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These web pages provide a practical introduction to lambda reduction, with a few pointers to more esoteric issues. I'm a linguist, and I have linguists in mind for my audience, so linguistic issues will be emphasized (e.g., a discussion of the interaction of lambda with other binding operators such as ∃ "exists" and ∀ "forall").
Our goal today is to introduce a new operator into our theory { the lambda operator, symbolized by the Greek letter ‘ ’ { and show some of the natural language constructions it can be used to analyze.
(iii) The inclusion of the operation of “functional application” or “function-argument application”, the application of a function to its argument. (iv) The use of lambda-expressions. The lambda-operator is the basic tool for building expressions which denote functions.
15 lut 2023 · Introducing the lambda-operator and restricting occurrences of definite descriptions to arguments of lambda-atoms has a potential of simplifying the mentioned tableau systems for these theories.
In Formal Linguistics we are mostly interested in lambda conversion and abstraction. Moreover, we work only with typed-lambda calculus and even more, only with a fragment of it.
Lambda-conversion: A principle concerning the application of λ-expressions to arguments. Examples: λ x [ x 2 + 1] (5) = 5 2 + 1 = 26 λ x [ run ( x )]( b ) ≡ run ( b )
Overview for today Recap: Predicate Logic Lambda abstraction Types Syntax and Semantics Application and beta reduction Reading: Coppock, E., and Champollion, L. (2021). Invitation to formal semantics. Manuscript, Boston University and New York University (Ch.5) fo.petukhova; nddascalug@lsv.uni-saarland.de Introduction to Formal Semantics ...
