multiply(f2(), f2())), "constant * constant");
+		assert_eq!(format(multiply(f3(), f3())), "f(a) * f(a)");
+		assert_eq!(format(multiply(f4(), f4())), "function(a, b, c) * function(a, b, c)");
+		assert_eq!(format(function("f", vec![multiply(constant("a"), constant("b"))])), "f(a * b)");
+		assert_eq!(format(
+			function("f", vec![multiply(constant("a"), constant("b")),
+				multiply(constant("c"), constant("d")), multiply(constant("e"), constant("f"))])),
+			"f(a * b, c * d, e * f)");
+
+		assert_eq!(format(divide(f1(), f1())), "a / a");
+		assert_eq!(format(divide(f2(), f2())), "constant / constant");
+		assert_eq!(format(divide(f3(), f3())), "f(a) / f(a)");
+		assert_eq!(format(divide(f4(), f4())), "function(a, b, c) / function(a, b, c)");
+		assert_eq!(format(function("f", vec![divide(constant("a"), constant("b"))])), "f(a / b)");
+		assert_eq!(format(
+			function("f", vec![divide(constant("a"), constant("b")),
+				divide(constant("c"), constant("d")), divide(constant("e"), constant("f"))])),
+			"f(a / b, c / d, e / f)");
+
+		assert_eq!(format(modulo(f1(), f1())), "a % a");
+		assert_eq!(format(modulo(f2(), f2())), "constant % constant");
+		assert_eq!(format(modulo(f3(), f3())), "f(a) % f(a)");
+		assert_eq!(format(modulo(f4(), f4())), "function(a, b, c) % function(a, b, c)");
+		assert_eq!(format(function("f", vec![modulo(constant("a"), constant("b"))])), "f(a % b)");
+		assert_eq!(format(
+			function("f", vec![modulo(constant("a"), constant("b")),
+				modulo(constant("c"), constant("d")), modulo(constant("e"), constant("f"))])),
+			"f(a % b, c % d, e % f)");
+
+		assert_eq!(format(add(f1(), f1())), "a + a");
+		assert_eq!(format(add(f2(), f2())), "constant + constant");
+		assert_eq!(format(add(f3(), f3())), "f(a) + f(a)");
+		assert_eq!(format(add(f4(), f4())), "function(a, b, c) + function(a, b, c)");
+		assert_eq!(format(function("f", vec![add(constant("a"), constant("b"))])), "f(a + b)");
+		assert_eq!(format(
+			function("f", vec![add(constant("a"), constant("b")),
+				add(constant("c"), constant("d")), add(constant("e"), constant("f"))])),
+			"f(a + b, c + d, e + f)");
+
+		assert_eq!(format(subtract(f1(), f1())), "a - a");
+		assert_eq!(format(subtract(f2(), f2())), "constant - constant");
+		assert_eq!(format(subtract(f3(), f3())), "f(a) - f(a)");
+		assert_eq!(format(subtract(f4(), f4())), "function(a, b, c) - function(a, b, c)");
+		assert_eq!(format(function("f", vec![subtract(constant("a"), constant("b"))])), "f(a - b)");
+		assert_eq!(format(
+			function("f", vec![subtract(constant("a"), constant("b")),
+				subtract(constant("c"), constant("d")), subtract(constant("e"), constant("f"))])),
+			"f(a - b, c - d, e - f)");
+	}
+
+	#[test]
+	fn format_combination_absolute_value_and_lower()
+	{
+		assert_eq!(format(absolute_value(absolute_value(constant("a")))), "||a||");
+		assert_eq!(format(absolute_value(negative(constant("a")))), "|-a|");
+		assert_eq!(format(negative(absolute_value(constant("a")))), "-|a|");
+		assert_eq!(format(absolute_value(add(constant("a"), constant("b")))), "|a + b|");
+		assert_eq!(format(
+			add(absolute_value(constant("a")), absolute_value(constant("b")))),
+			"|a| + |b|");
+		assert_eq!(format(absolute_value(subtract(constant("a"), constant("b")))), "|a - b|");
+		assert_eq!(format(
+			subtract(absolute_value(constant("a")), absolute_value(constant("b")))),
+			"|a| - |b|");
+		assert_eq!(format(absolute_value(multiply(constant("a"), constant("b")))), "|a * b|");
+		assert_eq!(format(
+			multiply(absolute_value(constant("a")), absolute_value(constant("b")))),
+			"|a| * |b|");
+		assert_eq!(format(absolute_value(divide(constant("a"), constant("b")))), "|a / b|");
