An axiomatic theory for partial functions
Kuper, Jan (1993) An axiomatic theory for partial functions. Information and Computation, 107 (1). pp. 104150. ISSN 08905401

PDF
1MB 
Abstract:  We describe an axiomatic theory for the concept of oneplace, partial function, where function is taken in its extensional sense. The theory is rather general; i.e., concepts such as natural number and set are definable, and topics such as nonstrictness and self application can he handled. It contains a model of the (extensional) lambda calculus, and commonly applied mechanisms (such as currying and inductive delinability) are possible. Furthermore, the theory is equiconsistent with and equally powerful as ZF Set Theory. The theory (called Axiomatic Function Theory, AFT) is described in the language of classical first order predicate logic with equality and one nonlogical predicate symbol for function application. By means of some notational conventions, we describe a method within this logic to handle undefinedness in a natural way. 
Item Type:  Article 
Copyright:  © 1993 Elsevier Science 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/17947 
Official URL:  http://dx.doi.org/10.1006/inco.1993.1063 
Export this item as:  BibTeX EndNote HTML Citation Reference Manager 
Repository Staff Only: item control page
Metis ID: 118466