## linear topology

<*theory*>

A linear topology on a left A-module M is a topology on M that is invariant under translations and admits a fundamental system of neighborhood of 0 that consists of submodules of M. If there is such a topology, M is said to be linearly topologized. If A is given a discrete topology, then M becomes a topological A-module with respect to a linear topology.

[Wikipedia]

Last updated: 2014-06-30

## linear transformation

## linear type

1. An attribute of values which are used exactly once: they are neither duplicated nor destroyed. Such values require no garbage collection, and can safely be updated in place, even if they form part of a data structure.

Linear types are related to the linear logic of J.-Y Girard. They extend Schmidt's notion of single threading, provide an alternative to Hudak and Bloss' update analysis, and offer a practical complement to Lafont and Holmström's elegant linear languages.

['Use-Once' Variables and Linear Objects - Storage Management,
Reflection and Multi-Threading, Henry Baker.
*http://home.pipeline.com/~hbaker1/Use1Var.html*].

["Linear types can change the world!", Philip Wadler, "Programming Concepts and Methods", April 1990, eds. M. Broy, C. Jones, pub. North-Holland, IFIP TC2 Working Conference on Programming Concepts and Methods, Sea of Galilee, Israel].

Last updated: 1995-03-03

### Nearby terms:

linear space ♦ **linear topology** ♦ linear transformation ♦ linear type

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