This chapter, describes GTC, an alternative approach to the use of type classes that avoids the problems associated with context reduction, while retaining much of the flexibility of HTC. In addition, GTC benefits from a remarkably clean and efficient implementation that does not require sophisticated compile-time analysis or transformation. As in the previous chapter we concentrate more on implementation details than on formal properties of GTC.

An early description of GTC was distributed to the Haskell mailing list in February 1991 and subsequently used as a basis for Gofer, a small experimental system based on Haskell and described in (Jones, 1991c). The two languages are indeed very close, and many programs that are written with one system in mind can be used with the other with little or no changes. On the other hand, the underlying type systems are slightly different: Using explicit type signature declarations it is possible to construct examples that are well typed in one but not in the other.

Section 8.1 describes the basic principles of GTC and its relationship to HTC. The only significant differences between the two systems are in the methods used to simplify the context part of an inferred type. While HTC relies on the use of context reduction, GTC adopts a weaker form of simplification that does not make use of the information provided in instance declarations.

Section 8.2 describes the implementation of dictionaries used in the current version of Gofer. As an alternative to the treatment of dictionaries as tuples of values in the previous chapter, we give a representation which guarantees that the translation of each member function definition requires at most one dictionary parameter.

The principal aim of this chapter is to show how the concept of evidence can be used to give a semantics for OML programs with implicit overloading.

Outline of chapter

We begin by describing a version of the polymorphic λ-calculus called OP that includes the constructs for evidence application and abstraction described in the previous chapter (Section 5.1). One of the main uses of OP is as the target of a translation from OML with the semantics of each OML term being defined by those of its translation. In Section 5.2 we show how the OML typing derivations for a term E can be interpreted as OP derivations for terms with explicit overloading, each of which is a potential translation for E. It is immediate from this construction that every well-typed OML term has a translation and that all translations obtained in this way are well-typed in OP.

Given that each OML typing typically has many distinct derivations it follows that there will also be many distinct translations for a given term and it is not clear which should be chosen to represent the original term. The OP term corresponding to the derivation produced by the type inference algorithm in Section 3.4 gives one possible choice but it seems rather unnatural to base a definition of semantics on any particular type inference algorithm. A better approach is to show that any two translations of a term are semantically equivalent so that an implementation is free to use whichever translation is more convenient in a particular situation while retaining the same, well-defined semantics.

This chapter expands on the implementation of type classes in Haskell using dictionary values as proposed by Wadler and Blott (1989) and sketched in Section 4.5. For brevity, we refer to this approach to the use of type classes as HTC. The main emphasis in this chapter is on concrete implementation and we adopt a less rigourous approach to formal properties of HTC than in previous chapters. In particular, we describe a number of optimisations that are necessary to obtain an efficient implementation of HTC - i.e. to minimise the cost of overloading. We do not consider the more general problems associated with the efficient implementation of non-strict functional languages like Haskell which are beyond the scope of this thesis.

Section 7.1 describes an important aspect of the system of type classes in Haskell which means that only a particularly simple form of predicate expression can be used in the type signature of an overloaded function. The set of predicates in a Haskell type signature is usually referred to as the context and hence we will use the term context reduction to describe the process of reducing the context to an acceptable form. Context reduction usually results in a small context, acts as a partial check of satisfiability and helps to guarantee decidability of predicate entailment. Unfortunately, it can also interfere with the use of data abstraction and limits the possibilities for extending the Haskell system of type classes.

The main ideas used in the implementation of HTC are described in Section 7.2 including the treatment of default definitions which were omitted from our previous descriptions.

In this thesis we have developed a general formulation of overloading based on the use of qualified types. Applications of qualified types can be described by choosing an appropriate system of predicates and we have illustrated this with particular examples including Haskell type classes, explicit subtyping and extensible records. We have shown how these ideas can be extended to construct a system that combines ML-style polymorphism and overloading in an implicitly typed programming language. Using the concept of evidence we have extended this work to describe the semantics of overloading in this language, establishing sufficient conditions to guarantee that the meaning of a given term is well-defined. Finally, we have described techniques that can be used to obtain efficient concrete implementations of systems based on this framework.

