Correspondence between ALGOL 60 and Church's Lambda-notation: part I
Communications of the ACM
Revised report on the algorithm language ALGOL 60
Communications of the ACM
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
Mechanical construction of type-checking predicates for extensible data types
ACM '74 Proceedings of the 1974 annual conference - Volume 1
Survey: A survey of state vectors
Computer Science Review
| Hi-index | 48.22 |
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.