Refining specifications to logic programs

The refinement calculus provides a framework for the stepwise development of imperative programs from specifications. In this paper we study a refinement calculus for deriving logic programs. Dealing with logic programs rather than imperative programs has the dual advantages that, due to the expressive power of logic programs, the final program is closer to the original specification, and each refinement step can achieve more. Together these reduce the overall number of derivation steps. We present a logic programming language extended with specification constructs (including general predicates, assertions, and types and invariants) to form a wide-spectrum language. General predicates allow non-executable properties to be included in specifications. Assertions, types and invariants make assumptions about the intended inputs of a procedure explicit, and can be used during refinement to optimize the constructed logic program. We provide a semantics for the extended logic programming language and derive a set of refinement laws. Finally we apply these to an example derivation.

Speech disorder in preschool children exposed to Cantonese and English

Speech disorder in monolingual Cantonese- or English-speaking children has been well described in the literature. There appear to be no reports, however, that describe speech-disordered children who have been exposed to both languages. Here we report on the error patterns of two preschool speech-disordered children who were learning two languages. Both children's first language was Cantonese, but they were also exposed to English through the media and child care. Their disorders were of unknown aetiology. The following questions were asked of the data: (a) Do bilingual children, suspected of having speech problems, make errors in Cantonese and English that reflect delay or disorder when compared with normative data on monolingual speech development in each language? (b) How does the children's speech differ from other bilingual children from the same language learning background? (c) Are the children's speech difficulties apparent in both languages? (d) Is the pattern of errors the same in both languages or do language-specific processes operate? The results bear on theories of acquisition, disorder and bilingualism; they also have clinical implications for speech-language pathologists whose caseloads include bilingual preschool children.