Related papers: Dijkstra Monads for Free
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
While methods of code abstraction and reuse are widespread and well researched, methods of proof abstraction and reuse are still emerging. We consider the use of dependent types for this purpose, introducing a completely mechanical approach…
This paper develops a general method of inference for fixed effects models which is (i) automatic, (ii) computationally inexpensive, (iii) tuning parameter-free, and (iv) highly model agnostic. Specifically, we show how to combine a…
Performing an additive decomposition of arbitrary functions of random elements is paramount for global sensitivity analysis and, therefore, the interpretation of black-box models. The well-known seminal work of Hoeffding characterized the…
Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defines deterministic…
Modal types -- types that are derived from proof systems of modal logic -- have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds…
Shallow embeddings that use monads to represent effects are popular in proof-oriented languages because they are convenient for formal verification. Once shallowly embedded programs are verified, they are often extracted to mainstream…
This work presents a novel posterior inference method for models with intractable evidence and likelihood functions. Error-guided likelihood-free MCMC, or EG-LF-MCMC in short, has been developed for scientific applications, where a…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
Monads are a useful tool for structuring effectful features of computation such as state, non-determinism, and continuations. In the last decade, several generalisations of monads have been suggested which provide a more fine-grained model…
We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…
A long-standing open problem in the semantics of programming languages supporting probabilistic choice is to find a commutative monad for probability on the category DCPO. In this paper we present three such monads and a general…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
We extend Homotopy Type Theory with a novel modality that is simultaneously a monad and a comonad. Because this modality induces a non-trivial endomap on every type, it requires a more intricate judgemental structure than previous modal…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
Awodey, later with Newstead, showed how polynomial functors with extra structure (termed ``natural models'') hold within them the categorical semantics for dependent type theory. Their work presented these ideas clearly but ultimately led…
Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…
For every finitary monad $T$ on sets and every endofunctor $F$ on the category of $T$-algebras we introduce the concept of an ffg-Elgot algebra for $F$, that is, an algebra admitting coherent solutions for finite systems of recursive…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…