Affiliations: Computer Science Department Boston University Boston,
MA 02215, USA. E-mail: {chiyan;shearer;hwxi}@cs.bu.edu
Abstract: The notion of program transformation is ubiquitous in programming
language studies on interpreters, compilers, partial evaluators, etc. In order
to implement a program transformation, we need to choose a representation in
the meta language, that is, the programming language in which we construct
programs, for representing object programs, that is, the programs in the object
language on which the program transformation is to be performed. In practice,
most representations chosen for typed object programs are typeless in the sense
that the type of an object program cannot be reflected in the type of its
representation. This is unsatisfactory as such typeless representations make it
impossible to capture in the type system of the meta language various
invariants in a program transformation that are related to the types of object
programs. In this paper, we propose an approach to implementing program
transformations that makes use of a first-order typeful program representation,
where the type of an object program as well as the types of the free variables
in the object program can be reflected in the type of the representation of the
object program. We introduce some programming techniques needed to handle this
typeful program representation, and then present an implementation of a CPS
transform function where the relation between the type of an object program and
that of its CPS transform is captured in the type system of DML. In a broader
context, we claim to have taken a solid step along the line of research on
constructing certifying compilers.
Keywords: Typeful Program Transformation, Dependent Types, Applied Type System, ATS, Continuation Passing Style, CPS, Closure Conversion
