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

Typed Generic Traversal With Term Rewriting Strategies

A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S'_{gamma}. The calculus employs a many-sorted type system extended by designated generic strategy types gamma. We consider two generic strategy types, namely the types of type-preserving and type-unifying strategies. S'_{gamma} offers traversal combinators to construct traversals or schemes thereof from many-sorted and generic strategies. The traversal combinators model different forms of one-step traversal, that is, they process the immediate subterms of a given term without anticipating any scheme of recursion into terms. To inhabit generic types, we need to add a fundamental combinator to lift a many-sorted strategy $s$ to a generic type gamma. This step is called strategy extension. The semantics of the corresponding combinator states that s is only applied if the type of the term at hand fits, otherwise the extended strategy fails. This approach dictates that the semantics of strategy application must be type-dependent to a certain extent. Typed strategic term rewriting with coverage of generic term traversal is a simple but expressive model of generic programming. It has applications in program transformation and program analysis.Comment: 85 pages, submitted for publication to the Journal of Logic and Algebraic Programmin

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

Transformation of structure-shy programs : applied to XPath queries and strategic functions

Various programming languages allow the construction of structure-shy programs. Such programs are defined generically for many different datatypes and only specify specific behavior for a few relevant subtypes. Typical examples are XML query languages that allow selection of subdocuments without exhaustively specifying intermediate element tags. Other examples are languages and libraries for polytypic or strategic functional programming and for adaptive object-oriented programming. In this paper, we present an algebraic approach to transformation of declarative structure-shy programs, in particular for strategic functions and XML queries. 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. We show how subsets of these laws can be used to construct effective rewrite systems for specialization, generalization, and optimization of structure-shy programs. We present a type-safe encoding of these rewrite systems in Haskell which itself uses strategic functional programming techniques.(undefined

Rascal: From Algebraic Specification to Meta-Programming

Algebraic specification has a long tradition in bridging the gap between specification and programming by making specifications executable. Building on extensive experience in designing, implementing and using specification formalisms that are based on algebraic specification and term rewriting (namely Asf and Asf+Sdf), we are now focusing on using the best concepts from algebraic specification and integrating these into a new programming language: Rascal. This language is easy to learn by non-experts but is also scalable to very large meta-programming applications. We explain the algebraic roots of Rascal and its main application areas: software analysis, software transformation, and design and implementation of domain-specific languages. Some example applications in the domain of Model-Driven Engineering (MDE) are described to illustrate this.Comment: In Proceedings AMMSE 2011, arXiv:1106.596

Scrap your boilerplate with object algebras

htmlabstractTraversing complex Abstract Syntax Trees (ASTs) typically requires large amounts of tedious boilerplate code. For many operations most of the code simply walks the structure, and only a small portion of the code implements the functional- ity that motivated the traversal in the first place. This paper presents a type-safe Java framework called Shy that removes much of this boilerplate code. In Shy Object Algebras are used to describe complex and extensible AST structures. Using Java annotations Shy generates generic boilerplate code for various types of traversals. For a concrete traversal, users of Shy can then inherit from the generated code and over- ride only the interesting cases. Consequently, the amount of code that users need to write is significantly smaller. Moreover, traversals using the Shy framework are also much more structure shy, becoming more adaptive to future changes or extensions to the AST structure. To prove the effectiveness of the approach, we applied Shy in the implementation of a domain-specific questionnaire language. Our results show that for a large number of traversals there was a significant reduction in the amount of user-defined code

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

Various programming languages allow the construction of structure-shy programs. Such programs are defined generically for many different datatypes and only specify specific behavior for a few relevant subtypes. Typical examples are XML query languages that allow selection of subdocuments without exhaustively specifying intermediate element tags. Other examples are languages and libraries for polytypic or strategic functional programming and for adaptive object-oriented programming. In this paper, we present an algebraic approach to transformation of declarative structure-shy programs, in particular for strategic functions and XML queries. 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. We show how subsets of these laws can be used to construct effective rewrite systems for specialization, generalization, and optimization of structure-shy programs. We present a type-safe encoding of these rewrite systems in Haskell which itself uses strategic functional programming techniques. We discuss the application of these rewrite systems for XPath query optimization and for query migration in the context of schema evolution

Variable elimination for building interpreters

In this paper, we build an interpreter by reusing host language functions instead of recoding mechanisms of function application that are already available in the host language (the language which is used to build the interpreter). In order to transform user-defined functions into host language functions we use combinatory logic : lambda-abstractions are transformed into a composition of combinators. We provide a mechanically checked proof that this step is correct for the call-by-value strategy with imperative features.Comment: 33 page

Programming errors in traversal programs over structured data

Traversal strategies \'a la Stratego (also \'a la Strafunski and 'Scrap Your Boilerplate') provide an exceptionally versatile and uniform means of querying and transforming deeply nested and heterogeneously structured data including terms in functional programming and rewriting, objects in OO programming, and XML documents in XML programming. However, the resulting traversal programs are prone to programming errors. We are specifically concerned with errors that go beyond conservative type errors; examples we examine include divergent traversals, prematurely terminated traversals, and traversals with dead code. Based on an inventory of possible programming errors we explore options of static typing and static analysis so that some categories of errors can be avoided. This exploration generates suggestions for improvements to strategy libraries as well as their underlying programming languages. Haskell is used for illustrations and specifications with sufficient explanations to make the presentation comprehensible to the non-specialist. The overall ideas are language-agnostic and they are summarized accordingly