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We define BioScapeL, a stochastic pi-calculus in 3D-space. A novel aspect of BioScapeL is that entities have programmable locations. The programmer can specify a particular location where to place an entity, or a location relative to the current location of the entity. The motivation for the extension comes from the need to describe the evolution of populations of biochemical species in space, while keeping a sufficiently high level description, so that phenomena like diffusion, collision, and confinement can remain part of the semantics of the calculus. Combined with the random diffusion movement inherited from BioScape, programmable locations allow us to capture the assemblies of configurations of polymers, oligomers, and complexes such as microtubules or actin filaments. Further new aspects of BioScapeL include random translation and scaling. Random translation is instrumental in describing the location of new entities relative to the old ones. For example, when a cell secretes a hydronium ion, the ion should be placed at a given distance from the originating cell, but in a random direction. Additionally, scaling allows us to capture at a high level events such as division and growth; for example, daughter cells after mitosis have half the size of the mother cell.
Provenance is an increasing concern due to the ongoing revolution in sharing and processing scientific data on the Web and in other computer systems. It is proposed that many computer systems will need to become provenance-aware in order to provide satisfactory accountability, reproducibility, and trust for scientific or other high-value data. To date, there is not a consensus concerning appropriate formal models or security properties for provenance. In previous work, we introduced a formal framework for provenance security and proposed formal definitions of properties called disclosure and obfuscation. In this article, we study refined notions of positive and negative disclosure and obfuscation in a concrete setting, that of a general-purpose programing language. Previous models of provenance have focused on special-purpose languages such as workflows and database queries. We consider a higher-order, functional language with sums, products, and recursive types and functions, and equip it with a tracing semantics in which traces themselves can be replayed as computations. We present an annotation-propagation framework that supports many provenance views over traces, including standard forms of provenance studied previously. We investigate some relationships among provenance views and develop some partial solutions to the disclosure and obfuscation problems, including correct algorithms for disclosure and positive obfuscation based on trace slicing.
We study a dependently typed extension of a multi-stage programming language `a la MetaOCaml, which supports quasi-quotation and cross-stage persistence for manipulation of code fragments as first-class values and an evaluation construct for execution of programs dynamically generated by this code manipulation. Dependent types are expected to bring to multi-stage programming enforcement of strong invariant -- beyond simple type safety -- on the behavior of dynamically generated code. An extension is, however, not trivial because such a type system would have to take stages of types -- roughly speaking, the number of surrounding quotations -- into account. To rigorously study properties of such an extension, we develop $lambda^{MD}$, which is an extension of Hanada and Igarashis typed calculus $lambda^{triangleright%} $ with dependent types, and prove its properties including preservation, confluence, strong normalization for full reduction, and progress for staged reduction. Motivated by code generators that generate code whose type depends on a value from outside of the quotations, we argue the significance of cross-stage persistence in dependently typed multi-stage programming and certain type equivalences that are not directly derived from reduction rules.
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying the extension of definitions and results on pure computations to an effectful setting. Additionally, we show a number of algebraic and order-theoretic laws on diagrams, this way laying the foundations for a diagrammatic calculus of algebraic effects. We give a formal foundation for such a calculus in terms of Lawvere theories and generic effects.
The polymorphic RPC calculus allows programmers to write succinct multitier programs using polymorphic location constructs. However, until now it lacked an implementation. We develop an experimental programming language based on the polymorphic RPC calculus. We introduce a polymorphic Client-Server (CS) calculus with the client and server parts separated. In contrast to existing untyped CS calculi, our calculus is not only able to resolve polymorphic locations statically, but it is also able to do so dynamically. We design a type-based slicing compilation of the polymorphic RPC calculus into this CS calculus, proving type and semantic correctness. We propose a method to erase types unnecessary for execution but retaining locations at runtime by translating the polymorphic CS calculus into an untyped CS calculus, proving semantic correctness.
Differential lambda-calculus was first introduced by Thomas Ehrhard and Laurent Regnier in 2003. Despite more than 15 years of history, little work has been done on a differential calculus with integration. In this paper, we shall propose a differential calculus with integration from programming point of view. We show its good correspondence with mathematics, which is manifested by how we construct these reduction rules and how we preserve important mathematical theorems in our calculus. Moreover, we highlight applications of the calculus in incremental computation, automatic differentiation, and computation approximation.