## Paper: A Linear Logical Framework (at LICS 1996)

*Winner of the Test-of-Time Award in 2016***Iliano Cervesato Frank Pfenning**

### Abstract

We present the linear type theory LLF as the formal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of Mini-ML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cut-elimination.

### BibTeX

@InProceedings{CervesatoPfenning-ALinearLogicalFrame, author = {Iliano Cervesato and Frank Pfenning}, title = {A Linear Logical Framework}, booktitle = {Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science (LICS 1996)}, year = {1996}, month = {July}, pages = {264--275}, location = {New Brunswick, NJ, USA}, publisher = {IEEE Computer Society Press} }