Abstract
This paper is an exposition of the basic ideas of the mathematical theory of sketches and a detailed description of some of the ways in which this theory can be used in theoretical computer science to specify datatypes. In particular, this theory provides a convenient way of introducing datatypes which have variants, for example in case of errors or nil pointers. The semantics is a generalization of initial algebra semantics which in some cases allows initial algebras depending on a parameter such as a bound for overflow.
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Wells, C., Barr, M. (1988). The formal description of data types using sketches. In: Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Language Semantics. MFPS 1987. Lecture Notes in Computer Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19020-1_27
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