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The Recursion Scheme from the Cofree Recursive Comonad

Tarmo Uustalu, Varmo Vene
2011 Electronical Notes in Theoretical Computer Science  
Differently from the scheme based on the cofree comonad on F in a similar fashion, this scheme allows not only recursive calls on elements structurally smaller than the given argument, but also subsidiary  ...  We instantiate the general comonad-based construction of recursion schemes for the initial algebra of a functor F to the cofree recursive comonad on F .  ...  scheme from the cofree recursive comonad Cofree recursive comonads Recursive comonads, dualizing the completely iterative monads of Aczel, Adámek et al  ... 
doi:10.1016/j.entcs.2011.02.020 fatcat:yql7ngvdkvdjrmqxos57omvjiu

Recursive coalgebras from comonads

Venanzio Capretta, Tarmo Uustalu, Varmo Vene
2006 Information and Computation  
We discuss Osius's [22] concept of a recursive coalgebra of a functor from the perspective of programming semantics and give some new sufficient conditions for the recursiveness of a functor-coalgebra  ...  that are based on comonads, comonad-coalgebras and distributive laws.  ...  schemes for initial algebras derivable from comonads (cf. also the dual result stated in [4, 7] ; we note that in [28] , the substitution and solution theorems of [20, 1] were proved from this result  ... 
doi:10.1016/j.ic.2005.08.005 fatcat:xlxme6iodffxrec4zkjbekczcy

Recursive Coalgebras from Comonads

Venanzio Capretta, Tarmo Uustalu, Varmo Vene
2004 Electronical Notes in Theoretical Computer Science  
We discuss Osius's [22] concept of a recursive coalgebra of a functor from the perspective of programming semantics and give some new sufficient conditions for the recursiveness of a functor-coalgebra  ...  that are based on comonads, comonad-coalgebras and distributive laws.  ...  schemes for initial algebras derivable from comonads (cf. also the dual result stated in [4, 7] ; we note that in [28] , the substitution and solution theorems of [20, 1] were proved from this result  ... 
doi:10.1016/j.entcs.2004.02.034 fatcat:nxqxm7l3vvgpjdcielxo2v2nfy

Unifying structured recursion schemes

Ralf Hinze, Nicolas Wu, Jeremy Gibbons
2013 Proceedings of the 18th ACM SIGPLAN international conference on Functional programming - ICFP '13  
Until now, these two unified schemes have appeared incompatible. We show that this appearance is illusory: in fact, adjoint folds subsume recursion schemes from comonads.  ...  There have also been attempts to unify the various generalisations: two prominent such unifications are the 'recursion schemes from comonads' of Uustalu, Vene and Pardo, and our own 'adjoint folds'.  ...  For instance, a largely orthogonal extension of standard folds are recursion schemes from comonads." Recursion schemes from comonads Recursion schemes from comonads are due to Uustalu et al. [30] .  ... 
doi:10.1145/2500365.2500578 dblp:conf/icfp/HinzeWG13 fatcat:3et7dpxknbcb7mdhzj7pgyji3y

Unifying structured recursion schemes

Ralf Hinze, Nicolas Wu, Jeremy Gibbons
2013 SIGPLAN notices  
Until now, these two unified schemes have appeared incompatible. We show that this appearance is illusory: in fact, adjoint folds subsume recursion schemes from comonads.  ...  There have also been attempts to unify the various generalisations: two prominent such unifications are the 'recursion schemes from comonads' of Uustalu, Vene and Pardo, and our own 'adjoint folds'.  ...  For instance, a largely orthogonal extension of standard folds are recursion schemes from comonads." Recursion schemes from comonads Recursion schemes from comonads are due to Uustalu et al. [30] .  ... 
doi:10.1145/2544174.2500578 fatcat:hslrjndwarawbek7a4x2qiqq4i

Histo- and dynamorphisms revisited

Ralf Hinze, Nicolas Wu
2013 Proceedings of the 9th ACM SIGPLAN workshop on Generic programming - WGP '13  
In this paper, we revisit and relate these schemes and show how they can be expressed in terms of recursion schemes from comonads, as well as from recursive coalgebras.  ...  as well as one that uses recursion schemes.  ...  between recursion schemes from comonads and the adjoint folds [6] .  ... 
doi:10.1145/2502488.2502496 dblp:conf/icfp/HinzeW13 fatcat:o7vaczc4mve4lczjl5ap4iewde

Page 6801 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
schemes from comonads.  ...  over the comonad) that together encode the recursive call pattern of a par- ticular recursion scheme for this inductive type.  ... 

