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Published byTy Crozier Modified over 2 years ago

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Announcements See web page for talk schedule Dire consequences if I dont hear from you by Monday Schedule next week: Monday – class as usual Wednesday – class as usual immediately after class – I go to Chicago for data mining conference, return Sunday (will be checking ) Friday – class as usual: Les LaCroix from ITS will talk about scripting languages

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Scheme Lists Lists are a special form of S- Expressions () represents the empty list (A) represents list contains A (A) is really (A. ()) (A B) is really (A. (B. () ) ) (picture on blackboard)

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Function Calls Function calls represented as lists (A B C) means evaluate A to a function, evaluate B and C as parameters Use the value returned by the call as the "meaning" of (A B C) Why does (car (1 2)) fail? (1 2) looks like a function call, but 1 isn't a function. quote function says "don't evaluate" (car (quote (1 2))) shorthand: (car '(1 2))

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User-defined functions The list (lambda (args) (body)) creates an anonymous function (lambda (x y) (+ x y)) ((lambda (x y) (+ x y)) 5 6) => 11

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User-defined functions The scheme command define binds values and functions to symbols (define pi ) (define add-two-nums (lambda (x y) (+ x y))) Abbreviated as (define add-two-nums (x y) (+ x y)) Functions in Scheme are first-class objects – treated just like any other data type

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Recursion Breaks a problem down into simpler or smaller problems Mentality: If trivial case then supply answer else supply part of answer combined with solution of smaller problem

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Example: nth function

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(define (nth input n) (if (= n 0) (car input) (nth (cdr input) (- n 1))))

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Example: copy-list

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(define (copy-list input) (cond ((= (length input) 0) ()) ((= (length input) 1) (list (car input))) (else (cons (car input) (copy-list (cdr input))))))

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Let and side effects let is used to create local variables example in DrScheme let is good for preventing functions from affecting the outside world A side effect is when a function changes either one if its parameters or a global variable Scheme uses the ! as a convention to indicate that a function changes an argument

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Subsets How can we define a Scheme function to create a subset? (subsets (1 2 3)) => ( () (1) (2) (3) (1 2) (1 3) (2 3) (1 2 3)) Number of subsets of n+1 values is twice as many as subsets of n values If we have subsets of (1 2), get subsets of (1 2 3) by duplicating all subsets of (1 2) and adding 3

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Subsets Define distrib function to add a new element to a list of lists (distrib (() (1) (2) (1 2)) 3) => ( (3) (3 1) (3 2) (3 1 2)) (define (distrib L E) (if (null? L) () (cons (cons E (car L)) (distrib (cdr L) E)))) Then define an extend function to attach these two together:

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Subsets (define (extend L E) (append L (distrib L E))) Then defining the subsets code is easy: (define (subsets L) (if (null? L) (list ()) (extend (subsets (cdr L)) (car L))))

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Accessing elements of a list (list-tail L k) returns tail of a list after removing first k elements (list-ref L k) pulls off the k-th element Both of these can be slow since lists are linked lists

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Still have not heard from a handful of people No language or date, but paired Mark Peralta / Chris Middleton Language but no date: Robin Smogor / Jenny Cooper Paired? Language? Date? Scott OReilly / Thorin Tatge No contact at all Kevin DeRonne Shaun Reynolds Ryan Wakeham Chris Ghere Steve Fritzdixon Looking for partner Akira Matoba If you have not contacted me at all by the end of the day today (via ), drop a letter grade on the talk If you do not have a language and date scheduled before class on Wednesday, same penalty

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Vectors Better to use vectors if accessing multiple elements of a list: (define x #(1 2.0 three)) (vector-ref x 2) vector->list and list->vector convert back and forth -> is Scheme convention for a conversion function

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Lookup tables Scheme function assoc does lookup in a list (define my-list ( (a 10) (b 20) (c 30)) (assoc b my-list) Can do it with non-atomic keys too (define price-list ( ( (subaru forester) 21000) ( (toyota rav4) 23000) ( (honda cr-v) 21200) )) (assoc (toyota rav4) price-list)

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Nasty Scheme functions set-car! set-cdr! examples

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Scoping Scheme has lexical scoping. Any variables which are non-local are bound to containing lambda parameters, let values, or globally defined values. Example: (define (f x) (lambda (y) (+ x y))) f takes one parameter, x. It returns a function of y. (f 10) => (lambda (y) (+ 10 y))

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Scoping Unbound symbols are assumed to be globals Let is a good way to encapsulate internal variables (define cnt (let ( (I 0) ) (lambda () (set! I (+ I 1)) I))) Try it by executing the function (cnt) repeatedly

