Provide term type deduction function

This implements a function for retrieving the return type of terms, that
is, both the domain to which the expression evaluates to as well as
whether it’s an empty, unit, or general set with multiple values.

include/anthem/Type.h

@@ -0,0 +1,166 @@
+#ifndef __ANTHEM__TYPE_H
+#define __ANTHEM__TYPE_H
+
+#include <anthem/AST.h>
+#include <anthem/Utils.h>
+
+namespace anthem
+{
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+//
+// Type
+//
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+struct DefaultVariableDomainAccessor
+{
+	Domain operator()(const ast::Variable &variable)
+	{
+		return variable.declaration->domain;
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template <class VariableDomainAccessor = DefaultVariableDomainAccessor, class... Arguments>
+Type type(const ast::Term &term, Arguments &&... arguments);
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template <class VariableDomainAccessor = DefaultVariableDomainAccessor>
+struct TermTypeVisitor
+{
+	template <class... Arguments>
+	static Type visit(const ast::BinaryOperation &binaryOperation, Arguments &&... arguments)
+	{
+		const auto leftType = type<VariableDomainAccessor>(binaryOperation.left, std::forward<Arguments>(arguments)...);
+		const auto rightType = type<VariableDomainAccessor>(binaryOperation.right, std::forward<Arguments>(arguments)...);
+
+		// Binary operations on empty sets return an empty set (also with division)
+		if (leftType.setSize == SetSize::Empty || rightType.setSize == SetSize::Empty)
+			return {Domain::Unknown, SetSize::Empty};
+
+		// Binary operations on nonintegers return an empty set (also with division)
+		if (leftType.domain == Domain::Noninteger || rightType.domain == Domain::Noninteger)
+			return {Domain::Unknown, SetSize::Empty};
+
+		// Binary operations on unknown types return an unknown set
+		if (leftType.domain == Domain::Unknown || rightType.domain == Domain::Unknown)
+			return {Domain::Unknown, SetSize::Unknown};
+
+		// Divisions return an unknown set
+		if (binaryOperation.operator_ == ast::BinaryOperation::Operator::Division)
+			return {Domain::Integer, SetSize::Unknown};
+
+		// Binary operations on integer sets of unknown size return an integer set of unknown size
+		if (leftType.setSize == SetSize::Unknown || rightType.setSize == SetSize::Unknown)
+			return {Domain::Integer, SetSize::Unknown};
+
+		// Binary operations on integer sets with multiple elements return an integer set with multiple elements
+		if (leftType.setSize == SetSize::Multi || rightType.setSize == SetSize::Multi)
+			return {Domain::Integer, SetSize::Multi};
+
+		// Binary operations on plain integers return a plain integer
+		return {Domain::Integer, SetSize::Unit};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::Boolean &, Arguments &&...)
+	{
+		return {Domain::Noninteger, SetSize::Unit};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::Function &function, Arguments &&...)
+	{
+		// TODO: check that functions cannot return sets
+
+		return {function.declaration->domain, SetSize::Unit};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::Integer &, Arguments &&...)
+	{
+		return {Domain::Integer, SetSize::Unit};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::Interval &interval, Arguments &&... arguments)
+	{
+		const auto fromType = type<VariableDomainAccessor>(interval.from, std::forward<Arguments>(arguments)...);
+		const auto toType = type<VariableDomainAccessor>(interval.to, std::forward<Arguments>(arguments)...);
+
+		// Intervals with empty sets return an empty set
+		if (fromType.setSize == SetSize::Empty || toType.setSize == SetSize::Empty)
+			return {Domain::Unknown, SetSize::Empty};
+
+		// Intervals with nonintegers return an empty set
+		if (fromType.domain == Domain::Noninteger || toType.domain == Domain::Noninteger)
+			return {Domain::Unknown, SetSize::Empty};
+
+		// Intervals with unknown types return an unknown set
+		if (fromType.domain == Domain::Unknown || toType.domain == Domain::Unknown)
+			return {Domain::Unknown, SetSize::Unknown};
+
+		// Intervals with integers generally return integer sets
+		// TODO: handle 1-element intervals such as 1..1 and empty intervals such as 2..1
+		return {Domain::Integer, SetSize::Unknown};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::SpecialInteger &, Arguments &&...)
+	{
+		return {Domain::Noninteger, SetSize::Unit};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::String &, Arguments &&...)
+	{
+		return {Domain::Noninteger, SetSize::Unit};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::UnaryOperation &unaryOperation, Arguments &&... arguments)
+	{
+		assert(unaryOperation.operator_ == ast::UnaryOperation::Operator::Absolute);
+
+		const auto argumentType = type<VariableDomainAccessor>(unaryOperation.argument, std::forward<Arguments>(arguments)...);
+
+		// Absolute value of an empty set returns an empty set
+		if (argumentType.setSize == SetSize::Empty)
+			return {Domain::Unknown, SetSize::Empty};
+
+		// Absolute value of nonintegers returns an empty set
+		if (argumentType.domain == Domain::Noninteger)
+			return {Domain::Unknown, SetSize::Empty};
+
+		// Absolute value of integers returns the same type
+		if (argumentType.domain == Domain::Integer)
+			return argumentType;
+
+		return {Domain::Unknown, SetSize::Unknown};
+	}
+
+	template <class... Arguments>
+	static Type visit(const ast::Variable &variable, Arguments &&... arguments)
+	{
+		const auto domain = VariableDomainAccessor()(variable, std::forward<Arguments>(arguments)...);
+
+		return {domain, SetSize::Unit};
+	}
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template <class VariableDomainAccessor, class... Arguments>
+Type type(const ast::Term &term, Arguments &&... arguments)
+{
+	return term.accept(TermTypeVisitor<VariableDomainAccessor>(), std::forward<Arguments>(arguments)...);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+}
+
+#endif

include/anthem/Utils.h

@@ -42,6 +42,24 @@ enum class Domain
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////
 
+enum class SetSize
+{
+	Empty,
+	Unit,
+	Multi,
+	Unknown,
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
+struct Type
+{
+	Domain domain{Domain::Unknown};
+	SetSize setSize{SetSize::Unknown};
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+
 }
 
 #endif