The Essence of Dataflow Programming [chapter]

Tarmo Uustalu, Varmo Vene
2006 Lecture Notes in Computer Science  
In fact, comonads are even better, as there is more structure to comonads than to arrow types. Arrow types are too general.  ...  We propose a novel, comonadic approach to dataflow (streambased) computation.  ...  recursion schemes, see e.g., [39, 28, 9] .  ... 
doi:10.1007/11894100_5 fatcat:4x6vw6hgwjb33eckue3637bnqi

The Essence of Dataflow Programming [chapter]

Tarmo Uustalu, Varmo Vene
2005 Lecture Notes in Computer Science  
In fact, comonads are even better, as there is more structure to comonads than to arrow types. Arrow types are too general.  ...  We propose a novel, comonadic approach to dataflow (streambased) computation.  ...  recursion schemes, see e.g., [39, 28, 9] .  ... 
doi:10.1007/11575467_2 fatcat:ymlesan5vfdkfcrkx7lrwlijyu

Relational semantics of linear logic and higher-order model-checking [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
scheme.  ...  schemes.  ...  recursion scheme G.  ... 
arXiv:1501.04789v3 fatcat:4yd3ryhkpzgzfhpy52fctlmglq

Conjugate Hylomorphisms -- Or

Ralf Hinze, Nicolas Wu, Jeremy Gibbons
2015 SIGPLAN notices  
We show that many basic adjunctions induce useful recursion schemes. In fact, almost every structured recursion scheme seems to arise as an instance of the conjugate rule.  ...  The past decades have witnessed an extensive study of structured recursion schemes.  ...  Indeed, in many ways the present work extends the unification of structured recursion schemes presented in [13] , which showed that recursion schemes from comonads [31] are subsumed by adjoint folds  ... 
doi:10.1145/2775051.2676989 fatcat:ilkugd6olvenpebplq3yymkvj4

Conjugate Hylomorphisms -- Or

Ralf Hinze, Nicolas Wu, Jeremy Gibbons
2015 Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '15  
We show that many basic adjunctions induce useful recursion schemes. In fact, almost every structured recursion scheme seems to arise as an instance of the conjugate rule.  ...  The past decades have witnessed an extensive study of structured recursion schemes.  ...  Indeed, in many ways the present work extends the unification of structured recursion schemes presented in [13] , which showed that recursion schemes from comonads [31] are subsumed by adjoint folds  ... 
doi:10.1145/2676726.2676989 dblp:conf/popl/HinzeWG15 fatcat:zo2sbmkynra5pexg62yur2dhzu

Comonadic Notions of Computation

Tarmo Uustalu, Varmo Vene
2008 Electronical Notes in Theoretical Computer Science  
This continues the work in the early 90s by Brookes, Geva and Van Stone on the use of computational comonads in intensional semantics.  ...  We argue that symmetric (semi)monoidal comonads provide a means to structure context-dependent notions of computation such as notions of dataflow computation (computation on streams) and of tree relabelling  ...  Recursion (both general recursion and guarded recursion) and finer and coarser alternatives to comonads analogous to Lawvere theories and arrows are important special topics that we plan to address elsewhere  ... 
doi:10.1016/j.entcs.2008.05.029 fatcat:cyunhgexjrbdflj6wo4zypbv2m

Finitary semantics of linear logic and higher-order model-checking [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
Given a higher-order recursion scheme G, the finiteness of its interpretation in the model enables us to associate to any MSO formula phi a new higher-order recursion scheme G_phi resolving the selection  ...  The main idea is to start from an infinitary and colored relational semantics of the lambdaY-calculus already formulated, and to replace it by its finitary counterpart based on finite prime-algebraic lattices  ...  recursion schemes.  ... 
arXiv:1502.05147v2 fatcat:lseygm2skzcorilqj7s7o55n4m

Scientific Modelling with Coalgebra-Algebra Homomorphisms [article]

Baltasar Trancón y Widemann, Michael Hauhs
2015 arXiv   pre-print
We show the general applicability of the approach by discussing a surprisingly broad collection of instances from real-world modelling practice.  ...  Besides the well-known applications in recursive functional programming, several basic modes of reasoning about scientific models have been demonstrated to admit such an exact meta-theory.  ...  Section 2 introduces our dual pair of recursion schemes of interest. Sections 3 and 4 discuss two application domains per scheme.  ... 
arXiv:1506.07290v1 fatcat:ogbblkrosncxbnvqymysxgic3m
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