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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 H on a category C , 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 [12] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete...

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