  What is Sequence Algebra? This is a question that any teacher or student of
mathematics or computer science can engage with. Sequences are in Calculus,
Combinatorics, Statistics and Computation. They are foundational, a step up
from number arithmetic. Sequence operations are easy to implement from scratch
(in Haskell) and afford a wide variety of testing and experimentation. When
bits and pieces of sequence algebra are pulled together from the literature,
there emerges a claim for status as a substantial pre-analysis topic. Here we
set the stage by bringing together a variety of sequence algebra concepts for
the first time in one paper. This provides a novel economical overview,
intended to invite a broad mathematical audience to cast an eye over the
subject. A complete, yet succinct, basic implementation of sequence operations
is presented, ready to play with. The implementation also serves as a benchmark
for introducing Haskell by mathematical example.
