Abstract
After an introduction to the syntax of Godel systemT, we present its naive denotational semantics in the domain of lazy natural numbers and show an adequacy property relating syntax and semantics. We recall the natural restrictions of systemT delineating primitive recursion as a subsystem. We discuss the weakness of primitive recursion by exhibiting a simple unary algorithm whose denotation is not the semantics of a primitive recursive algorithm. This algorithm can nevertheless be programmed in systemT by using the power of higher-order (functional) definitions. Generalizing this example, we obtain a representation theorem, asserting that every “reasonable” algorithm of typeN →N can be programmed in systemT. We conclude by discussing what is known in the case of higher arities.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
