Remove unneeded trait methods

Implement name parsing

Start parsing terms

Implement word boundaries

Implement strings

Add pipe character to allowed word boundaries

Implement booleans

Require word boundaries around names

Implement variable parsing

Finish implementing term parsing

Add term parsing test

Test associativity of multiplication

Make parse feature the default

Fix term parsing and finish tests

Start parsing formulas

Continue parsing formulas

Finish implementing formula parsing

Move boolean parser to separate module

Move integer parser to separate module

Move special integer parser to separate module

Move string parser to separate module

Address warnings

Fix negation parser

Refactor term parser tests

Address clippy warning

Disallow reserved keywords as names

Add missing word boundary character

Check that names don’t start with special characters

Minor refactoring

Add note

Test conjunction parser

Test disjunction parser

Parentheses for stronger checks

Add note

Fix implication parser and output

Split formatting functionality into two files

Test term formatting

Add unit test for function declaration formatting

Work in progress

Fix implication formatting

Refactor precedence rules

Start testing formula formatter

Minor formatting

Test remaining formula types

Add unit tests for precedence-0 formulas and lower

Before larger refactoring

Refactor precedence rules for formulas

Remove ChildPosition enum

Fix

Address warnings

Remove unneeded precedence implementation

Test negation

Test quantified formulas

Clean up tests

Clean up tests

Test conjunction

Test disjunction

Start testing implications

Refactor parenthesis requirement check

Fix precedence of implication

Continue testing implication

Test biconditionals

Experimental method for testing all permutations

Rewrite tests for clarity

Rewrite tests for clarity

Add type annotations

Rewrite tests for clarity

Reorganize tests

Finish testing biconditionals

Support empty n-aries

Support quantified expressions with 0 parameters

Rewrite term formatting tests for clarity

Reorganize term formatter tests

Refactor parenthesis rules for terms

Remove unneeded parentheses enum

Refactoring

Refactoring

Minor clean-up

Minor clean-up

Simplify representation of quantified formulas

Remove redundant indirection

Remove redundant indirection

.github/workflows/main.yml

@@ -0,0 +1,32 @@
+name: Rust
+
+on:
+  push:
+    branches: [master]
+  pull_request:
+    branches: [master]
+
+jobs:
+  test:
+    name: Test
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        build: [stable, beta, nightly]
+        include:
+          - build: stable
+            rust: stable
+          - build: beta
+            rust: beta
+          - build: nightly
+            rust: nightly
+
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install Rust (rustup)
+        run: rustup update ${{ matrix.rust }} --no-self-update && rustup default ${{ matrix.rust }}
+        shell: bash
+      - name: Build
+        run: cargo build --verbose
+      - name: Run tests
+        run: cargo test --verbose

Cargo.toml

@@ -11,3 +11,6 @@ keywords = ["logic"]
 categories = ["data-structures", "science"]
 license = "MIT"
 edition = "2018"
+
+[dependencies]
+log = "0.4"

src/ast.rs

@@ -1,5 +1,8 @@
+use crate::flavor::{FunctionDeclaration as _, PredicateDeclaration as _};
+
 // Operators
 
+#[derive(Clone, Copy, Eq, Hash, Ord, PartialEq, PartialOrd)]
 pub enum BinaryOperator
 {
 	Add,
@@ -10,6 +13,7 @@ pub enum BinaryOperator
 	Exponentiate,
 }
 
+#[derive(Clone, Copy, Eq, Hash, Ord, PartialEq, PartialOrd)]
 pub enum ComparisonOperator
 {
 	Greater,
@@ -20,12 +24,22 @@ pub enum ComparisonOperator
 	Equal,
 }
 
+#[derive(Clone, Copy, Eq, Hash, Ord, PartialEq, PartialOrd)]
 pub enum UnaryOperator
 {
 	AbsoluteValue,
 	Negative,
 }
 
+// ImplicationDirection
+
+#[derive(Clone, Copy, Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub enum ImplicationDirection
+{
+	LeftToRight,
+	RightToLeft,
+}
+
 // Primitives
 
 #[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
@@ -47,7 +61,8 @@ impl FunctionDeclaration
 	}
 }
 
-pub type FunctionDeclarations = std::collections::BTreeSet<std::rc::Rc<FunctionDeclaration>>;
+pub type FunctionDeclarations<F> =
+	std::collections::BTreeSet<std::rc::Rc<<F as crate::flavor::Flavor>::FunctionDeclaration>>;
 
 #[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
 pub struct PredicateDeclaration
@@ -68,7 +83,8 @@ impl PredicateDeclaration
 	}
 }
 
-pub type PredicateDeclarations = std::collections::BTreeSet<std::rc::Rc<PredicateDeclaration>>;
+pub type PredicateDeclarations<F> =
+	std::collections::BTreeSet<std::rc::Rc<<F as crate::flavor::Flavor>::PredicateDeclaration>>;
 
 pub struct VariableDeclaration
 {
@@ -78,10 +94,10 @@ pub struct VariableDeclaration
 impl std::cmp::PartialEq for VariableDeclaration
 {
 	#[inline(always)]
-	fn eq(&self, other: &VariableDeclaration) -> bool
+	fn eq(&self, other: &Self) -> bool
 	{
-		let l = self as *const VariableDeclaration;
-		let r = other as *const VariableDeclaration;
+		let l = self as *const Self;
+		let r = other as *const Self;
 
 		l.eq(&r)
 	}
@@ -115,6 +131,17 @@ impl std::cmp::Ord for VariableDeclaration
 	}
 }
 
+impl std::hash::Hash for VariableDeclaration
+{
+	#[inline(always)]
+	fn hash<H: std::hash::Hasher>(&self, state: &mut H)
+	{
+		let p = self as *const VariableDeclaration;
+
+		p.hash(state);
+	}
+}
+
 impl VariableDeclaration
 {
 	pub fn new(name: String) -> Self
@@ -126,20 +153,26 @@ impl VariableDeclaration
 	}
 }
 
-pub type VariableDeclarations = Vec<std::rc::Rc<VariableDeclaration>>;
+pub type VariableDeclarations<F> =
+	Vec<std::rc::Rc<<F as crate::flavor::Flavor>::VariableDeclaration>>;
 
 // Terms
 
-pub struct BinaryOperation
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct BinaryOperation<F>
+where
+	F: crate::flavor::Flavor,
 {
 	pub operator: BinaryOperator,
-	pub left: Box<Term>,
-	pub right: Box<Term>,
+	pub left: Box<Term<F>>,
+	pub right: Box<Term<F>>,
 }
 
-impl BinaryOperation
+impl<F> BinaryOperation<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(operator: BinaryOperator, left: Box<Term>, right: Box<Term>) -> Self
+	pub fn new(operator: BinaryOperator, left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self
 		{
@@ -150,42 +183,53 @@ impl BinaryOperation
 	}
 }
 
-pub struct Function
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct Function<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub declaration: std::rc::Rc<FunctionDeclaration>,
-	pub arguments: Vec<Box<Term>>,
+	pub declaration: std::rc::Rc<F::FunctionDeclaration>,
+	pub arguments: Terms<F>,
 }
 
-impl Function
+impl<F> Function<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(declaration: &std::rc::Rc<FunctionDeclaration>, arguments: Vec<Box<Term>>) -> Self
+	pub fn new(declaration: std::rc::Rc<F::FunctionDeclaration>, arguments: Terms<F>) -> Self
 	{
-		assert_eq!(declaration.arity, arguments.len(),
-			"function has a different number of arguments then declared");
+		assert_eq!(declaration.arity(), arguments.len(),
+			"function has a different number of arguments than declared");
 
 		Self
 		{
-			declaration: std::rc::Rc::clone(declaration),
+			declaration,
 			arguments,
 		}
 	}
 }
 
+#[derive(Clone, Copy, Eq, Hash, Ord, PartialEq, PartialOrd)]
 pub enum SpecialInteger
 {
 	Infimum,
 	Supremum,
 }
 
-pub struct UnaryOperation
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct UnaryOperation<F>
+where
+	F: crate::flavor::Flavor,
 {
 	pub operator: UnaryOperator,
-	pub argument: Box<Term>,
+	pub argument: Box<Term<F>>,
 }
 
-impl UnaryOperation
+impl<F> UnaryOperation<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(operator: UnaryOperator, argument: Box<Term>) -> Self
+	pub fn new(operator: UnaryOperator, argument: Box<Term<F>>) -> Self
 	{
 		Self
 		{
@@ -195,34 +239,44 @@ impl UnaryOperation
 	}
 }
 
-pub struct Variable
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct Variable<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub declaration: std::rc::Rc<VariableDeclaration>,
+	pub declaration: std::rc::Rc<F::VariableDeclaration>,
 }
 
-impl Variable
+impl<F> Variable<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(declaration: &std::rc::Rc<VariableDeclaration>) -> Self
+	pub fn new(declaration: std::rc::Rc<F::VariableDeclaration>) -> Self
 	{
 		Self
 		{
-			declaration: std::rc::Rc::clone(declaration),
+			declaration,
 		}
 	}
 }
 
 // Formulas
 
-pub struct Compare
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct Compare<F>
+where
+	F: crate::flavor::Flavor,
 {
 	pub operator: ComparisonOperator,
-	pub left: Box<Term>,
-	pub right: Box<Term>,
+	pub left: Box<Term<F>>,
+	pub right: Box<Term<F>>,
 }
 
-impl Compare
+impl<F> Compare<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(operator: ComparisonOperator, left: Box<Term>, right: Box<Term>) -> Self
+	pub fn new(operator: ComparisonOperator, left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self
 		{
@@ -233,15 +287,20 @@ impl Compare
 	}
 }
 
-pub struct Exists
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct QuantifiedFormula<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub parameters: std::rc::Rc<VariableDeclarations>,
-	pub argument: Box<Formula>,
+	pub parameters: std::rc::Rc<VariableDeclarations<F>>,
+	pub argument: Box<Formula<F>>,
 }
 
-impl Exists
+impl<F> QuantifiedFormula<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(parameters: std::rc::Rc<VariableDeclarations>, argument: Box<Formula>) -> Self
+	pub fn new(parameters: std::rc::Rc<VariableDeclarations<F>>, argument: Box<Formula<F>>) -> Self
 	{
 		Self
 		{
@@ -251,76 +310,54 @@ impl Exists
 	}
 }
 
-pub struct ForAll
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct Implies<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub parameters: std::rc::Rc<VariableDeclarations>,
-	pub argument: Box<Formula>,
+	pub direction: ImplicationDirection,
+	pub antecedent: Box<Formula<F>>,
+	pub implication: Box<Formula<F>>,
 }
 
-impl ForAll
+impl<F> Implies<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(parameters: std::rc::Rc<VariableDeclarations>, argument: Box<Formula>) -> Self
-	{
-		Self
-		{
-			parameters,
-			argument,
-		}
-	}
-}
-
-pub struct IfAndOnlyIf
-{
-	pub left: Box<Formula>,
-	pub right: Box<Formula>,
-}
-
-impl IfAndOnlyIf
-{
-	pub fn new(left: Box<Formula>, right: Box<Formula>) -> Self
-	{
-		Self
-		{
-			left,
-			right,
-		}
-	}
-}
-
-pub struct Implies
-{
-	pub antecedent: Box<Formula>,
-	pub implication: Box<Formula>,
-}
-
-impl Implies
-{
-	pub fn new(antecedent: Box<Formula>, implication: Box<Formula>) -> Self
+	pub fn new(direction: ImplicationDirection, antecedent: Box<Formula<F>>,
+		implication: Box<Formula<F>>)
+		-> Self
 	{
 		Self
 		{
+			direction,
 			antecedent,
 			implication,
 		}
 	}
 }
 
-pub struct Predicate
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub struct Predicate<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub declaration: std::rc::Rc<PredicateDeclaration>,
-	pub arguments: Vec<Box<Term>>,
+	pub declaration: std::rc::Rc<F::PredicateDeclaration>,
+	pub arguments: Terms<F>,
 }
 
-impl Predicate
+impl<F> Predicate<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn new(declaration: &std::rc::Rc<PredicateDeclaration>, arguments: Vec<Box<Term>>) -> Self
+	pub fn new(declaration: std::rc::Rc<F::PredicateDeclaration>, arguments: Terms<F>) -> Self
 	{
-		assert_eq!(declaration.arity, arguments.len(),
-			"predicate has a different number of arguments then declared");
+		assert_eq!(declaration.arity(), arguments.len(),
+			"predicate has a different number of arguments than declared");
 
 		Self
 		{
-			declaration: std::rc::Rc::clone(declaration),
+			declaration,
 			arguments,
 		}
 	}
@@ -328,33 +365,38 @@ impl Predicate
 
 // Variants
 
-pub enum Term
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub enum Term<F>
+where
+	F: crate::flavor::Flavor,
 {
-	BinaryOperation(BinaryOperation),
+	BinaryOperation(BinaryOperation<F>),
 	Boolean(bool),
-	Function(Function),
+	Function(Function<F>),
 	Integer(i32),
 	SpecialInteger(SpecialInteger),
 	String(String),
-	UnaryOperation(UnaryOperation),
-	Variable(Variable),
+	UnaryOperation(UnaryOperation<F>),
+	Variable(Variable<F>),
 }
 
-pub type Terms = Vec<Box<Term>>;
+pub type Terms<F> = Vec<Term<F>>;
 
-impl Term
+impl<F> Term<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn absolute_value(argument: Box<Term>) -> Self
+	pub fn absolute_value(argument: Box<Term<F>>) -> Self
 	{
 		Self::unary_operation(UnaryOperator::AbsoluteValue, argument)
 	}
 
-	pub fn add(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn add(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::binary_operation(BinaryOperator::Add, left, right)
 	}
 
-	pub fn binary_operation(operator: BinaryOperator, left: Box<Term>, right: Box<Term>) -> Self
+	pub fn binary_operation(operator: BinaryOperator, left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::BinaryOperation(BinaryOperation::new(operator, left, right))
 	}
@@ -364,12 +406,12 @@ impl Term
 		Self::Boolean(value)
 	}
 
