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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'.  ...  Acknowledgments This work has been funded by EPSRC grant number EP/J010995/1, on Unifying Theories of Generic Programming.  ... 
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'.  ...  Acknowledgments This work has been funded by EPSRC grant number EP/J010995/1, on Unifying Theories of Generic Programming.  ... 
doi:10.1145/2544174.2500578 fatcat:hslrjndwarawbek7a4x2qiqq4i

The Unified Algorithmic Platform for Solving Complex Problems of Computational Geometry [chapter]

Vasyl Tereshchenko, Igor Budjak, Andrey Fisunenko
2013 Lecture Notes in Computer Science  
Keywords Unified algorithmic platform, complex tasks, parallel-and-recursive algorithm, computational geometry, weighted concatenable queue.  ...  In this way our scheme can conventionally be divided into the following stages: preliminary processing, recursive partitioning (recursive descent),merging subsets' results (recursive ascent).  ...  Unlike the described classical approach we decided to create system having single universal data structure unified for all tasks.  ... 
doi:10.1007/978-3-642-39958-9_39 fatcat:wp6pjbjqlzedzp5uye6czzaa6u

Quasi-destructive graph unification

Hideto Tomabechi
1991 Proceedings of the 29th annual meeting on Association for Computational Linguistics -  
We have developed a scheme to attain these two elements without expensive overhead through temporarily modifying graphs during unification to eliminate copying during unification.  ...  recursion as unifying.  ...  Experiments 19h may be slightly slower becauseour unification recurses twice on a graph: once to unify and once to copy, whereas in incremental unification schemes copying is performed during the same  ... 
doi:10.3115/981344.981385 dblp:conf/acl/Tomabechi91 fatcat:lgezczt56rdzjgdlwiyzfnt6lm

Signature-check based unification filter

Alfredo M. Maeda, Jun-Ichi Aoe, Hideto Tomabechi
1994 Software, Practice & Experience  
In this paper we present what we call a unification filter or U-filter, that preprocesses the feature structures to be unified.  ...  If the U-filter succeeds, unification is then skipped because the attempt to unify the involved structures would result in failure.  ...  Structures that pass U-filtering must be unified in the traditional way, and may or may not unify.  ... 
doi:10.1002/spe.4380240702 fatcat:g5n7xnc3e5e7vme4727k4ybgme

Design of Efficient Unification for Natural Language

Hideto Tomabechi
1995 Journal of Natural Language Processing  
We propose a scheme to attain these criteria without expensive overhead for reversing the changes made to the graph node structures based on the notion of quasi-destructive unification.  ...  Thus, fully delaying copying in incremental schemes to avoid early copying would make their control structures essentially no different from Q-D and reversible (Karttunen's) schemes.  ...  This way, we can see that unification of these feature structures is possible and actually trivial using the Q-D scheme.  ... 
doi:10.5715/jnlp.2.2_23 fatcat:b7qhprnvibdanlx3n26uqx35re

Finite Memory Structure Filtering and Smoothing for Target Tracking in Wireless Network Environments

Pyung Soo Kim
2019 Applied Sciences  
by the recursive infinite memory structure (IMS) filtering such as Kalman filter.  ...  Firstly, a unified algorithm of finite memory structure (FMS) filtering and smoothing is proposed for a discrete-time state-space model.  ...  Moreover, in contrast to the recursive IMS filter such as the Kalman filter, the proposed unified algorithm can have intrinsic robustness due to its finite memory structure.  ... 
doi:10.3390/app9142872 fatcat:leok2irw5bblhpgspgd7hzvtt4

Optimal unified IIR architectures for time-recursive discrete sinusoidal transforms

K.J.R. Liu, C.T. Chiu, R.K. Kolagotla, J.F. JaJa
1993 IEEE International Conference on Acoustics Speech and Signal Processing  
This structure uses only half as many multipliers as the previous best known scheme [l]. The proposed architecture is regular, modular, and locally-connected.  ...  An optimal unified architecture that can efficiently compute the Discrete Cosine, Sine, Hartley, Fourier, Lapped Orthogonal, and Complex Lapped transforms for a continuous input data stream is proposed  ...  OPTIMAL TIME-RECURSIVE ARCHITECTURES Optimal Unified IIR Structures Input data arrive serially in most real-time signal processing applications.  ... 
doi:10.1109/icassp.1993.319438 dblp:conf/icassp/LiuCKJ93 fatcat:ooh2u7aiejhdld4dpl2fetwzzi

