7. Visibility

Recursion tables externalize some of the structure we would otherwise have to keep track of while reading a recursive definition.

For simple examples, two questions become especially visible:

Have all constructor cases been handled?

and:

When recursion occurs, does it move toward structurally smaller data?

Base cases and recursive cases become visually distinguishable.

Recursive reduction can be compared directly with the structure represented in the row and column headers.

This can reduce part of the cognitive burden of understanding a definition.

A recursion table does not by itself show that a definition is correct or that every relevant assumption has been made explicit.

This is what recursion tables are meant to add.

They may be useful pedagogically because they give a reader something compact to inspect before moving to more formal reasoning.