We propose regular expression types as a foundation for statically typed XML processing languages. Regular expression types, like most schema languages for XML, introduce regular expression notations such as repetition (*), alternation (|), etc., to describe XML documents. The novelty of our type system is a semantic presentation of subtyping, as inclusion between the sets of documents denoted by two types. We give several examples illustrating the usefulness of this form of subtyping in XML processing. The decision problem for the subtype relation reduces to the inclusion problem between tree automata, which is known to be exptime-complete. To avoid this high complexity in typical cases, we develop a practical algorithm that, unlike classical algorithms based on determinization of tree automata, checks the inclusion relation by a top-down traversal of the original type expressions. The main advantage of this algorithm is that it can exploit the property that type expressions being compared often share portions of their representations. Our algorithm is a variant of Aiken and Murphy’s set-inclusion constraint solver, to which are added several new implementation techniques, correctness proofs, and preliminary performance measurements on some small programs in the domain of typed XML processing.

Generalized algebraic data types (GADTs), sometimes known as “guarded recursive data types ” or “first-class phantom types”, are a simple but powerful generalization of the data types of Haskell and ML. Recent works have given compelling examples of the utility of GADTs, although type inference is known to be difficult. Our contribution is to show how to exploit programmer-supplied type annotations to make the type inference task almost embarrassingly easy. Our main technical innovation is wobbly types, which express in a declarative way the uncertainty caused by the incremental nature of typical type-inference algorithms.

This paper describes a new approach to generic functional programming, which allows us to define functions generically for all datatypes expressible in Haskell. A generic function is one that is defined by induction on the structure of types. Typical examples include pretty printers, parsers, and comparison functions. The advanced type system of Haskell presents a real challenge: datatypes may be parameterized not only by types but also by type constructors, type definitions may involve mutual recursion, and recursive calls of type constructors can be arbitrarily nested. We show that--- despite this complexity---a generic function is uniquely defined by giving cases for primitive types and type constructors (such as disjoint unions and cartesian products). Given this information a generic function can be specialized to arbitrary Haskell datatypes. The key idea of the approach is to model types by terms of the simply typed -calculus augmented by a family of recursion operators. While co...

Abstract. Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes describe the basic constructs of Generic Haskell and highlight the underlying theory. Generic programming aims at making programming more effective by making it more general. Generic programs often embody non-traditional kinds of polymorphism. Generic Haskell is an extension of Haskell [38] that supports the construction of generic programs. Generic Haskell adds to Haskell the notion of structural polymorphism, the ability to define a function (or a type) by induction on the structure of types. Such a function is generic in the sense that it works not only for a specific type but for a whole class of types. Typical examples include equality, parsing and pretty printing, serialising, ordering, hashing, and so on. The lecture notes on Generic Haskell are organized into two parts. This first part motivates the need for genericity, describes the basic constructs of Generic Haskell, puts Generic Haskell into perspective, and highlights the underlying theory. The second part entitled “Generic Haskell: applications ” delves deeper into the language discussing three non-trivial applications of Generic Haskell: generic dictionaries, compressing XML documents, and a generic version of the zipper data type. The first part is organized as follows. Section 1 provides some background discussing type systems in general and the type system of Haskell in particular. Furthermore, it motivates the basic constructs of Generic Haskell. Section 2 takes a closer look at generic definitions and shows how to define some popular generic functions. Section 3 highlights the theory underlying Generic Haskell and discusses its implementation. Section 4 concludes. 1

Research in dependent type theories [M-L71a] has, in the past, concentrated on its use in the presentation of theorems and theorem-proving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs may readily be specified and established. In particular, it develops technology for programming with dependent inductive families of datatypes and proving those programs correct. It demonstrates the considerable advantage to be gained by indexing data structures with pertinent characteristic information whose soundness is ensured by typechecking, rather than human effort. Type theory traditionally presents safe and terminating computation on inductive datatypes by means of elimination rules which serve as induction principles and, via their associated reduction behaviour, recursion operators [Dyb91]. In the programming language arena, these appear somewhat cumbersome and give rise to unappealing code, complicated by the inevitable interaction between case analysis on dependent types and equational reasoning on their indices which must appear explicitly in the terms. Thierry Coquand’s proposal [Coq92] to equip type theory directly with the kind of

this paper into several sections. As an overview, in Section 2, I try and classify meta-programs into groups. The purpose of this is to provide a common vocabulary which we can use to describe meta-programming systems in the rest of the paper

We develop an explicit two level system that allows programmers to reason about the behavior of effectful programs. The first level is an ordinary ML-style type system, which confers standard properties on program behavior. The second level is a conservative extension of the first that uses a logic of type refinements to check more precise properties of program behavior. Our logic is a fragment of intuitionistic linear logic, which gives programmers the ability to reason locally about changes of program state. We provide a generic resource semantics for our logic as well as a sound, decidable, syntactic refinement-checking system. We also prove that refinements give rise to an optimization principle for programs. Finally, we illustrate the power of our system through a number of examples.

Grammatical Framework (GF) is a special-purpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate run-time errors in language processing. In the same way as an LF, GF uses...

Abstract. We present the Mobile Resource Guarantees framework: a system for ensuring that downloaded programs are free from run-time violations of resource bounds. Certificates are attached to code in the form of efficiently checkable proofs of resource bounds; in contrast to cryptographic certificates of code origin, these are independent of trust networks. A novel programming language with resource constraints encoded in function types is used to streamline the generation of proofs of resource usage. 1

Abstract We show how higher kinded generic programming can be represented faithfully within a dependently typed programming system. This development has been implemented using the Oleg system. The present work can be seen as evidence for our thesis that extensions of type systems can be done by programming within a dependently typed language, using data as codes for types. 1.