// Operators

pub enum BinaryOperator
{
	Addition,
	Subtraction,
	Multiplication,
	Division,
	Modulo,
	Exponentiation,
}

pub enum ComparisonOperator
{
	Greater,
	Less,
	LessOrEqual,
	GreaterOrEqual,
	NotEqual,
	Equal,
}

pub enum UnaryOperator
{
	AbsoluteValue,
	Negation,
}

// Primitives

pub struct FunctionDeclaration
{
	pub name: String,
	pub arity: usize,
}

pub struct PredicateDeclaration
{
	pub name: String,
	pub arity: usize,
}

#[derive(Eq, Hash, PartialEq)]
pub struct VariableDeclaration
{
	pub name: String,
}

pub type VariableDeclarations = std::collections::HashSet<std::rc::Rc<VariableDeclaration>>;

pub struct VariableDeclarationStack
{
	pub free_variable_declarations: VariableDeclarations,
	bound_variable_declaration_stack: Vec<std::rc::Rc<VariableDeclarations>>,
}

impl VariableDeclarationStack
{
	pub fn find(&self, variable_name: &str) -> Option<std::rc::Rc<VariableDeclaration>>
	{
		for variable_declarations in self.bound_variable_declaration_stack.iter().rev()
		{
			if let Some(variable_declaration) = variable_declarations.iter().find(|x| x.name == variable_name)
			{
				return Some(std::rc::Rc::clone(&variable_declaration));
			}
		}

		if let Some(variable_declaration) = self.free_variable_declarations.iter().find(|x| x.name == variable_name)
		{
			return Some(std::rc::Rc::clone(&variable_declaration));
		}

		None
	}

	pub fn find_or_create(&mut self, variable_name: &str) -> std::rc::Rc<VariableDeclaration>
	{
		if let Some(variable_declaration) = self.find(variable_name)
		{
			return variable_declaration;
		}

		let variable_declaration = VariableDeclaration
		{
			name: variable_name.to_owned(),
		};
		let variable_declaration = std::rc::Rc::new(variable_declaration);

		self.free_variable_declarations.insert(std::rc::Rc::clone(&variable_declaration));

		variable_declaration
	}

	pub fn push(&mut self, bound_variable_declarations: std::rc::Rc<VariableDeclarations>)
	{
		self.bound_variable_declaration_stack.push(bound_variable_declarations);
	}

	pub fn pop(&mut self)
	{
		// TODO: return error instead
		self.bound_variable_declaration_stack.pop().expect("bound variable is empty, cannot pop last element");
	}
}

// Terms

pub struct BinaryOperation
{
	pub operator: BinaryOperator,
	pub left: Box<Term>,
	pub right: Box<Term>,
}

pub struct Function
{
	pub declaration: std::rc::Rc<FunctionDeclaration>,
	pub arguments: Vec<Box<Term>>,
}

pub enum SpecialInteger
{
	Infimum,
	Supremum,
}

pub struct UnaryOperation
{
	pub operator: UnaryOperator,
	pub argument: Box<Term>,
}

pub struct Variable
{
	pub declaration: std::rc::Rc<VariableDeclaration>,
}

// Formulas

pub struct Biconditional
{
	pub left: Box<Formula>,
	pub right: Box<Formula>,
}

pub struct Comparison
{
	pub operator: ComparisonOperator,
	pub left: Box<Term>,
	pub right: Box<Term>,
}

pub struct Exists
{
	pub parameters: Vec<std::rc::Rc<VariableDeclaration>>,
	pub argument: Box<Formula>,
}

pub struct ForAll
{
	pub parameters: Vec<std::rc::Rc<VariableDeclaration>>,
	pub argument: Box<Formula>,
}

pub struct Implies
{
	pub antecedent: Box<Formula>,
	pub implication: Box<Formula>,
}

pub struct Predicate
{
	pub declaration: std::rc::Rc<PredicateDeclaration>,
	pub arguments: Vec<Box<Term>>,
}

// Variants

pub enum Term
{
	BinaryOperation(BinaryOperation),
	Boolean(bool),
	Function(Function),
	Integer(i32),
	SpecialInteger(SpecialInteger),
	String(String),
	Symbolic(String),
	UnaryOperation(UnaryOperation),
	Variable(Variable),
}

pub type Terms = Vec<Box<Term>>;

pub enum Formula
{
	And(Formulas),
	Biconditional(Biconditional),
	Boolean(bool),
	Comparison(Comparison),
	Exists(Exists),
	ForAll(ForAll),
	Implies(Implies),
	Not(Box<Formula>),
	Or(Formulas),
	Predicate(Predicate),
}

pub type Formulas = Vec<Box<Formula>>;