Development of a Translator from LLVM to ACL2

In our current work a library of formally verified software components is to be created, and assembled, using the Low-Level Virtual Machine (LLVM) intermediate form, into subsystems whose top-level assurance relies on the assurance of the individual components. We have thus undertaken a project to build a translator from LLVM to the applicative subset of Common Lisp accepted by the ACL2 theorem prover. Our translator produces executable ACL2 formal models, allowing us to both prove theorems about the translated models as well as validate those models by testing. The resulting models can be translated and certified without user intervention, even for code with loops, thanks to the use of the def::ung macro which allows us to defer the question of termination. Initial measurements of concrete execution for translated LLVM functions indicate that performance is nearly 2.4 million LLVM instructions per second on a typical laptop computer. In this paper we overview the translation process and illustrate the translator's capabilities by way of a concrete example, including both a functional correctness theorem as well as a validation test for that example.Comment: In Proceedings ACL2 2014, arXiv:1406.123

A Step-Indexing Approach to Partial Functions

We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive definitions or recursion operators which are not available in ACL2 and they provide little, if any, support for executing the resulting definitions. We use step-indexing as the underlying implementation technology, enabling the definitions to be carried out in first order logic. We also show how recent enhancements to ACL2's guard feature can be used to enable the efficient execution of partial recursive functions.Comment: In Proceedings ACL2 2013, arXiv:1304.712

Origins of the extragalactic background at 1mm from a combined analysis of the AzTEC and MAMBO data in GOODS-N

We present a study of the cosmic infrared background, which is a measure of the dust obscured activity in all galaxies in the Universe. We venture to isolate the galaxies responsible for the background at 1mm; with spectroscopic and photometric redshifts we constrain the redshift distribution of these galaxies. We create a deep 1.16mm map (sigma ~ 0.5mJy) by combining the AzTEC 1.1mm and MAMBO 1.2mm datasets in GOODS-N. This combined map contains 41 secure detections, 13 of which are new. By averaging the 1.16mm flux densities of individually undetected galaxies with 24um flux densities > 25uJy, we resolve 31--45 per cent of the 1.16mm background. Repeating our analysis on the SCUBA 850um map, we resolve a higher percentage (40--64 per cent) of the 850um background. A majority of the background resolved (attributed to individual galaxies) at both wavelengths comes from galaxies at z > 1.3. If the ratio of the resolved submillimeter to millimeter background is applied to a reasonable scenario for the origins of the unresolved submillimeter background, 60--88 per cent of the total 1.16mm background comes from galaxies at z > 1.3.Comment: 12 pages, 10 figures. Accepted by MNRAS. The combined map is publicly available at http://www.astro.umass.edu/~pope/goodsn_mm