Abstract
We are studying here the computations over free algebras that can be done in a constant number of complete developments of the pure λ-calculus. In the following, such computations will be called constant time parallel computations (considering that all redexes in a λ-term are reduced “at the same time” to produce its complete development). This has obviously nothing to do with a realistic definition of constant time parallel computation, but the set K Λ of numeric functions that are computable in this way enjoys good closure properties making it close in some sense to the class of elementary functions. We prove that a function over free algebras is computable in parallel constant time in the pure λ-calculus, iff it is representable in the simply typed λ-calculus Λ → . In considering the latter, the full type structures of Λ → prove to be serious tools for an extensional study of the functions λ-representable with constant parallel runtime, giving us in particular a full description of the λ-representable predicates.
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.