From a theoretical perspective, some of the main contributions of this thesis are:

• The formulation of a general purpose system that can be used to describe a number of different applications of overloading.

• The extension of standard results, for example the existence of principal types, to the type system of OML.

• A new approach to the proof of coherence, based on the use of conversions.

From a practical perspective, we mention:

• The implementation of overloading using the template-based approach, and the closely related implementation of type class overloading in Gofer.

• A new implementation for extensible records, based on the use of evidence.

• The use of information about satisfiability of predicate sets to obtain more informative inferred types.

The key feature of a system of qualified types that distinguishes it from other systems based solely on parametric polymorphism is the use of a language of predicates to describe sets of types (or more generally, relations between types). Exactly which sets of types and relations are useful will (of course) vary from one application to another and it does not seem appropriate to base a general theory on any particular choice. Our solution, outlined in this chapter, is to work in a framework where the properties of a (largely unspecified) language of predicates are described in terms of an entailment relation that is expected to satisfy a few simple laws. In this way, we are able to treat the choice of a language of predicates as a parameter for each of the type systems described in subsequent chapters. This approach also has the advantage that it enables us to investigate how the properties of particular type systems are affected by properties of the underlying systems of predicates.

The basic notation for predicates and entailment is outlined in Section 2.1. The remaining sections illustrate this general framework with applications to: Haskell-style type classes (Section 2.2), subtyping (Section 2.3) and extensible records (Section 2.4). Although we consider each of these examples independently, this work opens up the possibility of combining elements of each in a single concrete programming language.

Basic definitions

For much of this thesis we deal with an abstract language of predicates on types.

Type systems for programming languages

Many programming languages rely on the use of a system of types to distinguish between different kinds of value. This in turn is used to identify two classes of program; those which are well-typed and accepted by the type system, and those that it rejects. Many different kinds of type system have been considered but, in each case, the principal benefits are the same:

• The ability to detect program errors at compile time: A type discipline can often help to detect simple program errors such as passing an inappropriate number of parameters to a function.

• Improved performance: If, by means of the type system, it is possible to ensure that the result of a particular calculation will always be of a certain type, then it is possible to omit the corresponding runtime checks that would otherwise be needed before using that value. The resulting program will typically be slightly shorter and faster.

• Documentation: The types of the values defined in a program are often useful as a simple form of documentation. Indeed, in some situations, just knowing the type of an object can be enough to deduce properties about its behaviour (Wadler, 1989).

The main disadvantage is that no effective type system is complete; there will always be programs that are rejected by the type system, even though they would have produced welldefined results if executed without consideration of the types of the terms involved.

Introduction

The lexicon has come to occupy an increasingly central place in a variety of current linguistic theories, and it is equally important to work in natural language processing. The lexicon – the repository of information about words – has often proved to be a bottleneck in the design of large-scale natural language systems, given the tremendous number of words in the English language, coupled with the constant coinage of new words and shifts in the meanings of existing words. For this reason, there has been growing interest recently in building large-scale lexical knowledge bases automatically, or even semi-automatically, taking various on-line resources such as machine readable dictionaries (MRDs) and text corpora as a starting point, for instance, see the papers in Boguraev and Briscoe (1989) and Zernik (1989a). This chapter looks at the task of creating a lexicon from a different perspective, reviewing some of the advances in the understanding of the organization of the lexicon that have emerged from recent work in linguistics and sketching how the results of this work may be used in the design and creation of large-scale lexical knowledge bases that can serve a variety of needs, including those of natural language front ends, machine translation, speech recognition and synthesis, and lexicographers' and translators' workstations.

Although in principle on-line resources such as MRDs and text corpora would seem to provide a wealth of valuable linguistic information that could serve as a foundation for developing a lexical knowledge base, in practice it is often difficult to take full advantage of the information these existing resources contain.