+		assert_eq!(format(
+			divide(absolute_value(constant("a")), absolute_value(constant("b")))),
+			"|a| / |b|");
+		assert_eq!(format(absolute_value(modulo(constant("a"), constant("b")))), "|a % b|");
+		assert_eq!(format(
+			modulo(absolute_value(constant("a")), absolute_value(constant("b")))),
+			"|a| % |b|");
+		assert_eq!(format(absolute_value(exponentiate(constant("a"), constant("b")))), "|a ** b|");
+		assert_eq!(format(
+			exponentiate(absolute_value(constant("a")), absolute_value(constant("b")))),
+			"|a| ** |b|");
+	}
+
+	#[test]
+	fn format_combination_negative_and_lower()
+	{
+		assert_eq!(format(negative(negative(constant("a")))), "--a");
+		assert_eq!(format(add(negative(constant("a")), negative(constant("b")))), "-a + -b");
+		assert_eq!(format(negative(add(constant("a"), constant("b")))), "-(a + b)");
+		assert_eq!(format(subtract(negative(constant("a")), negative(constant("b")))), "-a - -b");
+		assert_eq!(format(negative(subtract(constant("a"), constant("b")))), "-(a - b)");
+		assert_eq!(format(multiply(negative(constant("a")), negative(constant("b")))), "-a * -b");
+		assert_eq!(format(negative(multiply(constant("a"), constant("b")))), "-(a * b)");
+		assert_eq!(format(divide(negative(constant("a")), negative(constant("b")))), "-a / -b");
+		assert_eq!(format(negative(divide(constant("a"), constant("b")))), "-(a / b)");
+		assert_eq!(format(modulo(negative(constant("a")), negative(constant("b")))), "-a % -b");
+		assert_eq!(format(negative(modulo(constant("a"), constant("b")))), "-(a % b)");
+		assert_eq!(format(exponentiate(negative(constant("a")), negative(constant("b")))), "-a ** -b");
+		assert_eq!(format(negative(exponentiate(constant("a"), constant("b")))), "-(a ** b)");
+	}
+
+	#[test]
+	fn format_combination_exponentiate_and_lower()
+	{
+		assert_eq!(format(
+			exponentiate(
+				exponentiate(constant("a"), constant("b")),
+				exponentiate(constant("c"), constant("d")))),
+			"(a ** b) ** c ** d");
+		assert_eq!(format(
+			exponentiate(
+				multiply(constant("a"), constant("b")),
+				multiply(constant("c"), constant("d")))),
+			"(a * b) ** (c * d)");
+		assert_eq!(format(
+			multiply(
+				exponentiate(constant("a"), constant("b")),
+				exponentiate(constant("c"), constant("d")))),
+			"a ** b * c ** d");
+		assert_eq!(format(
+			exponentiate(
+				divide(constant("a"), constant("b")),
+				divide(constant("c"), constant("d")))),
+			"(a / b) ** (c / d)");
+		assert_eq!(format(
+			divide(
+				exponentiate(constant("a"), constant("b")),
+				exponentiate(constant("c"), constant("d")))),
+			"a ** b / c ** d");
+		assert_eq!(format(
+			exponentiate(
+				modulo(constant("a"), constant("b")),
+				modulo(constant("c"), constant("d")))),
+			"(a % b) ** (c % d)");
+		assert_eq!(format(
+			modulo(
+				exponentiate(constant("a"), constant("b")),
+				exponentiate(constant("c"), constant("d")))),
+			"a ** b % c ** d");
+		assert_eq!(format(
+			exponentiate(
+				add(constant("a"), constant("b")),
+				add(constant("c"), constant("d")))),
+			"(a + b) ** (c + d)");
+		assert_eq!(format(
+			add(
+				exponentiate(constant("a"), constant("b")),
+				exponentiate(constant("c"), constant("d")))),
+			"a ** b + c ** d");
+		assert_eq!(format(
+			exponentiate(
+				subtract(constant("a"), constant("b")),
+				subtract(constant("c"), constant("d")))),
+			"(a - b) ** (c - d)");
+		assert_eq!(format(
+			subtract(
+				exponentiate(constant("a"), constant("b")),
+				exponentiate(constant("c"), constant("d")))),
+			"a ** b - c ** d");
+	}
+
+	#[test]
+	fn format_combination_multiplicative_binary_operations_and_lower()
+	{
+		assert_eq!(format(
+			multiply(
