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Which data types have ω-complete initial algebra specifications?

By J.A. Bergstra and J. Heering


An algebraic specification is called ω-complete or inductively complete if all (open as well as closed)\ud equations valid in its initial model are equationally derivable from it, i.e., if the equational theory of\ud the initial model is identical to the equational theory of the specification, As the latter is recursively\ud enumerable, the initial model of an ω-complete algebraic specification is a data type with a recursively\ud enumerable equational theory. We show that if hidden sorts and functions are allowed in the\ud specification, the converse is also true: every data type with a recursively enumerable equational\ud theory has an ω-complete initial algebra specification with hidden sorts and functions. We also show\ud that in the case of finite data types the hidden sorts can be dispensed with

Topics: Wijsbegeerte
Year: 1994
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