recitation 1: scheme expressions

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primitive expressions

    self-evaluating expressions (constants)
      boolean:  #t, #f
      numbers:  0, 1, -5, 6.001, 76120398235983942, ....
      strings: "hello", "world", "6.001", ...

    built-in procedures: +, *, sqrt, odd?, zero?, ..

    variables (check lookup table)
      - initial: defines built-in procedures
      - add to lookup table with define
      - means of abstraction

compound expressions (things in parens)

    combinations
       - prefix notation (vs. postfix or infix)
       - variable number of arguments
       - expressions as trees

    special forms
       define -global definitions
       and
       or
       if
       lambda

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identifiers 
    - can't start with a number 
    - can't have white-space
    - can be upper/lower case

reserved keywords 
    =>, and, begin, case, cond, define, delay, else, 
    if, lambda, let, let*, letrec, quasiquote, quote, 
    set! unquote, unquote-splicing

variables
    - In Scheme we don't have to declare the type 
      (e.g. int, boolean, floating point, ...)

use ";"  for comments

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Rules for evaluation 
1. If self-evaluating, return value. 
2. If a name, return value associated with name in environment. 
3. If a special form, do something special. 
4. If a combination, then 
   a. Evaluate all of the subexpressions of 
      combination (in any order) 
   b. Apply the operator to the values of the 
      operands (arguments) and return result

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Mantra Review

   1. Every expression has a value (except for errors, 
      infinite loops and the define special form)
   2. To find the value of a combination,
      * Find values of all subexpressions in any order
      * Apply the value of the first to the values of the rest
   3. The value of a lambda expression is a procedure 

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To find the value of a COMBINATION:
  a.  first, find the value of the ___________
  b,  then, APPLY the value of the ________ to the ___________

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(* 2 3) =>

(*2 3) =>

((*2 3)) =>

(define a 5) =>

(define b (+ a 2)) =>

(define a 3) =>

a =>

b =>

(a) =>

(define define 4) =>

(and #t) =>

(and #t #f) =>

(and #t #f (4)) =>

(define and 5) =>