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Backtracking with cut via a distributive law and left-zero monoids

MACIEJ PIRÓG, SAM STATON
2017 Journal of functional programming  
We give two descriptions of the resulting monad: as the monad of free left-zero monoids, and as a composition via a distributive law of the list monad and the 'unary idempotent operation' monad.  ...  The scope delimiter of cut arises as a handler.  ...  Research supported by a Royal Society University Research Fellowship and EPSRC Grant EP/N007387/1.  ... 
doi:10.1017/s0956796817000077 fatcat:ziro3piclvg6hgwrc5xvmxx6pq

Eilenberg–Moore Monoids and Backtracking Monad Transformers

Maciej Piróg
2016 Electronic Proceedings in Theoretical Computer Science  
Finally, we construct an Eilenberg--Moore monoid of endomorphisms, which, via the codensity monad construction, yields a continuation-based implementation a la Hinze.  ...  From this, we obtain a number of results, including the facts that the list monad transformer is indeed a monad, a transformer, and an instance of the MonadPlus class.  ...  Acknowledgements I would like to thank Tom Schrijvers for his remarks on an early draft of this paper, and the anonymous reviewers for their detailed comments and helpful suggestions.  ... 
doi:10.4204/eptcs.207.2 fatcat:x44pue7ydfatjmljsquyiod26u

Comprehending Ringads [chapter]

Jeremy Gibbons
2016 Lecture Notes in Computer Science  
List comprehensions are a widely used programming construct, in languages such as Haskell and Python and in technologies such as Microsoft's Language Integrated Query.  ...  When the monad has the additional structure of a so-called ringad, corresponding to 'empty' and 'union' operations, then it can be seen as some kind of collection type, and the comprehension notation can  ...  Acknowledgements I am very grateful to Ralf Hinze, Nicolas Wu, Fritz Henglein, Tarmo Uustalu, and Oleg Kiselyov for their helpful discussions, to Eerke Boiten for finding a copy of Wadler's note (Wadler  ... 
doi:10.1007/978-3-319-30936-1_7 fatcat:lvtbq6upxjhazmmrnzhrz436de

Transformation of structure-shy programs with application to XPath queries and strategic functions

Alcino Cunha, Joost Visser
2011 Science of Computer Programming  
We formulate a rich set of algebraic laws, not just for transformation of structure-shy programs, but also for their conversion into structure-sensitive programs and vice versa.  ...  Such programs are defined generically for many different datatypes and only specify specific behavior for a few relevant subtypes.  ...  We have modeled the core of the XPath language in terms of strategic program combinators, augmented with a universal node type and associated operations.  ... 
doi:10.1016/j.scico.2010.01.003 fatcat:kz3666fm3rd4nmrpdh7gk3muha

On The Resolution Semiring

Marc Bagnol
2014 Zenodo  
It provides us with an algebraicand abstract setting, while being presented in a syntactic and concrete way, inwhich a theoretical study of computation can be carried on.We will review first the interactive  ...  In this thesis, we study a semiring structure with a product based on theresolution rule of logic programming.  ...  From this perspective, a proof of A B can be seen as a program that inputs (through the cut rule) a proof of A and outputs (via the cut-elimination procedure) a cut-free proof of B.  ... 
doi:10.5281/zenodo.806771 fatcat:klgfbxmvfrf3xhad2pb4tq56ee

Subject index volumes 1–200

1999 Theoretical Computer Science  
, 1251 zero-knowledge, see also ZK interactive protocol. 1573 proof, 25 IO protocols, 1573 zero-one law, 3652 for algorithmically random sequences, 3652 zeros, 2170, 2264.2523,2526,2734 at infinity, common  ...  zero-characteristic field, 3400 zero-cost tile rotation problem, 3493 zero-dimensional spaces, 2525 strongly -, 836 topological space. 836 tree, 1586 zero-divisor-free, 1718 zero- ComputerScience  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Categorifying measure theory: a roadmap [article]

G. Rodrigues
2009 arXiv   pre-print
A program for categorifying measure theory is outlined.  ...  To motivate and explain such an interpretation is a long voyage with a couple of false starts, the inevitable detours and a good deal of backtracking. In the words of W.  ...  If µ : 2 X −→ A is a cosheaf, then it factors via χ as dµ : PShv(X) −→ A by taking the left Kan extension Lan χ µ.  ... 
arXiv:0912.4914v1 fatcat:biunlrnctrfinbdazdhhprnomi

Counting Successes: Effects and Transformations for Non-deterministic Programs [chapter]

