Confluence via strong normalisation in an algebraic λ-calculus with rewriting

Details Confluence via strong normalisation in an algebraic λ-calculus with rewriting Confluence via strong normalisation in an algebraic λ-calculus with rewriting

2011-02-03

arxiv.org/abs/1102.0749v3

EPTCS 81, 2012, pp. 16-29

Computer Science

Logic in Computer Science

In Proceedings LSFA 2011, arXiv:1203.5423

Scientific paper

10.4204/EPTCS.81.2

The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while the latter uses equalities. When given by rewrites, algebraic lambda-calculi are not confluent unless further restrictions are added. We provide a type system for the linear-algebraic lambda-calculus enforcing strong normalisation, which gives back confluence. The type system allows an abstract interpretation in System F.

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