Related papers: Formal Verification of Monad Transformers
In model-driven development, an ordered model transformation is a nested set of transformations between source and target classes, in which each transformation is governed by its own pre and post- conditions, but structurally dependent on…
The classical powerset construction is a standard method converting a non-deterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that…
Inspired by the classical theory of modules over a monoid, we give a first account of the natural notion of module over a monad. The associated notion of morphism of left modules ("Linear" natural transformations) captures an important…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can be constructed from oplax bicolimits and bicoequalizers of…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…
Although some work has been done on the metamathematics of Metamath, there has not been a clear definition of a model for a Metamath formal system. We define the collection of models of an arbitrary Metamath formal system, both for…
Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about…
ACL2 has long supported user-defined simplifiers, so-called metafunctions and clause processors, which are installed when corresponding rules of class :meta or :clause-processor are proved. Historically, such simplifiers could access the…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
In this paper, we prove correctness of parallelizing a string matcher using Haskell as a theorem prover. We use refinement types to specify correctness properties, Haskell terms to express proofs and Liquid Haskell to check correctness of…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I,…
As the groupoid model of Hofmann and Streicher proves, identity proofs in intensional Martin-L\"of type theory cannot generally be shown to be unique. Inspired by a theorem by Hedberg, we give some simple characterizations of types that do…
In this work, we study 'reduction monads', which are essentially the same as monads relative to the free functor from sets into multigraphs. Reduction monads account for two aspects of the lambda calculus: on the one hand, in the monadic…