20 December 2010 - 14h00
Cartesian Programming (HDR defence) (HDR)
by John Plaice from University of New South Wales
Abstract: We present a new form of declarative programming inspired by the Cartesian coordinate sys-
tem. This Cartesian programming, illustrated by the TransLucid language, assumes that all
programmed entities vary with respect to all possible dimensions, or degrees of freedom. This
model is immediately applicable to areas of science, engineering and business in which working
with multiple dimensions is common. It is also well suited to specification and programming in
situations where a problem is not fully understood, and, with refinement, more parameters will
be taken into consideration as time progresses.
In the Cartesian model, these dimensions include, for all entities, all possible parameters, be
these explicit or implicit, visible or hidden. As a result, defining the aggregate semantics of an
entire system is simplified, much as the use of the universal relation simplifies the semantics of a
relational database system. Evolution through time is handled through the use of a special time
dimension that does not allow access to the future.
In TransLucid, any atomic value may be used as a dimension. A context maps each dimension
to its corresponding ordinate. A context delta is the partial equivalent. An expression is evaluated
in a given context, and this context may be queried, dimension by dimension, or perturbed by a
A variable in TransLucid may have several definitions, and given a current context, the bestfit
(most specific) definitions with respect to that context are chosen and evaluated separately, and
the results are combined together. The set of definitions for a variable define a hyperdaton, which
can be understood as an arbitrary-dimensional array of arbitrary extent.
Functional abstraction in TransLucid requires two kinds of parameters: value parameters, with
call-by-value semantics, are used to pass dimensions and constants; named parameters, with call-
by-name semantics, are used to pass hyperdatons. Where clauses, used for local definitions, define
both new variables and new dimensions of variance.
This thesis presents the full development of Cartesian programming and of TransLucid, com-
plete with a historical overview leading to their conception. Both the denotational and operational
semantics are presented, as is the implementation, designed as a library. One important result is
that the operational semantics requires only the evaluation and caching of relevant dimensions,
thereby ensuring that space usage is kept to a minimum. Two applications using the TransLucid
library are presented, one a standalone interpreter, the other an interactive code browser and
The set of equations defining a TransLucid system can vary over time, a special dimension. At
each instant, the set of equations may be modified, but in so doing can only affect the present and
future of the system. Timing semantics is always synchronous. There are several possible ways
for multiple TransLucid systems to interact.
The caching mechanism provided in the operational semantics allows for the efficient imple-
mentation of systems whose calling structure is highly irregular. For more regular structures, it
is possible to create even more efficient bottom-up solutions, in which recursive instantiations of
functions are eliminated, with clear bounds on memory usage and computation.
Cartesian programming is not just designed as a standalone paradigm, but as a means of better
understanding other paradigms. We examine imperative programming and side-effects, and show
that these, under certain conditions, can be translated into TransLucid, thereby allowing the
design of new imperative constructs in the original language.