Parametric Types for Typed Attribute-Value Logic

Parametric polymorphism has been combined with inclusional polymorphism to provide natural type systems for Prolog (DH88), HiLog (YFS92), and cofistraint resolution languages (Smo89), and, in linguistics, by HPSG-tike grammars to classify lists and sets of linguistic objects (PS94), and by phonologists in representations of hierarchical structure (Kle91). This paper summarizes the incorporation of parametric types into the typed attribute-value logic of (Car92), thus providing a natural extension to the type system for ALE (CP96). Following (Car92), the concern here is not with models of feature terms themselves, but with how to compute with parametric types, and what different kinds of information one can represent relative to a signature with parametric types, than relative to a signature without them. This enquiry has yielded a more flexible interpretation of parametric types with several specific properties necessary to conform to their current usage by linguists and implementors who work with feature-based formalisms. 1 M o t i v a t i o n Linguists who avail themselves of attributevalue logic normally choose whether to encode information with subtypes or features on the aesthetic basis of what seems intuitively to capture their generalizations better. Linguists working in LFG typically use one implicit type for objects that bear features, and other types (atoms) for only featureless objects. In HPSG, the si tuation is less clear, both historically (semantic relations, for example, used to be values of a RELN attribute, and are now subtypes of a more general semantic type), and synchronically (verbs, for example, are identified as (un)inverted and (non-)auxiliaries by two boolean-valued features, AUX and INV, whereas their form, e.g., finite, infinitive, gerund, is identified by a subtype of a single vform type). That it makes, or at least should make, no difference from a formal or implementational point of view which encoding is used has been argued elsewhere (Mos96; Pen-f). HPSG's type system also includes parametric types, e.g., Figure 1, from (PS94). In contrast word 7)hrase ~list ~,nelist(X)~ r \ fl I / HEAD:J21 ~ / _ L¢~_. TAIL: l i s t ( X ) si j t X an t i s [ ) . . .