![]() Therefore, we will now give a short sketch of some of the central ideas involved in an interpreted simply typed -calculus.Įvery expression gets assigned a unique type in simply typed -calculus. Nevertheless, the two points just mentioned are very important theoretical topics concerning the use of -calculus in formal semantics. (In fact -calculus was originally designed to investigate function definition, function application and recursion.)Īs regards the first point: The version of -calculus we're going to use is untyped, and we'll argue below that we don't have to interpret any -expressions for our purposes. ![]() In this calculus, expressions get assigned types that regulate function application.įunctions: -expressions can be given an interpretation in terms of functions over a system of complex domains. ![]() Types: The version of -calculus most commonly used in linguistics is simply typed -calculus. If you've heard about -Calculus before in other semantics textbooks or lectures, you will probably feel that we have left out a discussion of at least two points: We 've been viewing it simply as a tool for controlling substitutions, without caring much what single -expressions actually mean. The perspective we've been taking on -calculus so far has been a very technical one. In this section we discuss two topics that are important in connection with -calculus, but that have been ommited so far: Types and the semantics of -expressions in terms of functions.
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