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We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on Fraenkel-Mostowski (FM) set theory how to address this through first-class names: in this paper we present a dependent type theory for programming and reasoning with such names. Our development is… (More)

We consider programming language aspects of algorithms that operate on data too large to fit into memory. In previous work we have introduced IntML, a functional programming language with primitives that support the implementation of such algorithms. We have shown that IntML can express all LOGSPACE functions but have left open the question how easy it is… (More)

In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. in Ghica's approach to hardware synthesis, or in joint work with Dal Lago on programming with sublinear space. This paper relates such semantically… (More)

A number of complexity classes, most notably PTIME, have been characterised by subsystems of linear logic. In this paper we show that the functions computable in logarithmic space can also be characterised by a restricted version of linear logic. We introduce Stratified Bounded Affine Logic (SBAL), a restricted version of Bounded Linear Logic, in which not… (More)

We consider the problem of functional programming with data in external memory, in particular as it appears in sublinear space computation. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot compose functions directly for lack of space for the intermediate result,… (More)

- Ulrich Schöpp
- 2006

We study pointer programs as a model of structured computation within logspace. Pointer programs capture the common description of logspace algorithms as programs that take as input some structured data (e.g. a graph) and that store in memory only a constant number of pointers to the input (e.g. to the graph nodes). Starting from pure pointer programs, in… (More)

We present a sequent calculus for formally verifying modal µ-calculus properties of concurrent processes. Building on work by Dam and Gurov, the proof system contains rules for the explicit manipulation of fixed-point approximants. We develop a new syntax for approximants, incorporating, in particular, modalities for approximant modification. We make… (More)

Many logspace algorithms are naturally described as programs that operate on a structured input (e.g., a graph), that store in memory only a constant number of pointers (e.g., to graph nodes) and that do not use pointer arithmetic. Such “pure pointer algorithms” thus are a useful abstraction for studying the nature of logspace-computation.
In… (More)

In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used by a number of authors for the design of compilation methods, in particular for applications where resource control is important. The work in this area has focused on call-by-name languages. In this… (More)