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TeIL: a type-safe imperative Tensor Intermediate Language

Reference

Norman A. Rink, Jeronimo Castrillon, "TeIL: a type-safe imperative Tensor Intermediate Language" , Proceedings of the 6th ACM SIGPLAN International Workshop on Libraries, Languages, and Compilers for Array Programming (ARRAY), ACM, pp. 57–68, New York, NY, USA, Jun 2019. [doi]

Abstract

Each of the popular tensor frameworks from the machine learning domain comes with its own language for expressing tensor kernels. Since these tensor languages lack precise specifications, it is impossible to understand and reason about tensor kernels that exhibit unexpected behaviour. In this paper, we give examples of such kernels. The tensor languages are superficially similar to the well-known functional array languages, for which formal definitions often exist. However, the tensor languages are inherently imperative. In this paper we present TeIL, an imperative tensor intermediate language with precise formal semantics. For the popular tensor languages, TeIL can serve as a common ground on the basis of which precise reasoning about kernels becomes possible. Based on TeIL s formal semantics we develop a type-safety result in the Coq proof assistant.

Bibtex

@InProceedings{rink_array19,
author = {Norman A. Rink and Jeronimo Castrillon},
title = {{TeIL}: a type-safe imperative {Tensor Intermediate Language}},
booktitle = {Proceedings of the 6th ACM SIGPLAN International Workshop on Libraries, Languages, and Compilers for Array Programming (ARRAY)},
year = {2019},
series = {ARRAY 2019},
pages = {57--68},
address = {New York, NY, USA},
month = jun,
publisher = {ACM},
doi = {10.1145/3315454.3329959},
url = {http://doi.acm.org/10.1145/3315454.3329959},
acmid = {3329959},
isbn = {978-1-4503-6717-2/19/06},
location = {Phoenix, AZ, USA},
numpages = {12},
abstract = {Each of the popular tensor frameworks from the machine learning domain comes with its own language for expressing tensor kernels. Since these tensor languages lack precise specifications, it is impossible to understand and reason about tensor kernels that exhibit unexpected behaviour. In this paper, we give examples of such kernels.
The tensor languages are superficially similar to the well-known functional array languages, for which formal definitions often exist. However, the tensor languages are inherently imperative. In this paper we present TeIL, an imperative tensor intermediate language with precise formal semantics. For the popular tensor languages, TeIL can serve as a common ground on the basis of which precise reasoning about kernels becomes possible. Based on TeIL's formal semantics we develop a type-safety result in the Coq proof assistant.},
}

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