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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