  Motivated by a need for a model of reversible computation appropriate for a
Brownian molecular architecture, the $\aleph$ calculus is introduced. This
novel model is declarative, concurrent, and term-based--encapsulating all
information about the program data and state within a single structure in order
to obviate the need for a von Neumann-style discrete computational 'machine', a
challenge in a molecular environment. The name is inspired by the Greek for
'not forgotten', due to the emphasis on (reversibly) learning and un-learning
knowledge of different variables. To demonstrate its utility for this purpose,
as well as its elegance as a programming language, a number of examples are
presented; two of these examples, addition/subtraction and
squaring/square-rooting, are furnished with designs for abstract molecular
implementations. A natural by-product of these examples and accompanying
syntactic sugar is the design of a fully-fledged programming language, alethe,
which is also presented along with an interpreter. Efficiently simulating
$\aleph$ on a deterministic computer necessitates some static analysis of
programs within the alethe interpreter in order to render the declarative
programs sequential. Finally, work towards a type system appropriate for such a
reversible, declarative model of computation is presented.
