The Sketch of a Polymorphic Symphony

In previous work, we have introduced functional strategies, that is, first-class generic functions that can traverse into terms of any type while mixing uniform and type-specific behaviour. In the present paper, we give a detailed description of one particular Haskell-based model of functional strategies. This model is characterised as follows. Firstly, we employ first-class polymorphism as a form of second-order polymorphism as for the mere types of functional strategies. Secondly, we use an encoding scheme of run-time type case for mixing uniform and type-specific behaviour. Thirdly, we base all traversal on a fundamental combinator for folding over constructor applications. Using this model, we capture common strategic traversal schemes in a highly parameterised style. We study two original forms of parameterisation. Firstly, we design parameters for the specific control-flow, data-flow and traversal characteristics of more concrete traversal schemes. Secondly, we use overloading to postpone commitment to a specific type scheme of traversal. The resulting portfolio of traversal schemes can be regarded as a challenging benchmark for setups for typed generic programming. The way we develop the model and the suite of traversal schemes, it becomes clear that parameterised + typed strategic programming is best viewed as a potent combination of certain bits of parametric, intensional, polytypic, and ad-hoc polymorphism

Strategic polymorphism requires just two combinators!

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term rewriting strategies (with coverage of traversal) to the functional programming paradigm. Meanwhile, a number of Haskell-based models and combinator suites were proposed to support generic programming with functional strategies. In the present paper, we provide a compact and matured reconstruction of functional strategies. We capture strategic polymorphism by just two primitive combinators. This is done without commitment to a specific functional language. We analyse the design space for implementational models of functional strategies. For completeness, we also provide an operational reference model for implementing functional strategies (in Haskell). We demonstrate the generality of our approach by reconstructing representative fragments of the Strafunski library for functional strategies.Comment: A preliminary version of this paper was presented at IFL 2002, and included in the informal preproceedings of the worksho

RepLib: A library for derivable type classes

Some type class instances can be automatically derived from the structure of types. As a result, the Haskell language includes the deriving mechanism to automatic generates such instances for a small number of built-in type classes. In this paper, we present RepLib, a GHC library that enables a similar mechanism for arbitrary type classes. Users of RepLib can define the relationship between the structure of a datatype and the associated instance declaration by a normal Haskell functions that pattern-matches a representation types. Furthermore, operations defined in this manner are extensible-instances for specific types not defined by type structure may also be incorporated. Finally, this library also supports the definition of operations defined by parameterized types

Strategic polymorphism requires just two combinators!

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term rewriting strategies (with coverage of traversal) to the functional programming paradigm. Meanwhile, a number of Haskell-based models and combinator suites were proposed to support generic programming with functional strategies. In the present paper, we provide a compact and matured reconstruction of functional strategies. We capture strategic polymorphism by just two primitive combinators. This is done without commitment to a specific functional language. We analyse the design space for implementational models of functional strategies. For completeness, we also provide an operational reference model for implementing functional strategies (in Haskell). We demonstrate the generality of our approach by reconstructing representative fragments of the Strafunski library for functional strategies

Boxes Go Bananas: Encoding Higher-Order Abstract Syntax With Parametric Polymorphism (Extended Version)

Higher-order abstract syntax is a simple technique for implementing languages with functional programming. Object variables and binders are implemented by variables and binders in the host language. By using this technique, one can avoid implementing common and tricky routines dealing with variables, such as capture-avoiding substitution. However, despite the advantages this technique provides, it is not commonly used because it is difficult to write sound elimination forms (such as folds or catamorphisms) for higher-order abstract syntax. To fold over such a datatype, one must either simultaneously define an inverse operation (which may not exist) or show that all functions embedded in the datatype are parametric. In this paper, we show how first-class polymorphism can be used to guarantee the parametricity of functions embedded in higher-order abstract syntax. With this restriction, we implement a library of iteration operators over data-structures containing functionals. From this implementation, we derive fusion laws that functional programmers may use to reason about the iteration operator. Finally, we show how this use of parametric polymorphism corresponds to the Schürmann, Despeyroux and Pfenning method of enforcing parametricity through modal types. We do so by using this library to give a sound and complete encoding of their calculus into System Fω. This encoding can serve as a starting point for reasoning about higher-order structures in polymorphic languages

Proceedings of the ACM SIGPLAN Workshop on Approaches and Applications of Inductive Programming (AAIP 2009)

