@misc{lob-paper,
author = {Jason Gross and Jack Gallagher and Benya Fallenstein},
title = {L{\"o}b's Theorem: A functional pearl of dependently typed quining},
month = {March},
year = {2016},
note = {Submitted to \href{http://conf.researchr.org/home/icfp-2016/}{ICFP 2016}},
bibliography = {https://people.csail.mit.edu/jgross/personal-website/papers/lob-bibliography.html},
abstract = {L{\"o}b's theorem states that to prove that a proposition is provable, it
is sufficient to prove the proposition under the assumption that it is
provable. The Curry-Howard isomorphism identifies formal proofs with
abstract syntax trees of programs; L{\"o}b's theorem thus implies, for
total languages which validate it, that self-interpreters are
impossible. We formalize a few variations of L{\"o}b's theorem in Agda
using an inductive-inductive encoding of terms indexed over types. We
verify the consistency of our formalizations relative to Agda by
giving them semantics via interpretation functions.},
artifact-zip = {https://people.csail.mit.edu/jgross/personal-website/papers/lob-paper/supplemental-nonymous.zip},
code-agda = {https://people.csail.mit.edu/jgross/personal-website/papers/lob-paper/lob.lagda},
code-github = {https://github.com/JasonGross/lob-paper},
code-html = {https://people.csail.mit.edu/jgross/personal-website/papers/lob-paper/html/lob.html},
url = {https://people.csail.mit.edu/jgross/personal-website/papers/2016-lob-icfp-2016-draft.pdf}
}
@misc{parsing-parse-trees,
author = {Jason Gross and Adam Chlipala},
title = {Parsing Parses: A Pearl of (Dependently Typed) Programming and Proof},
month = {August},
year = {2015},
note = {Submitted to \href{http://icfpconference.org/icfp2015/cfp.html}{ICFP
2015}},
abstract = {We present a functional parser for arbitrary context-free grammars,
together with soundness and completeness proofs, all inside Coq.
By exposing the parser in the right way with parametric polymorphism
and dependent types, we are able to use the parser to prove its own
soundness, and, with a little help from relational parametricity,
prove its own completeness, too. Of particular interest is one strange
instantiation of the type and value parameters: by parsing \emph{parse
trees} instead of strings, we convince the parser to generate its
own completeness proof. We conclude with highlights of our experiences
iterating through several versions of the Coq development, and some
general lessons about dependently typed programming.},
owner = {Jason},
timestamp = {2015.03.14},
url = {https://people.csail.mit.edu/jgross/personal-website/papers/2015-parsing-parse-trees.pdf}
}
@misc{pldi-15-fiat-to-facade,
author = {Cl\'ement Pit--Claudel and Peng Wang and Jason Gross and Ben Delaware and Adam Chlipala},
title = {Correct-by-Construction Program Derivation from Specifications to
Assembly Language},
month = {June},
year = {2015},
note = {Submitted to PLDI 2015},
abstract = {We present a Coq-based system to certify the entire process of implementing
declarative mathematical specifications with efficient assembly code.
That is, we produce formal assembly-code libraries with proofs, in
the style of Hoare logic, demonstrating compatibility with relational
specifications in higher-order logic. Most code-generation paths
from high-level languages involve the introduction of garbage collection
and other runtime support for source-level abstractions, but we generate
code suitable for resource-constrained embedded systems, using manual
memory management and in-place updating of heap-allocated data structures.
We start from very high-level source code, applying the Fiat framework
to refine set-theory expressions into functional programs; then we
further apply Fiat's refinement tools to translate functional programs
into Facade, a simple imperative language without a heap or aliasing;
and finally we plug into the assembly-generation features of the
Bedrock framework, where we link with handwritten data-structure
implementations and their associated proofs. Each program refinement
leads to a proved Hoare-logic specification for an assembly function,
with no trust dependencies on any aspect of our synthesis process,
which is highly automated.},
owner = {Jason},
timestamp = {2014.11.17},
url = {https://people.csail.mit.edu/jgross/personal-website/papers/2015-fiat-to-facade.pdf}
}
@misc{partial-evaluation-rewriting,
author = {Jason Gross and Adam Chlipala and Andres Erbsen},
title = {A Framework for Building Verified Partial Evaluators},
month = {January},
year = {2021},
note = {Submitted to \href{https://popl21.sigplan.org/}{POPL 2021}},
abstract = {\emph{Partial evaluation} is a classic technique for generating lean, customized code from libraries that start with more bells and whistles.
It is also an attractive approach to creation of \emph{formally verified} systems, where theorems can be proved about libraries, yielding correctness of all specializations ``for free.''
However, it can be challenging to make library specialization both performant (at compile time and runtime) and trustworthy.
We present a new approach, prototyped in the Coq proof assistant, which supports specialization at the speed of native-code execution, without adding to the trusted code base.
Our extensible engine, which combines the traditional concepts of tailored term reduction and automatic rewriting from hint databases, is also of interest to replace these ingredients in proof assistants' proof checkers and tactic engines, at the same time as it supports extraction to standalone compilers from library parameters to specialized code.},
artifact-tar-gz = {https://people.csail.mit.edu/jgross/personal-website/papers/2021-rewriting-popl-draft.tar.gz},
code-github = {https://github.com/mit-plv/rewriter},
url = {https://people.csail.mit.edu/jgross/personal-website/papers/2021-rewriting-popl-draft.pdf}
}
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