FACILE: A symmetric integration of concurrent and functional programming

Domain theory is the mathematical theory underlying denotational semantics. This thesis presents a formalization of domain theory in the Higher Order Logic (HOL) theorem proving system along with a mechanization of proof functions and other tools to support reasoning about the denotations of functional programs. By providing a fixed point operator for functions on certain domains which have a special undefined (bottom) element, this extension of HOL supports the definition of recursive functions which are not also primitive recursive. Thus, it provides an approach to the long-standing and important problem of defining non-primitive recursive functions in the HOL system.<br /> <br />Our philosophy is that there must be a direct correspondence between elements of complete partial orders (domains) and elements of HOL types, in order to allow the reuse of higher order logic and proof infrastructure already available in the HOL system. Hence, we are able to mix domain theoretic reasoning with reasoning in the set theoretic HOL world to advantage, exploiting HOL types and tools directly. Moreover, by mixing domain and set theoretic reasoning, we are able to eliminate almost all reasoning about the bottom element of complete partial orders that makes the LCF theorem prover, which supports a first order logic of domain theory, difficult and tedious to use. A thorough comparison with LCF is provided.<br /> <br />The advantages of combining the best of the domain and set theoretic worlds in the same system are demonstrated in a larger example, showing the correctness of a unification algorithm. A major part of the proof is conducted in the set theoretic setting of higher order logic, and only at a late stage of the proof domain theory is introduced to give a recursive definition of the algorithm, which is not primitive recursive. Furthermore, a total well-founded recursive unification function can be defined easily in pure HOL by proving that the unification algorithm (defined in domain theory) always terminates; this proof is conducted by a non-trivial well-founded induction. In such applications, where non-primitive recursive HOL functions are defined via domain theory and a proof of termination, domain theory constructs only appear temporarily.

Concurrent Clean is an experimental, lazy, higher-order parallel functional programming language based on term graph rewriting. An important difference with other languages is that in Clean graphs are manipulated and not terms. This can be used by the programmer to control communication and sharing of computation. Cyclic structures can be defined. Concurrent Clean furthermore allows to control the (parallel) order of evaluation to make efficient evaluation possible. With help of sequential annotations the default lazy evaluation can be locally changed into eager evaluation. The language enables the definition of partially strict data structures which make a whole new class of algorithms feasible in a functional language. A powerful and fast strictness analyser is incorporated in the system. The quality of the code generated by the Clean compiler has been greatly improved such that it is one of the best code generators for a lazy functional language. Two very powerful parallel annotations enable the programmer to define concurrent functional programs with arbitrary process topologies. Concurrent Clean is set up in such a way that the efficiency achieved for the sequential case can largely be maintained for a parallel implementation on loosely coupled parallel machine architectures.

A type theoretic programming language is introduced that is based on lambda calculus with coproducts, products and inductive types, and additionally allows the definition of recursive functions in the way that is common in most functional programming languages. A formal system is presented that checks whether such a definition is structurally recursive and a soundness theorem is shown for this system. Thus all functions passing this check are ensured to terminate on all inputs. For the moment only non-mutual recursive functions are considered.

Automatic parallelization of recursive functions with rewriting rules

Datalog is a carefully restricted logic programming language. What makes Datalog attractive is its declarative fixpoint semantics: Datalog queries consist of simple Horn clauses, yet Datalog solvers efficiently compute all derivable tuples even for recursive queries. However, as we argue in this paper, Datalog is ill-suited as a programming language and Datalog programs are hard to write and maintain. We propose a “new” frontend for Datalog: functional programming with sets called functional IncA. While programmers write recursive functions over algebraic data types and sets, we transparently translate all code to Datalog relations. However, we retain Datalog’s strengths: Functions that generate sets can encode arbitrary relations and mutually recursive functions have fixpoint semantics. We also ensure that the generated Datalog program terminates whenever the original functional program terminates, so that we can apply off-the-shelve bottom-up Datalog solvers. We demonstrate the versatility and ease of use of functional IncA by implementing a type checker, a program transformation, an interpreter of the untyped lambda calculus, two data-flow analyses, and clone detection of Java bytecode.

