This issue of the Journal of Functional Programming is dedicated to work presented at
the Workshop on Implicit Computational Complexity in Programming Languages,
affiliated with the 1998 meeting of the International Conference on Functional
Programming in Baltimore.Several machine-independent approaches to computational complexity have been
developed in recent years; they establish a correspondence linking computational
complexity to conceptual and structural measures of complexity of declarative
programs and of formulas, proofs and models of formal theories. Examples include
descriptive complexity of finite models, restrictions on induction in arithmetic and
related first order theories, complexity of set-existence principles in higher order
logic, and specifications in linear logic. We refer to these approaches collectively as
Implicit Computational Complexity. This line of research provides a framework for
a streamlined incorporation of computational complexity into areas such as formal
methods in software development, programming language theory, and database
theory.A fruitful thread in implicit computational complexity is based on exploring the
computational complexity consequences of introducing various syntactic control
mechanisms in functional programming, including restrictions (akin to static typing)
on scoping, data re-use (via linear modalities), and iteration (via ramification of
data). These forms of control, separately and in combination, can certify bounds
on the time and space resources used by programs. In fact, all results in this area
establish that each restriction considered yields precisely a major computational
complexity class. The complexity classes thus obtained range from very restricted
ones, such as NC and Alternating logarithmic time, through the central classes Poly-Time and Poly-Space, to broad classes such as the Elementary and the Primitive
Recursive functions.Considerable effort has been invested in recent years to relax as much as possible
the structural restrictions considered, allowing for more exible programming and
proof styles, while still guaranteeing the same resource bounds. Notably, more
exible control forms have been developed for certifying that functional programs
execute in Poly-Time.The 1998 workshop covered both the theoretical foundations of the field and steps
toward using its results in various implemented systems, for example in controlling
the computational complexity of programs extracted from constructive proofs. The
five papers included in this issue nicely represent this dual concern of theory and
practice. As they are going to print, we should note that the field of Implicit
Computational Complexity continues to thrive: successful workshops dedicated to
it were affiliated with both the LICS'99 and LICS'00 conferences. Special issues, of
Information and Computation dedicated to the former, and of Theoretical Computer
Science to the latter, are in preparation.
Probabilistic Recursion Theory and Implicit Computational Complexity
