We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science --- LICS'96 (E. Clarke editor), pp. 264--275, New Brunswick, NJ, July 27--30 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of Mini-ML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cut-elimination. 1 Introduction A logical framework is a formal system desig...

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Refinement is a mathematically-based technique for developing a program from an abstract specification so that the program satisfies the specification. The aim of the Program Refinement Tool project is to develop a generic refinement tool suitable for supporting a methodology for the interactive development of programs based on the refinement calculus. This report summarizes our investigation into an appropriate engine to use for the refinement calculator and theorem prover in this tool. Contents 1 Introduction 2 2 Refinement Engine 3 2.1 Structure of Refinement Rules : : : : : : : : : : : : : : : : : : 3 2.2 Applicability Conditions : : : : : : : : : : : : : : : : : : : : : 5 2.3 Parameters : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.4 Monotonicity : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.5 Proving Refinement Rules : : : : : : : : : : : : : : : : : : : : 8 2.6 Schematic Developments : : : : : : : : : : : : : : : : : : : : : 8 2.7 Customizing t...