A program logic for higher-order procedural variables and non-local jumps

Relying on the formulae-as-types paradigm for classical logic, we define a program logic for an imperative language with higher-order procedural variables and non-local jumps. Then, we show how to derive a sound program logic for this programming language. As a by-product, we obtain a non-dependent type system which is more permissive than what is usually found in statically typed imperative languages. As a generic example, we encode imperative versions of delimited continuations operators shift and reset

Refinement of higher-order logic programs

A refinement calculus provides a method for transforming specifications to executable code, maintaining the correctness of the code with respect to its specification. In this paper we extend the refinement calculus for logic programs to include higher-order programming capabilities in specifications and programs, such as procedures as terms and lambda abstraction. We use a higher-order type and term system to describe programs, and provide a semantics for the higher-order language and refinement. The calculus is illustrated by refinement examples

Hailstorm : A Statically-Typed, Purely Functional Language for IoT Applications

With the growing ubiquity of Internet of Things (IoT), more complex logic is being programmed on resource-constrained IoT devices, almost exclusively using the C programming language. While C provides low-level control over memory, it lacks a number of high-level programming abstractions such as higher-order functions, polymorphism, strong static typing, memory safety, and automatic memory management.We present Hailstorm, a statically-typed, purely functional programming language that attempts to address the above problem. It is a high-level programming language with a strict typing discipline. It supports features like higher-order functions, tail-recursion and automatic memory management, to program IoT devices in a declarative manner. Applications running on these devices tend to be heavily dominated by I/O. Hailstorm tracks side effects like I/O in its type system using resource types. This choice allowed us to explore the design of a purely functional standalone language, in an area where it is more common to embed a functional core in an imperative shell. The language borrows the combinators of arrowized FRP, but has discrete-time semantics. The design of the full set of combinators is work in progress, driven by examples. So far, we have evaluated Hailstorm by writing standard examples from the literature (earthquake detection, a railway crossing system and various other clocked systems), and also running examples on the GRiSP embedded systems board, through generation of Erlang

Invited Talk: Towards a Principled Multi-Language Infrastructure

AbstractSun's Java architecture introduced a safe virtual machine (VM) in which an ensemble of software components developed independently could smoothly interoperate. The goal of Microsoft's Common Language Runtime (CLR) is to generalize this approach and allow components in many source languages to interoperate safely. CLR supports flexible interoperation by compiling various source languages into a common intermediate language and by using a unified type system. However, the type system in CLR (and Java VM) enforces only conventional type safety in an object-oriented system. Therefore, higher-level specifications (e.g., resource bounds, generalized access control, formal software protocols) cannot be enforced. Because conventional type systems are too inflexible for real applications, developers often bypass the type system, producing code that steps outside the managed part of the VM; such components cannot be verified.At Yale we have been developing typed common intermediate languages (named FLINT) that can support safely not only the standard object-oriented model, but also higher-order generic (polymorphic) programming and Java-style reflection (introspection). Unlike CLR, our type system is independent of any particular programming model, yet it is capable of expressing all valid propositions and proofs in higher-order predicate logic (so it can be used to capture and verify advanced program properties). The rich type system of FLINT makes it possible to typecheck both compiler intermediate code and low level machine code; this allows typechecking to take place at any phase of compilation, even after optimizations and register allocation. It also leads to a smaller and more extensible VM because low-level native routines that would otherwise be in VM can now be verified and moved into a certified library. This talk describes our vision of the FLINT system, outline our approach to its design, and survey the technologies that can be brought to support its implementation

An Elementary Affine λ-Calculus with Multithreading and Side Effects

International audienceLinear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main contributions are as follows. First, we introduce a modal call-by-value λ-calculus with multithreading and side effects. Second, we provide a combinatorial proof of termination in elementary time for the language. Third, we introduce an elementary affine type system that guarantees the standard subject reduction and progress properties. Finally, we illustrate the programming of iterative functions with side effects in the presented formalism

The design and implementation of a relational programming system.

