By Henry F. Ledgard
Communications of the ACM,
November 1972,
Vol. 15 No. 11, Pages 956-966
10.1145/355606.361876
Comments
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.
The full text of this article is premium content
No entries found
Log in to Read the Full Article
Need Access?
Please select one of the options below for access to premium content and features.
Create a Web Account
If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.
Join the ACM
Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.
Subscribe to Communications of the ACM Magazine
Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.
Purchase the Article
Non-members can purchase this article or a copy of the magazine in which it appears.