-	pub fn divide(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn divide(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::binary_operation(BinaryOperator::Divide, left, right)
 	}
 
-	pub fn exponentiate(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn exponentiate(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::binary_operation(BinaryOperator::Exponentiate, left, right)
 	}
@@ -379,8 +421,7 @@ impl Term
 		Self::boolean(false)
 	}
 
-	pub fn function(declaration: &std::rc::Rc<FunctionDeclaration>, arguments: Vec<Box<Term>>)
-		-> Self
+	pub fn function(declaration: std::rc::Rc<F::FunctionDeclaration>, arguments: Terms<F>) -> Self
 	{
 		Self::Function(Function::new(declaration, arguments))
 	}
@@ -395,17 +436,17 @@ impl Term
 		Self::Integer(value)
 	}
 
-	pub fn modulo(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn modulo(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::binary_operation(BinaryOperator::Modulo, left, right)
 	}
 
-	pub fn multiply(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn multiply(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::binary_operation(BinaryOperator::Multiply, left, right)
 	}
 
-	pub fn negative(argument: Box<Term>) -> Self
+	pub fn negative(argument: Box<Term<F>>) -> Self
 	{
 		Self::unary_operation(UnaryOperator::Negative, argument)
 	}
@@ -420,7 +461,7 @@ impl Term
 		Self::String(value)
 	}
 
-	pub fn subtract(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn subtract(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::binary_operation(BinaryOperator::Subtract, left, right)
 	}
@@ -435,39 +476,42 @@ impl Term
 		Self::boolean(true)
 	}
 
-	pub fn unary_operation(operator: UnaryOperator, argument: Box<Term>) -> Self
+	pub fn unary_operation(operator: UnaryOperator, argument: Box<Term<F>>) -> Self
 	{
 		Self::UnaryOperation(UnaryOperation::new(operator, argument))
 	}
 
-	pub fn variable(declaration: &std::rc::Rc<VariableDeclaration>) -> Self
+	pub fn variable(declaration: std::rc::Rc<F::VariableDeclaration>) -> Self
 	{
 		Self::Variable(Variable::new(declaration))
 	}
 }
 
-pub enum Formula
+#[derive(Eq, Hash, Ord, PartialEq, PartialOrd)]
+pub enum Formula<F>
+where
+	F: crate::flavor::Flavor,
 {
-	And(Formulas),
+	And(Formulas<F>),
 	Boolean(bool),
-	Compare(Compare),
-	Exists(Exists),
-	ForAll(ForAll),
-	IfAndOnlyIf(IfAndOnlyIf),
-	Implies(Implies),
-	Not(Box<Formula>),
-	Or(Formulas),
-	Predicate(Predicate),
+	Compare(Compare<F>),
+	Exists(QuantifiedFormula<F>),
+	ForAll(QuantifiedFormula<F>),
+	IfAndOnlyIf(Formulas<F>),
+	Implies(Implies<F>),
+	Not(Box<Formula<F>>),
+	Or(Formulas<F>),
+	Predicate(Predicate<F>),
 }
 
-pub type Formulas = Vec<Box<Formula>>;
+pub type Formulas<F> = Vec<Formula<F>>;
 
-impl Formula
+impl<F> Formula<F>
+where
+	F: crate::flavor::Flavor,
 {
-	pub fn and(arguments: Formulas) -> Self
+	pub fn and(arguments: Formulas<F>) -> Self
 	{
-		assert!(!arguments.is_empty());
-
 		Self::And(arguments)
 	}
 
@@ -476,19 +520,17 @@ impl Formula
 		Self::Boolean(value)
 	}
 
-	pub fn compare(operator: ComparisonOperator, left: Box<Term>, right: Box<Term>) -> Self
+	pub fn compare(operator: ComparisonOperator, left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::Compare(Compare::new(operator, left, right))
 	}
 
-	pub fn exists(parameters: std::rc::Rc<VariableDeclarations>, argument: Box<Formula>) -> Self
+	pub fn exists(parameters: std::rc::Rc<VariableDeclarations<F>>, argument: Box<Formula<F>>) -> Self
 	{
-		assert!(!parameters.is_empty());
-
-		Self::Exists(Exists::new(parameters, argument))
+		Self::Exists(QuantifiedFormula::new(parameters, argument))
 	}
 
-	pub fn equal(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn equal(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::compare(ComparisonOperator::Equal, left, right)
 	}
@@ -498,62 +540,58 @@ impl Formula
 		Self::boolean(false)
 	}
 
-	pub fn for_all(parameters: std::rc::Rc<VariableDeclarations>, argument: Box<Formula>) -> Self
+	pub fn for_all(parameters: std::rc::Rc<VariableDeclarations<F>>, argument: Box<Formula<F>>) -> Self
 	{
-		assert!(!parameters.is_empty());
-
-		Self::ForAll(ForAll::new(parameters, argument))
+		Self::ForAll(QuantifiedFormula::new(parameters, argument))
 	}
 
-	pub fn greater(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn greater(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::compare(ComparisonOperator::Greater, left, right)
 	}
 
-	pub fn greater_or_equal(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn greater_or_equal(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::compare(ComparisonOperator::GreaterOrEqual, left, right)
 	}
 
-	pub fn if_and_only_if(left: Box<Formula>, right: Box<Formula>) -> Self
+	pub fn if_and_only_if(arguments: Formulas<F>) -> Self
 	{
-		Self::IfAndOnlyIf(IfAndOnlyIf::new(left, right))
+		Self::IfAndOnlyIf(arguments)
 	}
 
-	pub fn implies(antecedent: Box<Formula>, consequent: Box<Formula>) -> Self
+	pub fn implies(direction: ImplicationDirection, antecedent: Box<Formula<F>>,
+		consequent: Box<Formula<F>>) -> Self
 	{
-		Self::Implies(Implies::new(antecedent, consequent))
+		Self::Implies(Implies::new(direction, antecedent, consequent))
 	}
 
-	pub fn less(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn less(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::compare(ComparisonOperator::Less, left, right)
 	}
 
-	pub fn less_or_equal(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn less_or_equal(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::compare(ComparisonOperator::LessOrEqual, left, right)
 	}
 
-	pub fn not(argument: Box<Formula>) -> Self
+	pub fn not(argument: Box<Formula<F>>) -> Self
 	{
 		Self::Not(argument)
 	}
 
-	pub fn not_equal(left: Box<Term>, right: Box<Term>) -> Self
+	pub fn not_equal(left: Box<Term<F>>, right: Box<Term<F>>) -> Self
 	{
 		Self::compare(ComparisonOperator::NotEqual, left, right)
 	}
 
-	pub fn or(arguments: Formulas) -> Self
+	pub fn or(arguments: Formulas<F>) -> Self
 	{
-		assert!(!arguments.is_empty());
-
 		Self::Or(arguments)
 	}
 
-	pub fn predicate(declaration: &std::rc::Rc<PredicateDeclaration>, arguments: Vec<Box<Term>>)
-		-> Self
+	pub fn predicate(declaration: std::rc::Rc<F::PredicateDeclaration>, arguments: Terms<F>) -> Self
 	{
 		Self::Predicate(Predicate::new(declaration, arguments))
 	}
@@ -563,3 +601,11 @@ impl Formula
 		Self::boolean(true)
 	}
 }
+
+pub struct OpenFormula<F>
+where
+	F: crate::flavor::Flavor,
+{
+	pub free_variable_declarations: std::rc::Rc<VariableDeclarations<F>>,
+	pub formula: Formula<F>,
+}

src/flavor.rs

@@ -0,0 +1,85 @@
+pub trait FunctionDeclaration
+{
+	fn display_name(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result;
+	fn arity(&self) -> usize;
+	fn matches_signature(&self, other_name: &str, other_arity: usize) -> bool;
+}
+
+impl FunctionDeclaration for crate::FunctionDeclaration
+{
+	fn display_name(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		write!(formatter, "{}", self.name)
+	}
+
+	fn arity(&self) -> usize
+	{
+		self.arity
+	}
+
+	fn matches_signature(&self, other_name: &str, other_arity: usize) -> bool
+	{
+		self.name == other_name && self.arity == other_arity
+	}
+}
+
+pub trait PredicateDeclaration
+{
+	fn display_name(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result;
+	fn arity(&self) -> usize;
+	fn matches_signature(&self, other_name: &str, other_arity: usize) -> bool;
+}
+
+impl PredicateDeclaration for crate::PredicateDeclaration
+{
+	fn display_name(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		write!(formatter, "{}", self.name)
+	}
+
+	fn arity(&self) -> usize
+	{
+		self.arity
+	}
+
+	fn matches_signature(&self, other_name: &str, other_arity: usize) -> bool
+	{
+		self.name == other_name && self.arity == other_arity
+	}
+}
+
+pub trait VariableDeclaration
+{
+	fn display_name(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result;
+	fn matches_name(&self, other_name: &str) -> bool;
+}
+
+impl VariableDeclaration for crate::VariableDeclaration
+{
+	fn display_name(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		write!(formatter, "{}", self.name)
+	}
+
+	fn matches_name(&self, other_name: &str) -> bool
+	{
+		self.name == other_name
+	}
+}
+
+pub trait Flavor
+{
+	type FunctionDeclaration: FunctionDeclaration + std::cmp::Eq + std::cmp::Ord + std::hash::Hash;
+	type PredicateDeclaration:
+		PredicateDeclaration + std::cmp::Eq + std::cmp::Ord + std::hash::Hash;
+	type VariableDeclaration: VariableDeclaration + std::cmp::Eq + std::cmp::Ord + std::hash::Hash;
+}
+
+pub struct DefaultFlavor;
+
+impl Flavor for DefaultFlavor
+{
+	type FunctionDeclaration = crate::FunctionDeclaration;
+	type PredicateDeclaration = crate::PredicateDeclaration;
+	type VariableDeclaration = crate::VariableDeclaration;
+}