The declarative class of computer languages consists mainly of two paradigms - the logic and the functional. Much research has been devoted in recent years to the integration of the two with the aim of securing the advantages of both without retaining their disadvantages. To date this research has, arguably, been less fruitful than initially hoped. A large number of composite functional/logical languages have been proposed but have generally been marred by the lack of a firm, cohesive, mathematical basis. More recently new declarative paradigms, equational and constraint languages, have been advocated. These however do not fully encompass those features we perceive as being central to functional and logic languages. The crucial functional features are higher-order definitions, static polymorphic typing, applicative expressions and laziness. The crucial logic features are ability to reason about both functional and non-functional relationships and to handle computations involving search. This thesis advocates a new declarative paradigm which lies midway between functional and logic languages - the so-called relational paradigm. In a relationallanguage program and data alike are denoted by relations. All expressions are relations constructed from simpler expressions using operators which form a relational algebra. The impetus for use of relations in a declarative language comes from observations concerning their connection to functional and logic programming. Relations are mathematically more general than functions modelling non-functional as well as functional relationships. They also form the basis of many logic languages, for example, Prolog. This thesis proposes a new relational language based entirely on binary relations, named Drusilla. We demonstrate the functional and logic aspects of Drusilla. It retains the higher-order objects and polymorphism found in modern functional languages but handles non-determinism and models relationships between objects in the manner of a logic language with notion of algorithm being composed of logic and control elements. Different programming styles - functional, logic and relational- are illustrated. However, such expressive power does not come for free; it has associated with it a high cost of implementation. Two main techniques are used in the necessarily complex language interpreter. A type inference system checks programs to ensure they are meaningful and simultaneously performs automatic representation selection for relations. A symbolic manipulation system transforms programs to improve. efficiency of expressions and to increase the number of possible representations for relations while preserving program meaning

Multiparadigm programming: Novel devices for implementing functional and logic programming constructs in C++

Constructs for functional and logic programming can be smoothly integrated into an existing object-oriented language. We demonstrate this in the context of C++ (a statically-typed object-oriented language with effects and parametric polymorphism) via two libraries: FC++ and LC++. FC++ is a library for functional programming in C++; FC++ supports higher-order polymorphic functions, lazy lists, and a small lambda language; it also contains a large library of useful functions, datatypes, combinators, and monads. LC++ is a library for logic programming in C++; LC++ provides the same general functionality as Prolog, including the ability to return query results lazily (one at a time). Both libraries are embedded in C++ so that they share C++'s static type system, and the library interfaces provide straightforward ways for code from within one paradigm to ``call out' to another. Our work describes the techniques used to implement these libraries in C++ and shows that the resulting multiparadigm language has useful applications in real-world domains. We also describe how many of the implementation techniques can be generalized from C++ and applied to other programming languages to yield similar results.Ph.D.Committee Chair: Yannis Smaragdakis; Committee Member: Mary Jean Harrold; Committee Member: Olin Shivers; Committee Member: Philip Wadler; Committee Member: Spencer Rugabe

Deliverables: a categorical approach to program development in type theory

This thesis considers the problem of program correctness within a rich theory of dependent types, the Extended Calculus of Constructions (ECC). This system contains a powerful programming language of higher-order primitive recursion and higher-order intuitionistic logic. It is supported by Pollack's versatile LEGO implementation, which I use extensively to develop the mathematical constructions studied here. I systematically investigate Burstall's notion of deliverable, that is, a program paired with a proof of correctness. This approach separates the concerns of programming and logic, since I want a simple program extraction mechanism. The Sigma-types of the calculus enable us to achieve this. There are many similarities with the subset interpretation of Martin-Löf type theory. I show that deliverables have a rich categorical structure, so that correctness proofs may be decomposed in a principled way. The categorical combinators which I define in the system package up much logical book-keeping, allowing one to concentrate on the essential structure of algorithms. I demonstrate our methodology with a number of small examples, culminating in a machine-checked proof of the Chinese remainder theorem, showing the utility of the deliverables idea. Some drawbacks are also encountered. I consider also semantic aspects of deliverables, examining the definitions in an abstract setting, again firmly based on category theory. The aim is to overcome the clumsiness of the language of categorical combinators, using dependent type theories and their interpretation in fibrations. I elaborate a concrete instance based on the category of sets, which generalises to an arbitrary topos. In the process, I uncover a subsystem of ECC within which one may speak of deliverables defined over the topos. In the presence of enough extra structure, the interpretation extends to the whole of ECC. The wheel turns full circle