نتایج جستجو برای: monad theory

تعداد نتایج: 783100  

Journal: :Theor. Comput. Sci. 2015
Bart Jacobs

The Dijkstra and Hoare monads have been introduced recently for capturing weakest precondition computations and computations with preand post-conditions, within the context of program verification, supported by a theorem prover. Here we give a more general description of such monads in a categorical setting. We first elaborate the recently developed view on program semantics in terms of a trian...

2012
Ralf Hinze

Many program optimisations involve transforming a program in direct style to an equivalent program in continuation-passing style. This paper investigates the theoretical underpinnings of this transformation in the categorical setting of monads. We argue that so-called absolute Kan Extensions underlie this program optimisation. It is known that every Kan extension gives rise to a monad, the code...

Journal: :CoRR 2013
Paul-André Melliès Noam Zeilberger

The concept of refinement in type theory is a way of reconciling the “intrinsic” and the “extrinsic” meanings of types. We begin with a rigorous analysis of this concept, settling on the simple conclusion that the type-theoretic notion of “type refinement system” may be identified with the category-theoretic notion of “functor”. We then use this correspondence to give an equivalent type-theoret...

2011
Rasmus Ejlers Møgelberg Sam Staton

We investigate the phenomenon that every monad is a linear state monad. We do this by studying a fully-complete state-passing translation from an impure call-by-value language to a new linear type theory: the enriched call-by-value calculus. The results are not specific to store, but can be applied to any computational effect expressible using algebraic operations, even to effects that are not ...

2012
BACHUKI MESABLISHVILI ROBERT WISBAUER

For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguières and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads). In a recent joint paper with S. Lack the same authors define the notion of a pre-Hopf monad by requiring only a special form of the fusion operator to be invertible. In previous papers it was observed by the presen...

2013
David Michael Roberts DAVID M. ROBERTS

The universal bundle functor W : sGrp(C) → sC for simplicial groups in a category C with finite products lifts to a monad on sGrp(C) landing in contractible simplicial groups. The construction extends to simplicial algebras for any multisorted Lawvere theory.

2010
Richard Blute

This paper establishes a relation between the notion of a codifferential category and the more classic theory of Kähler differentials in commutative algebra. A codifferential category is an additive symmetric monoidal category with a monad T , which is furthermore an algebra modality, i.e. a natural assignment of an associative algebra structure to each object of the form T (C). Finally, a codi...

2006
Matthew Fluet

These two quotations represent the key ideas behind two major research agendas. The first captures the essence of monadic I/O, which is the fundamental abstraction used to provide input/output and concurrency in the lazy, purely-functional language (Concurrent) Haskell. The second captures the essence of first-class synchronous events, which is the fundamental abstraction used to provide concur...

2015
Soshichi Uchii

I have developed an informational interpretation of Leibniz’s metaphysics and dynamics, but in this paper I will concentrate on his theory of time. According to my interpretation, each monad is an incorporeal automaton programed by God, and likewise each organized group of monads is a cellular automaton (in von Neumann’s sense) governed by a single dominant monad (entelechy). The activities of ...

Journal: :Archive of Formal Proofs 2017
Andreas Lochbihler

The notion of a monad cannot be expressed within higher-order logic (HOL) due to type system restrictions. We show that if a monad is used with values of only one type, this notion can be formalised in HOL. Based on this idea, we develop a library of effect specifications and implementations of monads and monad transformers. Hence, we can abstract over the concrete monad in HOL definitions and ...

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