comp_314_lambda_definitions_1_03 - Comp 314 λ-calculus...

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Unformatted text preview: Comp 314 λ-calculus definitions and notes Version 1.03 Chris Stephenson March 14, 2009 1 Grammar In this grammar for the λ-calculus, i represents one of an infinite number of names. You can think of i as representing a Scheme identifier. There are an infinite number of Scheme identifiers. But Scheme identifiers are formed from a finite alpahabet. We could embed the regular grammar for Scheme identifiers in the context free grammar of the λ-calculus to give us a grammar with a finite alphabet, but an infinite number of names. Expanded in this way, our λ-calculus definition below obeys the rules for a formal language by having a finite alphabet. The definition below with an apparently infinite alphabet is simply a convenient shorthand. Λ → i Λ → (Λ Λ) Λ → ( λ i Λ) 2 Free Identifiers Definition of FI(Λ), the free identifiers of a λ-sentence. Λ = i ⇒ FI (Λ) = { i } Λ = ( M N ) ⇒ FI (Λ) = FI ( M ) ∪ FI ( N ) Λ = ( λ i M ) ⇒ FI (Λ) = FI ( M ) \ { i } 1 3 β-reduction...
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comp_314_lambda_definitions_1_03 - Comp 314 λ-calculus...

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