Nick Benton, Andrew Kennedy, Martin Hofmann, Vivek Nigam
2016 Lecture Notes in Computer Science  
A relational semantics for the effect system establishes the soundness of both the analysis and its use in effect-based program transformations.  ...  We give a simple effect system for non-deterministic programs, tracking static approximations to the number of results that may be produced by each computation.  ...  We thank the referees for their thorough and helpful comments.  ... 
doi:10.1007/978-3-319-30936-1_3 fatcat:dx3sffxt2jd7vdw44axu4iwidq

This Week's Finds in Mathematical Physics (51-100) [article]

John C. Baez
2022 arXiv   pre-print
These issues discuss quantum gravity, topological quantum field theory and other topics in mathematics and physics.  ...  They also include two expository series: one on ADE classifications and one on categories and higher categories. They were typeset in 2020 by Tim Hosgood.  ...  The eigenvalues are all nonnegative, so all the quantities exp(−tλ i ) go to zero except for the zero eigenvalues, and we're left with str(exp(−tH)) being equal to the alternating sum of the dimensions  ... 
arXiv:2203.02631v1 fatcat:mhrjnnmee5a7nljvh4jt4qyou4

A dynamical perspective on shear-bend coordinates [article]

Aaron Fenyes
2018 arXiv   pre-print
On a surface with punctures, Gaiotto, Hollands, Moore and Neitzke's "abelianization" process computes the shear-bend coordinates of a twisted SL_2 C local system without reference to its hyperbolic geometry  ...  Bonahon and Thurston's "shear-bend coordinates" parameterize these local systems of charts.  ...  We'll say a horogeodesic curve is non-backtracking if it never makes two left turns or two right turns in a row.  ... 
arXiv:1510.05757v2 fatcat:hlvkms2ugfggva2gixozzzq2ru

Testing isomorphism of graded algebras [article]

Peter A. Brooksbank, E. A. O'Brien, James B. Wilson
2019 arXiv   pre-print
We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma.  ...  We present a new algorithm to decide isomorphism between finite graded algebras.  ...  A bi-additive map (or just bimap) is a tuple U * = U 2 , U 1 , U 0 , • where the U i are abelian groups and • : U 2 × U 1 U 0 is a function satisfying the following two-sided distributive law: (u 2 + u  ... 
arXiv:1708.08873v2 fatcat:jj6gefndxbc5netvo77grg2cya

On the complexity of Cockett-Seely polarized games [article]

J. R. B. Cockett, C. A. Pastro
2004 arXiv   pre-print
The final section of the paper points out that, despite the apparent complexity of the formulas, there is, for the initial polarized logic with all the connectives (additives, multiplicatives, and exponentials  ...  The structure of the internal hom object can be exploited and, using dynamic programming techniques, one can reduce the cost of finding a strategy in such a formula to the order of the product of the sizes  ...  As, in the worst case, this is the very least one must do this is a hard bound.  ... 
arXiv:math/0402441v2 fatcat:rxzc2aa7i5h3bgxzstr5zhg5si

ENFrame: A Platform for Processing Probabilistic Data [article]

Sebastiaan J. van Schaik and Dan Olteanu and Robert Fink
2013 arXiv   pre-print
We introduce sequential and distributed algorithms for computing the probability of interconnected events exactly or approximately with error guarantees.  ...  Using ENFrame, users can write programs in a fragment of Python with constructs such as bounded-range loops, list comprehension, aggregate operations on lists, and calls to external database engines.  ...  The dfs procedure is called using a non-zero error budget 2ε, and it assigns half of the budget to the newly created left branch of the decision tree.  ... 
arXiv:1309.0373v1 fatcat:mqv5xq53srhgrf4k6hiw2qxnxy

Rules and strategies for program transformation [chapter]

Alberto Pettorossi, Maurizio Proietti
1993 Lecture Notes in Computer Science  
We present an overview of the program transformation methodology, focusing our attention on the so-called 'rules + strategies' approach in the case of functional and logic programs.  ...  A.  ...  Partsch for their suggestions and comments. Finally we would like to thank Dr. O. Aioni for her careful reading of a previous draft of this paper.  ... 
doi:10.1007/3-540-57499-9_23 fatcat:xe6263rjmnd7vojj2wzbjgqtsq

Recent progress in coalescent theory [article]

Nathanael Berestycki
2009 arXiv   pre-print
These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and other fields such as spin glass models.  ...  The emphasis is on recent work concerning in particular the connection of these processes to continuum random trees and spatial models such as coalescing random walks.  ...  The converse uses a zero-one law for Π along the lines of Blumenthal's zero-one law (details in [131] ).  ... 
arXiv:0909.3985v1 fatcat:2vccjcadrbauffhdjq5gdm4hsq
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