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Semantics for Algebraic Operations

✍ Scribed by Gordon Plotkin; John Power

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
170 KB
Volume
45
Category
Article
ISSN
1571-0661

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✦ Synopsis

Given a category C with finite products and a strong monad T on C, we investigate axioms under which an ObC-indexed family of operations of the form Ξ± x : (T x) n -β†’ T x provides a definitive semantics for algebraic operations added to the computational Ξ»-calculus. We recall a definition for which we have elsewhere given adequacy results for both big and small step operational semantics, and we show that it is equivalent to a range of other possible natural definitions of algebraic operation. We outline examples and non-examples and we show that our definition is equivalent to one for call-by-name languages with effects too.

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