src/format.rs

@@ -1,431 +1,2 @@
-trait Precedence
-{
-	fn precedence(&self) -> i32;
-}
-
-impl Precedence for crate::Term
-{
-	fn precedence(&self) -> i32
-	{
-		match &self
-		{
-			Self::Boolean(_)
-			| Self::Function(_)
-			| Self::SpecialInteger(_)
-			| Self::Integer(_)
-			| Self::String(_)
-			| Self::Variable(_)
-				=> 0,
-			Self::UnaryOperation(
-				crate::UnaryOperation{operator: crate::UnaryOperator::Negative, ..})
-				=> 1,
-			Self::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Exponentiate, ..})
-				=> 2,
-			Self::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Multiply, ..})
-			| Self::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Divide, ..})
-			| Self::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Modulo, ..})
-				=> 3,
-			Self::BinaryOperation(crate::BinaryOperation{operator: crate::BinaryOperator::Add, ..})
-			| Self::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Subtract, ..})
-				=> 4,
-			Self::UnaryOperation(
-				crate::UnaryOperation{operator: crate::UnaryOperator::AbsoluteValue, ..})
-				=> 5,
-		}
-	}
-}
-
-impl Precedence for crate::Formula
-{
-	fn precedence(&self) -> i32
-	{
-		match &self
-		{
-			Self::Predicate(_)
-			| Self::Boolean(_)
-			| Self::Compare(_)
-				=> 0,
-			Self::Exists(_)
-			| Self::ForAll(_)
-				=> 1,
-			Self::Not(_)
-				=> 2,
-			Self::And(_)
-				=> 3,
-			Self::Or(_)
-				=> 4,
-			Self::Implies(_)
-				=> 5,
-			Self::IfAndOnlyIf(_)
-				=> 6,
-		}
-	}
-}
-
-impl std::fmt::Debug for crate::FunctionDeclaration
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{}/{}", &self.name, self.arity)
-	}
-}
-
-impl std::fmt::Display for crate::FunctionDeclaration
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{:?}", &self)
-	}
-}
-
-impl std::fmt::Debug for crate::PredicateDeclaration
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{}/{}", &self.name, self.arity)
-	}
-}
-
-impl std::fmt::Display for crate::PredicateDeclaration
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{:?}", &self)
-	}
-}
-
-impl std::fmt::Debug for crate::VariableDeclaration
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{}", &self.name)
-	}
-}
-
-impl std::fmt::Display for crate::VariableDeclaration
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{:?}", &self)
-	}
-}
-
-struct TermDisplay<'term>
-{
-	parent_precedence: Option<i32>,
-	term: &'term crate::Term,
-}
-
-fn display_term(term: &crate::Term, parent_precedence: Option<i32>) -> TermDisplay
-{
-	TermDisplay
-	{
-		parent_precedence,
-		term,
-	}
-}
-
-impl<'term> std::fmt::Debug for TermDisplay<'term>
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		let precedence = self.term.precedence();
-		let requires_parentheses = match self.parent_precedence
-		{
-			Some(parent_precedence) => precedence > parent_precedence,
-			None => false,
-		};
-		let precedence = Some(precedence);
-
-		if requires_parentheses
-		{
-			write!(format, "(")?;
-		}
-
-		match &self.term
-		{
-			crate::Term::Boolean(true) => write!(format, "true"),
-			crate::Term::Boolean(false) => write!(format, "false"),
-			crate::Term::SpecialInteger(crate::SpecialInteger::Infimum) => write!(format, "#inf"),
-			crate::Term::SpecialInteger(crate::SpecialInteger::Supremum) => write!(format, "#sup"),
-			crate::Term::Integer(value) => write!(format, "{}", value),
-			crate::Term::String(value) => write!(format, "\"{}\"", value),
-			crate::Term::Variable(variable) => write!(format, "{:?}", variable.declaration),
-			crate::Term::Function(function) =>
-			{
-				write!(format, "{}", function.declaration.name)?;
-
-				assert!(function.declaration.arity == function.arguments.len(),
-					"number of function arguments differs from declaration (expected {}, got {})",
-					function.declaration.arity, function.arguments.len());
-
-				if function.arguments.len() > 0
-				{
-					write!(format, "{}(", function.declaration.name)?;
-
-					let mut separator = "";
-
-					for argument in &function.arguments
-					{
-						write!(format, "{}{:?}", separator, display_term(&argument, None))?;
-
-						separator = ", ";
-					}
-
-					write!(format, ")")?;
-				}
-
-				Ok(())
-			},
-			crate::Term::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Add, left, right})
-				=> write!(format, "{:?} + {:?}", display_term(left, precedence),
-					display_term(right, precedence)),
-			crate::Term::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Subtract, left, right})
-				=> write!(format, "{:?} - {:?}", display_term(left, precedence),
-					display_term(right, precedence)),
-			crate::Term::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Multiply, left, right})
-				=> write!(format, "{:?} * {:?}", display_term(left, precedence),
-					display_term(right, precedence)),
-			crate::Term::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Divide, left, right})
-				=> write!(format, "{:?} / {:?}", display_term(left, precedence),
-					display_term(right, precedence)),
-			crate::Term::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Modulo, left, right})
-				=> write!(format, "{:?} % {:?}", display_term(left, precedence),
-					display_term(right, precedence)),
-			crate::Term::BinaryOperation(
-				crate::BinaryOperation{operator: crate::BinaryOperator::Exponentiate, left, right})
-				=> write!(format, "{:?} ** {:?}", display_term(left, precedence),
-					display_term(right, precedence)),
-			crate::Term::UnaryOperation(
-				crate::UnaryOperation{operator: crate::UnaryOperator::Negative, argument})
-				=> write!(format, "-{:?}", display_term(argument, precedence)),
-			crate::Term::UnaryOperation(
-				crate::UnaryOperation{operator: crate::UnaryOperator::AbsoluteValue, argument})
-				=> write!(format, "|{:?}|", display_term(argument, precedence)),
-		}?;
-
-		if requires_parentheses
-		{
-			write!(format, ")")?;
-		}
-
-		Ok(())
-	}
-}
-
-impl<'term> std::fmt::Display for TermDisplay<'term>
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{:?}", self)
-	}
-}
-
-struct FormulaDisplay<'formula>
-{
-	parent_precedence: Option<i32>,
-	formula: &'formula crate::Formula,
-}
-
-fn display_formula(formula: &crate::Formula, parent_precedence: Option<i32>) -> FormulaDisplay
-{
-	FormulaDisplay
-	{
-		parent_precedence,
-		formula,
-	}
-}
-
-impl<'formula> std::fmt::Debug for FormulaDisplay<'formula>
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		let precedence = self.formula.precedence();
-		let requires_parentheses = match self.parent_precedence
-		{
-			Some(parent_precedence) => precedence > parent_precedence,
-			None => false,
-		};
-		let precedence = Some(precedence);
-
-		if requires_parentheses
-		{
-			write!(format, "(")?;
-		}
-
-		match &self.formula
-		{
-			crate::Formula::Exists(exists) =>
-			{
-				assert!(!exists.parameters.is_empty());
-
-				write!(format, "exists")?;
-
-				let mut separator = " ";
-
-				for parameter in exists.parameters.iter()
-				{
-					write!(format, "{}{:?}", separator, parameter)?;
-
-					separator = ", "
-				}
-
-				write!(format, " {:?}", display_formula(&exists.argument, precedence))?;
-			},
-			crate::Formula::ForAll(for_all) =>
-			{
-				assert!(!for_all.parameters.is_empty());
-
-				write!(format, "forall")?;
-
-				let mut separator = " ";
-
-				for parameter in for_all.parameters.iter()
-				{
-					write!(format, "{}{:?}", separator, parameter)?;
-
-					separator = ", "
-				}
-
-				write!(format, " {:?}", display_formula(&for_all.argument, precedence))?;
-			},
-			crate::Formula::Not(argument) => write!(format, "not {:?}",
-				display_formula(argument, precedence))?,
-			crate::Formula::And(arguments) =>
-			{
-				let mut separator = "";
-
-				assert!(!arguments.is_empty());
-
-				for argument in arguments
-				{
-					write!(format, "{}{:?}", separator, display_formula(argument, precedence))?;
-
-					separator = " and "
-				}
-			},
-			crate::Formula::Or(arguments) =>
-			{
-				let mut separator = "";
-
-				assert!(!arguments.is_empty());
-
-				for argument in arguments
-				{
-					write!(format, "{}{:?}", separator, display_formula(argument, precedence))?;
-
-					separator = " or "
-				}
-			},
-			crate::Formula::Implies(crate::Implies{antecedent, implication})
-				=> write!(format, "{:?} -> {:?}", display_formula(antecedent, precedence),
-					display_formula(implication, precedence))?,
-			crate::Formula::IfAndOnlyIf(crate::IfAndOnlyIf{left, right})
-				=> write!(format, "{:?} <-> {:?}", display_formula(left, precedence),
-					display_formula(right, precedence))?,
-			crate::Formula::Compare(
-				crate::Compare{operator: crate::ComparisonOperator::Less, left, right})
-				=> write!(format, "{:?} < {:?}", display_term(left, None),
-					display_term(right, None))?,
-			crate::Formula::Compare(
-				crate::Compare{operator: crate::ComparisonOperator::LessOrEqual, left, right})
-				=> write!(format, "{:?} <= {:?}", display_term(left, None),
-					display_term(right, None))?,
-			crate::Formula::Compare(
-				crate::Compare{operator: crate::ComparisonOperator::Greater, left, right})
-				=> write!(format, "{:?} > {:?}", display_term(left, None),
-					display_term(right, None))?,
-			crate::Formula::Compare(
-				crate::Compare{operator: crate::ComparisonOperator::GreaterOrEqual, left, right})
-				=> write!(format, "{:?} >= {:?}", display_term(left, None),
-					display_term(right, None))?,
-			crate::Formula::Compare(
-				crate::Compare{operator: crate::ComparisonOperator::Equal, left, right})
-				=> write!(format, "{:?} = {:?}", display_term(left, None),
-					display_term(right, None))?,
-			crate::Formula::Compare(
-				crate::Compare{operator: crate::ComparisonOperator::NotEqual, left, right})
-				=> write!(format, "{:?} != {:?}", display_term(left, None),
-					display_term(right, None))?,
-			crate::Formula::Boolean(true) => write!(format, "#true")?,
-			crate::Formula::Boolean(false) => write!(format, "#false")?,
-			crate::Formula::Predicate(predicate) =>
-			{
-				write!(format, "{}", predicate.declaration.name)?;
-
-				if !predicate.arguments.is_empty()
-				{
-					write!(format, "(")?;
-
-					let mut separator = "";
-
-					for argument in &predicate.arguments
-					{
-						write!(format, "{}{:?}", separator, display_term(argument, None))?;
-
-						separator = ", "
-					}
-
-					write!(format, ")")?;
-				}
-			},
-		}
-
-		if requires_parentheses
-		{
-			write!(format, ")")?;
-		}
-
-		Ok(())
-	}
-}
-
-impl<'formula> std::fmt::Display for FormulaDisplay<'formula>
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{:?}", self)
-	}
-}
-
-impl std::fmt::Debug for crate::Formula
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{:?}", display_formula(&self, None))
-	}
-}
-
-impl std::fmt::Display for crate::Formula
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{}", display_formula(&self, None))
-	}
-}
-
-impl std::fmt::Debug for crate::Term
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{:?}", display_term(&self, None))
-	}
-}
-
-impl std::fmt::Display for crate::Term
-{
-	fn fmt(&self, format: &mut std::fmt::Formatter) -> std::fmt::Result
-	{
-		write!(format, "{}", display_term(&self, None))
-	}
-}
+pub mod formulas;
+pub mod terms;

src/lib.rs

@@ -1,4 +1,11 @@
 mod ast;
-pub mod format;
+pub mod flavor;
+mod format;
+mod parse;
+mod utils;
 
 pub use ast::*;
+pub use format::{formulas::FormulaDisplay, terms::TermDisplay};
+pub use flavor::{DefaultFlavor, Flavor};
+pub use utils::*;
+pub use parse::{DefaultParser, Parser};

src/parse.rs

@@ -0,0 +1,142 @@
+pub mod error;
+pub mod formulas;
+pub mod terms;
+pub mod tokens;
+
+pub use error::Error;
+
+use crate::flavor::{FunctionDeclaration as _, PredicateDeclaration as _, VariableDeclaration as _};
+
+pub trait Parser: Sized
+{
+	type Flavor: crate::flavor::Flavor;
+
+	fn find_or_create_function_declaration(&self, name: &str, arity: usize)
+		-> std::rc::Rc<<Self::Flavor as crate::flavor::Flavor>::FunctionDeclaration>;
+
+	fn find_or_create_predicate_declaration(&self, name: &str, arity: usize)
+		-> std::rc::Rc<<Self::Flavor as crate::flavor::Flavor>::PredicateDeclaration>;
+
+	fn new_variable_declaration(name: String)
+		-> <Self::Flavor as crate::flavor::Flavor>::VariableDeclaration;
+
+	fn find_or_create_variable_declaration(
+		variable_declaration_stack_layer: &crate::VariableDeclarationStackLayer<Self::Flavor>,
+		variable_name: &str)
+		-> std::rc::Rc<<Self::Flavor as crate::flavor::Flavor>::VariableDeclaration>
+	{
+		match variable_declaration_stack_layer
+		{
+			crate::VariableDeclarationStackLayer::Free(free_variable_declarations) =>
+			{
+				if let Some(variable_declaration) = free_variable_declarations.borrow().iter()
+					.find(|x| x.matches_name(variable_name))
+				{
+					return std::rc::Rc::clone(&variable_declaration);
+				}
+
+				let variable_declaration = Self::new_variable_declaration(variable_name.to_owned());
+				let variable_declaration = std::rc::Rc::new(variable_declaration);
+
+				free_variable_declarations.borrow_mut()
+					.push(std::rc::Rc::clone(&variable_declaration));
+
+				variable_declaration
+			},
+			crate::VariableDeclarationStackLayer::Bound(bound_variable_declarations) =>
+			{
+				if let Some(variable_declaration) = bound_variable_declarations
+					.variable_declarations.iter()
+					.find(|x| x.matches_name(variable_name))
+				{
+					return std::rc::Rc::clone(&variable_declaration);
+				}
+
+				Self::find_or_create_variable_declaration(bound_variable_declarations.parent,
+					variable_name)
+			},
+		}
+	}
+
+	fn parse_formula(&self, input: &str)
+		-> Result<crate::OpenFormula<Self::Flavor>, crate::parse::Error>
+	{
+		formulas::formula(input, self)
+	}
+}
+
+pub struct DefaultParser
+{
+	function_declarations:
+		std::cell::RefCell<crate::FunctionDeclarations<<Self as Parser>::Flavor>>,
+	predicate_declarations:
+		std::cell::RefCell<crate::PredicateDeclarations<<Self as Parser>::Flavor>>,
+}
+
+impl DefaultParser
+{
+	pub fn new() -> Self
+	{
+		Self
+		{
+			function_declarations: std::cell::RefCell::new(
+				crate::FunctionDeclarations::<<Self as Parser>::Flavor>::new()),
+			predicate_declarations: std::cell::RefCell::new(
+				crate::PredicateDeclarations::<<Self as Parser>::Flavor>::new()),
+		}
+	}
+}
+
+impl Parser for DefaultParser
+{
+	type Flavor = crate::flavor::DefaultFlavor;
+
+	fn new_variable_declaration(name: String)
+		-> <Self::Flavor as crate::flavor::Flavor>::VariableDeclaration
+	{
+		crate::VariableDeclaration
+		{
+			name,
+		}
+	}
+
+	fn find_or_create_function_declaration(&self, name: &str, arity: usize)
+		-> std::rc::Rc<<Self::Flavor as crate::flavor::Flavor>::FunctionDeclaration>
+	{
+		let mut function_declarations = self.function_declarations.borrow_mut();
+
+		match function_declarations.iter().find(|x| x.matches_signature(name, arity))
+		{
+			Some(declaration) => std::rc::Rc::clone(&declaration),
+			None =>
+			{
+				let declaration = crate::FunctionDeclaration::new(name.to_string(), arity);
+				let declaration = std::rc::Rc::new(declaration);
+
+				function_declarations.insert(std::rc::Rc::clone(&declaration));
+
+				declaration
+			},
+		}
+	}
+
+	fn find_or_create_predicate_declaration(&self, name: &str, arity: usize)
+		-> std::rc::Rc<<Self::Flavor as crate::flavor::Flavor>::PredicateDeclaration>
+	{
+		let mut predicate_declarations = self.predicate_declarations.borrow_mut();
+
+		match predicate_declarations.iter().find(|x| x.matches_signature(name, arity))
+		{
+			Some(declaration) => std::rc::Rc::clone(&declaration),
+			None =>
+			{
+				let declaration = crate::PredicateDeclaration::new(name.to_string(), arity);
+				let declaration = std::rc::Rc::new(declaration);
+
+				predicate_declarations.insert(std::rc::Rc::clone(&declaration));
+
+				declaration
+			},
+		}
+	}
+}

