Monad (category theory) ≈ Monad (category theory)
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A logical relation for monadic encapsulation of state: proving contextual equivalences in the presence of runST Open
We present a logical relations model of a higher-order functional programming language with impredicative polymorphism, recursive types, and a Haskell-style ST monad type with runST. We use our logical relations model to show that runST pr…
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Towards a Calculus of State-based Software Components Open
This paper introduces a calculus of state-based software components modelled as concrete coalgebras for some Set endofunctors, with specified initial conditions. The calculus is parametrized by a notion of behaviour, introduced as a strong…
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Monadic refinements for relational cost analysis Open
Formal frameworks for cost analysis of programs have been widely studied in the unary setting and, to a limited extent, in the relational setting. However, many of these frameworks focus only on the cost aspect, largely side-lining functio…
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Quotient Inductive-Inductive Types Open
Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the\ndefinition of datatypes which have constructors for equalities over the defined\ntype. HITs generalise quotient types and allow to define types which are not\nsets in …
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A graded dependent type system with a usage-aware semantics Open
Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive sum…
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Iterated Covariant Powerset is not a Monad Open
We prove that the double covariant powerset functor PP does not admit any monad structure. The same applies to the n-fold composition of P for any n>1.
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Effekt: Capability-passing style for type- and effect-safe, extensible effect handlers in Scala Open
Effect handlers are a promising way to structure effectful programs in a modular way. We present the Scala library Effekt , which is centered around capability passing and implemented in terms of a monad for multi-prompt delimited continua…
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LWeb: information flow security for multi-tier web applications Open
This paper presents LWeb, a framework for enforcing label-based, information flow policies in database-using web applications. In a nutshell, LWeb marries the LIO Haskell IFC enforcement library with the Yesod web programming framework. Th…
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Sound and robust solid modeling via exact real arithmetic and continuity Open
Algorithms for solid modeling, i.e., Computer-Aided Design (CAD) and computer graphics, are often specified on real numbers and then implemented with finite-precision arithmetic, such as floating-point. The result is that these implementat…
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Evolving Heterotic Gauge Backgrounds: Genetic Algorithms versus Reinforcement Learning Open
The immensity of the string landscape and the difficulty of identifying solutions that match the observed features of particle physics have raised serious questions about the predictive power of string theory. Modern methods of optimisatio…
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Equivalences for free: univalent parametricity for effective transport Open
Homotopy Type Theory promises a unification of the concepts of equality and equivalence in Type Theory, through the introduction of the univalence principle. However, existing proof assistants based on type theory treat this principle as a…
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Combining probabilistic and non-deterministic choice via weak distributive laws Open
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A unifying type-theory for higher-order (amortized) cost analysis Open
This paper presents λ-amor, a new type-theoretic framework for amortized cost analysis of higher-order functional programs and shows that existing type systems for cost analysis can be embedded in it. λ-amor introduces a new modal type for…
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Homotopy-coherent algebra via Segal conditions Open
Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an "algebraic pattern", by which we mean an ∞-category equipped with a factorization system and a collection of "elementary" objects.…
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An effectful way to eliminate addiction to dependence Open
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Parallel Philosophy for MetaOrganizations With MetaOperations: From Leibniz’s Monad to HanoiDAO Open
Welcome to the third issue of IEEE Transactions on Computational Social Systems (TCSS) of 2022. According to the latest update of CiteScoreTracker from Elsevier Scopus released on April 6, 2022, the CitesSore of IEEE TCSS has reached a his…
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Partiality, Revisited: The Partiality Monad as a Quotient Inductive-Inductive Type Open
Capretta's delay monad can be used to model partial computations, but it has the "wrong" notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the "right" notion of equality, weak bisimilarity. …
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Reaching for the Star: Tale of a Monad in Coq Open
Monadic programming is an essential component in the toolbox of functional programmers. For the pure and total programmers, who sometimes navigate the waters of certified programming in type theory, it is the only means to concisely implem…
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Enriched Meanings: Natural Language Semantics with Category Theory Open
1: Introduction Part I: Background 2: Enriched meanings in semantics and pragmatics 3: Category theory Part II: Case Studies 4: Conventional implicature 5: Perspectival reference 6: Uncertainty and conjunction fallacies Part III: Compositi…
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Program Synthesis using Abstraction Refinement Open
We present a new approach to example-guided program synthesis based on counterexample-guided abstraction refinement. Our method uses the abstract semantics of the underlying DSL to find a program $P$ whose abstract behavior satisfies the e…
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Commutative Monads for Probabilistic Programming Languages Open
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Choice Trees: Representing Nondeterministic, Recursive, and Impure Programs in Coq Open
This paper introduces ctrees, a monad for modeling nondeterministic, recursive, and impure programs in Coq. Inspired by Xia et al.'s itrees, this novel data structure embeds computations into coinductive trees with three kind of nodes: ext…
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The Quantum Monad on Relational Structures Open
Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction, and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in …
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Relational algebra by way of adjunctions Open
Bulk types such as sets, bags, and lists are monads, and therefore support a notation for database queries based on comprehensions. This fact is the basis of much work on database query languages. The monadic structure easily explains most…
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All $(\infty,1)$-toposes have strict univalent universes Open
We prove the conjecture that any Grothendieck $(\infty,1)$-topos can be presented by a Quillen model category that interprets homotopy type theory with strict univalent universes. Thus, homotopy type theory can be used as a formal language…
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Signals and Comonads Open
We propose a novel discipline for programming stream functions and for the semantic description of stream manipulation languages based on the observation that both general and causal stream functions can be characterized as coKleisli arrow…
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Dijkstra monads forever: termination-sensitive specifications for interaction trees Open
This paper extends the Dijkstra monad framework, designed for writing specifications over effectful programs using monadic effects, to handle termination sensitive specifications over interactive programs. We achieve this by introducing ba…
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Monads on dagger categories Open
The theory of monads on categories equipped with a dagger (a contravariant identity-on-objects involutive endofunctor) works best when everything respects the dagger: the monad and adjunctions should preserve the dagger, and the monad and …
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Desugaring Haskell's do-notation into applicative operations Open
Monads have taken the world by storm, and are supported by do-notation (at least in Haskell). Programmers are increasingly waking up to the usefulness and ubiquity of Applicatives, but they have so far been hampered by the absence of suppo…
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Weakest Preconditions in Fibrations Open
Weakest precondition transformers are useful tools in program verification. One of their key properties is compositionality, that is, the weakest precondition predicate transformer (wppt for short) associated to program f;g should be equal…