Related papers: Really Natural Linear Indexed Type Checking
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is…
Deep Learning systems (DL) based on Deep Neural Networks (DNNs) are more and more used in various aspects of our life, including unmanned vehicles, speech processing, and robotics. However, due to the limited dataset and the dependence on…
A long-standing shortcoming of statically typed functional languages is that type checking does not rule out pattern-matching failures (run-time match exceptions). Refinement types distinguish different values of datatypes; if a program…
Linear programming is a fundamental tool in a wide range of decision systems. However, without privacy protections, sharing the solution to a linear program may reveal information about the underlying data used to formulate it, which may be…
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…
Expressing class specifications via executable constraints is important for various software engineering tasks such as test generation, bug finding and automated debugging, but developers rarely write them. Techniques that infer…
We present an extension of System F with call-by-name exceptions. The type system is enriched with two syntactic constructs: a union type for programs whose execution may raise an exception at top level, and a corruption type for programs…
A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…
This work introduces the novel concept of kind refinement, which we develop in the context of an explicitly polymorphic ML-like language with type-level computation. Just as type refinements embed rich specifications by means of…
This paper presents a novel approach to automatically verify properties of pure data-parallel programs with non-linear indexing -- expressed as pre- and post-conditions on functions. Programs consist of nests of second-order array…
The need to increase accuracy in detecting sophisticated cyber attacks poses a great challenge not only to the research community but also to corporations. So far, many approaches have been proposed to cope with this threat. Among them,…
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
Refinement types turn typechecking into lightweight verification. The classic form of refinement type is the datasort refinement, in which datasorts identify subclasses of inductive datatypes. Existing type systems for datasort refinements…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
Runtime predictive analyses enhance coverage of traditional dynamic analyses based bug detection techniques by identifying a space of feasible reorderings of the observed execution and determining if any of these witnesses the violation of…
It is a strength of graph-based data formats, like RDF, that they are very flexible with representing data. To avoid run-time errors, program code that processes highly-flexible data representations exhibits the difficulty that it must…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
In this paper we introduce a fuzzy constraint linear discriminant analysis (FC-LDA). The FC-LDA tries to minimize misclassification error based on modified perceptron criterion that benefits handling the uncertainty near the decision…