src/parse/error.rs

@@ -0,0 +1,182 @@
+pub type Source = Box<dyn std::error::Error>;
+
+pub struct Location
+{
+	start: usize,
+	end: Option<usize>,
+}
+
+impl Location
+{
+	pub fn new(start: usize, end: Option<usize>) -> Self
+	{
+		Self
+		{
+			start,
+			end,
+		}
+	}
+}
+
+pub enum Kind
+{
+	UnmatchedParenthesis,
+	CharacterNotAllowed(char),
+	ParseNumber(String),
+	MixedImplicationDirections(Location),
+	ExpectedVariableDeclaration,
+	UnexpectedToken,
+	EmptyExpression,
+	ExpectedLogicalConnectiveArgument(String),
+	ExpectedTerm,
+	MultipleComparisonOperators(crate::ComparisonOperator, crate::ComparisonOperator),
+}
+
+pub struct Error
+{
+	pub kind: Kind,
+	pub location: Location,
+	pub source: Option<Source>,
+}
+
+impl Error
+{
+	pub(crate) fn new(kind: Kind, location: Location) -> Self
+	{
+		Self
+		{
+			kind,
+			location,
+			source: None,
+		}
+	}
+
+	pub(crate) fn with<S: Into<Source>>(mut self, source: S) -> Self
+	{
+		self.source = Some(source.into());
+		self
+	}
+
+	pub(crate) fn new_unmatched_parenthesis(location: Location) -> Self
+	{
+		Self::new(Kind::UnmatchedParenthesis, location)
+	}
+
+	pub(crate) fn new_character_not_allowed(character: char, location: Location) -> Self
+	{
+		Self::new(Kind::CharacterNotAllowed(character), location)
+	}
+
+	pub(crate) fn new_parse_number<I: Into<String>, S: Into<Source>>(input: I, location: Location,
+		source: S)
+		-> Self
+	{
+		Self::new(Kind::ParseNumber(input.into()), location).with(source)
+	}
+
+	pub(crate) fn new_mixed_implication_directions(location_1: Location, location_2: Location)
+		-> Self
+	{
+		Self::new(Kind::MixedImplicationDirections(location_2), location_1)
+	}
+
+	pub(crate) fn new_expected_variable_declaration(location: Location) -> Self
+	{
+		Self::new(Kind::ExpectedVariableDeclaration, location)
+	}
+
+	pub(crate) fn new_unexpected_token(location: Location) -> Self
+	{
+		Self::new(Kind::UnexpectedToken, location)
+	}
+
+	pub(crate) fn new_empty_expression(location: Location) -> Self
+	{
+		Self::new(Kind::EmptyExpression, location)
+	}
+
+	pub(crate) fn new_expected_logical_connective_argument(logical_connective_name: String,
+		location: Location)
+		-> Self
+	{
+		Self::new(Kind::ExpectedLogicalConnectiveArgument(logical_connective_name), location)
+	}
+
+	pub(crate) fn new_expected_term(location: Location) -> Self
+	{
+		Self::new(Kind::ExpectedTerm, location)
+	}
+
+	pub(crate) fn new_multiple_comparison_operators(
+		comparison_operator_1: crate::ComparisonOperator,
+		comparison_operator_2: crate::ComparisonOperator, location: Location)
+		-> Self
+	{
+		Self::new(Kind::MultipleComparisonOperators(comparison_operator_1, comparison_operator_2),
+			location)
+	}
+}
+
+impl std::fmt::Debug for Error
+{
+	fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		if let Some(end) = self.location.end
+		{
+			write!(formatter, "parsing error at {}:{}: ", self.location.start, end)?;
+		}
+		else
+		{
+			write!(formatter, "parsing error at {}: ", self.location.start)?;
+		}
+
+		match &self.kind
+		{
+			Kind::UnmatchedParenthesis => write!(formatter, "unmatched parenthesis")?,
+			Kind::CharacterNotAllowed(character) =>
+				write!(formatter, "character not allowed: ‘{}’", character)?,
+			Kind::ParseNumber(input) => write!(formatter, "could not “{}” as number", input)?,
+			// TODO: print second location properly
+			Kind::MixedImplicationDirections(_location_2) =>
+				write!(formatter, "-> and <- implications may not be mixed within the same scope")?,
+			Kind::ExpectedVariableDeclaration =>
+				write!(formatter, "expected a variable declaration")?,
+			Kind::UnexpectedToken => write!(formatter, "unexpected token")?,
+			Kind::EmptyExpression => write!(formatter, "empty expression")?,
+			Kind::ExpectedLogicalConnectiveArgument(ref logical_connective_name) =>
+				write!(formatter, "this “{}” logical connective is missing an argument",
+					logical_connective_name)?,
+			Kind::ExpectedTerm => write!(formatter, "expected a term")?,
+			Kind::MultipleComparisonOperators(comparison_operator_1, comparison_operator_2) =>
+				write!(formatter, "chained comparisons aren’t supported (found “{:?}” and “{:?}” in the same formula), consider separating them with “and”",
+					comparison_operator_1, comparison_operator_2)?,
+		}
+
+		if let Some(source) = &self.source
+		{
+			write!(formatter, "\nerror source: {}", source)?;
+		}
+
+		Ok(())
+	}
+}
+
+impl std::fmt::Display for Error
+{
+	fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		write!(formatter, "{:?}", self)
+	}
+}
+
+impl std::error::Error for Error
+{
+	fn source(&self) -> Option<&(dyn std::error::Error + 'static)>
+	{
+		match &self.source
+		{
+			Some(source) => Some(source.as_ref()),
+			None => None,
+		}
+	}
+}

