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Higher-Order type-level programming in Haskell

PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2019年第ICFP期3卷 1-26页

作者： Kiss, Csongor Field, Tony Eisenbach, Susan Jones, Simon Peyton Imperial Coll London Dept Comp 180 Queens Gate London SW7 1AZ England Imperial Coll London Comp 180 Queens Gate London SW7 1AZ England Microsoft Res 21 Stn Rd Cambridge CB1 2FB England

type family applications in Haskell must be fully saturated. This means that all type-level functions have to be first-order, leading to code that is both messy and longwinded. In this paper we detail an extension to GHC that removes this restriction. We augment Haskell's existing type arrow, ->, with an unmatchable arrow, ->, that supports partial application of type families without compromising soundness. A soundness proof is provided. We show how the techniques described can lead to substantial code-size reduction (circa 80%) in the type-level logic of commonly-used type-level libraries whilst simultaneously improving code quality and readability.

关键词： type-level programming type families Higher-order functions

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Graded Monads and type-level programming for Dependence Analysis 14

Graded Monads and Type-Level Programming for Dependence Anal...

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14th ACM SIGPLAN International Symposium on Haskell (Haskell)

作者： Keating, Finnbar Gale, Michael B. Univ Warwick Coventry W Midlands England

ISBN: (纸本)9781450386159

Programmers make assumptions about the order of memory operations, which are not captured in the operations' types and therefore cannot be enforced statically by a compiler. This can lead programmers to accidentally violate those assumptions if they are not careful. To address this issue, we encode the memory locations that are accessed by a given computation using a graded monad. We use the data flow dependencies which arise from this to construct a type-level graph that we analyse to automatically order the computations so that no dependencies are violated. This also allows for computations which have no dependencies on each other to be run concurrently.

关键词： dependence analysis graded monads type-level programming concurrency

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Attribute grammars fly first-class... safer!: dealing with DSL errors in type-level programming 19

Attribute grammars fly first-class... safer!: dealing with D...

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Proceedings of the 31st Symposium on Implementation and Application of Functional Languages

作者： Juan García-Garland Alberto Pardo Marcos Viera Universidad de la República Montevideo Uruguay

ISBN: (纸本)9781450375627

AspectAG is a domain specific language embedded in Haskell to represent modular attribute grammars. In AspectAG attribute grammar fragments can be defined independently (even in separate modules) and then combined in a safe way. This flexibility is achieved through the use of extensible records, which are implemented using type-level programming ***-level programming support has remarkably evolved in Haskell since the first version of AspectAG was designed; having incorporated new features like data promotion and kind polymorphism, among others, which allows to program in a "strongly typed" way at the level of types in a similar way as when programming at the level of *** this paper we redefine AspectAG applying the new type-level programming techniques. As a consequence, we obtain a more robust system with better error messages.

关键词： type-level programming EDSL attribute grammars Haskell

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Deriving Compositional Random Generators 31

Deriving Compositional Random Generators

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31st Symposium on Implementation and Application of Functional Languages (IFL)

作者： Mista, Agustin Russo, Alejandro Chalmers Univ Technol Gothenburg Sweden

ISBN: (纸本)9781450375627

Generating good random values described by algebraic data types is often quite intricate. State-of-the-art tools for synthesizing random generators serve the valuable purpose of helping with this task, while providing different levels of invariants imposed over the generated values. However, they are often not built for composability nor extensibility, a useful feature when the shape of our random data needs to be adapted while testing different properties or sub-systems. In this work, we develop an extensible framework for deriving compositional generators, which can be easily combined in different ways in order to fit developers' demands using a simple typelevel description language. Our framework relies on familiar ideas from the a la Carte technique for writing composable interpreters in Haskell. In particular, we adapt this technique with the machinery required in the scope of random generation, showing how concepts like generation frequency or terminal constructions can also be expressed in the same type-level fashion. We provide an implementation of our ideas, and evaluate its performance using realworld examples.

关键词： random testing type-level programming Haskell

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Attribute Grammars Fly First-Class How to do Aspect Oriented programming in Haskell

Attribute Grammars Fly First-Class How to do Aspect Oriented...

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14th ACM SIGPLAN International Conference on Functional programming

作者： Viera, Marcos Swierstra, S. Doaitse Swierstra, Wouter Univ Republica Inst Computac Montevideo Uruguay

ISBN: (纸本)9781605583327

Attribute Grammars (AGs), a general-purpose formalism for describing recursive computations over data types, avoid the trade-off which arises when building software incrementally: should it be easy to add new data types and data type alternatives or to add new operations on existing data types? However, AGs are usually implemented as a pre-processor, leaving e.g. type checking to later processing phases and making interactive development, proper error reporting and debugging difficult. Embedding AG into Haskell as a combinator library solves these problems. Previous attempts at embedding AGs as a domain-specific language were based on extensible records and thus exploiting Haskell's type system to check the well-formedness of the AG, but fell short in compactness and the possibility to abstract over oft occurring AG patterns. Other attempts used a very generic mapping for which the AG well-formedness could not be statically checked. We present a typed embedding of AG in Haskell satisfying all these requirements. The key lies in using HList-like typed heterogeneous collections (extensible polymorphic records) and expressing AG well-formedness conditions as type-level predicates (i.e., type-class constraints). By further type-level programming we can also express common programming patterns, corresponding to the typical use cases of monads such as Reader, Writer and State. The paper presents a realistic example of type-class-based type-level programming in Haskell.