Functional programming (FP) is regularly touted as the way forward for bringing parallel, concurrent, and distributed programming to the mainstream. The popularity of the rationale behind this viewpoint has even led to a number of object-oriented (OO) programming languages outside the Smalltalk tradition adopting functional features such as lambdas and thereby function closures. However, despite this established viewpoint of FP as an enabler, reliably distributing function closures over a network, or using them in concurrent environments nonetheless remains a challenge across FP and OO languages. This paper takes a step towards more principled distributed and concurrent programming by introducing a new closure-like abstraction and type system, called spores, that can guarantee closures to be serializable, thread-safe, or even have custom user-defined properties. Crucially, our system is based on the principle of encoding type information corresponding to captured variables in the type of a spore. We prove our type system sound, implement our approach for Scala, evaluate its practicality through a small empirical study, and show the power of these guarantees through a case analysis of real-world distributed and concurrent frameworks that this safe foundation for closures facilitates.

In this thesis, we explore techniques for the development and verification of programs in a high-level, expressive, and safe programming language. Our programs can express problems over unbounded domains and over recursive and mutable data structures. We present an implementation language flexible enough to build interesting and useful systems. We mostly maintain a core shared language for the specifications and the implementation, with only a few extensions specific to expressing the specifications. Extensions of the core shared language include imperative features with state and side effects, which help when implementing efficient systems. Our language is a subset of the Scala programming language. Once verified, programs can be compiled and executed using the existing Scala tools. We present algorithms for verifying programs written in this language. We take a layer-based approach, where we reduce, at each step, the program to an equivalent program in a simpler language. We first purify functions by transforming away mutations into explicit return types in the functions' signatures. This step rewrites all mutations of data structures into cloning operations. We then translate local state into a purely functional code, hence eliminating all traces of imperative programming. The final language is a functional subset of Scala, on which we apply verification. We integrate our pipeline of translations into Leon, a verifier for Scala. We verify the core functional language by using an algorithm already developed inside Leon. The program is encoded into equivalent first-order logic formulas over a combination of theories and recursive functions. The formulas are eventually discharged to an external SMT solver. We extend this core language and the solving algorithm with support for both infinite-precision integers and bit-vectors. The algorithm takes into account the semantics gap between the two domains, and the programmer is ultimately responsible to use the proper type to represent the data. We build a reusable interface for SMT-LIB that enables us to swap solvers transparently in order to validate the formulas emitted by Leon. We experiment with writing solvers in Scala; they could offer both a better and safer integration with the rest of the system. We evaluate the cost of using a higher-order language to implement such solvers, traditionally written in C/C++. Finally, we experiment with the system by building fully working and verified applications. We rely on the intersection of many features including higher-order functions, mutable data structures, recursive functions, and nondeterministic environment dependencies, to build concise and verified applications.

Concurrency has been with us almost from the beginning of computing. Managing and programming for concurrency is a difficult problem and various solutions have been suggested over the years. Debates on message passing vs. remote procedure call, synchronous vs. asynchronous message passing, bounded vs. unbounded buffers, active vs. passive objects etc. still continue. No solution is entirely satisfactory. Concurrent programming usually depends heavily on the nature of the problem at hand and the architecture of the target machine.

