A Type System for the Vectorial Aspect of the Linear-Algebraic Lambda-Calculus

Pablo Arrighi (1, 2, 3) , Alejandro Díaz-Caro (4, 5) , Benoît Valiron (5, 6)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 CAPP - Calculs algorithmes programmes et preuves
3 LIG - Laboratoire d'Informatique de Grenoble
4 LIG - Laboratoire d'Informatique de Grenoble
5 LIPN - Laboratoire d'Informatique de Paris-Nord
6 CIS - Department of Computer and Information Science [Pennsylvania]

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms resulting from the reduction of programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We show that the resulting typed lambda-calculus is strongly normalizing and features a weak subject-reduction.

Domaines: Logique en informatique [cs.LO]

Pablo Arrighi, Alejandro Díaz-Caro, Benoît Valiron. A Type System for the Vectorial Aspect of the Linear-Algebraic Lambda-Calculus. DCM - 7th International Workshop on Developments of Computational Methods - 2011, Jul 2011, Zurich, Swaziland. pp.1-15, ⟨10.4204/EPTCS.88.1⟩. ⟨hal-00924926⟩