Relationships between equational and inductive data types

Authors:
Eric G. Wagner
Affiliations:
Wagner Mathematics, Garrison, NY
Venue:
Formal Methods in Software and Systems Modeling
Year:
2005

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Abstract

This paper explores the relationship between equational algebraic specifications (using initial algebra semantics) and specifications based on simple inductive types (least fixed points of equations using just products and coproducts, e.g. N≅1+N). The main result is a proof that computable data type (one in which the corresponding algebra is computable in the sense of Mal'cev) can be specified inductively. This extends an earlier result of Bergstra and Tucker showing that any computable data type can be specified equationally.