Related papers: Call-by-name Gradual Type Theory
Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form $x\,y$ which decompose a compound data structure into its…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…
Within a component-based approach allowing dynamic reconfigurations, sequences of successive reconfiguration operations are expressed by means of reconfiguration paths, possibly infinite. We show that a subclass of such paths can be…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It…
We formalize a new type system for Elixir, a dynamically typed functional programming language of growing popularity that runs on the Erlang virtual machine. Our system combines gradual typing with semantic subtyping to enable precise,…
We introduces a category-theoretic framework for modelling trust as applied to trusted computation systems and remote attestation. By formalizing elements, claims, results, and decisions as objects within a category, and the processes of…
The complexity of the operating environment and required technologies for highly automated driving is unprecedented. A different type of threat to safe operation besides the fault-error-failure model by Laprie et al. arises in the form of…
Type classes are an elegant extension to traditional, Hindley-Milner based typing systems. They are used in modern, typed languages such as Haskell to support controlled overloading of symbols. Haskell 98 supports only single-parameter and…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing…
We investigate, in the context of functional prototype-based lan- guages, a calculus of objects which might extend themselves upon receiving a message, a capability referred to by Cardelli as a self-inflicted operation. We present a sound…
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…