+				multiply(constant("a"), constant("b")),
+				multiply(constant("c"), constant("d")))),
+			"a * b * c * d");
+		assert_eq!(format(
+			multiply(
+				divide(constant("a"), constant("b")),
+				divide(constant("c"), constant("d")))),
+			"a / b * c / d");
+		assert_eq!(format(
+			multiply(
+				modulo(constant("a"), constant("b")),
+				modulo(constant("c"), constant("d")))),
+			"a % b * (c % d)");
+		assert_eq!(format(
+			divide(
+				multiply(constant("a"), constant("b")),
+				multiply(constant("c"), constant("d")))),
+			"a * b / (c * d)");
+		assert_eq!(format(
+			divide(
+				divide(constant("a"), constant("b")),
+				divide(constant("c"), constant("d")))),
+			"a / b / (c / d)");
+		assert_eq!(format(
+			divide(
+				modulo(constant("a"), constant("b")),
+				modulo(constant("c"), constant("d")))),
+			"a % b / (c % d)");
+		assert_eq!(format(
+			modulo(
+				multiply(constant("a"), constant("b")),
+				multiply(constant("c"), constant("d")))),
+			"a * b % (c * d)");
+		assert_eq!(format(
+			modulo(
+				divide(constant("a"), constant("b")),
+				divide(constant("c"), constant("d")))),
+			"a / b % (c / d)");
+		assert_eq!(format(
+			modulo(
+				modulo(constant("a"), constant("b")),
+				modulo(constant("c"), constant("d")))),
+			"a % b % (c % d)");
+		assert_eq!(format(
+			multiply(
+				add(constant("a"), constant("b")),
+				add(constant("c"), constant("d")))),
+			"(a + b) * (c + d)");
+		assert_eq!(format(
+			add(
+				multiply(constant("a"), constant("b")),
+				multiply(constant("c"), constant("d")))),
+			"a * b + c * d");
+		assert_eq!(format(
+			multiply(
+				subtract(constant("a"), constant("b")),
+				subtract(constant("c"), constant("d")))),
+			"(a - b) * (c - d)");
+		assert_eq!(format(
+			subtract(
+				multiply(constant("a"), constant("b")),
+				multiply(constant("c"), constant("d")))),
+			"a * b - c * d");
+		assert_eq!(format(
+			divide(
+				add(constant("a"), constant("b")),
+				add(constant("c"), constant("d")))),
+			"(a + b) / (c + d)");
+		assert_eq!(format(
+			add(
+				divide(constant("a"), constant("b")),
+				divide(constant("c"), constant("d")))),
+			"a / b + c / d");
+		assert_eq!(format(
+			divide(
+				subtract(constant("a"), constant("b")),
+				subtract(constant("c"), constant("d")))),
+			"(a - b) / (c - d)");
+		assert_eq!(format(
+			subtract(
+				divide(constant("a"), constant("b")),
+				divide(constant("c"), constant("d")))),
+			"a / b - c / d");
+		assert_eq!(format(
+			modulo(
+				add(constant("a"), constant("b")),
+				add(constant("c"), constant("d")))),
+			"(a + b) % (c + d)");
+		assert_eq!(format(
+			add(
+				modulo(constant("a"), constant("b")),
+				modulo(constant("c"), constant("d")))),
+			"a % b + c % d");
+		assert_eq!(format(
+			modulo(
+				subtract(constant("a"), constant("b")),
+				subtract(constant("c"), constant("d")))),
+			"(a - b) % (c - d)");
+		assert_eq!(format(
+			subtract(
+				modulo(constant("a"), constant("b")),
+				modulo(constant("c"), constant("d")))),
+			"a % b - c % d");
+	}
+
+	#[test]
+	fn format_combination_additive_binary_operations_and_lower()
+	{
+		assert_eq!(format(
+			add(
+				add(constant("a"), constant("b")),
+				add(constant("c"), constant("d")))),
+			"a + b + c + d");
+		assert_eq!(format(
+			add(
+				subtract(constant("a"), constant("b")),
+				subtract(constant("c"), constant("d")))),
+			"a - b + c - d");
+		assert_eq!(format(
+			subtract(
+				add(constant("a"), constant("b")),
+				add(constant("c"), constant("d")))),
+			"a + b - (c + d)");
+		assert_eq!(format(
+			subtract(
+				subtract(constant("a"), constant("b")),
+				subtract(constant("c"), constant("d")))),
+			"a - b - (c - d)");
+	}
+}