src/parse/formulas.rs

@@ -0,0 +1,564 @@
+use super::terms::*;
+use super::tokens::*;
+
+pub fn formula<P>(input: &str, parser: &P)
+	-> Result<crate::OpenFormula<P::Flavor>, crate::parse::Error>
+where
+	P: super::Parser,
+{
+	let variable_declaration_stack = crate::VariableDeclarationStackLayer::free();
+
+	let formula_str = FormulaStr::new(input, parser, &variable_declaration_stack);
+	let formula = formula_str.parse(0)?;
+
+	let free_variable_declarations = match variable_declaration_stack
+	{
+		crate::VariableDeclarationStackLayer::Free(free_variable_declarations) =>
+			std::rc::Rc::new(free_variable_declarations.into_inner()),
+		_ => unreachable!(),
+	};
+
+	Ok(crate::OpenFormula
+	{
+		formula,
+		free_variable_declarations,
+	})
+}
+
+pub(crate) fn predicate_name(identifier: &str) -> Option<(&str, &str)>
+{
+	function_name(identifier)
+}
+
+#[derive(Clone, Copy, Eq, PartialEq)]
+enum LogicalConnective
+{
+	And,
+	IfAndOnlyIf,
+	ImpliesLeftToRight,
+	ImpliesRightToLeft,
+	Or,
+}
+
+impl LogicalConnective
+{
+	fn level(&self) -> usize
+	{
+		match self
+		{
+			Self::And => 1,
+			Self::Or => 2,
+			Self::ImpliesLeftToRight
+			| Self::ImpliesRightToLeft => 3,
+			Self::IfAndOnlyIf => 4,
+		}
+	}
+}
+
+impl std::fmt::Debug for LogicalConnective
+{
+	fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		match &self
+		{
+			Self::And => write!(formatter, "and"),
+			Self::IfAndOnlyIf => write!(formatter, "<->"),
+			Self::ImpliesLeftToRight => write!(formatter, "->"),
+			Self::ImpliesRightToLeft => write!(formatter, "<-"),
+			Self::Or => write!(formatter, "or"),
+		}
+	}
+}
+
+struct FormulaStr<'i, 'd, 'p, 'v, P>
+where
+	P: super::Parser,
+{
+	input: &'i str,
+	parser: &'d P,
+	variable_declaration_stack: &'v crate::VariableDeclarationStackLayer<'p, P::Flavor>,
+}
+
+impl<'i, 'd, 'p, 'v, P> FormulaStr<'i, 'd, 'p, 'v, P>
+where
+	P: super::Parser,
+{
+	pub fn new(input: &'i str, parser: &'d P,
+		variable_declaration_stack: &'v crate::VariableDeclarationStackLayer<'p, P::Flavor>)
+		-> Self
+	{
+		Self
+		{
+			input,
+			parser,
+			variable_declaration_stack,
+		}
+	}
+
+	fn logical_connectives(&self) -> Tokens<'i, impl FnMut(Token<'i>) -> Option<LogicalConnective>>
+	{
+		let functor = |token| match token
+		{
+			Token::Identifier("and") => Some(LogicalConnective::And),
+			Token::Identifier("or") => Some(LogicalConnective::Or),
+			Token::Symbol(Symbol::ArrowLeft) => Some(LogicalConnective::ImpliesRightToLeft),
+			Token::Symbol(Symbol::ArrowLeftAndRight) => Some(LogicalConnective::IfAndOnlyIf),
+			Token::Symbol(Symbol::ArrowRight) => Some(LogicalConnective::ImpliesLeftToRight),
+			_ => None,
+		};
+
+		Tokens::new_filter_map(self.input, functor)
+	}
+
+	fn split_at_logical_connective(&self, logical_connective: LogicalConnective)
+		-> TokenSplit<Tokens<'i, impl FnMut(Token<'i>) -> Option<Token<'i>>>>
+	{
+		let predicate = move |token: &_| match token
+		{
+			Token::Identifier("and") => logical_connective == LogicalConnective::And,
+			Token::Identifier("or") => logical_connective == LogicalConnective::Or,
+			Token::Symbol(Symbol::ArrowLeft) =>
+				logical_connective == LogicalConnective::ImpliesRightToLeft,
+			Token::Symbol(Symbol::ArrowLeftAndRight) =>
+				logical_connective == LogicalConnective::IfAndOnlyIf,
+			Token::Symbol(Symbol::ArrowRight) =>
+				logical_connective == LogicalConnective::ImpliesLeftToRight,
+			_ => false,
+		};
+
+		Tokens::new_filter(self.input, predicate).split()
+	}
+
+	pub fn top_level_logical_connective(&self)
+		-> Result<Option<LogicalConnective>, crate::parse::Error>
+	{
+		let mut top_level_logical_connective = None;
+
+		for logical_connective in self.logical_connectives()
+		{
+			let (_, logical_connective) = logical_connective?;
+
+			top_level_logical_connective = match top_level_logical_connective
+			{
+				None => Some(logical_connective),
+				Some(top_level_logical_connective) =>
+				{
+					let implication_directions_are_mixed =
+						logical_connective == LogicalConnective::ImpliesLeftToRight
+							&& top_level_logical_connective == LogicalConnective::ImpliesRightToLeft
+						|| logical_connective == LogicalConnective::ImpliesRightToLeft
+							&& top_level_logical_connective == LogicalConnective::ImpliesLeftToRight;
+
+					if implication_directions_are_mixed
+					{
+						return Err(crate::parse::Error::new_mixed_implication_directions(
+							crate::parse::error::Location::new(0, Some(0)),
+							crate::parse::error::Location::new(0, Some(0))));
+					}
+
+					if logical_connective.level() > top_level_logical_connective.level()
+					{
+						Some(logical_connective)
+					}
+					else
+					{
+						Some(top_level_logical_connective)
+					}
+				},
+			}
+		}
+
+		Ok(top_level_logical_connective)
+	}
+
+	fn comparison_operators(&self) -> Tokens<'i, impl FnMut(Token<'i>)
+		-> Option<crate::ComparisonOperator>>
+	{
+		let functor = |token| match token
+		{
+			Token::Symbol(symbol) => match symbol
+			{
+				Symbol::Greater => Some(crate::ComparisonOperator::Greater),
+				Symbol::GreaterOrEqual => Some(crate::ComparisonOperator::GreaterOrEqual),
+				Symbol::Less => Some(crate::ComparisonOperator::Less),
+				Symbol::LessOrEqual => Some(crate::ComparisonOperator::LessOrEqual),
+				Symbol::Equal => Some(crate::ComparisonOperator::Equal),
+				Symbol::NotEqual => Some(crate::ComparisonOperator::NotEqual),
+				_ => None,
+			},
+			_ => None,
+		};
+
+		Tokens::new_filter_map(self.input, functor)
+	}
+
+	pub fn parse(&self, level: usize) -> Result<crate::Formula<P::Flavor>, crate::parse::Error>
+	{
+		let indentation = "  ".repeat(level);
+		let input = trim_start(self.input);
+
+		log::trace!("{}- parsing formula: {}", indentation, input);
+
+		match input.chars().next()
+		{
+			Some(')') => return Err(crate::parse::Error::new_unmatched_parenthesis(
+				crate::parse::error::Location::new(0, Some(0)))),
+			None => return Err(crate::parse::Error::new_empty_expression(
+				crate::parse::error::Location::new(0, Some(0)))),
+			_ => (),
+		}
+
+		// Parse logical infix connectives
+		if let Some(top_level_logical_connective) = self.top_level_logical_connective()?
+		{
+			log::trace!("{}  parsing “{:?}” logical connective", indentation,
+				top_level_logical_connective);
+
+			// Parse arguments of n-ary logical infix connectives
+			let arguments_n_ary = ||
+			{
+				// TODO: improve error handling if the formulas between the operators are invalid
+				self.split_at_logical_connective(top_level_logical_connective)
+					.map(|argument| FormulaStr::new(argument?, self.parser, self.variable_declaration_stack).parse(level + 1))
+					.collect::<Result<Vec<_>, _>>()
+			};
+
+			match top_level_logical_connective
+			{
+				LogicalConnective::And => return Ok(crate::Formula::and(arguments_n_ary()?)),
+				LogicalConnective::Or => return Ok(crate::Formula::or(arguments_n_ary()?)),
+				LogicalConnective::IfAndOnlyIf =>
+					return Ok(crate::Formula::if_and_only_if(arguments_n_ary()?)),
+				LogicalConnective::ImpliesLeftToRight =>
+					return self.implication_left_to_right(
+						self.split_at_logical_connective(top_level_logical_connective), level + 1),
+				LogicalConnective::ImpliesRightToLeft =>
+				{
+					let mut argument_iterator =
+						self.split_at_logical_connective(top_level_logical_connective);
+					let first_argument = argument_iterator.next().ok_or_else(||
+						crate::parse::Error::new_expected_logical_connective_argument(
+							"right-to-left implication".to_string(),
+							crate::parse::error::Location::new(0, Some(0))))?;
+					let first_argument = FormulaStr::new(first_argument?, self.parser, self.variable_declaration_stack).parse(level + 1)?;
+
+					return argument_iterator.try_fold(first_argument,
+						|accumulator, argument|
+						{
+							let argument = FormulaStr::new(argument?, self.parser, self.variable_declaration_stack).parse(level + 1)?;
+
+							Ok(crate::Formula::implies(crate::ImplicationDirection::RightToLeft,
+								Box::new(argument), Box::new(accumulator)))
+						});
+				},
+			}
+		}
+
+		// Parse quantified formulas
+		if let Some((identifier, input)) = identifier(input)
+		{
+			match identifier
+			{
+				"not" =>
+				{
+					let input = trim_start(input);
+					log::trace!("{}  parsing “not” formula body: {}", indentation, input);
+
+					let argument = FormulaStr::new(input, self.parser, self.variable_declaration_stack).parse(level + 1)?;
+
+					return Ok(crate::Formula::not(Box::new(argument)));
+				},
+				"true" =>
+				{
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					return Ok(crate::Formula::true_());
+				},
+				"false" =>
+				{
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					return Ok(crate::Formula::false_());
+				},
+				_ => (),
+			}
+
+			let quantifier = match identifier
+			{
+				"exists" => Some(Quantifier::Existential),
+				"forall" => Some(Quantifier::Universal),
+				_ => None,
+			};
+
+			if let Some(quantifier) = quantifier
+			{
+				let input = trim_start(input);
+				log::trace!("{}  parsing “{:?}” formula body: {}", indentation, quantifier, input);
+
+				return self.quantified_formula(input, quantifier, level + 1);
+			}
+		}
+
+		let mut comparison_operators = self.comparison_operators();
+
+		// Parse comparisons
+		if let Some(comparison_operator) = comparison_operators.next()
+		{
+			let (_, comparison_operator) = comparison_operator?;
+
+			// Comparisons with more than one comparison operator aren’t supported
+			if let Some(next_comparison_operator) = comparison_operators.next()
+			{
+				let (_, next_comparison_operator) = next_comparison_operator?;
+
+				return Err(crate::parse::Error::new_multiple_comparison_operators(
+					comparison_operator, next_comparison_operator,
+					crate::parse::error::Location::new(0, Some(0))));
+			}
+
+			log::trace!("{}  parsing “{:?}” comparison: {}", indentation, comparison_operator, input);
+
+			let mut comparison_operator_split = self.comparison_operators().split();
+
+			// There’s exactly one comparison operator in this formula, as we have verified above.
+			// Hence, the split is guaranteed to generate exactly these two elements
+			let input_left = comparison_operator_split.next().unwrap()?;
+			let input_right = comparison_operator_split.next().unwrap()?;
+			assert!(comparison_operator_split.next().is_none());
+
+			let argument_left =
+				TermStr::new(input_left, self.parser, self.variable_declaration_stack)
+					.parse(level + 1)?;
+			let argument_right =
+				TermStr::new(input_right, self.parser, self.variable_declaration_stack)
+					.parse(level + 1)?;
+
+			return Ok(crate::Formula::compare(comparison_operator, Box::new(argument_left),
+				Box::new(argument_right)));
+		}
+
+		// Parse predicates
+		if let Some((predicate_name, input)) = predicate_name(input)
+		{
+			log::trace!("{}  parsing predicate {}", indentation, predicate_name);
+
+			let input = trim_start(input);
+
+			// Parse arguments if there are any
+			let (arguments, input) = match parenthesized_expression(input)?
+			{
+				Some((parenthesized_expression, input)) =>
+				{
+					let functor = |token: &_| *token == Token::Symbol(Symbol::Comma);
+					let arguments = Tokens::new_filter(parenthesized_expression, functor).split()
+						.map(|argument| TermStr::new(argument?, self.parser,
+							self.variable_declaration_stack)
+								.parse(level + 1))
+						.collect::<Result<_, _>>()?;
+
+					(arguments, input)
+				}
+				None => (vec![], input),
+			};
+
+			if !input.trim().is_empty()
+			{
+				return Err(crate::parse::Error::new_unexpected_token(
+					crate::parse::error::Location::new(0, Some(0))))
+			}
+
+			let declaration = self.parser.find_or_create_predicate_declaration(predicate_name,
+				arguments.len());
+			return Ok(crate::Formula::predicate(declaration, arguments));
+		}
+
+		// Parse parenthesized formulas
+		if let Some((parenthesized_expression, input)) = parenthesized_expression(input)?
+		{
+			if !input.trim().is_empty()
+			{
+				return Err(crate::parse::Error::new_unexpected_token(
+					crate::parse::error::Location::new(0, Some(0))));
+			}
+
+			return FormulaStr::new(parenthesized_expression, self.parser, self.variable_declaration_stack).parse(level + 1);
+		}
+
+		Err(crate::parse::Error::new_unexpected_token(
+			crate::parse::error::Location::new(0, Some(0))))
+	}
+
+	// TODO: refactor
+	fn implication_left_to_right_inner<T>(&self, mut argument_iterator: T, level: usize)
+		-> Result<Option<crate::Formula<P::Flavor>>, crate::parse::Error>
+	where
+		T: std::iter::Iterator<Item = Result<&'i str, crate::parse::Error>>
+	{
+		match argument_iterator.next()
+		{
+			Some(argument) =>
+			{
+				// TODO: improve error handling if antecedent cannot be parsed
+				let argument = FormulaStr::new(argument?, self.parser, self.variable_declaration_stack).parse(level)?;
+				match self.implication_left_to_right_inner(argument_iterator, level)?
+				{
+					Some(next_argument) => Ok(Some(crate::Formula::implies(
+						crate::ImplicationDirection::LeftToRight, Box::new(argument),
+						Box::new(next_argument)))),
+					None => Ok(Some(argument)),
+				}
+			},
+			None => Ok(None),
+		}
+	}
+
+	fn implication_left_to_right<T>(&self, mut argument_iterator: T, level: usize)
+		-> Result<crate::Formula<P::Flavor>, crate::parse::Error>
+	where
+		T: std::iter::Iterator<Item = Result<&'i str, crate::parse::Error>>
+	{
+		match argument_iterator.next()
+		{
+			Some(argument) =>
+			{
+				// TODO: improve error handling if antecedent cannot be parsed
+				let argument = FormulaStr::new(argument?, self.parser, self.variable_declaration_stack).parse(level)?;
+				match self.implication_left_to_right_inner(argument_iterator, level)?
+				{
+					Some(next_argument) => Ok(crate::Formula::implies(
+						crate::ImplicationDirection::LeftToRight, Box::new(argument),
+						Box::new(next_argument))),
+					None => Err(crate::parse::Error::new_expected_logical_connective_argument(
+						"left-to-right implication".to_string(),
+						crate::parse::error::Location::new(0, Some(0)))),
+				}
+			},
+			None => Err(crate::parse::Error::new_expected_logical_connective_argument(
+				"left-to-right implication".to_string(),
+				crate::parse::error::Location::new(0, Some(0)))),
+		}
+	}
+
+	// TODO: refactor without input argument
+	fn quantified_formula(&self, input: &str, quantifier: Quantifier, level: usize)
+		-> Result<crate::Formula<P::Flavor>, crate::parse::Error>
+	{
+		let (parameters, input) = match variable_declarations::<P>(input)?
+		{
+			Some(variable_declarations) => variable_declarations,
+			None => return Err(crate::parse::Error::new_expected_variable_declaration(
+				crate::parse::error::Location::new(0, Some(0)))),
+		};
+		let parameters = std::rc::Rc::new(parameters);
+
+		let variable_declaration_stack = crate::VariableDeclarationStackLayer::bound(
+			self.variable_declaration_stack, std::rc::Rc::clone(&parameters));
+
+		let formula_str =
+			FormulaStr::new(input.trim(), self.parser, &variable_declaration_stack);
+		let formula = Box::new(formula_str.parse(level)?);
+
+		let formula = match quantifier
+		{
+			Quantifier::Existential => crate::Formula::exists(parameters, formula),
+			Quantifier::Universal => crate::Formula::for_all(parameters, formula),
+		};
+
+		Ok(formula)
+	}
+}
+
+#[derive(Clone, Copy, Eq, PartialEq)]
+pub(crate) enum Quantifier
+{
+	Existential,
+	Universal,
+}
+
+impl std::fmt::Debug for Quantifier
+{
+	fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		match &self
+		{
+			Self::Existential => write!(formatter, "exists"),
+			Self::Universal => write!(formatter, "forall"),
+		}
+	}
+}
+
+#[cfg(test)]
+mod tests
+{
+	use super::*;
+
+	#[test]
+	fn tokenize_formula_logical_connectives()
+	{
+		let parser = crate::parse::DefaultParser::new();
+		let variable_declaration_stack = crate::VariableDeclarationStackLayer::free();
+
+		let formula_str = |input| FormulaStr::new(input, &parser, &variable_declaration_stack);
+
+		let f = formula_str("((forall X exists Y (p(X) -> q(Y)) and false) or p) -> false");
+		assert_eq!(f.top_level_logical_connective().unwrap(),
+			Some(LogicalConnective::ImpliesLeftToRight));
+		let mut i = f.logical_connectives();
+		assert_eq!(i.next().unwrap().unwrap().1, LogicalConnective::ImpliesLeftToRight);
+		assert!(i.next().is_none());
+
+		let f = formula_str("forall X exists Y (p(X) -> q(Y)) and false or p -> false");
+		assert_eq!(f.top_level_logical_connective().unwrap(),
+			Some(LogicalConnective::ImpliesLeftToRight));
+		let mut i = f.logical_connectives();
+		assert_eq!(i.next().unwrap().unwrap().1, LogicalConnective::And);
+		assert_eq!(i.next().unwrap().unwrap().1, LogicalConnective::Or);
+		assert_eq!(i.next().unwrap().unwrap().1, LogicalConnective::ImpliesLeftToRight);
+		assert!(i.next().is_none());
+
+		let f = formula_str("  p -> forall X exists Y (p(X) -> q(Y)) and false or p -> false  ");
+		assert_eq!(f.top_level_logical_connective().unwrap(),
+			Some(LogicalConnective::ImpliesLeftToRight));
+		let mut i = f.split_at_logical_connective(LogicalConnective::ImpliesLeftToRight);
+		assert_eq!(i.next().unwrap().unwrap(), "p");
+		assert_eq!(i.next().unwrap().unwrap(), "forall X exists Y (p(X) -> q(Y)) and false or p");
+		assert_eq!(i.next().unwrap().unwrap(), "false");
+		assert!(i.next().is_none());
+
+		let f = formula_str("  p -> forall X exists Y (p(X) -> q(Y)) and false or p -> false  ");
+		assert_eq!(f.top_level_logical_connective().unwrap(),
+			Some(LogicalConnective::ImpliesLeftToRight));
+		let mut i = f.split_at_logical_connective(LogicalConnective::And);
+		assert_eq!(i.next().unwrap().unwrap(), "p -> forall X exists Y (p(X) -> q(Y))");
+		assert_eq!(i.next().unwrap().unwrap(), "false or p -> false");
+		assert!(i.next().is_none());
+
+		let f = formula_str("  p and forall X exists Y (p(X) -> q(Y)) and false or p or false  ");
+		assert_eq!(f.top_level_logical_connective().unwrap(), Some(LogicalConnective::Or));
+		let mut i = f.split_at_logical_connective(LogicalConnective::Or);
+		assert_eq!(i.next().unwrap().unwrap(), "p and forall X exists Y (p(X) -> q(Y)) and false");
+		assert_eq!(i.next().unwrap().unwrap(), "p");
+		assert_eq!(i.next().unwrap().unwrap(), "false");
+		assert!(i.next().is_none());
+
+		let f = formula_str(" (p and q) ");
+		assert!(f.top_level_logical_connective().unwrap().is_none());
+		let mut i = f.split_at_logical_connective(LogicalConnective::And);
+		assert_eq!(i.next().unwrap().unwrap(), "(p and q)");
+		assert!(i.next().is_none());
+
+		assert!(formula_str(" a -> b -> c ").parse(0).is_ok());
+		assert!(formula_str(" a -> b <- c ").parse(0).is_err());
+
+		assert!(formula_str("  p -> forall X exists Y (p(X) -> q(Y)) and false or p -> false  ")
+			.parse(0).is_ok());
+	}
+}

