On second-order iterative monads
نویسندگان
چکیده
منابع مشابه
On second-order iterative monads
B. Courcelle studied algebraic trees as precisely the solutions of all recursive program schemes for a given signature in Set. He proved that the corresponding monad is iterative. We generalize this to recursive program schemes over a given finitary endofunctor H of a ”suitable” category. A monad is called second-order iterative if every guarded recursive program scheme (w.r.t. H) has a unique ...
متن کاملIterative reflections of monads
Iterative monads, introduced by Calvin Elgot in the 1970’s, are those ideal monads in which every guarded system of recursive equations has a unique solution. For every ideal monad M we prove that an iterative reflection, i.e., an embedding M ↪−→ M̂ into an iterative monad with the expected universal property, exists. We also introduce the concept of iterativity for algebras for the monad M, fol...
متن کاملOn Rational Monads and Free Iterative Theories
For every finitary endofunctor H of Set a rational algebraic theory (or a rational finitary monad) R is defined by means of solving all finitary flat systems of recursive equations over H. This generalizes the result of Elgot and his coauthors, describing a free iterative theory of a polynomial endofunctor H as the theory R of all rational infinite trees. We present a coalgebraic proof that R i...
متن کاملCompletely iterative algebras and completely iterative monads
Completely iterative theories of Calvin Elgot formalize (potentially infinite) computations as solutions of recursive equations. One of the main results of Elgot and his coauthors is that infinite trees form a free completely iterative theory. Their algebraic proof of this result is extremely complicated. We present completely iterative algebras as a new approach to the description of free comp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2011
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2011.04.027