A type theory for memory allocation and data layout

Ordered type theory is an extension of linear type theory in which variables in the context may be neither dropped nor re-ordered. This restriction gives rise to a natural notion of adjacency. We show that a language based on ordered types can use this property to give an exact account of the layout of data in memory. The fuse constructor from ordered logic describes adjacency of values in memory, and the mobilitymodal describes pointers into the heap. We choose a particular allocation model based on a common implementation scheme for copying garbage collection and show how this permits us to separate out the allocation and initialization of memory locations in such a way as to account for optimizations such as the coalescing of multiple calls to the allocator. This material is based on work supported in part by NSF grants CCR-9984812 and CCR-0121633. Any opinions, findings, and conclusions or recommendations in this publication are those of the authors and do not reflect the views of this agency