Inductive programming is concerned with the automated construction of declarative, often functional, recursive programs from incomplete specifications such as input/output examples. The inferred program must be correct with respect to the provided examples in a generalising sense: it should be neither equivalent to them, nor inconsistent. Inductive programming algorithms are guided explicitly or implicitly by a language bias (the class of programs that can be induced) and a search bias (determining which generalised program is constructed first). Induction strategies are either generate-and-test or example-driven. In generate-and-test approaches, hypotheses about candidate programs are generated independently from the given specifications. Program candidates are tested against the given specification and one or more of the best evaluated candidates are developed further. In analytical approaches, candidate programs are constructed in an example-driven way. While generate-and-test approaches can -- in principle -- construct any kind of program, analytical approaches have a more limited scope. On the other hand, efficiency of induction is much higher in analytical approaches. Inductive programming is still mainly a topic of basic research, exploring how the intellectual ability of humans to infer generalised recursive procedures from incomplete evidence can be captured in the form of synthesis methods. Intended applications are mainly in the domain of programming assistance -- either to relieve professional programmers from routine tasks or to enable non-programmers to some limited form of end-user programming. Furthermore, in the future, inductive programming techniques might be applied to further areas such as supporting the inference of lemmata in theorem proving or learning grammar rules. Inductive automated program construction has been originally addressed by researchers in artificial intelligence and machine learning. During the last years, some work on exploiting induction techniques has been started also in the functional programming community. Therefore, the third workshop on |Approaches and Applications of Inductive Programming| took place for the first time in conjunction with the ACM SIGPLAN International Conference on Functional Programming (ICFP 2009). The first and second workshop were associated with the International Conference on Machine Learning (ICML 2005) and the European Conference on Machine Learning (ECML 2007). AAIP´09 aimed to bring together researchers from the functional programming and the artificial intelligence communities, working in the field of inductive functional programming, and advance fruitful interactions between these communities with respect to programming techniques for inductive programming algorithms, the identification of challenge problems and potential applications. For everybody interested in inductive programming we recommend to visit the website: www.inductive-programming.org

Typed open programming : a higher-order, typed approach to dynamic modularity and distribution

In this dissertation we develop an approach for reconciling open programming the development of programs that support dynamic exchange of higher-order values with other processes with strong static typing in programming languages. We present the design of a concrete programming language, Alice ML, that consists of a conventional functional language extended with a set of orthogonal features like higher-order modules, dynamic type checking, higher-order serialisation, and concurrency. On top of these a flexible system of dynamic components and a simple but expressive notion of distribution is realised. The central concept in this design is the package, a first-class value embedding a module along with its interface type, which is dynamically checked whenever the module is extracted. Furthermore, we develop a formal model for abstract types that is not invalidated by the presence of primitives for dynamic type inspection, as is the case for the standard model based on existential quantification. For that purpose, we present an idealised language in form of an extended -calculus, which can express dynamic generation of types. This calculus is the first to combine and explore the interference of sealing and type inspection with higher-order singleton kinds, a feature for expressing sharing constraints on abstract types. A novel notion of abstracton kinds classifies abstract types. Higher-order type and kind coercions allow for modular translucent encapsulation of values at arbitrary type.In dieser Dissertation entwickeln wir einen programmiersprachlichen Ansatz zur Verbindung offener Programmierung der Entwicklung von Programmen, die das dynamische Laden und Austauschen höherstufiger Werte mit anderen Prozessen erlauben mit starker statischer Typisierung. Wir stellen das Design einer konkreten Programmiersprache namens Alice ML vor. Sie besteht aus einer konventionellen funktionalen Sprache, die um einen Satz orthogonaler Konzepte wie höherstufige Modularisierung, dynamische Typüberprüfung, höherstufige Serialisierung und Nebenläufigkeit erweitert wurde. Darauf aufbauend ist ein flexibles System dynamischer Komponenten sowie ein einfacher aber expressiver Ansatz fur Verteilung verwirklicht. Zentral ist dabei das Konzept eines Pakets (package), welches ein Modul in Kombination mit seinem Schnittstellentyp in einen Wert einbettet, und bei der Extraktion des Moduls eine dynamische Typüberprüfung vornimmt. Weiterhin entwickeln wir einen theoretischen Ansatz zur Modellierung von abstrakten Typen, welcher im Gegensatz zum herkömmlichen formalen Modell existentieller Quantifizierung auch in Gegenwart dynamischer Typinspektion gültig ist. Zu diesem Zweck definieren wir eine idealisierte Sprache in Form eines erweiterten λ-Kalküls, der dynamische Typgenerierung ausdrucken kann. Der Kalkül kombiniert diese erstmals mit höherstufigen Singleton Kinds, einem Sprachkonstrukt, welches Gleichheit von Typen ausdrücken kann. Zur Klassifizierung abstrakter Typen werden Abstraktions-Kinds als verwandtes Konzept entwickelt. Höherstufige Konversionen auf Term- und Typebene erlauben zudem die nachträgliche modulare Enkapsulierung von Werten beliebigen Typs

Higher-Order Intensional Type Analysis

Intensional type analysis provides the ability to analyze abstracted types at run time. In this paper, we extend that ability to higherorder and kind-polymorphic type constructors. The resulting language is elegant and expressive. We show through examples how it extends the repertoire of polytypic denitions and the domain of valid types for those denitions

Higher-Order Intensional Type Analysis in Type-Erasure Semantics

Higher-order intensional type analysis is a way of defining type-indexed operations, such as map, fold and zip, based on run-time type information. However, languages supporting this facility are naturally defined with a type-passing semantics, which su#ers from a number of drawbacks. This paper, describes how to recast higher-order intensional type analysis in a type-erasure semantics. The resulting language is simple and easy to implement---we present a prototype implementation of the necessary machinery as a small Haskell library