src/parse/terms.rs

@@ -0,0 +1,651 @@
+use super::tokens::*;
+
+pub(crate) fn function_name(input: &str) -> Option<(&str, &str)>
+{
+	let (identifier, remaining_input) = identifier(input)?;
+
+	if is_keyword(identifier)
+	{
+		return None;
+	}
+
+	let mut characters = identifier.chars();
+
+	while let Some(character) = characters.next()
+	{
+		match character
+		{
+			'_' => continue,
+			_ if character.is_ascii_lowercase() => return Some((identifier, remaining_input)),
+			_ => return None,
+		}
+	}
+
+	None
+}
+
+fn variable_name(input: &str) -> Option<(&str, &str)>
+{
+	let (identifier, remaining_input) = identifier(input)?;
+
+	let mut characters = identifier.chars();
+
+	while let Some(character) = characters.next()
+	{
+		match character
+		{
+			'_' => continue,
+			_ if character.is_ascii_uppercase() => return Some((identifier, remaining_input)),
+			_ => return None,
+		}
+	}
+
+	None
+}
+
+pub fn is_function_name(identifier: &str) -> bool
+{
+	if is_keyword(identifier)
+	{
+		return false;
+	}
+
+	let mut characters = identifier.chars();
+
+	while let Some(character) = characters.next()
+	{
+		match character
+		{
+			'_' => continue,
+			_ if character.is_ascii_lowercase() => return true,
+			_ => return false,
+		}
+	}
+
+	false
+}
+
+fn is_variable_name(identifier: &str) -> bool
+{
+	let mut characters = identifier.chars();
+
+	while let Some(character) = characters.next()
+	{
+		match character
+		{
+			'_' => continue,
+			_ if character.is_ascii_uppercase() => return true,
+			_ => return false,
+		}
+	}
+
+	false
+}
+
+pub(crate) fn variable_declaration<P>(input: &str)
+	-> Option<(<P::Flavor as crate::flavor::Flavor>::VariableDeclaration, &str)>
+where
+	P: crate::parse::Parser,
+{
+	variable_name(input)
+		.map(|(variable_name, remaining_input)|
+			(<P as crate::parse::Parser>::new_variable_declaration(variable_name.to_string()),
+			remaining_input))
+}
+
+pub(crate) fn variable_declarations<P>(input: &str)
+	-> Result<Option<(crate::VariableDeclarations<P::Flavor>, &str)>, crate::parse::Error>
+where
+	P: crate::parse::Parser,
+{
+	let mut variable_declarations = vec![];
+
+	let (first_variable_declaration, mut input) = match variable_declaration::<P>(input)
+	{
+		Some(first_variable_declaration) => first_variable_declaration,
+		None => return Ok(None),
+	};
+
+	variable_declarations.push(std::rc::Rc::new(first_variable_declaration));
+
+	loop
+	{
+		input = trim_start(input);
+
+		input = match symbol(input)
+		{
+			Some((Symbol::Comma, input)) => input,
+			// TODO: detect redeclarations, such as in “exists X, Y, X”
+			_ => return Ok(Some((variable_declarations, input))),
+		};
+
+		input = trim_start(input);
+
+		let (variable_declaration, remaining_input) = match variable_declaration::<P>(input)
+		{
+			Some(variable_declaration) => variable_declaration,
+			None => return Err(crate::parse::Error::new_expected_variable_declaration(
+				crate::parse::error::Location::new(0, Some(0)))),
+		};
+
+		input = remaining_input;
+
+		variable_declarations.push(std::rc::Rc::new(variable_declaration));
+	}
+}
+
+#[derive(Clone, Copy, Eq, PartialEq)]
+pub(crate) enum ArithmeticOperatorClass
+{
+	Exponential,
+	Multiplicative,
+	Additive,
+}
+
+impl ArithmeticOperatorClass
+{
+	fn level(&self) -> usize
+	{
+		match self
+		{
+			Self::Exponential => 1,
+			Self::Multiplicative => 2,
+			Self::Additive => 3,
+		}
+	}
+}
+
+impl std::fmt::Debug for ArithmeticOperatorClass
+{
+	fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		match &self
+		{
+			Self::Exponential => write!(formatter, "exponential"),
+			Self::Multiplicative => write!(formatter, "multiplicative"),
+			Self::Additive => write!(formatter, "additive"),
+		}
+	}
+}
+
+pub(crate) struct TermStr<'i, 'd, 'v, 'p, P>
+where
+	P: super::Parser,
+{
+	input: &'i str,
+	parser: &'d P,
+	variable_declaration_stack: &'v crate::VariableDeclarationStackLayer<'p, P::Flavor>,
+}
+
+impl<'i, 'd, 'v, 'p, P> TermStr<'i, 'd, 'v, 'p, P>
+where
+	P: super::Parser,
+{
+	pub fn new(input: &'i str, parser: &'d P,
+		variable_declaration_stack: &'v crate::VariableDeclarationStackLayer<'p, P::Flavor>)
+		-> Self
+	{
+		Self
+		{
+			input,
+			parser,
+			variable_declaration_stack,
+		}
+	}
+
+	fn arithmetic_operator_classes(&self) -> Tokens<'i, impl FnMut(Token<'i>)
+		-> Option<ArithmeticOperatorClass>>
+	{
+		let functor = |token| match token
+		{
+			Token::Symbol(Symbol::Exponentiation) => Some(ArithmeticOperatorClass::Exponential),
+			Token::Symbol(Symbol::Multiplication) => Some(ArithmeticOperatorClass::Multiplicative),
+			Token::Symbol(Symbol::Division) => Some(ArithmeticOperatorClass::Multiplicative),
+			Token::Symbol(Symbol::Percent) => Some(ArithmeticOperatorClass::Multiplicative),
+			Token::Symbol(Symbol::Plus) => Some(ArithmeticOperatorClass::Additive),
+			Token::Symbol(Symbol::Minus) => Some(ArithmeticOperatorClass::Additive),
+			_ => None,
+		};
+
+		// TODO: refactor so that self.input is always set correctly
+		Tokens::new_filter_map(self.input, functor)
+	}
+
+	fn filter_by_arithmetic_operator_class(&self,
+		arithmetic_operator_class: ArithmeticOperatorClass)
+		-> Tokens<'i, impl FnMut(Token<'i>) -> Option<crate::BinaryOperator>>
+	{
+		let functor = move |token| match token
+		{
+			Token::Symbol(Symbol::Exponentiation) =>
+				if arithmetic_operator_class == ArithmeticOperatorClass::Exponential
+				{
+					Some(crate::BinaryOperator::Exponentiate)
+				}
+				else
+				{
+					None
+				},
+			Token::Symbol(Symbol::Multiplication) =>
+				if arithmetic_operator_class == ArithmeticOperatorClass::Multiplicative
+				{
+					Some(crate::BinaryOperator::Multiply)
+				}
+				else
+				{
+					None
+				},
+			Token::Symbol(Symbol::Division) =>
+				if arithmetic_operator_class == ArithmeticOperatorClass::Multiplicative
+				{
+					Some(crate::BinaryOperator::Divide)
+				}
+				else
+				{
+					None
+				},
+			Token::Symbol(Symbol::Percent) =>
+				if arithmetic_operator_class == ArithmeticOperatorClass::Multiplicative
+				{
+					Some(crate::BinaryOperator::Modulo)
+				}
+				else
+				{
+					None
+				},
+			Token::Symbol(Symbol::Plus) =>
+				if arithmetic_operator_class == ArithmeticOperatorClass::Additive
+				{
+					Some(crate::BinaryOperator::Add)
+				}
+				else
+				{
+					None
+				},
+			Token::Symbol(Symbol::Minus) =>
+				if arithmetic_operator_class == ArithmeticOperatorClass::Additive
+				{
+					Some(crate::BinaryOperator::Subtract)
+				}
+				else
+				{
+					None
+				},
+			_ => None,
+		};
+
+		Tokens::new_filter_map(self.input, functor)
+	}
+
+	pub fn top_level_arithmetic_operator_class(&self)
+		-> Result<Option<ArithmeticOperatorClass>, crate::parse::Error>
+	{
+		let mut top_level_arithmetic_operator_class = None;
+
+		for arithmetic_operator_class in self.arithmetic_operator_classes()
+		{
+			let (_, arithmetic_operator_class) = arithmetic_operator_class?;
+
+			top_level_arithmetic_operator_class = match top_level_arithmetic_operator_class
+			{
+				None => Some(arithmetic_operator_class),
+				Some(top_level_arithmetic_operator_class) =>
+				{
+					if arithmetic_operator_class.level()
+						> top_level_arithmetic_operator_class.level()
+					{
+						Some(arithmetic_operator_class)
+					}
+					else
+					{
+						Some(top_level_arithmetic_operator_class)
+					}
+				},
+			}
+		}
+
+		Ok(top_level_arithmetic_operator_class)
+	}
+
+	pub fn parse(&self, level: usize) -> Result<crate::Term<P::Flavor>, crate::parse::Error>
+	{
+		let indentation = "  ".repeat(level);
+		log::trace!("{}- parsing term: {}", indentation, self.input);
+
+		let input = trim_start(self.input);
+
+		match input.chars().next()
+		{
+			Some(')') => return Err(crate::parse::Error::new_unmatched_parenthesis(
+				crate::parse::error::Location::new(0, Some(0)))),
+			// TODO: implement absolute value function
+			Some('|') => unimplemented!(),
+			None => return Err(crate::parse::Error::new_empty_expression(
+				crate::parse::error::Location::new(0, Some(0)))),
+			_ => (),
+		}
+
+		// Parse arithmetic infix operations
+		if let Some(top_level_arithmetic_operator_class) =
+			self.top_level_arithmetic_operator_class()?
+		{
+			log::trace!("{}  parsing {:?} arithmetic term", indentation,
+				top_level_arithmetic_operator_class);
+
+			if top_level_arithmetic_operator_class == ArithmeticOperatorClass::Exponential
+			{
+				return self.exponentiate(
+					self.filter_by_arithmetic_operator_class(top_level_arithmetic_operator_class)
+						.split(), level + 1);
+			}
+
+			// Parse arguments of arithmetic infix operations
+			let mut argument_iterator =
+				self.filter_by_arithmetic_operator_class(top_level_arithmetic_operator_class);
+
+			let (first_argument, first_binary_operator) = argument_iterator.next().ok_or_else(||
+				crate::parse::Error::new_expected_term(
+					crate::parse::error::Location::new(0, Some(0))))??;
+			let first_argument =
+				TermStr::new(first_argument, self.parser, self.variable_declaration_stack)
+					.parse(level + 1)?;
+			// TODO: improve error handling if the terms between the operators are invalid
+
+			let (accumulator, last_binary_operator) =
+				argument_iterator.try_fold((first_argument, first_binary_operator),
+					|(accumulator, binary_operator), argument|
+					{
+						let (argument, next_binary_operator) = argument?;
+						let argument = TermStr::new(argument, self.parser,
+							self.variable_declaration_stack)
+								.parse(level + 1)?;
+						let binary_operation =
+							crate::BinaryOperation::new(binary_operator, Box::new(accumulator),
+								Box::new(argument));
+						let formula = crate::Term::BinaryOperation(binary_operation);
+
+						Ok((formula, next_binary_operator))
+					})?;
+
+			// The last item hasn’t been consumed yet, so it’s safe to unwrap it
+			let last_argument = argument_iterator.remaining_input().unwrap();
+			let last_argument =
+				TermStr::new(last_argument, self.parser, self.variable_declaration_stack)
+					.parse(level + 1)?;
+			let last_binary_operation =
+				crate::BinaryOperation::new(last_binary_operator, Box::new(accumulator),
+					Box::new(last_argument));
+
+			return Ok(crate::Term::BinaryOperation(last_binary_operation));
+		}
+
+		if let Some((number, input)) = number(input)?
+		{
+			if !input.trim().is_empty()
+			{
+				return Err(crate::parse::Error::new_unexpected_token(
+					crate::parse::error::Location::new(0, Some(0))));
+			}
+
+			return Ok(crate::Term::integer(number as i32));
+		}
+
+		if let Some((identifier, input)) = identifier(input)
+		{
+			match identifier
+			{
+				"inf" =>
+				{
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					return Ok(crate::Term::infimum());
+				},
+				"sup" =>
+				{
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					return Ok(crate::Term::supremum());
+				},
+				"true" =>
+				{
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					return Ok(crate::Term::true_());
+				},
+				"false" =>
+				{
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					return Ok(crate::Term::false_());
+				},
+				_ if is_variable_name(identifier) =>
+				{
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					let declaration = P::find_or_create_variable_declaration(
+						self.variable_declaration_stack, identifier);
+					return Ok(crate::Term::variable(declaration));
+				},
+				_ if is_function_name(identifier) =>
+				{
+					let function_name = identifier;
+					log::trace!("{}  parsing function {}", indentation, function_name);
+
+					let input = trim_start(input);
+
+					// Parse arguments if there are any
+					let (arguments, input) = match parenthesized_expression(input)?
+					{
+						Some((parenthesized_expression, input)) =>
+						{
+							let functor = |token: &_| *token == Token::Symbol(Symbol::Comma);
+							let arguments = Tokens::new_filter(parenthesized_expression, functor).split()
+								.map(|argument| TermStr::new(argument?, self.parser,
+									self.variable_declaration_stack)
+										.parse(level + 1))
+								.collect::<Result<_, _>>()?;
+
+							(arguments, input)
+						}
+						None => (vec![], input),
+					};
+
+					if !input.trim().is_empty()
+					{
+						return Err(crate::parse::Error::new_unexpected_token(
+							crate::parse::error::Location::new(0, Some(0))))
+					}
+
+					let declaration = self.parser.find_or_create_function_declaration(
+						function_name, arguments.len());
+					return Ok(crate::Term::function(declaration, arguments));
+				},
+				_ => (),
+			}
+		}
+
+		// TODO: parse negative value
+
+		// Parse parenthesized terms
+		if let Some((parenthesized_expression, input)) = parenthesized_expression(input)?
+		{
+			if !input.trim().is_empty()
+			{
+				return Err(crate::parse::Error::new_unexpected_token(
+					crate::parse::error::Location::new(0, Some(0))));
+			}
+
+			return TermStr::new(parenthesized_expression, self.parser,
+				self.variable_declaration_stack)
+					.parse(level + 1);
+		}
+
+		Err(crate::parse::Error::new_unexpected_token(
+			crate::parse::error::Location::new(0, Some(0))))
+	}
+
+	// TODO: refactor
+	fn exponentiate_inner<T>(&self, mut argument_iterator: T, level: usize)
+		-> Result<Option<crate::Term<P::Flavor>>, crate::parse::Error>
+	where
+		T: std::iter::Iterator<Item = Result<&'i str, crate::parse::Error>>
+	{
+		match argument_iterator.next()
+		{
+			Some(argument) =>
+			{
+				// TODO: improve error handling if antecedent cannot be parsed
+				let argument =
+					TermStr::new(argument?, self.parser, self.variable_declaration_stack)
+						.parse(level)?;
+				match self.exponentiate_inner(argument_iterator, level)?
+				{
+					Some(next_argument) => Ok(Some(crate::Term::exponentiate(Box::new(argument),
+						Box::new(next_argument)))),
+					None => Ok(Some(argument)),
+				}
+			},
+			None => Ok(None),
+		}
+	}
+
+	fn exponentiate<T>(&self, mut argument_iterator: T, level: usize)
+		-> Result<crate::Term<P::Flavor>, crate::parse::Error>
+	where
+		T: std::iter::Iterator<Item = Result<&'i str, crate::parse::Error>>
+	{
+		match argument_iterator.next()
+		{
+			Some(argument) =>
+			{
+				// TODO: improve error handling if antecedent cannot be parsed
+				let argument =
+					TermStr::new(argument?, self.parser, self.variable_declaration_stack)
+						.parse(level)?;
+				match self.exponentiate_inner(argument_iterator, level)?
+				{
+					Some(next_argument) =>
+						Ok(crate::Term::exponentiate(Box::new(argument), Box::new(next_argument))),
+					None => Err(crate::parse::Error::new_expected_term(
+						crate::parse::error::Location::new(0, Some(0)))),
+				}
+			},
+			None => Err(crate::parse::Error::new_expected_term(
+				crate::parse::error::Location::new(0, Some(0)))),
+		}
+	}
+}
+
+#[cfg(test)]
+mod tests
+{
+	use super::*;
+
+	#[test]
+	fn parse_variable_name()
+	{
+		assert_eq!(variable_name("X").unwrap(), ("X", ""));
+		assert_eq!(variable_name("_X").unwrap(), ("_X", ""));
+		assert_eq!(variable_name("__X").unwrap(), ("__X", ""));
+		assert_eq!(variable_name("Variable").unwrap(), ("Variable", ""));
+		assert_eq!(variable_name("_Variable").unwrap(), ("_Variable", ""));
+		assert_eq!(variable_name("__Variable").unwrap(), ("__Variable", ""));
+		assert_eq!(variable_name("X,").unwrap(), ("X", ","));
+		assert_eq!(variable_name("_X,").unwrap(), ("_X", ","));
+		assert_eq!(variable_name("__X,").unwrap(), ("__X", ","));
+		assert_eq!(variable_name("Variable,").unwrap(), ("Variable", ","));
+		assert_eq!(variable_name("_Variable,").unwrap(), ("_Variable", ","));
+		assert_eq!(variable_name("__Variable,").unwrap(), ("__Variable", ","));
+	}
+
+	#[test]
+	fn parse_variable_declaration()
+	{
+		let variable_declaration =
+			|x| super::variable_declaration::<crate::parse::DefaultParser>(x);
+
+		let v = variable_declaration("X").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("X", ""));
+		let v = variable_declaration("_X").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("_X", ""));
+		let v = variable_declaration("__X").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("__X", ""));
+		let v = variable_declaration("Variable").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("Variable", ""));
+		let v = variable_declaration("_Variable").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("_Variable", ""));
+		let v = variable_declaration("__Variable").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("__Variable", ""));
+		let v = variable_declaration("X,").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("X", ","));
+		let v = variable_declaration("_X,").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("_X", ","));
+		let v = variable_declaration("__X,").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("__X", ","));
+		let v = variable_declaration("Variable,").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("Variable", ","));
+		let v = variable_declaration("_Variable,").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("_Variable", ","));
+		let v = variable_declaration("__Variable,").unwrap();
+		assert_eq!((v.0.name.as_str(), v.1), ("__Variable", ","));
+	}
+
+	#[test]
+	fn parse_variable_declarations()
+	{
+		let variable_declarations =
+			|x| super::variable_declarations::<crate::parse::DefaultParser>(x);
+
+		let v = variable_declarations("X.").unwrap().unwrap();
+		assert_eq!(v.0.len(), 1);
+		assert_eq!(v.0[0].name.as_str(), "X");
+		assert_eq!(v.1, ".");
+
+		let v = variable_declarations("X,Y,Z.").unwrap().unwrap();
+		assert_eq!(v.0.len(), 3);
+		assert_eq!(v.0[0].name.as_str(), "X");
+		assert_eq!(v.0[1].name.as_str(), "Y");
+		assert_eq!(v.0[2].name.as_str(), "Z");
+		assert_eq!(v.1, ".");
+
+		let v = variable_declarations("X, Y, Z.").unwrap().unwrap();
+		assert_eq!(v.0.len(), 3);
+		assert_eq!(v.0[0].name.as_str(), "X");
+		assert_eq!(v.0[1].name.as_str(), "Y");
+		assert_eq!(v.0[2].name.as_str(), "Z");
+		assert_eq!(v.1, ".");
+
+		let v = variable_declarations("X , Y , Z.").unwrap().unwrap();
+		assert_eq!(v.0.len(), 3);
+		assert_eq!(v.0[0].name.as_str(), "X");
+		assert_eq!(v.0[1].name.as_str(), "Y");
+		assert_eq!(v.0[2].name.as_str(), "Z");
+		assert_eq!(v.1, ".");
+
+		assert!(variable_declarations("test").unwrap().is_none());
+		assert!(variable_declarations("X, test").is_err());
+		assert!(variable_declarations("X ,test").is_err());
+		assert!(variable_declarations("X,Y,Z, test").is_err());
+		assert!(variable_declarations("X,Y,Z ,test").is_err());
+	}
+}

