Related papers: Type System for Four Delimited Control Operators
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
Hutchins' Pure Subtype Systems (PSS) offer a unified framework for types and terms, promising significant advancements in language design for features like dependent types and higher-order subtyping. However, the theory has been hampered by…
We present a correspondence and bisimulation between variants of parametrically polymorphic type systems and variants of finite control automata, such as FSA, PDA, tree automata and Turing machine. Within this correspondence we show that…
We study increasingly expressive type systems, from $F^\mu$ -- an extension of the polymorphic lambda calculus with equirecursive types -- to $F^{\mu;}_\omega$ -- the higher-order polymorphic lambda calculus with equirecursive types and…
We describe a way to represent computable functions between coinductive types as particular transducers in type theory. This generalizes earlier work on functions between streams by P. Hancock to a much richer class of coinductive types.…
Type-level programming is an increasingly popular way to obtain additional type safety. Unfortunately, it remains a second-class citizen in the majority of industrially-used programming languages. We propose a new dependently-typed system…
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…
It was demonstrated in recent work that $d=4$ unitary CFT's satisfy a special property: if a scalar operator with conformal dimension $\Delta$ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary…
Session types have been proposed as a means of statically verifying implementations of communication protocols. Although prior work has been successful in verifying some classes of protocols, it does not cope well with parameterized,…
This paper studies a control method for switching stable coexisting attractors of a class of non-autonomous dynamical systems. The central idea is to introduce a continuous path for the system's trajectory to transition from its original…
We prove that a CPD unilateral weighted shift $W_{\lambda}$ of type III is a quasi-affine transform of the operator $M_z$ of multiplication by the independent variable on the $L^2(\rho)$-closure of analytic complex polynomials on the…
We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson's extension theorem. Next, we show that WEP is equivalent to a…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
This paper presents advanced symbolic time series analysis (ASTSA) for large data sets emanating from cyber physical systems (CPS). The definition of CPS most pertinent to this paper is: A CPS is a system with a coupling of the cyber…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
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…
Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical…
We present new proofs of termination of evaluation in reduction semantics (i.e., a small-step operational semantics with explicit representation of evaluation contexts) for System F with control operators. We introduce a modified version of…
In recent years, the interest in using proof assistants to formalise and reason about mathematics and programming languages has grown. Type-logical grammars, being closely related to type theories and systems used in functional programming,…