关键词： Attribute Grammars Class system Lazy evaluation type-level programming Haskell HList

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Monad Factory: type-Indexed Monads

Monad Factory: Type-Indexed Monads

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11th Symposium on Trends in Functional programming

作者： Snyder, Mark Alexander, Perry Univ Kansas Informat & Telecommun Technol Ctr Lawrence KS 66045 USA

ISBN: (纸本)9783642229404

Monads provide a greatly useful capability to pure languages in simulating side-effects, but implementations such as the Monad Transformer Library [1] in Haskell prohibit reuse of those side-effects such as threading through two different states without some explicit work-around. Monad Factory provides a straightforward solution for opening the non-proper morphisms by indexing monads at both the type-level and term-level, allowing 'copies' of the monads to be created and simultaneously used within even the same monadic transformer stack. This expands monads' applicability and mitigates the amount of boilerplate code we need for monads to work together, and yet we use them nearly identically to non-indexed monads.

关键词： monads Haskell type-level programming

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Generic record combinators with static type checking 10

Generic record combinators with static type checking

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12th International ACM SIGPLAN Symposium on Principles and Practice of Declarative programming, PPDP 2010

作者： Jeltsch, Wolfgang Brandenburgische Technische Universität Cottbus Lehrstuhl Programmiersprachen und Compilerbau Postfach 101344 03013 Cottbus Germany

ISBN: (纸本)9781450301329

Common record systems only provide access to individual record fields. However, it is often useful to have generic record combina-tors, that is, functions that work with complete records of varying structure. Traditionally, generic record combinators can only be implemented in dynamically typed languages. In this paper, we present a record system for Haskell that allows us to define generic record combinators without giving up static type checks. The system is implemented as a library so that it works without modifications to the language. We achieve this mainly by using advanced type system features such as type equality constraints, type families, and higher-rank polymorphism. A key contribution of our paper is a technique for emulating subkinds, including subkind polymorphism. We use this to give the record system additional expressiveness. Our system is not only useful in itself. It also shows what features should be taken into account when designing language support for records. © 2010 ACM.

关键词： type families type-level reification type-level programming higher-rank polymorphism induction type equality closed classes generic programming

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Structure verification of deep neural networks at compilation time

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JOURNAL OF COMPUTER LANGUAGES 2021年 67卷

作者： Pineyro, Leonardo Pardo, Alberto Viera, Marcos Univ Republica Inst Comp Montevideo Uruguay

This paper presents TensorSafe, a Haskell library that makes possible the definition and structural validation of deep neural network architectures. Nowadays, the development process of deep learning models has been notably simplified due to the availability of sophisticated tools in the industry. However, most of these tools do not provide any security controls at compilation time, making the developers deal with unexpected run-time errors and uncertainties. In particular, validating the structure of deep neural networks at compilation time is a complex subject that involves the mathematical validation of all operations that a deep learning model will perform. Moreover, this structural checking requires an advanced usage of types systems theories to manipulate abstract type definitions capable of modeling neural network constructions. Many different programming techniques were involved in the specification of TensorSafe. Primarily, the application of the functional programming paradigm and the use of type-level programming were of great importance for the development process and to probe the correctness of the neural network models. The experimental evaluation showed that by using TensorSafe it is possible to correctly create well-known deep neural network architectures, such as AlexNet or ResNet50.

关键词： type-level programming Neural networks Functional programming

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Injective type Families for Haskell

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ACM SIGPLAN NOTICES 2015年第12期50卷 118-128页

作者： Stolarek, Jan Jones, Simon Peyton Eisenberg, Richard A. Tech Univ Lodz PL-90924 Lodz Poland Microsoft Res Cambridge Cambridge England Univ Penn Philadelphia PA 19104 USA

Haskell, as implemented by the Glasgow Haskell Compiler (GHC), allows expressive type-level programming. The most popular typelevel programming extension is typeFamilies, which allows users to write functions on types. Yet, using type functions can cripple type inference in certain situations. In particular, lack of injectivity in type functions means that GHC can never infer an instantiation of a type variable appearing only under type functions. In this paper, we describe a small modification to GHC that allows type functions to be annotated as injective. GHC naturally must check validity of the injectivity annotations. The algorithm to do so is surprisingly subtle. We prove soundness for a simplification of our algorithm, and state and prove a completeness property, though the algorithm is not fully complete. As much of our reasoning surrounds functions defined by a simple pattern-matching structure, we believe our results extend beyond just Haskell. We have implemented our solution on a branch of GHC and plan to make it available to regular users with the next stable release of the compiler.

关键词： Haskell type-level programming type families functional dependencies injectivity

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Promoting Functions to type Families in Haskell

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ACM SIGPLAN NOTICES 2014年第12期49卷 95-106页

作者： Eisenberg, Richard A. Stolarek, Jan Univ Penn Philadelphia PA 19104 USA Tech Univ Lodz PL-90924 Lodz Poland

Haskell, as implemented in the Glasgow Haskell Compiler (GHC), is enriched with many extensions that support type-level programming, such as promoted datatypes, kind polymorphism, and type families. Yet, the expressiveness of the type-level language remains limited. It is missing many features present at the term level, including case expressions, anonymous functions, partially-applied functions, and let expressions. In this paper, we present an algorithm with a proof of correctness - to encode these term-level constructs at the type level. Our approach is automated and capable of promoting a wide array of functions to type families. We also highlight and discuss those term-level features that are not promotable. In so doing, we offer a critique on GHC's existing type system, showing what it is already capable of and where it may want improvement. We believe that delineating the mismatch between GHC's term level and its type level is a key step toward supporting dependently typed programming. We have implemented our approach as part of the singletons package, available online.

关键词： Haskell type-level programming defunctionalization

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