Introduction

This chapter presents an operational definition of computational lexicography, which is emerging as a discipline in its own right. In the context of one of its primary goals – facilitation of (semi-)automatic construction of lexical knowledge bases (aka computational lexicons) by extracting lexical data from on-line dictionaries – the concerns of dictionary analysis are related to those of lexical semantics. The chapter argues for a particular paradigm of lexicon construction, which relies crucially on having flexible access to fine-grained structural analyses of multiple dictionary sources. To this end, several related issues in computational lexicography are discussed in some detail.

In particular, the notion of structured dictionary representation is exemplified by looking at the wide range of functions encoded, both explicitly and implicitly, in the notations for dictionary entries. This allows the formulation of a framework for exploiting the lexical content of dictionary structure, in part encoded configurationally, for the purpose of streamlining the process of lexical acquisition.

A methodology for populating a lexical knowledge base with knowledge derived from existing lexical resources should not be in isolation from a theory of lexical semantics. Rather than promote any particular theory, however, we argue that without a theoretical framework the traditional methods of computational lexicography can hardly go further than highlighting the inadequacies of current dictionaries. We further argue that by reference to a theory that assumes a formal and rich model of the lexicon, dictionaries can be made to reveal – through guided analysis of highly structured isomorphs – a number of lexical semantic relations of relevance to natural language processing, which are only encoded implicitly and are distributed across the entire source.

Introduction

One of the major resources in the task of building a large-scale lexicon for a natural-language system is the machine-readable dictionary. Serious flaws (for the user-computer) have already been documented in dictionaries being used as machine-readable dictionaries in natural language processing, including a lack of systematicity in the lexicographers' treatment of linguistic facts; recurrent omission of explicit statements of essential facts; and variations in lexicographical decisions which, together with ambiguities within entries, militate against successful mapping of one dictionary onto another and hence against optimal extraction of linguistic facts.

Large-scale electronic corpora now allow us to evaluate a dictionary entry realistically by comparing it with evidence of how the word is used in the real world. For various lexical items, an attempt is made to compare the view of word meaning that a corpus offers with the way in which this is presented in the definitions of five dictionaries at present available in machine-readable form and being used in natural language processing (NLP) research; corpus evidence is shown to support apparently incompatible semantic descriptions. Suggestions are offered for the construction of a lexical database entry to facilitate the mapping of such apparently incompatible dictionary entries and the consequent maximization of useful facts extracted from these.

How ‘reliable’ are dictionary definitions?

Writing a dictionary is a salutary and humbling experience. It makes you very aware of the extent of your ignorance in almost every field of human experience.

Introduction

The structural units of phrasal intonation are frequently orthogonal to the syntactic constituent boundaries that are recognized by traditional grammar and embodied in most current theories of syntax. As a result, much recent work on the relation of intonation to discourse context and information structure has either eschewed syntax entirely (cf. Bolinger, 1972; Cutler and Isard, 1980; Gussenhoven, 1983; Brown and Yule, 1983), or has supplemented traditional syntax with entirely nonsyntactic string-related principles (cf. Cooper and Paccia-Cooper, 1980). Recently, Selkirk (1984) and others have postulated an autonomous level of “intonational structure” for spoken language, distinct from syntactic structure. Structures at this level are plausibly claimed to be related to discourse-related notions, such as “focus”. However, the involvement of two apparently uncoupled levels of structure in Natural Language grammar appears to complicate the path from speech to interpretation unreasonably, and thereby to threaten the feasibility of computational speech recognition and speech synthesis.

In Steedman (1991a), I argue that the notion of intonational structure formalized by Pierrehumbert, Selkirk, and others, can be subsumed under a rather different notion of syntactic surface structure, which emerges from the “Combinatory Categorial” theory of grammar (Steedman, 1987, 1990). This theory engenders surface structure constituents corresponding directly to phonological phrase structure. Moreover, the grammar assigns to these constituents interpretations that directly correspond to what is here called “information structure” – that is, the aspects of discourse-meaning that have variously been termed “topic” and “comment”, “theme” and “rheme”, “given” and “new” information, and/or “presupposition” and “focus”.