5 research outputs found
Basic Operational Preorders for Algebraic Effects in General, and for Combined Probability and Nondeterminism in Particular
International audienceThe "generic operational metatheory" of Johann, Simpson and Voigtländer (LiCS 2010) defines contextual equivalence, in the presence of algebraic effects, in terms of a basic operational preorder on ground-type effect trees. We propose three general approaches to specifying such preorders: (i) operational (ii) denotational, and (iii) axiomatic; coinciding with the three major styles of program semantics. We illustrate these via a nontrivial case study: the combination of probabilistic choice with nondeterminism, for which we show that natural instantiations of the three specification methods (operational in terms of Markov decision processes, denotational using a powerdomain, and axiomatic) all determine the same canonical preorder. We do this in the case of both angelic and demonic nondeterminism
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, rely on the
selection monad, to handle choice, augmented 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 base 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 base types for the case of rewards
without probability