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    Automating Recursive Type Definitions in Higher Order Logic

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    Identification of Streptococcus pneumoniae by a real-time PCR assay targeting SP2020.

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    Real-time PCR targeting lytA (the major autolysin gene) and piaB (permease gene of the pia ABC transporter) are currently used as the gold-standard culture-independent assays for Streptococcus pneumoniae identification. We evaluated the performance of a new real-time PCR assay - targeting SP2020 (putative transcriptional regulator gene) - and compared its performance with the assays previously described. A collection of 150 pneumococci, 433 non-pneumococci and 240 polymicrobial samples (obtained from nasopharynx, oropharynx, and saliva; 80 from each site) was tested. SP2020 and lytA-CDC assays had the best performance (sensitivity of 100% for each compared to 95.3% for piaB). The specificity for lytA and piaB was 99.5% and for SP2020 was 99.8%. Misidentifications occurred for the three genes: lytA, piaB and SP2020 were found in non-pneumococcal strains; piaB was absent in some pneumococci including a serotype 6B strain. Combining lytA and SP2020 assays resulted in no misidentifications. Most polymicrobial samples (88.8%) yielded concordant results for the three molecular targets. The remaining samples seemed to contain non-typeable pneumococci (0.8%), and non-pneumococci positive for lytA (1.7%) or SP2020 (8.7%). We propose that combined detection of both lytA-CDC and SP2020 is a powerful strategy for the identification of pneumococcus either in pure cultures or in polymicrobial samples

    Automating Recursive Type Definitions in Higher Order Logic

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    : The expressive power of higher order logic makes it possible to define a wide variety of types within the logic and to prove theorems that state the properties of these types concisely and abstractly. This paper contains a tutorial introduction to the logical basis for such type definitions. Examples are given of the formal definitions in logic of several simple types. A method is then described for systematically defining any instance of a certain class of commonly-used recursive types. The automation of this method in HOL, an interactive system for generating proofs in higher order logic, is also discussed. 1 To appear in Current Trends in Hardware Verification and Automated Theorem Proving, proceedings of the 1988 Banff Workshop on Hardware Verification, edited by G. Birtwistle and P. Subrahmanyam (Springer-Verlag, 1988). Revised 28 January Contents Introduction 5 1 Introduction to Higher Order Logic 6 1.1 Notation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ..
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