A model for type checking: with an application to ALGOL 60

Most current programming languages treat computation over different classes of objects (e.g. numbers, strings, labels and functions). For correct compilation and execution, the following question then arises: is a program properly constructed so that its operations and operands are compatible? The activity of answering this question is usually called type checking. This paper attempts to isolate the notion of type checking and presents a partial solution to the type checking problem based on the notions of abstraction and application of functions. In particular, a program is mapped into an expression within a decideable subset of the &lgr;-calculus, which characterizes the type relations within the program and eliminates all other information. The determination of the type-wise correctness or incorrectness of the program is resolved by reducing its corresponding &lgr;-calculus expression to one of two normal forms, the constant “correct” for a type-wise correct program or the constant “error.” An application to type checking in Algol 60 is made, and the attendant problems faced for any notion of type checking are discussed.

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