# Sequence-Based Specification (SBS)

If you have been given access to work on the advanced SBS work, click here...

- Theory: Prowell Axiom System
- Practice: Interrupts
- Tools: Aleph

## Axioms

Lets develop an axiomatic formulation for sequence enumeration and abstraction. There are several goals for this work.

- Unify sequence enumeration and sequence abstraction. Read more...
- Develop the mathematics for composition of enumerations. Read more...
- If possible, identify a classification system for abstractions based on formal properties. Read more...
- Correctly incorporate advanced refinement techniques such as interrupts. Read more...

This *should* lead to cleaner and simpler implementations of tools for SBS, along with better practices.

## Questions

Key questions are:

- How do we characterize notions of homomorphism and isomorphism in sequence enumerations? More...
- Should we introduce nondeterministic refinements to the framework? More...
- Is there a natural decomposition (composition) theory for abstractions? More...
- Is there an advantage to developing the theory using relations instead of functions? More...

In particular, lets develop the theory in the most general sense, with no assumptions of either *finiteness* or *discreteness*.

If you are interested in working on this, please create an account and contribute.

## Early Results

It seems that it is worthwhile to discuss a mathematically simpler object I call a *semienumeration* before tackling enumerations. It has only a few axioms, and does not associate sequences with values. It isolates the thing that may be most significant in an enumeration: the reduction relation.

Representation theorems abound. Some are potentially quite interesting. If we view each symbol as an operator on sets of sequences, we can transform them problem in to a sigma algebra and investigate properties of its operators (the symbols).