Abstract. At a fundamental level, functional and object-oriented programming languages are all ‘higher-order’, in the sense that they support computing with values that are themselves pieces of program code encapsulated with a local environment. In functional languages these ‘active’ values are functions, while in object-oriented languages they are objects. Both styles of higher-order language claim to provide good support for writing adaptable programs, but functional and object-oriented languages achieve this adaptability in different ways: functional programs rely on parameterisation at the value, type and module level, while object-oriented languages rely primarily on subtyping and implementation inheritance. Here we compare these two approaches, mainly in terms of the features and properties of their type systems, and consider the benefits and disadvantages of unifying (or merging) the two paradigms by adding object-oriented features to ML as a base language. We argue that while some of the simpler aspects of object-oriented languages are compatible with ML, adding a full- edged class-based object system to ML leads to an excessively complex type system and relatively little expressive gain, especially if we aim to preserve that mostly functional style of programming that is a major advantage of ML.

The design and implementation of a well-defined set of extensions to the UCSD Pascal System which support concurrent programming is described. The extensions provide for dynamic process creation and interprocess communication using messages. The extensions are designed to be consistent with the UCSD Pascal System philosophy of providing a compact, portable environment for microcomputer software development. The concurrent programming capability extends the range of applications of the UCSD Pascal System to distributed systems, real-time process control, and simulation of discrete processes.

A new declarative programming paradigm, constraint functional logic programming (CFLP) is presented, which unifies systematically all features of constraint, functional and logic programming. CFLP extends constraint functional programming (CFP), which supports equation solving over a functional program, to general constraint programming permitting the use of constraints for programming as well as for posing queries. It also generalises constraint logic programming (CLP), by admitting user-defined functions as a purely functional subsystem of a CLP language. This paper presents the motivation for designing CFLP and its semantics. Programming examples are given in the concrete CFLP language Falcon.KeywordsLogic ProgramLogic ProgrammingConstraint ProgrammingConstraint SystemFunctional ProgrammingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We introduce a novel way to integrate functional and concurrent programming based on intuitionistic linear logic. The functional core arises from interpreting proof reduction as computation. The concurrent core arises from interpreting proof search as computation. The two are tightly integrated via a monad that permits both sides to share the same logical meaning for the linear connectives while preserving their different computational paradigms. For example, concurrent computation synthesizes proofs which can be evaluated as functional programs. We illustrate our design with some small examples, including an encoding of the pi-calculus.KeywordsLink FailureLinear LogicIndex TermFibonacci NumberFunctional CoreThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Investigated is algorithmic learning, in the limit, of correct programs for recursive functions f from both input/output examples of f and several interesting varieties of approximate additional (algorithmic) information about f. Specifically considered, as such approximate additional information about f, are Rose's frequency computations for f and several natural generalizations from the literature, each generalization involving programs for restricted trees of recursive functions which have f as a branch. Considered as the types of trees are those with bounded variation, finite width, and finite rank.

Corecursive definitions are usually only meaningful in functional languages with lazy evaluation semantics, because their domain and range may contain cyclic data graphs. By inspection of the call stack, it is possible in a strict evaluation environment to detect cycles in a computation, and thus transform finite input graphs infinite time. This paper presents a virtual machine with suitable cycle handling primitives and operational semantics to implement strict evaluation of corecursive functions. We discuss the impact on calling conventions and definition constructs, and demonstrate the relevance of the introduced features by application to the domain of infinite precision decimal arithmetics.KeywordsVirtual MachineOutput ParameterRecursive FunctionFunctional LanguageCycle DetectionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

WITH REFINED LINEARITY TEST: AN EXAMPLE OF RECURSIVE NETWORK STRUCTURE IN FP2, A FUNCTIONAL PARALLEL PROGRAMMING LANGUAGE Ricardo Caferra and Philippe Jorrand LIFIA Laboratoire d 'Informatique Fondamentale et d'Intelligence Artificielle IMAG GRENOBLE FRANCE Unification of first order terms is an essential primitive not only in resolution-like theorem provers but also in most AI languages. A rigorous approach to the design of a unification process with a high degree of internal parallelism has been recently proposed in [I ]. Starting with a trivial unification algorithm described by a recursive function in FP2 (a Functional Parallel Programming language developped at LIFIA), that process is obtained through successive transformational steps: