# Walk as thread-able expression

Walk as thread-able expression is a method how we can treat walk in space and thread-able expression in arithmetic as the same thing.

## Informal examples

We will give below informal examples, it is based on a variant of Example 2a with $\displaystyle{ \mu = 1, \lambda = \ln 2 }$ and the assignment is $\displaystyle{ A = -\frac{x}{y} }$ which labeled as red numbers on below picture.

There are several walks from 1 to 3 marked by different colors

• the black line encoded the expression $\displaystyle{ 1 \times 8 - 5 = 3 }$
• the purple line encoded the expression $\displaystyle{ (1 - \frac{5}{8}) \times 8 = 3 }$
• the brown line encoded the expression $\displaystyle{ (((1 - \frac{1}{8}) \times 2 - \frac{1}{2}) \times 2 - 1) \times 2 = 3 }$
• the orange line encoded the expression with accumulated infinitesimal by additions and multiplications which is a special integral.

A formal description will involve the completeness of grid systems like above case.