Corpus ID: 237635352

How to write a coequation

  title={How to write a coequation},
  author={Fredrik Dahlqvist and Todd J. Schmid},
There is a large amount of literature on the topic of covarieties, coequations and coequational specifications, dating back to the early seventies. Nevertheless, coequations have not (yet) emerged as an everyday practical specification formalism for computer scientists. In this review paper, we argue that this is partly due to the multitude of syntaxes for writing down coequations, which seems to have led to some confusion about what coequations are and what they are for. By surveying the… Expand


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  • P. Aczel
  • Computer Science
  • CSLI lecture notes series
  • 1988
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