1. plt-2002-2 6/7/2014 3.2-1 Data Abstraction Programming Language Essentials 2nd edition Chapter 2.2 An Abstraction for Inductive Data Types

2. plt-2002-2 6/7/2014 3.2-2 define-datatype bintree bintree: 'Number' | '(' 'Symbol' bintree bintree ')' (define-datatype bintree bintree? (leaf-node (datum number?)) (interior-node (key symbol?) (left bintree?) (right bintree?))) predicate constructors

3. plt-2002-2 6/7/2014 3.2-3 Scheme 48 Image http://www.cs.indiana.edu/eopl/code.zip $ scheme48 >,open srfi-23 >,load r5rs.scm >,load sllgen.scm sllgen.scm 2000-09-25 11:48 >,load define-datatype.scm define-datatype.scm version J3 2002-01-02 >,dump eopl.image EOPL Writing eopl.image $ scheme48 -i eopl.image >

4. plt-2002-2 6/7/2014 3.2-4 Terminology aggregate: contains values of other types, e.g., array or record with named fields. union: values are of other types. discriminated union: value contains explanatory tag and value of union's types. variant record: discriminated union of record types. Scheme values are discriminated union of primitive types. Inductively defined data types can be represented as variant records.

5. plt-2002-2 6/7/2014 3.2-5 define-datatype Scheme extension (define-datatype type-name type-predicate-name (variant-name (field-name predicate) … ) … ) creates variant record type with one or more variants with zero or more fields type and variant names must be globally unique must be used at top level

6. plt-2002-2 6/7/2014 3.2-6 define-datatype (2) creates type-predicate-name predicate with one argument creates variant-name constructor with one argument per field (define-datatype bintree bintree? (leaf-node (datum number?)) (interior-node (key symbol?) (left bintree?) (right bintree?)))

7. plt-2002-2 6/7/2014 3.2-7 define-datatype (3) (leaf-node 29) (bintree? (leaf-node 29)) (interior-node 'foo (leaf-node 1) (leaf-node 2) ) (bintree? (interior-node 'foo (leaf-node 1) (leaf-node 2) )

8. plt-2002-2 6/7/2014 3.2-8 s-list s-list: '(' symbol-expression* ')' symbol-expression: 'Symbol' | s-list (define-datatype s-list s-list? (empty-s-list) (non-empty-s-list (first symbol-exp?) (rest s-list?))) (define-datatype symbol-exp symbol-exp? (symbol-symbol-exp (data symbol?)) (s-list-symbol-exp (data s-list?)))

9. plt-2002-2 6/7/2014 3.2-9 s-list based on Scheme lists (define-datatype s-list s-list? (an-s-list (data (list-of symbol-exp?)))) (define list-of ; returns predicate for list (lambda (pred) (lambda (val) (or (null? val) (and (pair? val) (pred (car val)) ((list-of pred) (cdr val)) ) ) ) ) )

10. plt-2002-2 6/7/2014 3.2-10 Examples (s-list? (empty-s-list)) (s-list? (non-empty-s-list (symbol-symbol-exp 'a) (empty-s-list) ) (s-list? (an-s-list '())) (s-list? (an-s-list (list (symbol-symbol-exp 'a))) ) (s-list? (an-s-list (cons (symbol-symbol-exp 'a) '() ) ) )

11. plt-2002-2 6/7/2014 3.2-11 Sum of leaves of bintree (define leaf-sum (lambda (tree) (cases bintree tree (leaf-node (datum) datum) (interior-node (key left right) (+ (leaf-sum left) (leaf-sum right)) ) ) (leaf-sum (interior-node 'foo (leaf-node 1) (leaf-node 2) )

12. plt-2002-2 6/7/2014 3.2-12 cases (cases type-name expression (variant-name (field-name …) body) … (else body) ) value of expression must be of type-name variant selects appropriate variant-name each field value is bound to field-name and body is executed without else, all variants must be specified

13. plt-2002-2 6/7/2014 3.2-13 Lambda Calculus Representation expr: 'Symbol' | '(' 'lambda' '(' 'Symbol' ')' expr ')' | '(' expr expr ')' (define-datatype expression expression? (var-exp (id symbol?)) (lambda-exp (id symbol?) (body expression?)) (app-exp (rator expression?) (rand expression?)))

14. plt-2002-2 6/7/2014 3.2-14 Examples (expression? (var-exp 'x) ) (expression? (lambda-exp 'x (var-exp 'x)) ) (expression? (app-exp (var-exp 'f) (var-exp 'x)) ) (expression? (lambda-exp 'x (app-exp (var-exp 'f) (var-exp 'x)) )

15. plt-2002-2 6/7/2014 3.2-15 Syntax and Representation BNF specifies concrete syntax, external representation define-datatype defines building blocks for abstract syntax, internal representation expr: 'Symbol' var-exp (id) | '(' 'lambda' '(' 'Symbol' ')' expr ')' lambda-exp (id body) | '(' expr expr ')' app-exp (rator rand)

16. plt-2002-2 6/7/2014 3.2-16 Abstract Syntax Tree lambda-exp id body x app-exp rator rand var-exp app-exp id rator rand f var-exp var-exp id id f x (lambda (x) (f (f x)))

17. plt-2002-2 6/7/2014 3.2-17 Programming without an AST (define occurs-free? (lambda (var exp) (cond ((symbol? exp) (eqv? var exp)) ((eqv? (car exp) 'lambda) (and (not (eqv? (caadr exp) var)) (occurs-free? var (caddr exp)))) (else (or (occurs-free? var (car exp)) (occurs-free? var (cadr exp)) ) ) ) ) ) plagued by c*r references

18. plt-2002-2 6/7/2014 3.2-18 Programming with an AST (define occurs-free? (lambda (var exp) (cases expression exp (var-exp (id) (eqv? id var)) (lambda-exp (id body) (and (not (eqv? id var)) (occurs-free? var body))) (app-exp (rator rand) (or (occurs-free? var rator) (occurs-free? var rand) ) ) ) ) )

19. plt-2002-2 6/7/2014 3.2-19 Example (occurs-free? 'f (lambda-exp 'x (app-exp (var-exp 'f) (var-exp 'x)) )

20. plt-2002-2 6/7/2014 3.2-20 unparse-expression (define unparse-expression (lambda (exp) (cases expression exp (var-exp (id) id) (lambda-exp (id body) (list 'lambda (list id) (unparse-expression body) ) ) (app-exp (rator rand) (list (unparse-expression rator) (unparse-expression rand) ) ) ) ) )

21. plt-2002-2 6/7/2014 3.2-21 Example (unparse-expression (lambda-exp 'x (app-exp (var-exp 'f) (var-exp 'x)) )

22. plt-2002-2 6/7/2014 3.2-22 parse-expression (define parse-expression (lambda (datum) (cond ((symbol? datum) (var-exp datum)) ((pair? datum) (if (eqv? (car datum) 'lambda) (lambda-exp (caadr datum) (parse-expression (caddr datum))) (app-exp (parse-expression (car datum)) (parse-expression (cadr datum)) ) ) ) (else (error 'parse-expression datum)) ) ) )

23. plt-2002-2 6/7/2014 3.2-23 Example (unparse-expression (parse-expression '(lambda (x) (f x)) )