Abstract
We develop an approach of partial computations for the lambda calculus. It produces a class of bounded functions (i.e., the co-domains are finite while the domains are possibly infinite), including self-applicable functions. We show that the bounded functions are recursive and have to be represented as lambda terms without head normal form in the lambda calculus. In parallel, we develop a language independently from the lambda calculus. It also represents the class of bounded functions and therefore can produce whatever a Turing machine produces provided that computation has finite time and space. We call such a language a database language because we can use the language to construct and query business objects in database practice. With the bounded functions, we are able to extend the lambda calculus to effectively reduce terms having weak head normal form in a manner similar to how the standard lambda calculus reduces terms that have normal form.
Sign-in/Register to access full text options 
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.
