Data struct:
    - expression
        - matrix
        - complex

        - polynomial

State Data struct:
    - function
    - variable



Instruction/line:
    if is '?' evaluate label else declare label.

instruction  ::= <label> '=' (<expr> | '?')


Declaration:
    label is a declaration of function or variable name

label        ::= <funcDecl> | <var>
funcDecl     ::= <var> '(' <var> ')'
var          ::= [a-zA-Z]+


Expression:

5. real imag matrix
4. + -
3. * / % **
2. ^
1. ( )    -- not an operator

expr         ::= <sum> | <imag> | <matrix> | <real> | <var> | <funcExpr>

Arithmetic:

sum          ::= <term>   (+ | -)           <sum>    | <term>
term         ::= <factor> (* | / | % | **)? <term>   | <factor>  -- default to '*'
factor       ::= <base>   '^'               <factor> | <base>
base         ::= '(' <expr> ')'                      | <expr>

Leaf:

real         ::= [0-9]+(\.[0-9]+)?
imag         ::= <real> '*'? 'i'
matrix       ::= '[' (<matrixRow> ';')* ']'
matrixRow    ::= '[' (<expr> ',')* ']'
fundExpr     ::= <var> '(' <expr> ')'

REPL:

1. read user input
2. parse it into an ast
3. reduce the ast to the minimum possible form
4.

every expression is a binary tree, except () which can be interpreted by changing the
structure of the tree.

operators and operand are both expression (tree nodes).

operators always need 2 operand  (not leaf node)
operand need 0                   (leaf node)

evaluation of operand return the operand
evaluation of operator, evaluate his childs, perform the operation on them, return the result

fold?
!monoid

    +
   / \
  *   \
 / \   \      3 * 4 + (5 - 3i)
3   4   -
       / \
      5   3i

Node +
|_ Node *
|  |_ Leaf 3
|  |_ Leaf 4
|
|_ Node -
   |_ Leaf 5
   |_ Leaf 3i


i^0 = 1
i^1 = sqrt(-1) = i
i^2 = -1
i^3 = -sqrt(-1) = -i
i^4 = 1





atoms:      evaluate to itself
- rational
- imaginary
- complex

containers:  evaluate contained
- matrix
- variable?
- f() ?

operations:
- +
- -
- *
- /
- %
- ^
- **