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Linear and substructural types are powerful tools, but adding them to standard functional programming languages often means introducing extra annotations and typing machinery. We propose a lightweight substructural type system design that…

We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…

In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

We present a new type system combining occurrence typing, previously used to type check programs in dynamically-typed languages such as Racket, JavaScript, and Ruby, with dependent refinement types. We demonstrate that the addition of…

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…

Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through…

Multiparty sessions with asynchronous communications and global types play an important role for the modelling of interaction protocols in distributed systems. In designing such calculi the aim is to enforce, by typing, good properties for…

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…

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…

Continual Learning (CL) enables machine learning models to learn from continuously shifting new training data in absence of data from old tasks. Recently, pretrained vision transformers combined with prompt tuning have shown promise for…

We propose an extension of pure type systems with an algebraic presentation of inductive and co-inductive type families with proper indices. This type theory supports coercions toward from smaller sorts to bigger sorts via explicit type…

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…

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.…

Sequence prediction and classification are ubiquitous and challenging problems in machine learning that can require identifying complex dependencies between temporally distant inputs. Recurrent Neural Networks (RNNs) have the ability, in…

Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make…

Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…

Mutexes (i.e., locks) are well understood in separation logic, and can be specified in terms of either protecting an invariant or atomically changing the state of the lock. In this abstract, we develop the same styles of specifications for…