Type Classes have met a large success in Haskell and Is-abelle, as a solution for sharing notations by overloading and for specifying with abstract structures by quantification on contexts. However, both systems are limited by second-class implementations of these constructs , and these limitations are only overcomed by ad-hoc extensions to the respective… (More)
This paper exhibits the power of programming with dependent types by dint of embedding three domain-specific languages: Cryptol, a language for cryptographic protocols; a small data description language; and relational algebra. Each example demonstrates particular design patterns inherent to dependently-typed programming. Documenting these techniques paves… (More)
This paper presents a method to translate a proof in an ex-tensional version of the Calculus of Constructions into a proof in the Calculus of Inductive Constructions extended with a few axioms. We use a specific equality in order to translate the extensional conversion relation into an intensional system.
We present a simple stochastic rule-based approach to multilevel modelling for computational systems biology. Populations are modelled using multilevel multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such multisets, but now allowing variables to occur (as well as species and… (More)
Plotkin and Pretnar's handlers for algebraic effects occupy a sweet spot in the design space of abstractions for effectful computation. By separating effect signatures from their implementation, algebraic effects provide a high degree of modularity, allowing programmers to express effectful programs independently of the concrete interpretation of their… (More)
This paper is concerned with the asymptotic properties of a restricted class of Petri nets equipped with stochastic mass action semantics. We establish a simple algebraic criterion for the existence of an equilibrium, that is to say an invariant probability that satisfies the detailed balance condition familiar from the thermodynamics of reaction networks.… (More)
We present a reduction of the Turing halting problem (in the simplified form of the Post correspondence problem) to the problem of whether a continuous-time Markov chain (CTMC) presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is… (More)
From the phosphorylation state of a molecule to the volume of a cell, parameters are ubiquitous in systems biology. At the same time, most models involve static or dynamic compartments, for example to separate cells from their environment. We introduce coloured stochastic multilevel multiset rewriting, an expressive formalism for modelling systems with… (More)