Global ETD Search
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Showing 1 to 18 of 18 for “"monad"”.
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Monadic and Higher-Order Structure
… In turn, this description leads naturally to a monad–theory correspondence for higher-order algebraic theories, subsuming the classical monad–theory correspondence, and providing a new, monadic understanding of higher-order structure. In proving the monad–theory correspondence for higher-order …
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State transformers and modes of computation
… to adjunctions in a 2-category. A calculus of monads in a 2-category is presented, and general lifting theorems are proved. Applications to constructions in categorical automata theory are given, and a representation theorem for strong monads into the monad of continuations is proved.
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Ultrafilters and compactification
… we show that the ultrafilter space forms a monad in the category of topological spaces. Furthermore, we show that rendering the ultrafilter space suitably separated results in a generation of separated compactifications which coincide with some well-known compactifications. When the …
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Modular Compilers and Their Correctness Proofs
… in terms of denotational semantics based on monads, monad transformers, and a new model of staged computation called metacomputations. A novel form of denotational specification called observational program specification and related proof techniques are developed to assist in modular compiler …
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Programming and static analysis with graded monads
… impure, side-effecting computation using monads. Recent research in program semantics has focussed on graded monads, a useful generalisation of monads which allow the programmer to establish useful properties of a computation purely from their type of a computation. They have been used to …
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Feasibility of Vector Instruction-Set Semantics Using Abstract Monads
… a general-purpose language, Haskell, using its monad and typeclass support to abstract over effects. Another member of the same family is the RISC-V V extension, which specifies instructions for operating on multiple data elements in a single instruction, which is useful for domains with high …
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An inductive approach to ω-categories and their computads
… familially represent the free strict ω-category monad on globular sets, giving in particular a structurally recursive description of the monad multiplication. The second part of the thesis introduces weak ω-categories and their computads. First, computads are defined mutually inductively with the …
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Categorical semantics and composition of tree transducers
… The second approach is based on free monads and monad transformers. In the same way as monoids are used in the theory of character string automata, we use monads in the theory of tree transducers. We generalize the notion of a tree transducer defining the monadic transducer, and we …
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Interactions of (co)monads in Agda
We study interaction laws of monads and comonads in the interactive theorem prover Agda. Effectful computations are modeled as monads, while comonads model computation-running machines. Interaction laws describe how computations may be uniformly run to yield values. We study monads and comonads on …
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Linear/non-Linear Types For Embedded Domain-Specific Languages
… state and concurrency can take advantage of the monad that arises from the LNL model. In Coq, the QWIRE quantum circuit language uses linearity to enforce the no-cloning axiom of quantum mechanics. In homotopy type theory, quantum transformations can be encoded as higher inductive types to …
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Random Variable Spaces: Mathematical Properties and an Extension to Programming Computable Functions
… to Category Theory with special attention to Monads and the Giry Monad. The crux of the dissertation lies in the detailed exploration of Random Variable Spaces. Their mathematical properties are studied, including the establishment of relationships between these spaces through functors based …
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Autonomous Pseudomonoids
… as an Eilenberg-Moore construction for certain monad. As an application we show that the Drinfel'd double of a finite-dimensional Hopf algebra is equivalent to the centre of the associated pseudomonoid. The next piece of theory we develop is a general Radford's formula for autonomous map …
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Names and higher-order functions.
… leads to categorical models that use a strong monad, and examples are devised based on functor categories. The idea of logical relations is used to derive powerful reasoning methods that capture some of the distinction between private and public names. These techniques are shown to be complete …
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The Dialectica Models of Type Theory
… the Dialectica category associated to the error monad as studied by Biering. This model has only weak dependent products. In order to get a model with full dependent products we use the idempotent splitting construction, which generalizes the Karoubi envelope of a category. Making sense of the …
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Second-Order Algebraic Theories
… are the existence of algebraic functors and monad morphisms in the second-order universe. Moreover, we define a notion of translation homomorphism that allows us to establish a 2-categorical type theory correspondence.
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Formally justified and modular Bayesian inference for probabilistic programs
… functional programming abstractions called monad transformers. We develop a compact Haskell library for probabilistic programming closely corresponding to the semantic construction, giving users a high level of assurance in the correctness of the implementation. We also demonstrate on a …
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Probabilistic completion of nondeterministic models
Motivated by Moggi's work [34] on how monads can be used to capture computational behavior, there has been a growing interest in finding monads which capture the precise computational effects generated when combining the theory of probabilistic choice and the theory of nondeterministic choice. The …
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Unhappy Consciousness: Recognition and Reification in Victorian Fiction
… subjective effects of capitalist alienation, a monad whose only intervention in the world is to link predictive results with opaque processes, to "produce" recognition scenes (the solutions to each case) as a salable commodity. He is a machine for retrospection who has no personal past. In …