4 research outputs found
Smart Choices and the Selection Monad
Describing systems in terms of choices and their resulting costs and rewards
offers the promise of freeing algorithm designers and programmers from
specifying how those choices should be made; in implementations, the choices
can be realized by optimization techniques and, increasingly, by machine
learning methods. We study this approach from a programming-language
perspective. We define two small languages that support decision-making
abstractions: one with choices and rewards, and the other additionally with
probabilities. We give both operational and denotational semantics.
In the case of the second language we consider three denotational semantics,
with varying degrees of correlation between possible program values and
expected rewards. The operational semantics combine the usual semantics of
standard constructs with optimization over spaces of possible execution
strategies.
The denotational semantics, which are compositional and can also be viewed as
an implementation by translation to a simpler language, rely on the selection
monad, to handle choice, combined with an auxiliary monad, to handle other
effects such as rewards or probability.
We establish adequacy theorems that the two semantics coincide in all cases.
We also prove full abstraction at ground types, with varying notions of
observation in the probabilistic case corresponding to the various degrees of
correlation. We present axioms for choice combined with rewards and
probability, establishing completeness at ground types for the case of rewards
without probability
The theory of traces for systems with nondeterminism and probability
This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the resulting semantics to known definitions of trace equivalences appearing in the literature. Most of our results are based on the exciting interplay between monads and their presentations via algebraic theories
The Theory of Traces for Systems with Nondeterminism, Probability, and Termination
This paper studies trace-based equivalences for systems combining
nondeterministic and probabilistic choices. We show how trace semantics for
such processes can be recovered by instantiating a coalgebraic construction
known as the generalised powerset construction. We characterise and compare the
resulting semantics to known definitions of trace equivalences appearing in the
literature. Most of our results are based on the exciting interplay between
monads and their presentations via algebraic theories.Comment: This paper is an extended version of a LICS 2019 paper "The Theory of
Traces for Systems with Nondeterminism and Probability". It contains all the
proofs, additional explanations, material, and example
The Theory of Traces for Systems with Nondeterminism and Probability
International audienceThis paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the resulting semantics to known definitions of trace equivalences appearing in the literature. Most of our results are based on the exciting interplay between monads and their presentations via algebraic theories