Data Types In Computational Phonology

This paper exanfines cer ta in aspects of phonological s t ruc ture from the v iewpoint of ahs t r ac t d a t a types, Our imnled ia te goal is to find a forma t for l)honological representa t ion which will be reasonably f,'fithful to the concerns of theoret i : cal phonology while I)eing rigorous enough to a(Irail a computa t iona l in ter l ) re ta t ion. The longer t e rm goal is to incorpora te such representa t ions i n t o all appropr ia te general framework for llatnral l anguage processing, i 1 I n t r o d u c t i o n One of the dominant paradignls ill cnrrel l | colnputat . ional l inguist ics is l)rovided by unificationbased g r a m m a r formalisms. Such formalisms (of. IShieber 1986; Kasper t~ Rounds 1986)) describe hierarchic~d feature s t l ' t l e t l l r e s , w h i c h iH i n a l l y ways would appear to be an ideal se l l ing [br formal phonological analyses. 1,'eature bundles have long been used l)y phonologists , and more recent work on so-called feature geonletry (e.~. (Clements 1985; Sagey 19,~6)) has in t roduced hierarchy into such represenla t ions . Nevertheless. there are reasons to step back from s tandard feature-based apl~roaches, and instead to adopl the algebraic perspec t ive of abs t rac l data types (AD'P) which has been widely adopted iu coml)uter science. One general mot ivat ion, which we shall not e.xplore here. is thai Ihe ac l iv i ly of gran t lnar wri t ing, viewed as a process of prog r a m m e specification, should be amenable Io sl~pwise refinement in which the set of {sol necessari ly isomorphic) n,odels admi t t ed by a loose IThe work reported in this paper has [)¢:~,1, ~;tl ried ollt its part of the research i)rf)glitli/lll(!S o{ l]l(' ].{llnl&l;[ (~oFiin/llllic&[iOll |lesea.rch (}(:Illl'C. sl/ppOl'led })3 the OK Economic and Social Rescalch (:ouncil aml the project Computational l)houoh)gy: .,I ('onst~aint-fh~s¢d Approach, funded by the IlV. ~qcience and Engineering I(t. search Council, under grant (;R/(;-22081. 1 am glalt'ful to Steven Bird. Kimba Newton and 'l'm/v Simou [m di> cussions relating to this work. AcrEs DE COLING-92, NAtc~S, 23-28 Ao~rr 1992 speci l icat ion is gradual ly narrowed down to a u,fiqtm 'algebra (cf. (Sannel la & Tarleeki 1987) for an overview, and (Newton in prep.) for the apldicat ion to g r ammar writ ing). A second mot ivat ion, discussed in detai l by (Beierle & P le t a t 1988; Beierle K~ P le t a t 1989; Beierle et al. 1988), is to use equat iona l ADTS to provide a ma thema t ical foundation for h~ature s t ructures . A third mot ivat ion, dominan t in this pal)er , is to use the AI)T appl'oach lo provide a richer array of explicit da t a types than are readily admi t t ed by "p'tlre' feature s t ruc ture approaches . Briefly, in their raw form, [eature te rms (i.e., fnrnlalislns for descr ibing h~alure stru(:tures) do not a lways provide a perspicuous format for represent ing strllct II re. On the ADT approach, complex d a t a types are built up from atomic types by means of c o n s t r u c t o r f u n c t i o n s . For example . . . . (where we use the underscore '_' to mark the posit ion of the f imction 's a rguments ) creates e lements of type L i s t . A dala type may also have s e l e c t o r f u n c t i o n s for tak ing data e lements apar t . Thus, selectors for lhe type L±s t are the func tions f i r s t and l a s t . S tandard feature-bossed encoding of l isls uses only selectors for the da ta type; i.e. the feature labels FIRST and LAST ill ( 1 ) FIRST : o" 1 17 LAST : (FIRST : o" 2 17 LAST : nil) t lowever, the list const ructor is left implici t , That is, the feature term encoding tells you how lists are pulled apar t , but does not say how they are built up. When we confine our a t len t ion jus t to lists, lhis is not much to worry about , ltowever, tile s i tuat ion becomes less sat isfactory when we atIelnpI' to encode a larger variety of da t a structures into one and the same feature term; say, for example , s tandard lis(s, associatiw~ lists (i.e. str ings), cons t i tuent s t ruc ture hierarchy, and au tosegmenta l association. In order to dis t inguish axtequately between e lements of such da ta types, we really need to know the logical propert ies of their respective constructors , and this is a w l 1 4 9 PRec. oF COLING-92. NANTES. AUG. 23-28. 