src/parse/tokens.rs

@@ -0,0 +1,641 @@
+fn substring_offset(substring: &str, string: &str) -> usize
+{
+	substring.as_ptr() as usize - string.as_ptr() as usize
+}
+
+pub fn trim_start(mut input: &str) -> &str
+{
+	loop
+	{
+		let original_input = input;
+
+		input = input.trim_start();
+
+		let mut input_characters = input.chars();
+
+		if let Some('#') = input_characters.next()
+		{
+			input = input_characters.as_str();
+
+			match (input.find('\n'), input.find('\r'))
+			{
+				(Some(newline_index), Some(carriage_return_index)) =>
+				{
+					let split_index = std::cmp::min(newline_index, carriage_return_index);
+					input = input.split_at(split_index).1;
+				},
+				(Some(split_index), _)
+				| (_, Some(split_index)) => input = input.split_at(split_index).1,
+				_ => input = &input[..input.len()],
+			}
+		}
+
+		if input.is_empty() || input == original_input
+		{
+			break;
+		}
+	}
+
+	input
+}
+
+#[derive(Clone, Copy, Eq, PartialEq)]
+pub(crate) enum Keyword
+{
+	And,
+	Exists,
+	False,
+	ForAll,
+	Infimum,
+	Not,
+	Or,
+	Supremum,
+	True,
+}
+
+impl std::fmt::Debug for Keyword
+{
+	fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		match &self
+		{
+			Self::And => write!(formatter, "and"),
+			Self::Exists => write!(formatter, "exists"),
+			Self::False => write!(formatter, "false"),
+			Self::ForAll => write!(formatter, "forall"),
+			Self::Infimum => write!(formatter, "inf"),
+			Self::Not => write!(formatter, "not"),
+			Self::Or => write!(formatter, "or"),
+			Self::Supremum => write!(formatter, "sup"),
+			Self::True => write!(formatter, "true"),
+		}
+	}
+}
+
+#[derive(Clone, Copy, Eq, PartialEq)]
+pub(crate) enum Symbol
+{
+	ArrowLeft,
+	ArrowLeftAndRight,
+	ArrowRight,
+	Comma,
+	Division,
+	Equal,
+	Exponentiation,
+	Greater,
+	GreaterOrEqual,
+	Less,
+	LessOrEqual,
+	Minus,
+	Multiplication,
+	NotEqual,
+	Percent,
+	Plus,
+	VerticalBar,
+}
+
+impl std::fmt::Debug for Symbol
+{
+	fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
+	{
+		match &self
+		{
+			Self::ArrowLeft => write!(formatter, "<-"),
+			Self::ArrowLeftAndRight => write!(formatter, "<->"),
+			Self::ArrowRight => write!(formatter, "->"),
+			Self::Comma => write!(formatter, ","),
+			Self::Division => write!(formatter, "/"),
+			Self::Equal => write!(formatter, "="),
+			Self::Exponentiation => write!(formatter, "**"),
+			Self::Greater => write!(formatter, ">"),
+			Self::GreaterOrEqual => write!(formatter, ">="),
+			Self::Less => write!(formatter, "<"),
+			Self::LessOrEqual => write!(formatter, "<="),
+			Self::Minus => write!(formatter, "-"),
+			Self::Multiplication => write!(formatter, "*"),
+			Self::NotEqual => write!(formatter, "!="),
+			Self::Percent => write!(formatter, "%"),
+			Self::Plus => write!(formatter, "+"),
+			Self::VerticalBar => write!(formatter, "|"),
+		}
+	}
+}
+
+#[derive(Clone, Copy, Eq, PartialEq)]
+pub(crate) enum Token<'i>
+{
+	Identifier(&'i str),
+	Number(usize),
+	ParenthesizedExpression(&'i str),
+	Symbol(Symbol),
+}
+
+fn is_identifier_start_character(character: char) -> bool
+{
+	character.is_ascii_alphabetic()
+}
+
+fn is_identifier_body_character(character: char) -> bool
+{
+	match character
+	{
+		'_' => true,
+		_ if character.is_ascii_alphanumeric() => true,
+		_ => false,
+	}
+}
+
+pub fn identifier(input: &str) -> Option<(&str, &str)>
+{
+	let mut characters = input.char_indices();
+
+	let first_character = loop
+	{
+		match characters.next()
+		{
+			Some((_, '_')) => continue,
+			Some((_, character)) => break Some(character),
+			None => break None,
+		}
+	}?;
+
+	if !is_identifier_start_character(first_character)
+	{
+		return None;
+	}
+
+	loop
+	{
+		match characters.next()
+		{
+			None => return Some((input, characters.as_str())),
+			Some((character_index, character)) =>
+			{
+				if !is_identifier_body_character(character)
+				{
+					return Some(input.split_at(character_index));
+				}
+			},
+		}
+	}
+}
+
+pub(crate) fn is_keyword(identifier: &str) -> bool
+{
+	match identifier
+	{
+		"and"
+		| "exists"
+		| "false"
+		| "forall"
+		| "inf"
+		| "not"
+		| "or"
+		| "sup"
+		| "true" => true,
+		_ => false,
+	}
+}
+
+fn number_string(input: &str) -> Option<(&str, &str)>
+{
+	let mut characters = input.char_indices();
+
+	let (_, character) = match characters.next()
+	{
+		Some(characters_next) => characters_next,
+		None => return None,
+	};
+
+	if !character.is_ascii_digit()
+	{
+		return None;
+	}
+
+	loop
+	{
+		match characters.next()
+		{
+			None => return Some((input, characters.as_str())),
+			Some((character_index, character)) =>
+			{
+				if !character.is_ascii_digit()
+				{
+					return Some(input.split_at(character_index));
+				}
+			},
+		}
+	}
+}
+
+pub fn number(input: &str) -> Result<Option<(usize, &str)>, crate::parse::Error>
+{
+	let (number_string, remaining_input) = match number_string(input)
+	{
+		Some(number_string) => number_string,
+		None => return Ok(None),
+	};
+
+	let number = number_string.parse()
+		.map_err(|error| crate::parse::Error::new_parse_number(input,
+			crate::parse::error::Location::new(0, Some(0)), error))?;
+
+	Ok(Some((number, remaining_input)))
+}
+
+pub(crate) fn symbol(input: &str) -> Option<(Symbol, &str)>
+{
+	let mut characters = input.char_indices();
+
+	let (_, character) = match characters.next()
+	{
+		Some(characters_next) => characters_next,
+		None => return None,
+	};
+
+	let remaining_input = characters.as_str();
+
+	match character
+	{
+		',' => Some((Symbol::Comma, remaining_input)),
+		// <->, <-, <=, <
+		'=' => Some((Symbol::Equal, remaining_input)),
+		// !=
+		'!' => match characters.next()
+		{
+			Some((_, '=')) => Some((Symbol::NotEqual, characters.as_str())),
+			_ => None,
+		},
+		'<' => match characters.next()
+		{
+			Some((_, '-')) =>
+			{
+				let remaining_input = characters.as_str();
+
+				match characters.next()
+				{
+					Some((_, '>')) => Some((Symbol::ArrowLeftAndRight, characters.as_str())),
+					_ => Some((Symbol::ArrowLeft, remaining_input)),
+				}
+			},
+			Some((_, '=')) => Some((Symbol::LessOrEqual, characters.as_str())),
+			_ => Some((Symbol::Less, remaining_input)),
+		},
+		// >=, >
+		'>' => match characters.next()
+		{
+			Some((_, '=')) => Some((Symbol::GreaterOrEqual, characters.as_str())),
+			_ => Some((Symbol::Greater, remaining_input)),
+		},
+		'+' => Some((Symbol::Plus, remaining_input)),
+		// ->, -
+		'-' => match characters.next()
+		{
+			Some((_, '>')) => Some((Symbol::ArrowRight, characters.as_str())),
+			_ => Some((Symbol::Minus, remaining_input)),
+		},
+		// **, *
+		'*' => match characters.next()
+		{
+			Some((_, '*')) => Some((Symbol::Exponentiation, characters.as_str())),
+			_ => Some((Symbol::Multiplication, remaining_input)),
+		},
+		'/' => Some((Symbol::Division, remaining_input)),
+		'%' => Some((Symbol::Percent, remaining_input)),
+		'|' => Some((Symbol::VerticalBar, remaining_input)),
+		_ => None,
+	}
+}
+
+pub(crate) fn parenthesized_expression(input: &str)
+	-> Result<Option<(&str, &str)>, crate::parse::Error>
+{
+	let mut characters = input.chars();
+
+	let (first_character, remaining_input) = match characters.next()
+	{
+		Some(first_character) => (first_character, characters.as_str()),
+		None => return Ok(None),
+	};
+
+	if first_character != '('
+	{
+		return Ok(None);
+	}
+
+	let mut characters = remaining_input.char_indices();
+	let mut number_of_open_parentheses = 1;
+
+	while let Some((character_index, character)) = characters.next()
+	{
+		match character
+		{
+			'(' => number_of_open_parentheses += 1,
+			')' => number_of_open_parentheses -= 1,
+			_ => (),
+		}
+
+		if number_of_open_parentheses == 0
+		{
+			let position_of_closing_parenthesis = character_index;
+			let (parenthesized_expression, _) =
+				remaining_input.split_at(position_of_closing_parenthesis);
+			let remaining_input = characters.as_str();
+
+			return Ok(Some((parenthesized_expression, remaining_input)));
+		}
+	}
+
+	Err(crate::parse::Error::new_unmatched_parenthesis(
+		crate::parse::error::Location::new(0, Some(1))))
+}
+
+pub(crate) struct Tokens<'i, F>
+{
+	original_input: &'i str,
+	input: &'i str,
+	previous_index: usize,
+	reached_end_of_stream: bool,
+	functor: F,
+}
+
+impl<'i> Tokens<'i, ()>
+{
+	pub fn new_iter(input: &'i str) -> Tokens<'i, impl FnMut(Token<'i>) -> Option<Token<'i>>>
+	{
+		Tokens::new_filter_map(input, |x| Some(x))
+	}
+
+	pub fn new_filter<P>(input: &'i str, mut predicate: P)
+		-> Tokens<'i, impl FnMut(Token<'i>) -> Option<Token<'i>>>
+	where
+		P: FnMut(&Token<'i>) -> bool,
+	{
+		Tokens::new_filter_map(input,
+			move |x|
+			{
+				if predicate(&x)
+				{
+					Some(x)
+				}
+				else
+				{
+					None
+				}
+			})
+	}
+}
+
+impl<'i, F> Tokens<'i, F>
+{
+	pub fn new_filter_map(input: &'i str, functor: F) -> Self
+	{
+		Self
+		{
+			original_input: input,
+			input,
+			previous_index: 0,
+			reached_end_of_stream: false,
+			functor,
+		}
+	}
+
+	fn next_token(&mut self) -> Option<Result<(usize, usize, Token<'i>), crate::parse::Error>>
+	{
+		self.input = trim_start(self.input);
+		let index_left = substring_offset(self.input, self.original_input);
+
+		let first_character = match self.input.chars().next()
+		{
+			None => return None,
+			Some(first_character) => first_character,
+		};
+
+		if self.input.starts_with(")")
+		{
+			return Some(Err(crate::parse::Error::new_unmatched_parenthesis(
+				crate::parse::error::Location::new(0, Some(1)))));
+		}
+
+		match parenthesized_expression(self.input)
+		{
+			Ok(Some((parenthesized_expression, remaining_input))) =>
+			{
+				self.input = remaining_input;
+				let index_right = substring_offset(self.input, self.original_input);
+
+				return Some(Ok((index_left, index_right,
+					Token::ParenthesizedExpression(parenthesized_expression))));
