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Reasoning About Functional Programs in Nuprl
 In Functional Programming, Concurrency, Simulation and Automated Reasoning
, 1993
"... . There are two ways of reasoning about functional programs in the constructive type theory of the Nuprl proof development system. Nuprl can be used in a conventional programverification mode, in which functional programs are written in a familiar style and then proven to be correct. It can als ..."
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. There are two ways of reasoning about functional programs in the constructive type theory of the Nuprl proof development system. Nuprl can be used in a conventional programverification mode, in which functional programs are written in a familiar style and then proven to be correct. It can also be used in an extraction mode, where programs are not written explicitly, but instead are extracted from mathematical proofs. Nuprl is the only constructive type theory to support both of these approaches. These approaches are illustrated by applying Nuprl to Boyer and Moore's "majority" algorithm. 1 Introduction A type system for a functional programming language can be syntactic or semantic. In a syntactically typed language, such as SML 1 [25], typing is a property of the syntax of expressions. Only certain combinations of language constructs are designated "welltyped", and only welltyped expressions are given a meaning. Each welltyped expression has a type which can be derive...
A Theory and its Metatheory in FS 0
"... . Feferman has proposed FS 0 , a theory of finitary inductive systems, as a framework theory that allows a user to reason both in and about an encoded theory. I look here at how practical FS 0 really is. To this end I formalise a sequent calculus presentation of classical propositional logic, and sh ..."
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. Feferman has proposed FS 0 , a theory of finitary inductive systems, as a framework theory that allows a user to reason both in and about an encoded theory. I look here at how practical FS 0 really is. To this end I formalise a sequent calculus presentation of classical propositional logic, and show this can be used for work in both the theory and the metatheory. the latter is illustrated with a discussion of a proof of Gentzen's Hauptsatz. Contents x 1 Introduction 2 x 1.1 Background : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 x 1.2 Outline of paper : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 x 2 The theory FS 0 and notational conventions 4 x 2.1 What is FS 0 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 x 3 An informal description of Gentzen's calculus 5 x 3.1 The language : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 x 3.2 The calculus for classical propositional logic : : : : : : : : : : : : 6 x 4 Formalising the ...