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Lists

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  1. Lists "One can even conjecture that Lisp owes its survival specifically to the fact that its programs are lists, which everyone, including me, has regarded as a disadvantage.“ - John McCarthy, "Early History of Lisp"

  2. List Representation (1) • "("followed by zero or more terms and a ")" • Examples: (3 4 5), (word (a-symbol 5) 6 "String"), (), (((4))), ((()) () (()) t ()) • May be arbitrarily long and contain arbitrary types, even other lists • May contain multiple instances of the same element • Elements are in strict order

  3. List Representation (2) • To LISP, a list is either nil or a cons-cell • A cons-cell is an item stored next to a not nil item (usually a pointer) • Classic linked list structure • Example: (A 255 CATS 4.53242)

  4. Constructing Lists with Cons • S-expression stands for Symbolic Expression • Basically, a LISP term • cons creates a dotted-pair of two evaluated S-expressions (cons S-expression S-expression) • Examples • (cons 3 4)→ (3 . 4) • (cons 3 (cons 4 (cons 5 nil))) → (3 4 5) • This is equivalent to (3 . (4 . (5 . nil)))

  5. Constructing Lists with Quote • cons is good for adding one element to the front of a list, but is tedious for long lists • quote provides some syntactic sugar 'S-expression >'(this is a list) (THIS IS A LIST) • quote does not evaluate its argument >'(cons 5 (* 6 7)) (CONS 5 (* 6 7))

  6. Constructing Lists with List • list is used to construct a list of elements that are the results of evaluated expressions • Takes arbitrary number of arguments (list S-expression*) • Examples: • (list 5 (+ 6 7))→ (5 13) • (list '* (+ 6 7) 'x) → (* 13 x) • (list '/ '(+ 6 7) ()) → (/ (+ 6 7) NIL)

  7. Constructing Lists with Append • If you have multiple lists, append can combine them into one list (append S-expression*) • Examples: • (append '(*) '(4 5)) → (* 4 5) • (append '(5 6) '(nil) '(3 (5 6))) → (5 6 NIL 3 (5 6)) • (append '(5 6) nil) → (5 6)

  8. Lists as Trees (1) • The sequence of links can be drawn as a tree

  9. Lists as Trees (2) • Because lists can contain lists, they actually are trees

  10. Deconstructing Lists • Machines on which LISP was originally implemented had two useful machine instructions: • car: contents of address register, the left cell • cdr: contents of decrement register, the right cell • For a linear list, car is like getData() and cdr is like getNext() • Because lists are actually trees, car is like getLeftChild() and cdr is like getRightChild()

  11. >(car '(3 . 5)) 3 >(cdr '(3 . 5)) 5 >(car '(3 4 5 6 7 8)) 3 >(cdr '(3 4 5 6 7 8)) (4 5 6 7 8) >(car (cdr '(2 3 4 5))) 3 Letters a and d can be embedded between c and r to compose multiple car/cdr calls (car (car '((2 . 7) . 3)) is (caar '((2 . 7) . 3)) (cdr (cdr '(4 5 6))) is (cddr '(4 5 6)) (car (cdr '(2 3 4 5))) is (cadr '(2 3 4 5)) Up to four levels of nesting supported Car and Cdr Examples

  12. Other Accessors (first S-expression) (rest S-expression) • first and rest are the same as car and cdr • second, third, fourth, … , tenth also defined (nth integer S-expression) • nth retrieves element indicated by integer • Zero based • Examples: >(nth 0 '(4 5 6 7)) 4 >(nth 2 '(r e (s f) y)) (S F)

  13. Association Lists • Used to represent mappings • Lists of dotted-pairs Example: ((+ . "add") (- . "subtract")) • assoc returns the pair associated with a given key, nil if not found >(assoc '- '((+ . "add") (- . "subtract"))) (- . "subtract")

  14. Types of Equality >(assoc '(4 5) '(((2 4) . A) ((4 5) . B))) NIL • Default equality test is eql • eq does a pointer comparison • eql same as eq, but can also compare numbers of the same type • = is for numbers only, but can compare numbers of different types, e.g. (= 3 3.0)→ T • equal is the most general, and compares structure (slowest) • Can get around this using keyword arguments >(assoc '(4 5) '(((2 4) . A) ((4 5) . B)) :test 'equal) ((4 5) . B) • We’ll learn more about these later

  15. Updating Association Lists • assoc returns the first pair matching the input • (assoc 'c '((c . 5) (c . 6))) → (C . 5) • To change an association, put a new pair in front of it >(cons (cons 'name "Jacob") '((name . "Eric"))) ((NAME . "Jacob") (NAME . "Eric")) • acons is a shortcut for this (acons key value association-list) >(acons 'name "Jacob" '((name . "Eric"))) ((NAME . "Jacob") (NAME . "Eric"))

  16. Predicates for Lists • consp returns T if its argument is a cons • atom returns T if the argument is not a cons • listp returns T if its argument is a list, meaning a cons or nil • null returns T if its argument is nil • endp is like null, but requires a list