  Parametricity is a property of the syntax of type theory implying, e.g., that
there is only one function having the type of the polymorphic identity
function. Parametricity is usually proven externally, and does not hold
internally. Internalising it is difficult because once there is a term
witnessing parametricity, it also has to be parametric itself and this results
in the appearance of higher dimensional cubes. In previous theories with
internal parametricity, either an explicit syntax for higher cubes is present
or the theory is extended with a new sort for the interval. In this paper we
present a type theory with internal parametricity which is a simple extension
of Martin-L\"of type theory: there are a few new type formers, term formers and
equations. Geometry is not explicit in this syntax, but emergent: the new
operations and equations only refer to objects up to dimension 3. We show that
this theory is modelled by presheaves over the BCH cube category. Fibrancy
conditions are not needed because we use span-based rather than relational
parametricity. We define a gluing model for this theory implying that external
parametricity and canonicity hold. The theory can be seen as a special case of
a new kind of modal type theory, and it is the simplest setting in which the
computational properties of higher observational type theory can be
demonstrated.
