Comonadic Notions of Computation

  • Authors:
  • Tarmo Uustalu;Varmo Vene

  • Affiliations:
  • Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, EE-12618 Tallinn, Estonia;Dept. of Computer Science, University of Tartu, J. Liivi 2, EE-50409 Tartu, Estonia

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2008

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Abstract

We argue that symmetric (semi)monoidal comonads provide a means to structure context-dependent notions of computation such as notions of dataflow computation (computation on streams) and of tree relabelling as in attribute evaluation. We propose a generic semantics for extensions of simply typed lambda calculus with context-dependent operations analogous to the Moggi-style semantics for effectful languages based on strong monads. This continues the work in the early 90s by Brookes, Geva and Van Stone on the use of computational comonads in intensional semantics.