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Practical Variable-Arity Polymorphism [chapter]

T. Stephen Strickland, Sam Tobin-Hochstadt, Matthias Felleisen
2009 Lecture Notes in Computer Science  
Our practical validation in the context of our extensive code base confirms the usefulness of the enriched type system. Practical Variable-Arity Polymorphism  ...  Statically typed languages also accommodate modest forms of variable-arity functions, but even ML and Haskell, languages with highly expressive type systems, cannot type check the wide variety of variable-arity  ...  Second, our design choices for variable-arity polymorphism mostly capture the programming style used in practice by working PLT Scheme programmers.  ... 
doi:10.1007/978-3-642-00590-9_3 fatcat:gibgrtzcq5hi5gypkao645r7vi

Making a faster Curry with extensional types

Paul Downen, Zachary Sullivan, Zena M. Ariola, Simon Peyton Jones
2019 Proceedings of the 12th ACM SIGPLAN International Symposium on Haskell - Haskell 2019  
And these extensional functions can stand side-by-side with functions native to practical programming languages, which do not use callby-name evaluation.  ...  We show how extensional, callby-name functions have the correct behavior for directly expressing the arity of curried functions.  ...  to polymorphism of nonuniform arities.  ... 
doi:10.1145/3331545.3342594 dblp:conf/haskell/DownenSAJ19 fatcat:jqng4jcdvnfyjkfmwvjcfu4xn4

Tractability in constraint satisfaction problems: a survey

Clément Carbonnel, Martin C. Cooper
2015 Constraints  
involving only two WNU polymorphisms of fixed arity [125] and a variant of the recognition algorithm used for near-unanimity polymorphisms.  ...  This constant bound on the arity of constraints ensures that tractability does not depend on the way in which constraint relations are encoded: although, in practice, constraint relations are often stored  ... 
doi:10.1007/s10601-015-9198-6 fatcat:fl7kxmceh5bqzpyd2c37rtohii

First-class polymorphism for ML [chapter]

Stefan Kahrs
1994 Lecture Notes in Computer Science  
Polymorphism in ML is implicit: type variables are silently introduced and eliminated.  ...  The lack of an explicit declaration of type variables restricts the expressiveness of parameterised modules (functors).  ...  Our goal is to make functors properly more powerful than polymorphic functions --not so much because this lacking power is badly missed in programming practice, but in pursuit of a better understanding  ... 
doi:10.1007/3-540-57880-3_22 fatcat:nurfxyxb7fgv5lgxcdai2pbnfa

Distinguishing Data Structures and Functions: The Constructor Calculus and Functorial Types [chapter]

C. Barry Jay
2001 Lecture Notes in Computer Science  
The expressive power is greatly increased by allowing the functors to be polymorphic in the number of arguments they take, i.e. in their arities.  ...  Typing of generic functions employs polymorphism over functors in a functorial type system.  ...  Now the functorial type system supports arity variables and polymorphism in the arities of functors, as well as in the functors themselves.  ... 
doi:10.1007/3-540-45413-6_19 fatcat:bco7kshvenao5llxtmscnmjije

Arity Raising in Manticore [chapter]

Lars Bergstrom, John Reppy
2010 Lecture Notes in Computer Science  
Compilers for polymorphic languages are required to treat values in programs in an abstract and generic way at the source level.  ...  We present a novel strategy that uses both control-flow and type information to provide an arity raising implementation addressing these problems.  ...  This set of transformations means that there are no polymorphic functions left at the time that arity raising is being performed.  ... 
doi:10.1007/978-3-642-16478-1_6 fatcat:njpbfpxuhrgdpmzms7vqjumr7i

The expressive power of valued constraints: Hierarchies and collapses

David A. Cohen, Peter G. Jeavons, Stanislav Živný
2008 Theoretical Computer Science  
We show that in some cases a large class of valued constraints, of all possible arities, can be expressed by using valued constraints of a fixed finite arity.  ...  We also show that some simple classes of valued constraints, including the set of all monotonic valued constraints with finite cost values, cannot be expressed by a subset of any fixed finite arity, and  ...  We show that some valued constraints of fixed arities can express constraints of all possible arities whereas some other sets of valued constraints cannot be expressed by any subset of fixed finite arity  ... 
doi:10.1016/j.tcs.2008.08.036 fatcat:keheyfls5nhh5f4sotzq2ce2ky

Modular polymorphic defunctionalization

Georgios Fourtounis, Nikolaos Papaspyrou, Panagiotis Theofilopoulos
2014 Computer Science and Information Systems  
In this paper, we formalize a modular variant of defunctionalization which can support separate compilation for a functional programming language with parametric polymorphism.  ...  In practice, this heuristic is dependent on the number of functions forming closures in the original program and the arities of these functions.  ...  type is reached). arity T (b) . = 0 arity T (t) . = 0 arity T (m.d τ * ) . = 0 arity T (τ 1 → τ 2 ) . = 1 + arity T (τ 2 ) -arity V (v) returns the arity of a top-level function or constructor (i.e.,  ... 
doi:10.2298/csis130923030f fatcat:tquan4zczfedtlyabq2wjzq3ai

