Parametric Compositional Data Types

In previous work we have illustrated the benefits that compositional data types (CDTs) offer for implementing languages and in general for dealing with abstract syntax trees (ASTs). Based on Swierstra's data types \'a la carte, CDTs are implemented as a Haskell library that enables the definition of recursive data types and functions on them in a modular and extendable fashion. Although CDTs provide a powerful tool for analysing and manipulating ASTs, they lack a convenient representation of variable binders. In this paper we remedy this deficiency by combining the framework of CDTs with Chlipala's parametric higher-order abstract syntax (PHOAS). We show how a generalisation from functors to difunctors enables us to capture PHOAS while still maintaining the features of the original implementation of CDTs, in particular its modularity. Unlike previous approaches, we avoid so-called exotic terms without resorting to abstract types: this is crucial when we want to perform transformations on CDTs that inspect the recursively computed CDTs, e.g. constant folding.Comment: In Proceedings MSFP 2012, arXiv:1202.240

Towards Nominal Formal Languages

We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages

Process Calculi Abstractions for Biology

Several approaches have been proposed to model biological systems by means of the formal techniques and tools available in computer science. To mention just a few of them, some representations are inspired by Petri Nets theory, and some other by stochastic processes. A most recent approach consists in interpreting the living entities as terms of process calculi where the behavior of the represented systems can be inferred by applying syntax-driven rules. A comprehensive picture of the state of the art of the process calculi approach to biological modeling is still missing. This paper goes in the direction of providing such a picture by presenting a comparative survey of the process calculi that have been used and proposed to describe the behavior of living entities. This is the preliminary version of a paper that was published in Algorithmic Bioprocesses. The original publication is available at http://www.springer.com/computer/foundations/book/978-3-540-88868-

Cyclic Datatypes modulo Bisimulation based on Second-Order Algebraic Theories

Cyclic data structures, such as cyclic lists, in functional programming are tricky to handle because of their cyclicity. This paper presents an investigation of categorical, algebraic, and computational foundations of cyclic datatypes. Our framework of cyclic datatypes is based on second-order algebraic theories of Fiore et al., which give a uniform setting for syntax, types, and computation rules for describing and reasoning about cyclic datatypes. We extract the "fold" computation rules from the categorical semantics based on iteration categories of Bloom and Esik. Thereby, the rules are correct by construction. We prove strong normalisation using the General Schema criterion for second-order computation rules. Rather than the fixed point law, we particularly choose Bekic law for computation, which is a key to obtaining strong normalisation. We also prove the property of "Church-Rosser modulo bisimulation" for the computation rules. Combining these results, we have a remarkable decidability result of the equational theory of cyclic data and fold.Comment: 38 page

BlenX-based compositional modeling of complex reaction mechanisms

Molecular interactions are wired in a fascinating way resulting in complex behavior of biological systems. Theoretical modeling provides a useful framework for understanding the dynamics and the function of such networks. The complexity of the biological networks calls for conceptual tools that manage the combinatorial explosion of the set of possible interactions. A suitable conceptual tool to attack complexity is compositionality, already successfully used in the process algebra field to model computer systems. We rely on the BlenX programming language, originated by the beta-binders process calculus, to specify and simulate high-level descriptions of biological circuits. The Gillespie's stochastic framework of BlenX requires the decomposition of phenomenological functions into basic elementary reactions. Systematic unpacking of complex reaction mechanisms into BlenX templates is shown in this study. The estimation/derivation of missing parameters and the challenges emerging from compositional model building in stochastic process algebras are discussed. A biological example on circadian clock is presented as a case study of BlenX compositionality

Formal mechanization of device interactions with a process algebra

The principle emphasis is to develop a methodology to formally verify correct synchronization communication of devices in a composed hardware system. Previous system integration efforts have focused on vertical integration of one layer on top of another. This task examines 'horizontal' integration of peer devices. To formally reason about communication, we mechanize a process algebra in the Higher Order Logic (HOL) theorem proving system. Using this formalization we show how four types of device interactions can be represented and verified to behave as specified. The report also describes the specification of a system consisting of an AVM-1 microprocessor and a memory management unit which were verified in previous work. A proof of correct communication is presented, and the extensions to the system specification to add a direct memory device are discussed