This paper gives a comprehensive description of a typed version of the\ud logic known as LPF. This logic is basic to formal specification and verified design in the software development method VDM. If appropriately\ud extended to deal with recursively defined functions, the data types used\ud in VDM, etc., it gives the VDM notation and its associated rules of reasoning. The paper provides an overview of the needed extensions and\ud examines some of them in detail. It is shown how this non-classical logic\ud - and the extensions - can be reconstructed classically by embeddings\ud into classical infinitary logic
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