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# PL6 - CSE233/CSE300 1 Lambda...

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1 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 1 CSE233/CSE300 Lambda Calculus

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2 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 2 Overview Motivation Syntax Semantics Axiomatic Operational Reduction Normal Applicative Properties Confluence
3 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 3 Motivation Lambda calculus Minimalist approach Preserve expressive power Very simple Untyped or typed What we gain Easier to study Time systems Semantics Tool to formalize semantics of other languages

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4 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 4 Lambda Calculus Syntax Very small Examples Expr :== <Expr> <Expr> :== <Id>.<Expr> λ :== ( <Expr> ) :== <Id> x y s (x) x y x. x λ x. y λ ( x. y) z λ
5 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 5 Associativity Application associates to the left f a b c d (((f a) b) c) d

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6 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 6 Scoping Scope of abstractions Extent to the right as far as possible x. y.M N λ λ x.( y.(M N)) λ λ
7 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 7 Abstraction The abstraction Represents a function definition λ Is the abstraction symbol The formal is the identifier x The body is the expression M x.M λ

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8 /Users/ldm/courses/Spring05_CSE300/lectures/PL8.sxi 8 Application The application The expression Is a function call Intuitive semantics M is an abstraction N is the argument The application consist of Replace the formal x by the argument N in the body P M N x.P λ
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PL6 - CSE233/CSE300 1 Lambda...

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