+			},
+			Ok(None) => (),
+			Err(error) => return Some(Err(error)),
+		}
+
+		match number(self.input)
+		{
+			Ok(Some((number, remaining_input))) =>
+			{
+				self.input = remaining_input;
+				let index_right = substring_offset(self.input, self.original_input);
+
+				return Some(Ok((index_left, index_right, Token::Number(number))));
+			},
+			Ok(None) => (),
+			Err(error) => return Some(Err(error)),
+		}
+
+		if let Some((identifier, remaining_input)) = identifier(self.input)
+		{
+			self.input = remaining_input;
+			let index_right = substring_offset(self.input, self.original_input);
+
+			return Some(Ok((index_left, index_right, Token::Identifier(identifier))));
+		}
+
+		if let Some((symbol, remaining_input)) = symbol(self.input)
+		{
+			self.input = remaining_input;
+			let index_right = substring_offset(self.input, self.original_input);
+
+			return Some(Ok((index_left, index_right, Token::Symbol(symbol))));
+		}
+
+		return Some(Err(crate::parse::Error::new_character_not_allowed(first_character,
+			crate::parse::error::Location::new(0, Some(0)))));
+	}
+
+	pub fn remaining_input(&mut self) -> Option<&'i str>
+	{
+		if self.reached_end_of_stream
+		{
+			return None;
+		}
+
+		let remaining_input = self.original_input[self.previous_index..].trim();
+		self.reached_end_of_stream = true;
+
+		Some(remaining_input)
+	}
+
+	pub fn split(self) -> TokenSplit<Self>
+	{
+		TokenSplit::new(self)
+	}
+}
+
+impl<'i, F, G> std::iter::Iterator for Tokens<'i, F>
+where
+	F: FnMut(Token<'i>) -> Option<G>,
+{
+	type Item = Result<(&'i str, G), crate::parse::Error>;
+
+	fn next(&mut self) -> Option<Self::Item>
+	{
+		if self.previous_index == self.original_input.len()
+		{
+			return None;
+		}
+
+		loop
+		{
+			match self.next_token()
+			{
+				Some(Ok((index_left, index_right, token))) =>
+				{
+					let token = match (self.functor)(token)
+					{
+						None => continue,
+						Some(token) => token,
+					};
+
+					let input_left = self.original_input[self.previous_index..index_left].trim();
+
+					self.previous_index = index_right;
+
+					return Some(Ok((input_left, token)));
+				},
+				Some(Err(error)) => return Some(Err(error)),
+				None => return None,
+			}
+		}
+	}
+}
+
+pub(crate) struct TokenSplit<T>
+{
+	tokens: T,
+}
+
+impl TokenSplit<()>
+{
+	pub fn new<T>(tokens: T) -> TokenSplit<T>
+	{
+		TokenSplit
+		{
+			tokens,
+		}
+	}
+}
+
+impl<'i, F, G> std::iter::Iterator for TokenSplit<Tokens<'i, F>>
+where
+	F: FnMut(Token<'i>) -> Option<G>,
+{
+	type Item = Result<&'i str, crate::parse::Error>;
+
+	fn next(&mut self) -> Option<Self::Item>
+	{
+		match self.tokens.next()
+		{
+			Some(Ok((input_before, _))) => Some(Ok(input_before)),
+			Some(Err(error)) => Some(Err(error)),
+			None => match self.tokens.remaining_input()
+			{
+				Some(remaining_input) => Some(Ok(remaining_input)),
+				None => None,
+			},
+		}
+	}
+}
+
+#[cfg(test)]
+mod tests
+{
+	use super::*;
+
+	#[test]
+	fn tokenize_identifier()
+	{
+		assert_eq!(identifier("test").unwrap(), ("test", ""));
+		assert_eq!(identifier("test2").unwrap(), ("test2", ""));
+		assert_eq!(identifier("Test").unwrap(), ("Test", ""));
+		assert_eq!(identifier("Test2").unwrap(), ("Test2", ""));
+		assert_eq!(identifier("_test").unwrap(), ("_test", ""));
+		assert_eq!(identifier("_test2").unwrap(), ("_test2", ""));
+		assert_eq!(identifier("__test").unwrap(), ("__test", ""));
+		assert_eq!(identifier("__test2").unwrap(), ("__test2", ""));
+		assert_eq!(identifier("test, test").unwrap(), ("test", ", test"));
+		assert_eq!(identifier("test2, test").unwrap(), ("test2", ", test"));
+		assert_eq!(identifier("Test, Test").unwrap(), ("Test", ", Test"));
+		assert_eq!(identifier("Test2, Test").unwrap(), ("Test2", ", Test"));
+		assert_eq!(identifier("_test, _test").unwrap(), ("_test", ", _test"));
+		assert_eq!(identifier("_test2, _test").unwrap(), ("_test2", ", _test"));
+		assert_eq!(identifier("__test, __test").unwrap(), ("__test", ", __test"));
+		assert_eq!(identifier("__test2, __test").unwrap(), ("__test2", ", __test"));
+		assert!(identifier("2test, test").is_none());
+		assert!(identifier("#test, test").is_none());
+		assert!(identifier("$test, test").is_none());
+		assert!(identifier(",test, test").is_none());
+	}
+
+	#[test]
+	fn tokenize_primitives()
+	{
+		assert_eq!(parenthesized_expression("(foo bar baz) test").unwrap(),
+			Some(("foo bar baz", " test")));
+		assert!(parenthesized_expression("( | asd#0231(asd|asd) test").is_err());
+		assert_eq!(parenthesized_expression("( | asd#0231(asd|asd) ) test").unwrap(),
+			Some((" | asd#0231(asd|asd) ", " test")));
+		assert_eq!(parenthesized_expression("( | a)sd#0231(asd|asd)  test").unwrap(),
+			Some((" | a", "sd#0231(asd|asd)  test")));
+
+		assert_eq!(number("1234, ").unwrap(), Some((1234, ", ")));
+		assert_eq!(number("1234.5, ").unwrap(), Some((1234, ".5, ")));
+		assert_eq!(number("-1234, ").unwrap(), None);
+		assert_eq!(number("a1234, ").unwrap(), None);
+
+		assert_eq!(symbol("<-"), Some((Symbol::ArrowLeft, "")));
+		assert_eq!(symbol("<->"), Some((Symbol::ArrowLeftAndRight, "")));
+		assert_eq!(symbol("->"), Some((Symbol::ArrowRight, "")));
+		assert_eq!(symbol(","), Some((Symbol::Comma, "")));
+		assert_eq!(symbol("/"), Some((Symbol::Division, "")));
+		assert_eq!(symbol("="), Some((Symbol::Equal, "")));
+		assert_eq!(symbol("**"), Some((Symbol::Exponentiation, "")));
+		assert_eq!(symbol(">"), Some((Symbol::Greater, "")));
+		assert_eq!(symbol(">="), Some((Symbol::GreaterOrEqual, "")));
+		assert_eq!(symbol("<"), Some((Symbol::Less, "")));
+		assert_eq!(symbol("<="), Some((Symbol::LessOrEqual, "")));
+		assert_eq!(symbol("-"), Some((Symbol::Minus, "")));
+		assert_eq!(symbol("*"), Some((Symbol::Multiplication, "")));
+		assert_eq!(symbol("!="), Some((Symbol::NotEqual, "")));
+		assert_eq!(symbol("+"), Some((Symbol::Plus, "")));
+		assert_eq!(symbol("|"), Some((Symbol::VerticalBar, "")));
+
+		assert_eq!(symbol("<-a"), Some((Symbol::ArrowLeft, "a")));
+		assert_eq!(symbol("<->a"), Some((Symbol::ArrowLeftAndRight, "a")));
+		assert_eq!(symbol("->a"), Some((Symbol::ArrowRight, "a")));
+		assert_eq!(symbol(",a"), Some((Symbol::Comma, "a")));
+		assert_eq!(symbol("/a"), Some((Symbol::Division, "a")));
+		assert_eq!(symbol("=a"), Some((Symbol::Equal, "a")));
+		assert_eq!(symbol("**a"), Some((Symbol::Exponentiation, "a")));
+		assert_eq!(symbol(">a"), Some((Symbol::Greater, "a")));
+		assert_eq!(symbol(">=a"), Some((Symbol::GreaterOrEqual, "a")));
+		assert_eq!(symbol("<a"), Some((Symbol::Less, "a")));
+		assert_eq!(symbol("<=a"), Some((Symbol::LessOrEqual, "a")));
+		assert_eq!(symbol("-a"), Some((Symbol::Minus, "a")));
+		assert_eq!(symbol("*a"), Some((Symbol::Multiplication, "a")));
+		assert_eq!(symbol("!=a"), Some((Symbol::NotEqual, "a")));
+		assert_eq!(symbol("+a"), Some((Symbol::Plus, "a")));
+		assert_eq!(symbol("|a"), Some((Symbol::VerticalBar, "a")));
+	}
+}

src/utils.rs

@@ -0,0 +1,102 @@
+use crate::flavor::VariableDeclaration as _;
+
+pub struct BoundVariableDeclarations<'p, F>
+where
+	F: crate::flavor::Flavor,
+{
+	pub parent: &'p VariableDeclarationStackLayer<'p, F>,
+	pub variable_declarations: std::rc::Rc<crate::VariableDeclarations<F>>,
+}
+
+impl<'p, F> BoundVariableDeclarations<'p, F>
+where
+	F: crate::flavor::Flavor,
+{
+	pub fn new(parent: &'p VariableDeclarationStackLayer<'p, F>,
+		variable_declarations: std::rc::Rc<crate::VariableDeclarations<F>>) -> Self
+	{
+		Self
+		{
+			parent,
+			variable_declarations,
+		}
+	}
+}
+
+pub enum VariableDeclarationStackLayer<'p, F>
+where
+	F: crate::flavor::Flavor,
+{
+	Free(std::cell::RefCell<crate::VariableDeclarations<F>>),
+	Bound(BoundVariableDeclarations<'p, F>),
+}
+
+impl<'p, F> VariableDeclarationStackLayer<'p, F>
+where
+	F: crate::flavor::Flavor,
+{
+	pub fn free() -> Self
+	{
+		Self::Free(std::cell::RefCell::new(vec![]))
+	}
+
+	pub fn bound(parent: &'p VariableDeclarationStackLayer<'p, F>,
+		variable_declarations: std::rc::Rc<crate::VariableDeclarations<F>>) -> Self
+	{
+		Self::Bound(BoundVariableDeclarations::new(parent, variable_declarations))
+	}
+
+	pub fn find(&self, variable_name: &str) -> Option<std::rc::Rc<F::VariableDeclaration>>
+	{
+		match self
+		{
+			VariableDeclarationStackLayer::Free(free_variable_declarations) =>
+			{
+				if let Some(variable_declaration) = free_variable_declarations.borrow().iter()
+					.find(|x| x.matches_name(variable_name))
+				{
+					return Some(std::rc::Rc::clone(&variable_declaration));
+				}
+
+				None
+			},
+			VariableDeclarationStackLayer::Bound(bound_variable_declarations) =>
+			{
+				if let Some(variable_declaration) = bound_variable_declarations
+					.variable_declarations.iter()
+					.find(|x| x.matches_name(variable_name))
+				{
+					return Some(std::rc::Rc::clone(&variable_declaration));
+				}
+
+				bound_variable_declarations.parent.find(variable_name)
+			},
+		}
+	}
+
+	pub fn free_variable_declarations_do_mut<F1, F2>(&self, f: F1) -> F2
+	where
+		F1: Fn(&mut crate::VariableDeclarations<F>) -> F2,
+	{
+		match self
+		{
+			VariableDeclarationStackLayer::Free(free_variable_declarations)
+				=> f(&mut free_variable_declarations.borrow_mut()),
+			VariableDeclarationStackLayer::Bound(bound_variable_declarations)
+				=> bound_variable_declarations.parent.free_variable_declarations_do_mut(f),
+		}
+	}
+
+	pub fn free_variable_declarations_do<F1, F2>(&self, f: F1) -> F2
+	where
+		F1: Fn(&crate::VariableDeclarations<F>) -> F2,
+	{
+		match self
+		{
+			VariableDeclarationStackLayer::Free(free_variable_declarations)
+				=> f(&free_variable_declarations.borrow()),
+			VariableDeclarationStackLayer::Bound(bound_variable_declarations)
+				=> bound_variable_declarations.parent.free_variable_declarations_do(f),
+		}
+	}
+}