# The probability of non-confluent systems

@inproceedings{DazCaro2013ThePO,
title={The probability of non-confluent systems},
author={Alejandro D{\'i}az-Caro and Gilles Dowek},
booktitle={DCM},
year={2013}
}
• Published in DCM 26 August 2013
• Computer Science, Mathematics
We show how to provide a structure of probability space to the set of execution traces on a non-confluent abstract rewrite system, by defining a variant of a Lebesgue measure on the space of traces. Then, we show how to use this probability space to transform a non-deterministic calculus into a probabilistic one. We use as example Lambda+, a recently introduced calculus defined through type isomorphisms.
8 Citations

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#### References

SHOWING 1-10 OF 37 REFERENCES
Normalisation of a Non-deterministic Type Isomorphic {\lambda}-calculus
• Mathematics, Computer Science
• 2013
We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is aExpand
Probabilistic /lambda-calculus and Quantitative Program Analysis
• Computer Science
• J. Log. Comput.
• 2005
It is shown how the framework of probabilistic abstract interpretation can be applied to statically analyse a Probabilistic version of the λ-calculus to allow for a more speculative use of its outcomes based on the consideration of statistically defined quantities. Expand
Probabilistic λ-calculus and Quantitative Program Analysis
• 2004
We show how the framework of probabilistic abstract interpretation can be applied to statically analyse a probabilistic version of the λ-calculus. The resulting analysis allows for a more speculativeExpand
The algebraic lambda calculus
• L. Vaux
• Computer Science, Mathematics
• Mathematical Structures in Computer Science
• 2009
An extension of the pure lambda calculus is introduced by endowing the set of terms with the structure of a vector space, or, more generally, of a module, over a fixed set of scalars, and it is proved it is confluent. Expand
Linearity in the Non-deterministic Call-by-Value Setting
• Mathematics, Computer Science
• WoLLIC
• 2012
A fine-grained type system is defined, capturing the right linearity present in such formalisms as the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. Expand
Non determinism through type isomorphism
• Mathematics, Computer Science
• LSFA
• 2012
An equivalence relation on propositions and a proof system where equivalent propositions have the same proofs are defined, which resembles several known non-deterministic and algebraic lambda-calculi. Expand
Rewriting Logic and Probabilities
• Computer Science, Mathematics
• RTA
• 2003
Whether there exists a notion of probabilistic rewrite system with an associated notion of Probabilistic rewriting logic is discussed. Expand
Call-by-Value Non-determinism in a Linear Logic Type Discipline
• Computer Science, Mathematics
• LFCS
• 2013
It is proved that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy call-by-value reduction. Expand
A relational semantics for parallelism and non-determinism in a functional setting
• Mathematics, Computer Science
• Ann. Pure Appl. Log.
• 2012
This paper introduces a λ -calculus extended with non-deterministic choice and parallel composition and defines its operational semantics (based on the may and must intuitions underlying the authors' two additional operations), and describes the interpretation of this calculus in this model. Expand
Process Algebra with Probabilistic Choice
This paper treats the problem of combining parallel composition with probability and with or without non-determinism in the setting of process algebra in the form of ACP to obtain the Basic Process Algebra with probabilistic choice prBPA and the axiom system for ACP+π. Expand