University of Virginia Computer Science
CS150: Computer Science, Fall 2005

28 October 2005

CS150 Notes 28 (28 October 2005)

Upcoming Schedule

Problem Sets 7 and 8
Problem Set 7 will be handed out Monday; Problem Set 8 is handed out today, and involves several deliverables with different due dates.

If you (1) have a team formed and (2) have an idea for what you want to do for PS8, it may make better sense for you to start working on your PS8 than to do PS7. To arrange this, you need to email me by 11:59pm on Wednesday, November 2 at list of your team members and what you want to do for PS8.

How do we prove a model of computation is equivalent to a Turing Machine?

Lambda Calculus

term ::= variable | term term | ( term ) | λ variable . term

Alpha Reduction: (renaming variables)

λ y . Mα λ v . M [y |→ v] where v does not occur in M.
We can can change the name of a lambda variable, but replacing all occurances of the variable in the body term with a new name that does not appear in the body term.

Beta Reduction: (substitution)

x . M) Nβ M [ x |→ N ]
Example (use back)

f . ((λ x . f (xx)) (λ x . f (xx)))) λ x . x

Making "Primitives" out of nothing but Glue


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CS 150: Computer Science
University of Virginia
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