My dissertation research at Yale focused on the design, metatheory, implementation and usage of a novel programming language and proof assistant, called VeriML. The goal behind VeriML is to enable scalable development of logical proofs; the main idea about how to achieve this goal is to have good support for writing proof-producing functions with precise, typed signatures.
More precisely, VeriML aims to provide a compelling alternative to tactic development compared to existing approaches, by leveraging a rich type system coupled with a rich ML-style programming model. I have also shown how generalizations of features of traditional proof assistants, such as interactive development of proofs and tactics, are a direct consequence of VeriML’s design. Thus the language can be viewed as a proof assistant in its entirety. Through the addition of a simple staging construct, VeriML provides extensible static checking of proofs and tactics, solving long-standing issues such as having a safe yet user-extensible conversion rule. Because of this support, users are free to extend the ‘background reasoning’ that the proof assistant uses to handle trivial details with domain-specific sophistication of arbitrary complexity; this simplifies the development of further proofs and automation, yielding an approach to formal proofs closer to informal practice.
VeriML: A dependently-typed, user-extensible and language-centric approach to proof assistants. This is my Ph.D. dissertation, submitted on November 2nd 2012. This is the canonical reference to VeriML presenting its design, metatheory, implementation and examples in detail.
Static and User-Extensible Proof Checking, Antonis Stampoulis and Zhong Shao, POPL 2012, January 25-27, 2012, Philadelphia, PA, USA. There is also the Extended Version, with full typing rules and extensive metatheory proofs.
VeriML: Typed Computation of Logical Terms inside a Language with Effects, Antonis Stampoulis and Zhong Shao, ICFP 2010, September 27-29, 2010, Baltimore, MD, USA, as well as the extended version.
- Ph.D. Defense, October 15, 2012
- POPL 2012, January 26, 2012, Philadelphia, PA, USA. PowerPoint file, ACM link with video
- TYPES 2011, September 9, 2011, Bergen, Norway. Using VeriML to have an alternative, safely user-extensible conversion rule.
- ICFP 2010, September 29, 2010, Baltimore, MD, USA. Video of the talk.
- DTP 2010, July 9, 2010, Edinburgh, UK
- VeriML version 0.5. A lot of big and small improvements and changes; the most major ones being that VeriML is now compiled through translation to ML (instead of interpreted) and that there is some inductive definition support.
- VeriML version 0.3. This reflects VeriML as described in our POPL 2012 paper.
- VeriML version 0.1. An older version corresponding to our ICFP 2010 paper.