# 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} }

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

Simply Typed Lambda-Calculus Modulo Type Isomorphisms

- Mathematics, Computer ScienceArXiv
- 2015

A simply typed, non-deterministic lambda-calculus where isomorphic types are equated and an equivalence relation is settled at the term level is defined and a proof of strong normalisation modulo equivalence is provided.

The vectorial λ-calculus

- Computer Science, MathematicsInf. Comput.
- 2017

It is proved that the resulting typed λ-calculus is strongly normalising and features weak subject reduction and it is shown how to naturally encode matrices and vectors in this typed calculus.

The Vectorial Lambda-Calculus

- Computer ScienceArXiv
- 2013

It is proved that the resulting typed lambda-calculus is strongly normalising and features a weak subject reduction and it is shown how to naturally encode matrices and vectors in this typed calculus.

L O ] 5 A ug 2 01 3 The Vectorial Lambda-Calculus

- 2014

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the linear-algebraic aspects of this extension of lambda-calculus: it is able to statically describe…

Functional Pearl: The Distributive $\lambda$-Calculus

- Computer Science, Mathematics
- 2020

It is shown that the new rules of the distributive $\lambda$-calculus with pairs satisfy subject reduction if types are considered up to the distributivity isomorphism, and that the main result is strong normalization for simple types up to distributivity.

Functional and Logic Programming: 15th International Symposium, FLOPS 2020, Akita, Japan, September 14–16, 2020, Proceedings

- Computer ScienceFLOPS
- 2020

The fundamental determinants of poor performance scaling by Coq’s proof engine are studied, and preliminary results on bottlenecks in key operations are sketches.

Fe b 20 20 Functional Pearl : The Distributive λ-Calculus

- 2020

Functional Pearl: The Distributive λ-Calculus

- Computer Science, MathematicsFLOPS
- 2020

A simple extension of the \(\lambda \)-calculus with pairs with pairs is introduced by adding a computational interpretation of the valid distributivity isomorphism \(A \Rightarrow (B\wedge C) \equiv (A\Rightarrow B) \wedge (A}\Rightarrow C) of simple types.

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