Functional Ownership through Fractional Uniqueness

Ownership and borrowing systems, designed to enforce safe memory management without the need for garbage collection, have been brought to the fore by the Rust programming language. Rust also aims to bring some guarantees offered by functional programming into the realm of performant systems code, but the type system is largely separate from the ownership model, with type and borrow checking happening in separate compilation phases. Recent models such as RustBelt and Oxide aim to formalise Rust in depth, but there is less focus on integrating the basic ideas into more traditional type systems. An approach designed to expose an essential core for ownership and borrowing would open the door for functional languages to borrow concepts found in Rust and other ownership frameworks, so that more programmers can enjoy their benefits. One strategy for managing memory in a functional setting is through uniqueness types, but these offer a coarse-grained view: either a value has exactly one reference, and can be mutated safely, or it cannot, since other references may exist. Recent work demonstrates that linear and uniqueness types can be combined in a single system to offer restrictions on program behaviour and guarantees about memory usage. We develop this connection further, showing that just as graded type systems like those of Granule and Idris generalise linearity, Rust's ownership model arises as a graded generalisation of uniqueness. We combine fractional permissions with grading to give the first account of ownership and borrowing that smoothly integrates into a standard type system alongside linearity and graded types, and extend Granule accordingly with these ideas.Comment: 23 pages + references. In submissio

Implementing functional programs using mutable abstract data types

Journal ArticleWe study the following problem in this paper. Suppose we have a purely functional program that uses a set of abstract data types by invoking their operations. Is there an order of evaluation of the operations in the program that preserves the applicative order of evaluation semantics of the program even when the abstract data types behave as mutable modules. An abstract data type is mutable if one of its operations destructively updates the object rather than returning a new object as a result. This problem is important for several reasons. It can help eliminate unnecessary copying of data structure states. It supports a methodology in which one can program in a purely functional notation for purposes of verification and clarity, and then automatically transform the program into one in a n object oriented, imperative language, such as CLU, ADA, Smalltalk, etc., that supports abstract data types. It allows accruing both the benefits of using abstract data types in programming, and allows modularity and verifiability

Q# as a Quantum Algorithmic Language

Q# is a standalone domain-specific programming language from Microsoft for writing and running quantum programs. Like most industrial languages, it was designed without a formal specification, which can naturally lead to ambiguity in its interpretation. We aim to provide a formal language definition for Q#, placing the language on a solid mathematical foundation and enabling further evolution of its design and type system. This paper presents $\lambda$-Q#, an idealized version of Q# that illustrates how we may view Q# as a quantum Algol (algorithmic language). We show the safety properties enforced by $\lambda$-Q#'s type system and present its equational semantics based on a fully complete algebraic theory by Staton.Comment: In Proceedings QPL 2022, arXiv:2311.0837

A functional approach to heterogeneous computing in embedded systems

Developing programs for embedded systems presents quite a challenge; not only should programs be resource efficient, as they operate under memory and timing constraints, but they should also take full advantage of the hardware to achieve maximum performance. Since performance is such a significant factor in the design of embedded systems, modern systems typically incorporate more than one kind of processing element to benefit from specialized processing capabilities. For such heterogeneous systems the challenge in developing programs is even greater.In this thesis we explore a functional approach to heterogeneous system development as a means to address many of the modularity problems that are typically found in the application of low-level imperative programming for embedded systems. In particular, we explore a staged hardware software co-design language that we name Co-Feldspar and embed in Haskell. The staged approach enables designers to build their applications from reusable components and skeletons while retaining control over much of the generated source code. Furthermore, by embedding the language in Haskell we can exploit its type classes to write not only hardware and software programs, but also generic programs with overloaded instructions and expressions. We demonstrate the usefulness of the functional approach for co-design on a cryptographic example and signal processing filters, and benchmark software and mixed hardware-software implementations. Co-Feldspar currently adopts a monadic interface, which provides an imperative functional programming style that is suitable for explicit memory management and algorithms that rely on a certain evaluation order. For algorithms that are better defined as pure functions operating on immutable values, we provide a signal and array library that extends a monadic language, like Co-Feldspar. These extensions permit a functional style of programming by composing high-level combinators. Our compiler transforms such high-level code into efficient programs with mutating code. In particular, we show how to execute an FFT safely in-place, and how to describe a FIR and IIR filter efficiently as streams. Co-Feldspar’s monadic interface is however quite invasive; not only is the burden of explicit memory management quite heavy on the user, it is also quite easy to shoot on eself in the foot. It is for these reasons that we also explore a dynamic memory management discipline that is based on regions but predictable enough to be of use for embedded systems. Specifically, this thesis introduces a program analysis which annotates values with dynamically allocated memory regions. By limiting our efforts to functional languages that target embedded software, we manage to define a region inference algorithm that is considerably simpler than traditional approaches