6.001 Tutorial 1, Spring 2004

Introduction:  (5min)

Me:
  bcr@mit.edu
  PhD student, computer vision
  Other bits: music, sports, outdoors
Students:
  Name? Year? Major? Programming background? Favorite thing to do?
  Favorite snack?
  
  Take photo of class holding up sign of their name

Logistics: (3min)

Deadlines:

PSET 1 - Due Tuesday midnight
Lecture 3 - Due Wednesday 9am
Project 1 - Due Friday

  ** Don't try to do psets 2 hours before they are due (10-midnight
  ** Tuesday), there is only one server and it bogs down

Questions?

Philosophy of the course:

* What is this course about?  How to think.

* Scheme:

* Why scheme?
  It's got VERY simple syntax - compare C++
  Very mathematical -- based on lambda calculus
  Can focus using language, not learning language
  Basis of Python
  Some real systems built with Scheme/LISP: 
    yahoo! store, airline scheduling, AI

* Syntax: (case insensitive)

* Self-evaluating:

e.g.
5 => 5
17 => 17
"foo" => "foo"

* Combination:
  (procedure argument argument ...)

Evaluation Rule:
  1) evaluate subexpressions in any order
  2) APPLY value of proc to value of arguments

Application Rule:
  1) if primitive procedure, then just do it!
  2) if compound procedure, then evalute the body of the procedure
     with each formal parameter replaced by the corresponding actual
     argument value.

e.g.
(+ 1 2)
(+ 1 (+ 2 3)) 
(mystery-box (something 7))

Terminology:

evaluation -- Give value to some input
application - substitution model
parameters
arguments
expression
value
printed representation

Special Forms - exceptions to the rule

Define:

(define name value-exp)
Evaluation rule:
  1) evaluate value-exp
  2) entry in table <name,value of value-exp>

[Terminology: bind, binding]

define is NOT = like in C
Used to CREATE bindings (entries in the table)
Only convenience that it also replaces an existing binding
Only allowed at the top level, or in a lambda body (more on this later)

(define x 3)
(define y (+ 1 2))
  contents of table?

Lambda:  (my favorite! -- can do almost all the rest with lambda)

(lambda param-list body)
param-list: (var var var)
body: scheme expressions (can be more than one, value of last is returned)

[Terminology: variable, name, procedure]

e.g.
(lambda (x) 
  (+ x 1))
(lambda () 1 2)
(lambda (x) 
  (define y 3) 
  (+ x y))

Evaluation rule:
  1) Create a double-bubble.  (draw picture)

DO NOT EVALUATE BODY (only evaluated when procedure applied!)

; Syntactic sugar:

(define (foo bar) (+ bar 1))
(define foo (lambda (bar) (+ bar 1)))
See the pattern?

; If:

(if test consequent alternative)
; does consequent if test evaluates to NOT #f.
(if 0 1 2)        ; 1
(if + 1 2)        ; 1

; Problems:

(+ 3 4 6)                   13
(- 1)                       -1
(/ 5)                       .2
(define x 3) (= x 3)        #t
(lambda (x) (+ x 1))        proc

; Preface: 2 types of examples: easy and hard.. guess which this is:
((lambda (x y) (y x)) (lambda () 3) (lambda (z) (+ (z) 3)))
;Value: 6
; Walk through step by step.. it isn't hard when you follow rules

; Fantasy football example:
; touchdown: 6pts
; reception yards: 20 yards per point
; fumbles: -1 pts
; fumbles lost: -2 pts

(define fantasy
  (lambda (t r f fl) 
    ((+ (* 6 t) (/ r 20) (* f -1) (* fl -2)))))

; Randy Moss' stats: tds=1; rec yds=150; fumbles=0; fumbles lost=0
(fantasy 1 150 0 0)

f(x) = m * x + b
(lambda (x) (+ (* m x) b))
Eg: (lambda (x) (+ (* 2 x) 3))

Teaser:
(define line-maker
  (lambda (m b)
     (lambda (x) (+ (* m x) b))))
(define f
  (line-maker 1 0))

(f 0)
(f 5)

Teaser:
Why does if need to be a special form?

(define true 
  (lambda (first second) first))
(define false 
  (lambda (first second) second))
(define my-if 
  (lambda (test tb fb) (test tb fb)))

; (can do substitution model to figure out)

; Where does it fail?
(my-if true 1 (/ 1 0))

; Questions? (if time)