# Generalizing Substitution

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 37, Issue: 4, page 315-336
- ISSN: 0988-3754

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topUustalu, Tarmo. "Generalizing Substitution." RAIRO - Theoretical Informatics and Applications 37.4 (2010): 315-336. <http://eudml.org/doc/92726>.

@article{Uustalu2010,

abstract = {
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 iterativeness), arises from the inverses of the final (A+H-)-coalgebras (if existing), i.e. , the algebras of
non-wellfounded H-terms. We show that, upon an appropriate
generalization of the notion of substitution, the same can more
generally be said about the initial T'(A,-)-algebras resp. the
inverses of the final T'(A,-)-coalgebras for any endobifunctor
T' on any category C such that the functors T'(-,X)
uniformly carry a monad structure.
},

author = {Uustalu, Tarmo},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Algebras of terms; non-wellfounded terms; substitution;
iteration of guarded substitution rules; monads; hyperfunctions;
finitely or possibly infinitely branching trees.; terms; guarded substitution},

language = {eng},

month = {3},

number = {4},

pages = {315-336},

publisher = {EDP Sciences},

title = {Generalizing Substitution},

url = {http://eudml.org/doc/92726},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Uustalu, Tarmo

TI - Generalizing Substitution

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 4

SP - 315

EP - 336

AB -
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 iterativeness), arises from the inverses of the final (A+H-)-coalgebras (if existing), i.e. , the algebras of
non-wellfounded H-terms. We show that, upon an appropriate
generalization of the notion of substitution, the same can more
generally be said about the initial T'(A,-)-algebras resp. the
inverses of the final T'(A,-)-coalgebras for any endobifunctor
T' on any category C such that the functors T'(-,X)
uniformly carry a monad structure.

LA - eng

KW - Algebras of terms; non-wellfounded terms; substitution;
iteration of guarded substitution rules; monads; hyperfunctions;
finitely or possibly infinitely branching trees.; terms; guarded substitution

UR - http://eudml.org/doc/92726

ER -

## References

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