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Chapter 2: Data Abstraction 2.2 An Abstraction for Inductive Data Types

Chapter 2: Data Abstraction 2.2 An Abstraction for Inductive Data Types. Recall inductive BNF definition of binary trees: <bintree> ::= <number> | (<symbol> <bintree> <bintree>) To write programs using bintree, we'll need:. constructors for different kinds of bintrees (like Java)

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Chapter 2: Data Abstraction 2.2 An Abstraction for Inductive Data Types

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  1. Chapter 2: Data Abstraction2.2 An Abstraction for Inductive Data Types • Recall inductive BNF definition of binary trees: • <bintree> ::= <number> | (<symbol> <bintree> <bintree>) • To write programs using bintree, we'll need: • constructors for different kinds of bintrees (like Java) • a predicate for telling whether an object is a bintree • (unlike Java, because Scheme types are dynamic) • a way of telling whether bintree is leaf or interior • a way of getting out the leaf or interior component

  2. An Abstraction for Inductive Data Types • Tell Dr. Racket to use the language extension from Essentials of Programming Languages (EOPL) textbook:

  3. An Abstraction for Inductive Data Types • Now we can use the define-datatype special form: (define-datatype bintree bintree? (leaf-node (datum number?)) (interior-node (key symbol?) (left bintree?) (right bintree?))) • What is this doing?

  4. Defines a datatype bintree, with predicate bintree? • (define-datatype bintree bintree? • A bintree is either • a leaf node consisting of a datum, which is a number • (leaf-node • (datum number?)) • an interior node consisting of a key that is a symbol, a left child that is a bintree, and a right child that is a bintree (interior-node (key symbol?) (left bintree?) (right bintree?)))

  5. Creates a dataype with the following interface: • (define-datatype bintree bintree? • A 1-argument procedure for constructing a leaf node, with a test to make sure that the argument is a number • (leaf-node • (datum number?)) • A 3-argument procedure for building an interior node, with a test for the first arg being a symbol and the second and third being a bintree (interior-node (key symbol?) (left bintree?) (right bintree?)))

  6. General format: (define-datatypetype-nametype-predicate-name {(variant-name {(field-namepredicate)}*}+) More on define-datatype (define-datatype bintree bintree? (leaf-node (datum number?))

  7. Determining variants via cases (define leaf-sum (lambda (tree) (cases bintree tree (leaf-node (datum) datum) (interior-node (key left right) (+ (leaf-sum left) (leaf-sum right)))))) (Essentially, a pattern-matcher)

  8. Determining variants via cases Supports type-checking: > (define tree-a (interior-node 'a (leaf-node 2) (leaf-node 3))) > (leaf-sum tree-a) 5 > (leaf-sum 'foo) case: not a bintree: foo

  9. Determining variants via cases General format: (casestype-nameexpression {(variant-name({field-name}*)consequent)}* (cases bintree tree (interior-node (key left right) (+ (leaf-sum left) (leaf-sum right))))))

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