Algebras of iteration theories
نویسندگان
چکیده
منابع مشابه
Iteration theories as monadic algebras
Iteration theories, as introduced by Stephen Bloom and Zoltán Ésik, are Lawvere theories equipped with a function assigning to every morphism e : n → n + k (representing a system of n recursive equations whose left-hand sides are variables and right-hand sides are terms in those n variables and k parameters) a morphism e† : n → k (representing a solution of those equations). This function is re...
متن کاملWhat Are Iteration Theories?
We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rationalΣ-tree signature. This supports the result that iteration theories axiomatize precisely the equational properties of least fixed points in domain theory: Rat is the monad of free rational theories and every free rational theory has a continuou...
متن کاملOn Algebras with Iteration
Several concepts of algebras with solutions of recursive equation systems are compared: CPO-enrichable algebras are proved to be iteration algebras of Z. Ésik, and iteration algebras are a special case of the recently introduced Elgot algebras (which are the monadic algebras for the free iterative monad). Another special case of iteration algebras are the iterative algebras of E. Nelson and J. ...
متن کاملamenability of banach algebras
chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...
15 صفحه اولElgot Theories: A New Perspective of Iteration Theories (Extended Abstract)
The concept of iteration theory of Bloom and Ésik summarizes all equational properties that iteration has in usual applications, e.g., in Domain Theory where to every system of recursive equations the least solution is assigned. However, this assignment in Domain Theory is also functorial. Yet, functoriality is not included in the definition of iteration theory. Pitty: functorial iteration theo...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1983
ISSN: 0022-0000
DOI: 10.1016/0022-0000(83)90044-2