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Understanding Higher-Order Functions and Polymorphism in µ-Scheme

This lecture explores the concepts of higher-order functions (HOF) and polymorphism in the µ-Scheme programming language. It covers the creation of set operations, insertion sort algorithms, and environment diagrams. Key topics include the construction of functions like `mk-set-ops` for list manipulation, and defining sorting functions such as `mk-insertion-sort`. The lecture emphasizes the theoretical underpinnings and practical applications of these concepts through examples and exercises. Students will also prepare for the next class by reading relevant material related to these topics.

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Understanding Higher-Order Functions and Polymorphism in µ-Scheme

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  1. CS603 Programming Language Organization • Lecture 16 • Spring 2004 • Department of Computer Science

  2. Overview • Questions • Finishing µ-Scheme • Reading for next time

  3. HOF for Polymorphism:List of Functions ->(val mk-set-ops (lambda (eqfun) (list2 (lambda (x s) ; member? (exists? ((curry eqfun) x) s)) (lambda (x s) ; add-element (if (exists? ((curry eqfun) x) s) s (cons x s))))) ->(val list-of-al-ops (mk-set-ops =alist?)) Pair Up: • Draw a diagram (of environment, cons cells and closures) for (val list-of-al-ops (mk-set-ops =alist?))

  4. Pair Up: What is the value of s? Pair Up: What is the value of s? HOF for Polymorphism:List of Functions -> (val al-member? (car list-of-al-ops)) -> (val al-add-element (cadr list-of-al-ops)) So uses will look like: ->(val emptyset ‘()) ->(val s (al-add-element ‘((U Thant)((I Ching))) emptyset) (((U Thant) (I Ching))) ->(val s (al-add-element ‘((E coli)(I Ching)) s)) (((E coli) (I Ching)) ((U Thang) (I Ching)))

  5. A polymorphic, higher-order sort ->(define mk-insertion-sort (lt) (letrec ( (insert (lambda (x l) (if (null? l) (list1 x) (if (lt x (car l)) (cons x l) (cons (car l) (insert x (cdr l))))))) (sort (lambda (l) (if (null? l) ’() (insert (car l) (sort (cdr l))))))) sort))

  6. A polymorphic, higher-order sort (cont.) ->(val sort< (mk-insertion-sort <)) ->(val sort> (mk-insertion-sort >)) ->(sort< ‘(6 9 1 7 4 3 8 5 2 10)) (1 2 3 4 5 6 7 8 9 10) ->(sort> ‘(6 9 1 7 4 3 8 5 2 10)) (10 9 8 7 6 5 4 3 2 1) ->(define pair< (p1 p2) (or (< (car p1) (car p2) (and (= (car p1) (car p2)) (< (cadr p1) (cadr p2))))) ->((mk-insertion-sort pair<) ‘((4 5) (2 9) (3 3) (8 1) (2 7))) ((2 7) (2 9) (3 3) (4 5) (8 1))

  7. µ-Scheme Concrete Syntax toplevel ::= exp | (usefile-name) | (valvariable-name exp) | (definefunction-name(formals)exp) exp ::= literal | variable-name | (ifexp exp exp) | (while exp exp) | (setvariable-name exp) | (begin {exp}) | (exp {exp}) | (let-keyword ({(variable-name exp)}) exp) | (lambda (formals)exp) | primitive let-keyword ::= let | let* | letrec

  8. µ-Scheme Concrete Syntax (cont.) formals ::= {variable-name} literal ::= integer | #t | #f | ‘S-exp | (quote S-exp) S-exp ::= literal| symbol-name| ({S-exp}) primitive ::= + | - | * | / | = | < | > | print | error | car | cdr | cons | number? | symbol? | pair? | null? | boolean? | procedure? integer ::= sequence of digits, possibly prefixed with a minus sign *-name ::= sequence of characters not an integer and not containing (, ), ;, or whitespace

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