CS99 Lecture4: Expressions and Statements
- week of 9/11

Statements
- like sentences
- each item in sentence is a token
- use language elements to build statements
- classifications
  - expression  * 
  - assignment  *
  - empty
  - quit 
  - selection
  - repetition
  - save
  - read
- (*) demo this today

* Expression
- like an operation, equation, formula
- something you want Maple to evaluate
- build using tokens (operators, integers, names, etc)
- entering an expression is an EXPRESSION STATEMENT
  ex) > 1+1;

Expression Tree
- use precedence and associativity
- decompose, or parse, tree into nodes and branches
- usually the nodes are operators, functions, numbers

* Assignments
- name := value
  (LHS)   (RHS)
- ways to say:
  name <- value
  name "gets" value
  name "stores" value	
  assign to name the value 
  assign the value to name
- sometimes NAME called a VARIABLE
  because assignment can change value
- other things to assign
  name := expr 
  (Maple evaluates expr, computes a result, stores in name)
  name1 := name2
  (Maple stores the symbolic name2 in name1)
- in fact, Maple has special ability:
  you may use a variable BEFORE assigning it!!!
- checking assignments
  > var
- remembering assignments
  assigned values persist until quitting Maple, assigning a new value,
  entering restart, or removing an assignment
- unassigning:
  > var := 'var'
- "=" vs ":="
  "=" is an equation, which is an expression
  ":=" is an assignment!

Worksheet Management
- need to know rules to handle assignments
- restart: clear all assignments
- kernel modes
  - shared (default) -- all worksheet know all values
  - parallel -- each worksheet runs independently 
- anames() -- show list of assigned names

Evaluating Expressions
- must understand how Maple's "brain" works
- automatic simplification and full evaluation

Automatic Simplification
- reduce "clearly" identical expressions
- > x-x; x+x; x/x;
- sometimes hard to predict

Full evaluation
- how Maple calculates (evaluates) results of an expression
- process:
  - convert expression into tree
  - replace all assigned names with expressions, which are also
    converted to trees
  - perform automatic simplification
  - perform mathematical operations and functions for subexpressions 
    until reaching the final answer
- works from bottom to top

Assignments Revisted
- how does Maple treat assignments during full evaluation?
  > expr;         fully evaluate expr
  > name:=expr    fully evaluate expr and store result in name
- what if expr contains a name n?
  if n is assigned, the assigned expression replaces n
  if n unassigned, n remains symbolic
  But Maple does not change any assignment INSIDE expr!
  example)
  > restart: x:=y+z: y:=1: x;
    output: 1+z
    explanation)
    clear assignments
    x gets y + z
    y gets 1   (the expression for x is still y+z: the assignment y:=1 only 
               changed y)
    evaluate x (Maple replaces y with 1 inside the expression for x 
               DURING full evaluation. So, x fully evaluates to 1+z,
               but x is NOT assigned to 1+z)
- Example 1: see figure 3-6
- Example 2: see figure 3-7

Unevaluation
- single quotes '' delay evaluation
- 'expr' tells Maple to first strip 'expr' of the quotes
- reason why unassignment works
  > a := 'a': 
  Maple strips left side of quotes, then Maple sees a:=a internally.
  So, the name a gets assigned to name a.