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

Bidirectionalization for Free with Runtime Recording: Or, a Light-Weight Approach to the View-Update Problem

A bidirectional transformation is a pair of mappings between source and view data objects, one in each direction. When the view is modified, the source is updated accordingly with respect to some laws. Over the years, a lot of effort has been made to offer better language support for programming such transformations. In particular, a technique known as bidirectionalization is able to analyze and transform unidirectional programs written in general purpose languages, and "bidirectionalize" them. Among others, a technique termed as semantic bidirectionalization proposed by Voigtländer stands out in term of user-friendliness. The unidirectional program can be written using arbitrary language constructs, as long as the function is polymorphic and the language constructs respect parametricity. The free theorems that follow from the polymorphic type of the program allow a kind of forensic examination of the transformation, determining its effect without examining its implementation. This is convenient, in the sense that the programmer is not restricted to using a particular syntax; but it does require the transformation to be polymorphic. In this paper, we lift this polymorphism requirement to improve the applicability of semantic bidirectionalization. Concretely, we provide a type class PackM γ α μ, which intuitively reads "a concrete datatype γ is abstracted to a type α, and the 'observations' made by a transformation on values of type γ are recorded by a monad μ". With PackM, we turn monomorphic transformations into polymorphic ones, that are ready to be bidirectionalized. We demonstrate our technique with a case study of standard XML queries, which were considered beyond semantic bidirectionalization because of their monomorphic nature

Static and dynamic semantics of NoSQL languages

We present a calculus for processing semistructured data that spans differences of application area among several novel query languages, broadly categorized as "NoSQL". This calculus lets users define their own operators, capturing a wider range of data processing capabilities, whilst providing a typing precision so far typical only of primitive hard-coded operators. The type inference algorithm is based on semantic type checking, resulting in type information that is both precise, and flexible enough to handle structured and semistructured data. We illustrate the use of this calculus by encoding a large fragment of Jaql, including operations and iterators over JSON, embedded SQL expressions, and co-grouping, and show how the encoding directly yields a typing discipline for Jaql as it is, namely without the addition of any type definition or type annotation in the code

Programming with heterogeneous structures: Manipulating XML data using bondi

Manipulating semistructured data, such as XML, does not fit well within conventional programming languages. A typical manipulation requires finding all occurrences of a structure matching a structured search pattern, whose context may be different in different places, and both aspects cause difficulty. If a special-purpose query language is used to manipulate XML, an interface to a more general programming environment is required, and this interface typically creates runtime overhead for type conversion. However, adding XML manipulation to a general-purpose programming language has proven difficult because of problems associated with expressiveness and typing. We show an alternative approach that handles many kinds of patterns within an existing strongly-typed general-purpose programming language called bondi. The key ideas are to express complex search patterns as structures of simple patterns, pass these complex patterns as parameters to generic data-processing functions and traverse heterogeneous data structures by a generalized form of pattern matching. These ideas are made possible by the language's support for pattern calculus, whose typing on structures and patterns enables path and pattern polymorphism. With this approach, adding a new kind of pattern is just a matter of programming, not language design. Copyright © 2006, Australian Computer Society, Inc

A Logical Approach To Deciding Semantic Subtyping

International audienceWe consider a type algebra equipped with recursive, product, function, intersection, union, and complement types together with type variables and implicit universal quantification over them. We consider the subtyping relation recently defined by Castagna and Xu over such type expressions and show how this relation can be decided in EXPTIME, answering an open question. The novelty, originality and strength of our solution reside in introducing a logical modeling for the semantic subtyping framework. We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system. This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful in the context of XML

Fling - A Fluent API Generator

We present the first general and practical solution of the fluent API problem - an algorithm, that given a deterministic language (equivalently, LR(k), k >= 0 language) encodes it in an unbounded parametric polymorphism type system employing only a polynomial number of types. The theoretical result is accompanied by an actual tool Fling - a fluent API compiler-compiler in the venue of YACC, tailored for embedding DSLs in Java