Type Checking, Coercion, and Inference

When a binary operator is reduced, as in our binop program, it is necessary to check the types of the arguments, possibly to coerce an argument to the correct type, and to infer the result type.

Suppose that X is real and I is integer.

Op	Arg1	Arg2	Op	New Arg1	New Arg2	Result
+	X	X	+	X	X	real
+	I	I	+	I	I	integer
+	I	X	+	(float I)	X	real
:=	I	X	:=	I	(fix X)	integer
<	I	X	<	(float I)	X	boolean

• For most operators, the ``higher'' type takes precedence. Numeric types may be organized in a type lattice where e.g. char < int < float < double.

• For assignment, the type of the left-hand side takes precedence.

• The result type is generally the operand type, but is always boolean for relational operators.

The result type is stored in the operator token.