Semantics for algebraic operations
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Date
2003Author
Plotkin, Gordon
Power, John
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Abstract
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 α_x : (Tx)n ! Tx provides a definitive semantics for algebraic operations added to
the computational λ-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.