Fantastic Morphisms and Where to Find Them: A Guide to Recursion Schemes [article]

Zhixuan Yang, Nicolas Wu
2022 arXiv   pre-print
Thus many generalisations have been proposed, which further lead to several unifying frameworks of structured recursion schemes.  ...  To fill this gap, this expository paper introduces structured recursion schemes from a practical point of view: a variety of recursion schemes are motivated and explained in contexts of concrete programming  ...  Contributions The existing literature [25, 26, 47] on unifying accounts to structured recursion schemes has focused on the categorical foundation of recursion schemes rather than their motivations or  ... 
arXiv:2202.13633v2 fatcat:224agn6lyvcubisbpwrj4n5rqe

Payments Systems Determination by Universal Financial Industry Message Scheme According to Single Euro Payments Area [chapter]

Slobodan Nikola Babić
2017 E-Business - State of the Art of ICT Based Challenges and Solutions  
, securities, trade services) by universal financial industry message scheme standard.  ...  This paper shows the determination of payment systems based on their structure (all the way from retail users up to the Central bank) and on the subject they are dealing with (payments, forex notifications  ...  It is quite clear that a recursive object can be represented by a recursive structure, too.  ... 
doi:10.5772/66250 fatcat:l7d4hi7vyfcpfoib47jjnflfya

Finding parallel functional pearls: Automatic parallel recursion scheme detection in Haskell functions via anti-unification

Adam D. Barwell, Christopher Brown, Kevin Hammond
2018 Future generations computer systems  
Unusually, we exploit anti-unification to expose these recursion schemes from source-level definitions whose structures match a recursion scheme, but which are not necessarily written directly in terms  ...  Higher-order functions enable simple and easily understood abstractions that can be used to implement a variety of common recursion schemes, such as maps and folds over traversable data structures.  ...  The only requirement is that the code structure matches the recursion schemes of interest, and that there are no unwanted side effects.  ... 
doi:10.1016/j.future.2017.07.024 fatcat:4wqcumg2nja7po2sj6e4i5kdtq

The Metalanguage λprolog and Its Implementation [chapter]

Gopalan Nadathur
2001 Lecture Notes in Computer Science  
Recursion Over Binding Structure Recognizing tail-recursiveness of arbitrary arity functions requires an explicit recursion over binding structure: • Given an expression of the form (fix (λf F)) analyze  ...  Realizing Higher-Order Unification Multiple most general unifiers may exist.  ... 
doi:10.1007/3-540-44716-4_1 fatcat:iq3a6msg3bc53f7qgtmb4dpsui

A Scheme-Driven Approach to Learning Programs from Input/Output Equations [article]

Jochen Burghardt
2018 arXiv   pre-print
By confining ourselves to structurally recursive definitions we obtain a fairly fast learning algorithm that often yields definitions close to intuitive expectations.  ...  simple structural recursion scheme.  ...  In Sect. 5.2, we discuss possible extensions of the structural recursion scheme, like simultaneous recursion.  ... 
arXiv:1802.01177v1 fatcat:ztpxgc4cn5clvcogmdtl2ps6xu

Induction of recursive program schemes [chapter]

Ute Schmid, Fritz Wysotzki
1998 Lecture Notes in Computer Science  
In this paper we present an approach to the induction of recursive structures from examples which is based on the notion of recursive program schemes.  ...  A recursive program scheme represents the class of structural identical programs and can be assigned different semantics by interpretation.  ...  The notion of RPSs enables us to model the acquisition of problem solving schemes and their use in analogical reasoning in a unified way (see [16] ). 3 Recursive Program Schemes (RPSs) The theoretical  ... 
doi:10.1007/bfb0026692 fatcat:fvhs7zimt5g3zdnfi6qpkokfxq

Page 607 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
The question whether countable recursion can be defined via a set of schemes remains open; the au- thor suggests, however, one possible scheme $14 for which known arguments for failure fail.  ...  Secondly, he answers a problem formulated by Hyland: Is a scheme of bar-recursion sufficient, together with S1-S9, to generate the countably recursive functionals?  ... 
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