Download CSC 4101: Programming Languages - Scheme and Functional Programming and more Assignments Programming Languages in PDF only on Docsity!
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SchemeScheme
Textbook, Sections 13.1 – 13.3, 13.
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Functional ProgrammingFunctional Programming
z Based on mathematical functions
z Take argument, return value
z Only function call, no assignment
z Functions are first-class values
z E.g., functions can return functions
z Requires garbage collection
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Lambda CalculusLambda Calculus
z Mathematical functional language
z Language constructs
- Variables: x
- *Primitive functions: **
- Function abstraction: λ ( x ) _xx_* or λ x****. _xx_*
- Function call: f ( x ) or f x
z Example
( λ ( x ) _xxx_** ) (2) yields 8
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SchemeScheme
z Dialect of LISP (from MIT, ca. 1975)
z Lists as built-in data type
z Same syntax for lists and programs
z Functions are (first-class) data
z Dynamic, strong typing
z Interaction ( read-eval-print ) loop
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Scheme SyntaxScheme Syntax
z S-expressions
s-expression ::= literals | symbols | ( s-expression... )
z Special forms for specific language
constructs
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Atomic Data TypesAtomic Data Types
z Numbers
z Booleans
#t, #f
z Characters, Strings
#\a, #\newline, "Hello World!"
z Symbols
f, x, +, *, foo, bar, null?, set!
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ListsLists
z Quotes
(quote x), ’x
z Empty list
’() , often assigned to the variable nil
z Nonempty list
’(1 2 3), ’(a b 3), ’(1 (2 3) 4)
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List RepresentationList Representation
The list ’(1 2) is stored as
cons /
1 cons /
2 ()
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List RepresentationList Representation
The list ’(1 (2 3) 4) is stored as cons /
1 cons /
cons cons / \ /
2 cons 4 () /
3 ()
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List FunctionsList Functions
z Predefined functions
car, cdr, cons
z Examples
(car ’(1 2)) returns 1 (cdr ’(1 2)) returns (2) (cons 1 ’(2)) returns (1 2) (cons 1 2) returns (1. 2)
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SS--ExpressionsExpressions
List Syntax S-Expression Syntax
Not a list (1. 2)
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More ExamplesMore Examples
Expression Value
(car (cdr ’(1 2 3))) 2 (cadr ’(1 2 3))) 2 (cons 1 ’()) (1) (cons 1 2) (1. 2) (cons ’() ’()) (()) (car ’(())) ()
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HigherHigher--Order Functions (cont’d)Order Functions (cont’d)
;; Curried version of twice (define (twice f) (lambda (x) (f (f x))))
(define quadruple (twice double)) (quadruple 2) ; returns 8 ((twice double) 2) ; returns 8 ((twice quadruple) 2) ; returns 32 ((twice (twice double)) 2) ; returns 32
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Curried Function in C SyntaxCurried Function in C Syntax
(int ()(int)) twice (int (f)(int)) { int foo (int x) { return f(f(x)); }
return foo; }
(twice(double))(2);
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ConditionalsConditionals
z If-then-else
(if (= x y) 1 2) ; in C: (x == y)? 1 : 2
z Cond
(cond ((= x y) 1) ((< x y) 2) (else 3))
z Anything non- #f is considered true
(if 1 2 3) ; returns 2
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EqualityEquality
Expression Value
(eq? x x) #t (eq? ’x ’x) #t (eq? ’() ’()) #t (eq? 2 2) undefined (eq? (list 1) ’(1)) #f
(eqv? 2 2) #t (equal? (list 1) ’(1)) #t
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RecursionRecursion
(define (fac n) (if (= n 0) 1 (* n (fac (- n 1)))))
(fac 5) ; returns 120 (fac 1000) ; that’s 2568 digits
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Map FunctionMap Function
(define (mymap f l) (if (null? l) ’() (cons (f (car l)) (mymap f (cdr l)))))
(mymap double ’(1 2 3 4 5)) ; returns (2 4 6 8 10) (mymap (lambda (x) (+ x 1)) ’(1 2)) ; returns (2 3)
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PartitioningPartitioning
(define (gt p ls) (filter (lambda (x) (> p x)) ls))
(define (le p ls) (filter (lambda (x) (<= p x)) ls))
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Filtering a ListFiltering a List
(define (filter pred ls) (cond ((null? ls) ’()) ((pred (car ls)) (cons (car ls) (filter pred (cdr ls)))) (else (filter pred (cdr ls)))))
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Assignment (but don’t use it)Assignment (but don’t use it)
Expression Value of x
(define x 3) 3 (set! x 5) 5
(define x (list 1 2)) (1 2) (set-car! x 3) (3 2) (set-cdr! x 4) (3. 4)
