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We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way is to specify a set of axiomatic equations, and allow proof…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
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…
Lambda calculi with algebraic data types lie at the core of functional programming languages and proof assistants, but conceal at least two fundamental theoretical problems already in the presence of the simplest non-trivial data type, the…
In their usual form, representation independence metatheorems provide an external guarantee that two implementations of an abstract interface are interchangeable when they are related by an operation-preserving correspondence. If our…
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type…
As artificial intelligence systems become increasingly prevalent in education, a fundamental challenge emerges: how can we verify if an AI truly understands how students think and reason? Traditional evaluation methods like measuring…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
Many formal languages include binders as well as operators that satisfy equational axioms, such as commutativity. Here we consider the nominal language, a general formal framework which provides support for the representation of binders,…
In this paper we use pre existing language support for type modifiers and object capabilities to enable a system for sound runtime verification of invariants. Our system guarantees that class invariants hold for all objects involved in…
We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
In deductive verification and software model checking, dealing with certain specification language constructs can be problematic when the back-end solver is not sufficiently powerful or lacks the required theories. One way to deal with this…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
$\mu$-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between $\mu$-Calculus and alternating tree automaton is used to solve the satisfiability and model checking…
Traditional category theory is typically based on set-theoretic principles and ideas, which are often non-constructive. An alternative approach to formalizing category theory is to use E-category theory, where hom sets become setoids. Our…
Andromeda is an LCF-style proof assistant where the user builds derivable judgments by writing code in a meta-level programming language AML. The only trusted component of Andromeda is a minimalist nucleus (an implementation of the…