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Lisp Internals

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  1. Lisp Internals

  2. A problem with lists • In Lisp, a list may “contain” another list • For example, (A (B C)) contains (B C) • So, how much storage do we need to allocate for a list? • If any list can contain any other list, there is no limit to the size of storage block we may need • This is impractical; we need another solution

  3. Pointers • Instead of actually putting one list inside another, we put a pointer to one list inside another • A pointer is a fixed, known size • This partially solves the problem, but... • A list can contain any number of elements • For example, the list ((A)(B)(A)(C)) contains four lists • This still leaves us needing arbitrarily large blocks of storage

  4. CAR and CDR • We can describe any list as the sum of two parts: its “head” (CAR) and its “tail” (CDR) • The head is the first thing in the list • The head could itself be an arbitrary list • The tail of a list is another (but shorter) list • Thus, any list can be described with just two pointers • This provides a complete solution to our problem of arbitrarily large storage blocks

  5. S-expressions • In Lisp, everything is an S-expression • An S-expression is an atom or a list • You can think of these as using two different kinds of storage locations--one kind for atoms, another kind for the parts of a list • This is an oversimplification, but it will do for now

  6. An atom is a simple thing, and we draw it in a simple way: Sometimes we don’t bother with the boxes: Atoms HELLO ABC NIL HELLO ABC NIL

  7. A list has two parts: a CAR and a CDR We draw this as a box , called a cons cell, with two compartments, called the car field and the cdr field In each of these compartments we put an arrow pointing to its respective value: car field car field cdr field value of car value of cdr Lists

  8. A NIL A NIL Example I ( A )

  9. A B C (B C) (C) NIL A B C NIL Example II ( A B C )

  10. A NIL B NIL Example III ((A) B)

  11. A NIL B NIL C D NIL Example IV ((A B) (C D))

  12. A B Dotted pairs • In a simple list, every right-pointing arrow points to a cons cell or to NIL • If a right-pointing arrow points to an atom, we have a dotted pair (A . B)

  13. A NIL Lisp lists are implemented with dotted pairs • Therefore, (A) = (A . NIL) • All structures in Lisp can be created from atoms and dotted pairs ( A ) = = (A . NIL)

  14. A B C D Example V ((A . B) . (C . D))

  15. Printing dotted pairs • A dotted pair is usually printed using parentheses and a dot: (A . B) • If the CDR of a dotted pair is NIL, the dot and the NIL are omitted:(A . NIL) = (A) • If the CDR is another cons cell, Lisp doesn’t print the dot or the parentheses • (A . (B . (C . NIL))) = (A B C) • (A . (B . (C . D))) = (A B C . D)

  16. (CDR L) L A (B C D E) Efficiency of CDR • Suppose L is the list (A B C D E) • Then (CDR L) is the list (B C D E) • Isn’t it expensive to create this new list? • Answer: NO! It’s incredibly cheap! • Lisp just copies a pointer:

  17. Here’s the cons cell we add to create the list (A B) A Here’s the list (B) Here’s the atom A B NIL Efficiency of CAR and CONS • CAR is just like CDR; you just copy a pointer • CONS takes more work; you have to allocate and fill one cons cell

  18. Sharing structure • List L and list (CDR L) are said to share structure • But if L = (A B C D E) and M = (CDR L), then when you change L, won’t M be changed? • Yes, but... • this is where the real genius of Lisp comes in... • You never changeL ! • None of the basic functions ever change anything that’s already there • Only CONS adds anything • The result is an extraordinarily efficient language!

  19. Memory • If you only add structure, and never change or delete anything, won’t you run out of memory? • Lisp uses garbage collection to recover structures that you are no longer using • More convenient for the programmer • Safer (less subject to human error) • Extremely effective in general

  20. Java isn’t Lisp • Although Lisp’s way of handling lists is elegant and efficient, it’s not the only way • Modifying the middle or end of a list is expensive • There are many ways we might implement lists in Java • Lisp’s implementation of lists is a great example, but not necessarily the final word

  21. A possible Java implementation • class Cell { } • class Atom extends Cell { String value; Atom(String value) { // constructor this.value = value; }} • class ConsCell extends Cell { Cell car; Cell cdr; ConsCell(Cell car, Cell cdr) { // constructor this.car = car; this.cdr = cdr; }}

  22. Another possible implementation • class Cell { boolean isAtom; String value; Cell car, cdr; • Cell(String value) { // constructor isAtom = true; this.value = value; } • Cell(Cell car, Cell cdr) { // constructor isAtom = false; this.car = car; this.cdr = cdr; }}

  23. Implementing the functions I • class Lisp { • static Cell car(Cell c) { return c.car;} • static Cell cdr(Cell c) { return c.cdr;} • static Cell cons(Cell c1, Cell c2) { return new Cell(c1, c2);}

  24. Implementing the functions II • static boolean atom(Cell c) { return c.isAtom;} • static boolean eq(Cell c1, Cell c2) { return c1.value.equals(c2.value);} • }

  25. The End