## Ordered Linear Logic and Applications (2001)

Citations: | 36 - 0 self |

### BibTeX

@TECHREPORT{Polakow01orderedlinear,

author = {Jeff Polakow and Harper John Reynolds},

title = {Ordered Linear Logic and Applications},

institution = {},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

This work is dedicated to my parents. Acknowledgments Firstly, and foremost, I would like to thank my principal advisor, Frank Pfenning, for his patience with me, and for teaching me most of what I know about logic and type theory. I would also like to acknowledge some useful discussions with Kevin Watkins which led me to simplify some of this work. Finally, I would like to thank my other advisor, John Reynolds, for all his kindness and support over the last five years. Abstract This thesis introduces a new logical system, ordered linear logic, which combines reasoning with unrestricted, linear, and ordered hypotheses. The logic conservatively extends (intuitionistic) linear logic, which contains both unrestricted and linear hypotheses, with a notion of ordered hypotheses. Ordered hypotheses must be used exactly once, subject to the order in which they were assumed (i.e., their order cannot be changed during the course of a derivation). This ordering constraint allows for logical representations of simple data structures such as stacks and queues. We construct ordered linear logic in the style of Martin-L"of from the basic notion of a hypothetical judgement. We then show normalization for the system by constructing a sequent calculus presentation and proving cut-elimination of the sequent system.