Completing partial combinatory algebras with unique head-normal forms
In this note, we prove that having unique head-normal forms is a sufficient condition on partial combinatory algebras to be completable. As application, we show that the pca of strongly normalizing CL-terms as well as the pca of natural numbers with partial recursive function application can be extended to total combinatory algebras.
|Mathematical Logic (acm F.4.1)|
|Partial algebras (msc 08A55), Combinatory logic and lambda-calculus (msc 03B40), Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (msc 16S15)|
|Department of Computer Science [CS]|
|Organisation||Specification and Analysis of Embedded Systems|
Bethke, I, Klop, J.W, & de Vrijer, R. (1995). Completing partial combinatory algebras with unique head-normal forms. Department of Computer Science [CS]. CWI.