A programming language type system includes, in a memory, a set of numeric type including integer types, fixed-point types and floating-point types, a set of type propagation rules to automatically determine result types of any combination of integer types, fixed-point types and floating-point types, constant annotations to explicitly specify a result type of a literal constant, context-sensitive constants whose type is determined from a context of a constant according to the set of type propagation rules, an assignment operator to explicitly specify a type of a value or computation, and operator annotations to explicitly specify a result type of a computation.