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This paper gives a reduction-preserving translation from Co-quand'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 recur-sive pattern matching programs, provides an implementable compilation technique in(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, simpliied, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure(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)
A retrospective study of 33 patients with cystosarcoma phyllodes was done. Eight of these patients had metastases, and the clinical and histologic criteria predicting the development of metastases were examined. The most reliable predictor was the presence of stromal overgrowth; this appears to be necessary for metastasis to occur. Other useful indicators(More)
84 patients with large operable breast cancer have been treated with primary medical chemotherapy rather than mastectomy in three sequential studies. 86% had tumours greater than 4 cm in diameter; median diameter was 6 cm (range 1-12). Median age was 46 years (range 23-66). In the first two studies 64 patients were treated with either CMF [cyclophosphamide(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)
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)