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Notions of computation and monads. (English) Zbl 0723.68073
Summary: The \(\lambda\)-calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with \(\lambda\)-terms. However, if one goes further and uses \(\beta\eta\)- conversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with total functions from values to values) that may jeopardise the applicability of theoretical results.
We introduce calculi, based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.

MSC:
68Q60 Specification and verification (program logics, model checking, etc.)
03B70 Logic in computer science
Software:
LCF
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