MoL-2012-06: Interaction, observation and denotation: A study of dialgebras for program semantics

MoL-2012-06: Blok, Alwin (2012) Interaction, observation and denotation: A study of dialgebras for program semantics. [Report]

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Abstract

We investigate the use of dialgebras for program semantics. Dialgebras generalise both algebras and coalgebras. As a result dialgebras can model compositional and interactive features of programs, in addition to program state and behaviour over time. We investigate the theory of universal dialgebra and use it to derive canonical denotational semantics from dialgebraic operational specifications. The greatest quotient of a dialgebraic operational semantics provides us with a denotational semantics that characterises behavioural equivalence. Subdialgebras on the other hand can provide small stand{alone denotations for programs. We extend the theory of universal dialgebra with a new result. We define minimisation and simplification sequences for dialgebras. When used with a dialgebraic operational semantics these sequences enable us to compute suitable denotations for programs. The technique can be used to decide equivalence of programs, if equivalence is decidable at all. The thesis is concluded with two examples. We provide a dialgebraic semantics for regular expressions that aligns with the classic semantics in which regular expressions are interpreted as deterministic automata. Finally we give a dialgebraic semantics for the synchronous CCS. In the coalgebraic semantics of the CCS the behaviour of individual processes is modelled. The dialgebraic semantics illustrates that dialgebras can model the behaviour of multiple processes at once, along with their interactions and resulting behaviour.

Item Type: Report
Report Nr: MoL-2012-06
Series Name: Master of Logic Thesis (MoL) Series
Year: 2012
Uncontrolled Keywords: Logic, Computation
Depositing User: Tanja Kassenaar
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/872

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