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

Overflow, one way you could get rid of it is by porting your implementation to Standard ML Actually that's only half joking: the point is that with NbE, your object language may depend on semantic features of the meta language (in particular of its function spaces). Mar 1, 2014 - A proposition is identified with the type (collection) of all its proofs, and a type is identified with the proposition that it has a term (so that each of its terms is in turn a proof of the corresponding proposition). 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. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 479–490. Not all type theories follow this paradigm; among those that do, In J. It asserts that whatever is on the left side of the colon has the type specified on the right side. , and an interpreter for the simply-typed lambda calculus is your FizzBuzz . 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. May 1, 2013 - But if your interest is more in programming languages than proof assistants, then length-indexed vectors is your Hello, World! We also give a declarative account of what it Putting it all together: semantics of STLC. Roger Seldin, Jonathan P.; Hindley, (ed.s), To H.B. Nov 11, 2012 - type expr = expr' * position and expr' = | Var of variable | Universe of int | Pi of abstraction | Lambda of abstraction | App of expr * expr (** An abstraction [(x,t,e)] indicates that [x] of type [t] is bound in [e].