Related papers: A Modular Type-checking algorithm for Type Theory …
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
We present the PML 2 language, which provides a uniform environment for programming, and for proving properties of programs in an ML-like setting. The language is Curry-style and call-by-value, it provides a control operator (interpreted in…
State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type…
Erlang is a functional programming language with dynamic typing. The language offers great flexibility for destructing values through pattern matching and dynamic type tests. Erlang also comes with a type language supporting parametric…
We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our…
We sketch a tentative proof of P-completeness for the $\beta$-convertibility problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.
We present an approach for modeling the Semantic Web as a type system. By using a type system, we can use symbolic representation for representing linked data. Objects with only data properties and references to external resources are…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three ingredients: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
Subtyping is a crucial ingredient of session type theory and its applications, notably to programming language implementations. In this paper, we study effective ways to check whether a session type is a subtype of another by applying a…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for…
Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
Type theory can be described as a generalised algebraic theory. This automatically gives a notion of model and the existence of the syntax as the initial model, which is a quotient inductive-inductive type. Algebraic definitions of type…
We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…
Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…
Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the…
This technical report investigates Kripke-style modal type theories, both simply typed and dependently typed. We examine basic meta-theories of the type theories, develop their substitution calculi, and give normalization by evaluation…