T-Tables

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.