lec9.pdf - lec9 Lambda Calculus Semantics CS3100 Fall 2019 Review Last time Lambda Calculus Syntax Today Lambda Calculus Semantics Reductions

lec9.pdf - lec9 Lambda Calculus Semantics CS3100 Fall 2019...

This preview shows page 1 - 5 out of 12 pages.

14/08/2019 lec9 1/12 Lambda Calculus : Semantics CS3100 Fall 2019 Review Last time Lambda Calculus: Syntax Today Lambda Calculus: Semantics Reductions, Church-Rosser Theorem. β-reduction Lambda Calculus we have been looking so far is untyped . No static semantics, only dynamic semantics! A term of the form is called a β-redex . The act of evaluating lambda calculus terms is called β-reduction . β-reduction replaces with . A term without β-reduxes is said to be in β-normal form . β-reduction, formally
Image of page 1
14/08/2019 lec9 2/12 Example Example Example Many steps of β-reduction Church-Rossser Theorem If and then there exists an such that and .
Image of page 2
14/08/2019 lec9 3/12 β-normal form "β-normal form" "contains no reduxes" Theorem (Uniqueness of β-normal forms). If and and and are in β-normal form, then . Proof. By Church-Rosser, obtain an such that and . But and are in β-normal form. Hence, . β-equivalence iff there exists an such that and . Possible Non-termination Some terms do not have a normal form
Image of page 3
14/08/2019 lec9 4/12 Such terms are said to diverge . Possible Non-termination Other terms may or may not terminate based on the redux chosen to reduce. Reduction Strategies Several different reduction strategies have been studied for lambda calculus. The β reduction we have seen so far is known as full β-reduction Any redex in the term can be reduced at any time.
Image of page 4
Image of page 5

You've reached the end of your free preview.

Want to read all 12 pages?

  • Fall '19

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors