Reconstructing a logic for inductive proofs of properties of functional programs

A logical framework consisting of a polymorphic call-by-value functional language and a first-order logic on the values is presented, which is a reconstruction of the logic of the verification system VeriFun. The reconstruction uses contextual semantics to define the logical value of equations. It equates undefinedness and non-termination, which is a standard semantical approach. The main results of this paper are: Meta-theorems about the globality of several classes of theorems in the logic, and proofs of global correctness of transformations and deduction rules. The deduction rules of VeriFun are globally correct if rules depending on termination are appropriately formulated. The reconstruction also gives hints on generalizations of the VeriFun framework: reasoning on nonterminating expressions and functions, mutual recursive functions and abstractions in the data values, and formulas with arbitrary quantifier prefix could be allowed

A Parallel semantics for normal logic programs plus time

It is proposed that Normal Logic Programs with an explicit time ordering are a suitable basis for a general purpose parallel programming language. Examples show that such a language can accept real-time external inputs and outputs, and mimic assignment, all without departing from its pure logical semantics. This paper describes a fully incremental bottom-up interpreter that supports a wide range of parallel execution strategies and can extract significant potential parallelism from programs with complex dependencies

The JStar language philosophy

This paper introduces the JStar parallel programming language, which is a Java-based declarative language aimed at discouraging sequential programming, en-couraging massively parallel programming, and giving the compiler and runtime maximum freedom to try alternative parallelisation strategies. We describe the execution semantics and runtime support of the language, several optimisations and parallelism strategies, with some benchmark results

Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file

Datalog as a parallel general purpose programming language

The increasing available parallelism of computers demands new programming languages that make parallel programming dramatically easier and less error prone. It is proposed that datalog with negation and timestamps is a suitable basis for a general purpose programming language for sequential, parallel and distributed computers. This paper develops a fully incremental bottom-up interpreter for datalog that supports a wide range of execution strategies, with trade-offs affecting efficiency, parallelism and control of resource usage. Examples show how the language can accept real-time external inputs and outputs, and mimic assignment, all without departing from its pure logical semantics