CS603 Programming Language Organization

1. CS603 Programming Language Organization • Lecture 11 • Spring 2003 • Department of Computer Science

2. Overview • Questions • Finishing µ-Scheme • µ-Scheme Operational Semantics • 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. 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

9. Abstract Syntax and Values • Same as last time, for toplevel, exp, lambda, and values, a separate structure, with a union element for each production Pair Up: • Draw an AST for (val list-of-al-ops (mk-set-ops =alist?))

10. Operational Semantics • Differences from Impcore • Single environment , not three • Environments bind names to locations, rather than to values. • Environments must be captured and it is never safe to mutate a binding in an environment. • State of abstract machine evaluating expression e is <e, , >

11. Operational Semantics (cont.) • We write <e, , > ⇓<v, ’> to mean • The result of evaluating expression e in environment  when the state of the store is , is the value v • The evaluation may update the store to produce a new state ’

12. µ-Scheme Judgments Pair Up: • Give me the tags for every production in toplevel and exp • Write up the corresponding judgment • Write judgment for (positive? 0) given: (define curry (f) (lambda (x) (lambda (y) (f x y))) (val zero? ((curry =) 0)) (zero? 0)

13. Reading for Next Time • Sections 3.12–3.14