Related papers: Refinement by interpretation in {\pi}-institutions
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their properties. Some of these interpretations are known, while…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
We investigate the value of extending the completeness of a decision model along different dimensions of refinement. Specifically, we analyze the expected value of quantitative, conceptual, and structural refinement of decision models. We…
Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation,…
Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…
In the present work, a natural sequel to \cite{MaPi1}, we further discuss the existence of adjunctions between categories of institutions and of $\pi$-institutions. This is done at both a foundational and an applied level. Firstly, we…
This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of the interpretation. In this way we are able to generalise…
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the…
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
In many real-world applications, the reward function is too complex to be manually specified. In such cases, reward functions must instead be learned from human feedback. Since the learned reward may fail to represent user preferences, it…
Current machine learning models are evaluated through behavioral snapshots, with benchmark accuracies, win rates and outcome-based metrics. Model explanations and evaluations, however, are fundamentally intertwined: understanding why a…
The refinement calculus for logic programs is a framework for deriving logic programs from specifications. It is based on a wide-spectrum language that can express both specifications and code, and a refinement relation that models the…
In this work we explore some applications of the notions of Institution and {\Pi}-Institution in the setting of propositional logics and establish a precise categorial relation between these notions, i.e., we provide a pair of functors that…
Recent deep-learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This chapter covers recent work aiming to interpret models by attributing…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…