James McKinna

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Pattern matching has proved an extremely powerful and durable notion in functional programming. This paper contributes a new programming notation for type theory which elaborates the notion in various ways. First, as is by now quite well-known in the type theory community, definition by pattern matching becomes a more discriminating tool in the presence of(More)
We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified proof of standardization for beta reduction that does not mention redex positions or residuals. Then we outline the meta theory of Pure(More)
This paper gives a reduction-preserving translation from Coquand’s dependent pattern matching [4] into a traditional type theory [11] with universes, inductive types and relations and the axiom K [22]. This translation serves as a proof of termination for structurally recursive pattern matching programs, provides an implementable compilation technique in(More)
Language designers have in recent years proposed a wealth of richer type systems for programming which seek to extend the range of statically enforced guarantees on data and code. Most such proposals have been evolutionary extensions of ML or Haskell, offering programmers a balanced compromise between expressive strength and existing well-understood(More)
This paper is about our hobby. For us, machine-checked mathematics is a passion, and constructive type theory (in the broadest sense) is the way to this objective. Efficient and correct type-checking programs are necessary, so a formal theory of type systems leading to verified type synthesis algorithms is a natural goal. For over a year the second author(More)
PURPOSE To subjectively and semiquantitatively evaluate color Doppler signals on images of breast lesions. MATERIALS AND METHODS A 5-MHz ultrasound (US) system was used to examine 210 new breast lesions. Signals were evaluated subjectively with an analog scale. A semiquantitative scoring system involved analysis of the average number of vessels per square(More)
Epidemiological and experimental evidence indicates that oestrogens are involved in the carcinogenic promotion of human breast cancer. We have undertaken a pilot trial of tamoxifen, an anti-oestrogen, compared to placebo given to 200 women at a high risk of developing breast cancer. The results of this trial show that acute toxicity is low and that accrual(More)