Axiomatic domain theory in categories of partial maps [E-Book] / Marcelo P. Fiore.
Fiore, Marcelo P., (author)
Cambridge : Cambridge University Press, 1996
1 online resource (xiii, 240 pages)
englisch
9780521602778
9780511526565
9780521571883
Distinguished dissertations in computer science
Full Text
Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) setting. In particular, the author develops theories of partiality and recursive types and applies them to the study of the metalanguage FPC; for example, enriched categorical models of the FPC are defined. Furthermore, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model. To conclude, for an axiomatisation of absolute non-trivial domain-theoretic models of FPC, operational and denotational semantics are related by means of computational soundness and adequacy results. To make the book reasonably self-contained, the author includes an introduction to enriched category theory.