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Generalizing substitution

Tarmo Uustalu — 2003

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

It is well known that, given an endofunctor H on a category , the initial ( A + H - ) -algebras (if existing), i.e., the algebras of (wellfounded) H -terms over different variable supplies A , give rise to a monad with substitution as the extension operation (the free monad induced by the functor H ). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness),...

Generalizing Substitution

Tarmo Uustalu — 2010

RAIRO - Theoretical Informatics and Applications

It is well known that, given an endofunctor on a category , the initial -algebras (if existing), , the algebras of (wellfounded) -terms over different variable supplies , give rise to a monad with substitution as the extension operation (the free monad induced by the functor ). Moss [17] and Aczel, Adámek, Milius and Velebil [12] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness),...

Coproducts of ideal monads

Neil GhaniTarmo Uustalu — 2004

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18–32],...

Coproducts of Ideal Monads

Neil GhaniTarmo Uustalu — 2010

RAIRO - Theoretical Informatics and Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly  [ (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, (2002) 18–32], and that of Hyland,...

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