The Complexity of General-Valued CSPs [article]

Vladimir Kolmogorov, Andrei Krokhin, Michal Rolinek
2017 arXiv   pre-print
An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables  ...  The goal is to find an assignment of labels to the variables that minimizes the sum.  ...  It can be checked that a generalized fractional polymorphism ρ of arity m → m can be converted into a fractional polymorphism ρ ′ of arity m, as follows: ρ ′ = g=(g1,...  ... 
arXiv:1502.07327v5 fatcat:652gahw3njcjxf73cormr2vijy

The Complexity of General-Valued CSPs

Vladimir Kolmogorov, Andrei Krokhin, Michal Rolínek
2017 SIAM journal on computing (Print)  
The goal is to find an assignment of labels to the variables that minimizes the sum.  ...  An instance of the valued constraint satisfaction problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables  ...  It can be checked that a generalized fractional polymorphism ρ of arity m → m can be converted into a fractional polymorphism ρ of arity m, as follows: ρ = g=(g1,...  ... 
doi:10.1137/16m1091836 fatcat:zfnnwzkui5fdljkba2kd7e2aou

On Backdoors to Tractable Constraint Languages [chapter]

Clément Carbonnel, Martin C. Cooper, Emmanuel Hebrard
2014 Lecture Notes in Computer Science  
In particular, we show that under the weak assumption that the polymorphisms are idempotent, the problem is unlikely to be FPT when the parameter is either r (the constraint arity) or k (the size of the  ...  In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property.  ...  Specifically, an operation f : D(Γ ) a → D(Γ ) of arity a is a polymorphism of Γ if for every R ∈ Γ of arity r and t 1 , . . . , t a ∈ R, f (t 1 , . . . , t a ) = (f (t 1 [1], . . . , t a [1]), . . . ,  ... 
doi:10.1007/978-3-319-10428-7_18 fatcat:nvc6gx5oi5ew7gbsg2bj6ldx3i

On Backdoors To Tractable Constraint Languages [article]

Clement Carbonnel, Martin C. Cooper, Emmanuel Hebrard
2014 arXiv   pre-print
In particular, we show that under the weak assumption that the polymorphisms are idempotent, the problem is unlikely to be FPT when the parameter is either r (the constraint arity) or k (the size of the  ...  In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property.  ...  Specifically, an operation f : D(Γ ) a → D(Γ ) of arity a is a polymorphism of Γ if for every R ∈ Γ of arity r and t 1 , . . . , t a ∈ R, f (t 1 , . . . , t a ) = (f (t 1 [1], . . . , t a [1]), . . . ,  ... 
arXiv:1404.3675v2 fatcat:tf2if2z3wjaprcezz247f7srn4

The Complexity of the Distributed Constraint Satisfaction Problem [article]

Silvia Butti, Victor Dalmau
2021 arXiv   pre-print
Specifically, we show that DCSP(Γ) is polynomial-time tractable if and only if Γ is invariant under symmetric polymorphisms of all arities.  ...  In this setting, variables and constraints are controlled by agents which communicate with each other by sending messages through fixed communication channels.  ...  Γ has symmetric polymorphisms of all arities. 2.  ... 
arXiv:2007.13594v2 fatcat:3gscejfnuncnlfopwi5r64zbli

Higher-Order Rewriting: Framework, Confluence and Termination [chapter]

Jean-Pierre Jouannaud
2005 Lecture Notes in Computer Science  
Here, the syntax forces us to write @(M, N ) when M is not a variable or is a variable with arity zero, and M (N ) when M is a variable with arity 1. More convincing advantages are discussed later.  ...  This is made possible by allowing us to control which variables can or cannot be captured through substitution when replacing a variable with arity: a substitute for a variable of arity n must be an abstraction  ... 
doi:10.1007/11601548_14 fatcat:iwdbwyqmbre2bkbza545hxkjfu

The complexity of finite-valued CSPs

Johan Thapper, Stanislav Zivny
2013 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13  
We show that every core language Γ either admits a binary idempotent and symmetric fractional polymorphism in which case the basic linear programming relaxation solves any instance of VCSP(Γ) exactly,  ...  ,ā m ). (2) Note that a fractional polymorphism of arity m is the same as a generalised fractional polymorphism of arity m → 1.  ...  Then ρ = P g ρ(g)χp•g is a binary symmetric fractional polymorphism of Γc of arity 2 → 2.  ... 
doi:10.1145/2488608.2488697 dblp:conf/stoc/ThapperZ13 fatcat:cehsaawevza7thx3wo45wzomta
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