Related papers: The Safe Lambda Calculus
Shielding is a prominent model-based technique to ensure safety of autonomous agents. Classical shielding aims to ensure that nothing bad ever happens and comes with strong guarantees about safety and maximal permissiveness. However,…
Terms in the lambda-calculus can be represented as planar trees decorated with symbols for abstraction and application, and having variables as leaves. In this paper, we concentrate on the branches of such trees, rather than on the trees…
The denotational semantics of the untyped lambda-calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent…
The confluence of untyped lambda-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of lambda-calculus with conditional rewriting and provide general results in…
We define a notion of normal form bisimilarity for the untyped call-by-value lambda calculus extended with the delimited-control operators shift and reset. Normal form bisimilarities are simple, easy-to-use behavioral equivalences which…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
Consider a scenario where a harmfulness evaluation metric intended to filter unsafe responses from a Large Language Model. When applied to individual harmful prompt-response pairs, it correctly flags them as unsafe by assigning a high-risk…
Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for…
Higher-order beta-matching is the following decision problem: given two simply typed lambda-terms, can the first term be instantiated to be beta-equivalent to the second term? This problem was formulated by Huet in the 1970s and shown…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
Safety is a critical feature of controller design for physical systems. When designing control policies, several approaches to guarantee this aspect of autonomy have been proposed, such as robust controllers or control barrier functions.…
It is quite challenging to ensure the safety of reinforcement learning (RL) agents in an unknown and stochastic environment under hard constraints that require the system state not to reach certain specified unsafe regions. Many popular…
In nonmonotonic reasoning from conditional belief bases, an inference operator satisfying syntax splitting postulates allows for taking only the relevant parts of a belief base into account, provided that the belief base splits into…
The notion of subtyping has gained an important role both in theoretical and applicative domains: in lambda and concurrent calculi as well as in programming languages. The soundness and the completeness, together referred to as the…
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
Host-acting agents promise a convenient interaction model in which users specify goals and the system determines how to realize them. We argue that this convenience introduces a distinct security problem: semantic under-specification in…
The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and…
Model-based safety analysis approaches aim at finding critical failure combinations by analysis of models of the whole system (i.e. software, hardware, failure modes and environment). The advantage of these methods compared to traditional…
Learning-based quadruped controllers achieve impressive agility but typically lack formal safety guarantees under model uncertainty, perception noise, and unstructured contact conditions. We introduce SafeMind, a differentiable stochastic…