Related papers: The Safe Lambda Calculus
We present a type system for an extension of lambda calculus with a conditional construction, named STAB, that characterizes the PSPACE class. This system is obtained by extending STA, a type assignment for lambda-calculus inspired by…
The design of metaprogramming languages requires appreciation of the tradeoffs that exist between important language characteristics such as safety properties, expressive power, and succinctness. Unfortunately, such tradeoffs are little…
Ensuring the safe alignment of large language models (LLMs) with human values is critical as they become integral to applications like translation and question answering. Current alignment methods struggle with dynamic user intentions and…
In this paper, we consider the problem of learning safe policies for probabilistic-constrained reinforcement learning (RL). Specifically, a safe policy or controller is one that, with high probability, maintains the trajectory of the agent…
Knapik et al. introduced the safety restriction which constrains both the types and syntax of the production rules defining a higher-order recursion scheme. This restriction gives rise to an equi-expressivity result between order-n pushdown…
Secure function computation has been thoroughly studied and optimized in the past decades. We extend techniques used for secure computation to simulate arbitrary protocols involving a mediator. The key feature of our notion of simulation is…
We observed that safety arguments are prone to stay too abstract, e.g. solutions refer to large packages, argument strategies to complex reasoning steps, contexts and assumptions lack traceability. These issues can reduce the confidence we…
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…
In this paper, we define a new 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. We also prove a completeness result of our realizability…
We present some lambda calculus with explicit substitutions and named variables. The characteristic feature of this calculus is as follows: renaming of bound variables when performing substitutions is done using special reductions and may…
Online-safety regulation under the UK Online Safety Act and the EU Digital Services Act increasingly treats scalar metrics as compliance evidence. Once announced, such a metric also becomes an optimization target: a strategic platform can…
Defining substitution for a language with binders like the simply typed $\lambda$-calculus requires repetition, defining substitution and renaming separately. To verify the categorical properties of this calculus, we must repeat the same…
This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
We give a rigorous characterization of what it means for a programming language to be memory safe, capturing the intuition that memory safety supports local reasoning about state. We formalize this principle in two ways. First, we show how…
Aligned language models face a significant limitation as their fine-tuning often results in compromised safety. To tackle this, we propose a simple method RESTA that performs LLM safety realignment. RESTA stands for REstoring Safety through…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety…
Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In…
Existing LLM agent frameworks lack formal semantics: there is no principled way to determine whether an agent configuration is well-formed or will terminate. We present $\lambda_A$, a typed lambda calculus for agent composition that extends…