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

Remember that for a calculus, you need to define two things: the syntax, which describes how valid expressions can be written in the calculus; and a set of rules that allow you to symbolically manipulate the expressions. Mar 13, 2014 - ****This is how John Divers presents the paradox in his fantastic book, Possible Worlds. Once you have even Montague's first order lambda calculus, you've got resources for a nice syntax-semantics interface. May 10, 2009 - Turns out, λ is logic free; it is an equational theory (directly quoted from Studies in logic and foundations of mathematics, The Lambda Calculus Its Syntax and Semantics by H.P. It asserts that whatever is on the left side of the colon has the type specified on the right side. It's easy to create in a look at LC. It's semantics are strong enough that we can do reasoning from it. Feb 29, 2012 - One of the really amazing things about this, which I'll show, is that a simply typed lambda calculus is completely semantically equivalent to an intuitionistic propositional logic: each type in the program is a proposition in the logic; The syntax part is easy. We add a ":" to the notation; the colon has an expression or variable binding on its left, and a type specification on its right. May 14, 2006 - Lambda calculus is great for a lot of reasons, among them: It's very simple. It is also combinatorially complete.