Abstract
The basis for this paper is a logic designed by Dana Scott [1] in 1969 for formalizing arguments about computable functions of higher type. This logic uses typed combinators, and we give a more or less direct translation into typed λ-calculus, which is an easier formalism to use, though not so easy for the metatheory because of the presence of bound variables. We then describe, by example only, a proof-checker program which has been implemented for this logic; the program is fully described in [2]. We relate the induction rule which is central to the logic to two more familiar rules - Recursion Induction and Structural Induction - showing that the former is a theorem of the logic, and that for recursively defined structures the latter is a derived rule of the logic. Finally we show how the syntax and semantics of a simple programming language may be described completely in the logic, and we give an example of a theorem which relates syntactic and semantic properties of programs and which can be stated and proved within the logic.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.