LaTiS and Abstract Mathematics

The goal is to build LaTiS on fundamental mathematical principles from Category Theory and Lambda Calculus. The Functions of the LaTiS data model are related to morphisms in category theory. The Functional Programming principles used in the LaTiS DSL can be related to ideas from Lambda Calculus. The three fundamental components of the LaTiS data model combined with the three basic constructs of lambda calculus should enable some really interesting abstract math. The LaTiS Algebra is being implemented as Operations in the DSL.

Until that goal is fully realized, the LaTiS model syntax currently lends itself to algebraic manipulation.

As an example, consider two data sets: a time series of temperature and a time series of humidity:

time -> temperature
time -> humidity

We can treat each of these as a LaTiS Variable (since a Function IS-A Variable) and combine them into a single Dataset as a Tuple:

(time -> temperature, time -> humidity)

If the time samples of both Functions are the same, we can factor out the common domain:

time -> (temperature, humidity)