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Let bindings can be subtle Notice the difference in behavior between these two programs: (define cnt (let ( (I 0) ) (lambda () (set! I (+ I 1)) I))) (define cnt (lambda () (let ( (I 0) ) (set! I (+ I 1)) I)))

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Sharing vs. Copying If there were no side effects, would never need to copy an object – just copy pointers If there are side effects, sometimes need to copy entire objects (define A (1 2)) (define B (cons A A)) B = ( (1 2) 1 2) show picture (set-car! (car B) 10)

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Copying Scheme objects (define (copy obj) (if (pair? obj) (cons (copy (car obj)) (copy (cdr obj))) obj))

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Shallow & Deep Copying Shallow copy – just copies a reference Deep copy – copies the entire object In Java (similar to C++): Object O1 = new Object(); Object O2; O2 = O1; // shallow copy Java has a clone operation: O2 = O1.clone();... but anything referenced by the object is shallow copied (unless you overload clone)

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Equality Checking Pointer equivalence – do the two operands point to the same address? Structural equivalence – do the two operands point to identical structures, even if in different locations? Pointer equivalence is faster but may not be what you want eqv? and eq? are pointer equivalence equal? is structural equivalence equal? is usually what you want (but slower)

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Loops Look like recursion (let loop ((x 1) (sum 0)) if (<= x 10) (loop (+ x 1) (+ sum x)) sum)) Sums the values from 1 to 10 and displays it Similar to for (x=1; x <= 10; sum += x, x++){}; cout << sum;

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Control Flow in Scheme Schemes control flow is normally simple and recursive: First argument is evaluated to get a function Remaining arguments are evaluated to get actual parameters Actual parameters are bound to functions formal parameters Function body is evaluated to obtain function call value Leads to deeply nested expression evaluation.

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Example: Multiply a list of integers (define (mult-list L) (if (null? L) 1 (* (car L) (mult-list (cdr L))))) The call (mult-list ( )) expands to (* 1 (* 2 (* 3 (* 4 (* 5 1))))) Get clever: if a 0 appears anywhere in the list, the product must be 0.

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Improved multiply (define (mult-list L) (cond ((null? L) 1) ((= 0 (car L)) 0) (else (* (car L) (mult-list (cdr L))))))) Better than above: but still do lots of unnecessary multiplications (until you hit zero) Can we escape from a sequence of nested calls once we know theyre unnecessary?

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Exceptions C++ handles this problem with exceptions struct Node { int val; Node *next; }

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C++ Exceptions int mult (Node *L) { try { return multNode(L); } catch (int returnCode) { return returnCode; } int multNode(Node *L) { if (L == NULL) return 1; else if (L->val == 0) throw 0; else return L->val * multNode(L->next); }

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Scheme Continuations A continuation is a Scheme mechanism for storing what you should do with a return value. Two different styles Implement your own Built in Scheme mechanisms

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Scheme continuations schintro_127.html#SEC171 schintro_127.html#SEC171 schintro_141.html#SEC264 schintro_141.html#SEC264 In most languages, calling a function creates a stack frame that holds return address for call and variable bindings In Scheme, everything is stored in garbage collected heap Whenever you call a function, you get a pointer to the calling function: partial continuation (draw picture)

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Scheme continuations Scheme actually lets you manipulate these continuations. This is weird! Scheme function: call-with-current-continuation can be abbreviated as call/cc Call/cc is used to call another function, but it passes along the current continuation as an argument.

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Continuations example (define (resumable-fun) (display 1) (display (call/cc abortable-fun)) (display 2)) (define (abortable-fun escape-fun) (display a) (if (bad-thing-happens) (escape-fun 0)) (display b)) (resumable-fun)

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Continuations with multiply Problem: how to use call/cc with an argument? (define (mult-list L) (call/cc mult-list-main L)) ;; this is bad code – cant take ;; a list Trick: have call/cc call an anonymous function (define (mult-list L) (call/cc (lambda (escape) (mult-list L escape)))

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Multiply with continuations (define (mult-list-main L escape) (cond ((null? L) 1) ((=0 (car L)) escape 0) (else (* (car L) (mult-list-main (cdr L) escape)))) (define (mult-list L) (call/cc (lambda (escape) (mult-list-main L escape)))

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Implement your own continuation ;; con has to be done multiplications (define (mult-list L con) (cond ((null? L) (con 1)) ((= 0 (car L) 0) (else (mult-list (cdr L) (lambda (n) (* n (con (car L))))))) To actually call the function: (define (id x) x) (mult-list (1 2 3) id)

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