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The Lambda Calculus. Its Syntax and Semantics Henk Barendregt
Publisher: College Publications

May 1, 2013 - But if your interest is more in programming languages than proof assistants, then length-indexed vectors is your Hello, World! The main idea behind these convolutions was to produce a . The λ calculus has exactly three kinds of expressions: Function definition: a function in λ calculus is an expression, written: λ param . We also give a declarative account of what it Putting it all together: semantics of STLC. But from the point of view of the poor soul who has to do any downstream processing, de Bruijn actually looks like a splendid idea, so we would prefer that. Dec 1, 2008 - One of the primary motivations behind SASyLF was to produce a tool which was easier to learn, had a higher level syntax (easier to read) and which gave more helpful error messages than Twelf. Body, which defines a function with one parameter. If it is not what is its relation with logic? Lambda calculus isn't much more complicated than what I showed, but it does require more than just an application context rule in its evaluation semantics. Jan 19, 2012 - It's Turing complete: if a function can be computed by any possible computing device, then it can be written in λ-calculus. Its semantics are strong enough that we can do reasoning from it. , and an interpreter for the simply-typed lambda calculus is your FizzBuzz . This should not be confused with "The Lambda Calculus, Its Syntax and Semantics", which is concerned with the untyped case and has an encyclopaedic scope.