The lambda -calculus is considered a useful mathematical tool in the study of programming languages. However, if one uses beta eta -conversion to prove equivalence of programs, then a gross simplification is introduced. The author gives a calculus based on a categorical semantics for computations, which provides a correct basis for proving equivalence of programs, independent from any specific computational model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Eugenio Moggi (2003) studied this question.