A T-Table sets up each step of the evaluation of an expression. The left-hand-side column holds the current version of the expression according to its current evaluation progress. The right-hand-side holds the operation and assignment of the current step.
The table is called a T-Table because each step assigns a variable starting with a t, short for temporary.
The list in operation column is called the T-Form of the expression.
Example
The following is the T-Table for the arithmetic expression x^2 + 5*x.
| Expression | Operation |
|---|---|
x^2 + 5*x |
|
t1 + 5*x |
t1 = x ^ 2 |
t1 + t2 |
t2 = 5 * x |
t3 |
t3 = t1 + t2 |
Thus, the T-Form of x^2 + 5*x is
t1 = x ^ 2
t2 = 5 * x
t3 = t1 + t2
Algorithm
The algorithm for creating a T-Form from an expression is the automatic programming algorithm.
1-to-1 mapping
It is possible to convert back and forth between an expression and its T-Form. This can be set up in a reverse T-Table.
Example
The reverse T-Table of
t1 = x ^ 2
t2 = 5 * x
t3 = t1 + t2
is
| Expression | Operation |
|---|---|
t3 |
t3 = t1 + t2 |
t1 + t2 |
t2 = 5 * x |
t1 + 5*x |
t1 = x ^ 2 |
x^2 + 5*x |
The expression is
x^2 + 5*x
Readability Parenthesis
If an expression constains a parenthesis that is added for readability, the paranthesis can be preserved using an assignment without an operator.
Example
a + (b*c):
| Expression | Operation |
|---|---|
a + (b*c) |
|
a + (t1) |
t1 = b*c |
a + t2 |
t2 = t1 |
t3 |
t3 = a + t2 |
The assignment to t2 is interpreted as a parenthesis.