Lists defined inductively ( A ) is the smallest set satisfying this - PowerPoint PPT Presentation

Jan 03, 2024 •280 likes •325 views

Lists defined inductively ( A ) is the smallest set satisfying this equation: LIST LIST ( A ) f (cons a as ) j a 2 A ; as 2 LIST ( A ) g f () g = [ Equivalently, LIST ( A ) is defined by these rules: (E MPTY ) 2 List ( A ) () a 2 A as 2

Lists defined inductively ( A ) is the smallest set satisfying this equation: LIST LIST ( A ) f (cons a as ) j a 2 A ; as 2 LIST ( A ) g f ’() g = [ Equivalently, LIST ( A ) is defined by these rules: (E MPTY ) 2 List ( A ) ’() a 2 A as 2 List ( A ) (C ONS ) (cons a as ) 2 List ( A )
One more inductive definition A list of A is one of: • The empty list ’() • (cons a as) , where a is an A and as is a list of A
Lists generalized: S-expressions An ordinary S-expression is one of: • An atom (symbol, number, Boolean) • A list of ordinary S-expressions Can write literally in source, with quote
� Scheme vs Impcore (Names stand for mutable locations—more to come.) New abstract syntax: LET (keyword, names, expressions, body) LAMBDAX (formals, body) APPLY (exp, actuals) New concrete syntax for LITERAL: (quote S-expression ) ’ S-expression

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Lists defined inductively ( A ) is the smallest set satisfying this equation: LIST ( A ) f (cons a

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