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This paper concerns the theory of partial maps under composition and more generally, the RC-semigroups introduced by Jackson and Stokes [Semigroup Forum 62 (2001) 279–310] (semigroups with a unary operation called (right) closure). Many of the motivating examples have a natural meet-semilattice structure; the inverse semigroup of all injective partial transformations of a set and the...This is an author’s version of an article published in Journal of Algebra. © 2003 Elsevier. [Journal Article]

We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory...This is an author’s version of an article published in the journal: International Journal of Algebra and Computation. ©2006 World Scientific Publishing Company, http://www.worldscinet.com/ijac/ijac.shtml [Journal Article]

The "if–then–else" construction is one of the most elementary programming commands, and its abstract laws have been widely studied, starting with McCarthy. Possibly, the most obvious extension of this is to include the operation of composition of programs, which gives a semigroup of functions (total, partial, or possibly general binary relations) that can be recombined using...Electronic version of an article published as International Journal of Algebra and Computation (IJAC), 19(7), 937-961, DOI:10.1142/S0218196709005354. © 2009 World Scientific Publishing Company. http://www.worldscinet.com/ijac/19/1907/S0218196709005354.html [Journal Article]

The semigroup of all partial maps on a set under the operation of composition admits a number of operations relating to the domain and range of a partial map. Of particular interest are the operations R and L returning the identity on the domain of a map and on the range of a map respectively. Schein [25] gave an axiomatic characterisation of the semigroups with R and L representable as systems... [Journal Article]

The "if–then–else" construction is one of the most elementary programming commands, and its abstract laws have been widely studied, starting with McCarthy. Possibly, the most obvious extension of this is to include the operation of composition of programs, which gives a semigroup of functions (total, partial, or possibly general binary relations) that can be recombined using... [Journal Article]