1992 ward when the const ructors are not made explicit . For compu ta t iona l phonoloKv, i t is not an unl ikely scenario to be confronted with such a var iety of d a t a s t ructures , since one may well wish to s tudy the complex in terac t ion between, say, non-l inear teml)oral relat ions and prosodic hierarchy. As a vehicle for computa t iona l implementa t ion , the uniformity of s tandard a t t r i b u t e / v a l u e no ta t ion is ex t remely usefld. As a vehicle for theory development , it can be ex t raord inar i ly uuperspicuous. The approach which we present here t rea ts phonological concepts as abs t r ac t d a t a types. A part icular ly convenient development environlnent is provided by the language OBJ (Goguen & Winkler 1988), which is based on order sorted equa, tionaJ logic, and all the examples given below (except where exp lMt ly iudicated to the con t rary) run in the version of OBJ3 released by sltI in 1988. The denota l iona l semant ics of a.n OB.] module is an algehra, while its opera t ional semant ics is based on order sorted rewrit iug. I 1 1.1 and 1.2 give a more deta i led in t roduct ion into the formal framework, while § 2 and 3 i lh ls t ra te the approach with some phonological examples. 1 .1 A b s t r a c t D a t a T y p e s A d a t a type consists of one or more domains of d a t a i tems, of which certaiu e lements are designated as basic, together wi th a set of opera t ious on the domains which suffice to generate al] d a t a i tems in the domains fl'om the I)asic i tems. A d a t a type is a b s t r a c t if it is independenl of any par t icu la r re t ) resentat ional scheme. A fundamen ta l claim of the ADJ group (cf. (Goguen. Tha tche r ,~ Wagner 1976)) and llluch subsequent work (cf. (Ehrig & MMn" 1985)) is t ha t abs t racl d a t a types are ( to be modelled as) algebras: and moreover, t ha t the models of abs t r ac t data types are ilfitial alget)ras. ~ The s i g n a t u r e o fa mauy-sor ted algebra is a l)air = consist ing of a signal are together wi th a set g of equat ions over terms cons t ruc ted from symbols in O and variables of the sorts in S. A m o d e l for a speciIica.tion is ~An initial algebra is characlerized uniquely up to |so morphism as the semantics of a specification: there is a unique homomorphisnl from the initial algebra inlo t'vely algebra of the specification. an algebra over the s igna ture which satisfies all the equat ions £. Ini t ia l algebras play a special role as the semant ics of an algebra. An ini t ia l a lgebra is minimal , in the sense expressed by the principles "no junk ' and 'no confusion' . 'No junk ' means tha t the a lgebra only contains d a t a which are denoted by variable-fl 'ee terms bui l t up from ol)eration symbols in the s ignature . 'No confusion' means tha t two such te rms t and t ~ denote the same object in the a lgebra only if the equation t = F is derivable from the equat ions of the specification. Specifications are wri t ten in a convent |ohM forma t consist ing of a declara t ion of s o r t s , operation symbols (op), and equat ions (oq). Preceding the equat ions we list all the variables ( v a r ) which figure in them. As an i l lus t ra t ion, we give below an OBJ sl)ecification of the d a t a type LIST1. (2) obj LIST1 i s s o r t s Ell L i s t op nil : -> List . op .~ : Eli List -> List . op head : List -> Eli . op tail : List -> List .