Computing with Contexts

  • Authors:
  • Ian A. Mason

  • Affiliations:
  • School of Mathematical and Computer Sciences, University of New England, NSW, Australia, 2351. iam@turing.une.edu.au

  • Venue:
  • Higher-Order and Symbolic Computation
  • Year:
  • 1999

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Abstract

We investigate a representation of contexts, expressionswith holes in them, that enables them to be meaningfully transformed,in particular α-converted and β-reduced. In particularwe generalize the set of λ-expressions to include holes, andon these generalized entities define β-reduction (i.e.,substitution) and filling so that these operations preserveα-congruence and commute. The theory is then applied to allowthe encoding of reduction systems and operational semantics ofcall-by-value calculi enriched with control, imperative andconcurrent features.