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://jasongross.github.io/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://jasongross.github.io/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://jasongross.github.io/papers/lob-paper/html/lob.html},
  url = {https://jasongross.github.io/papers/2016-lob-icfp-2016-draft.pdf}
  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
  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://jasongross.github.io/papers/2015-parsing-parse-trees.pdf}
  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://jasongross.github.io/papers/2015-fiat-to-facade.pdf}
  author = {Jason Gross and Andres Erbsen},
  title = {10 Years of Superlinear Slowness in {C}oq},
  month = {August},
  year = {2022},
  note = {Submitted to \href{https://coq-workshop.gitlab.io/2022/}{The Coq Workshop 2022}},
  abstract = {In most programming languages, asymptotic performance issues can almost always be explained by reference to the algorithm being implemented.
At most, the standard asymptotic performance of explicitly used operations on chosen data structures must be considered.
Even the constant factors in performance bottlenecks can often be explained without reference to the implementation of the interpreter, compiler, nor underlying machine.

In 10+ years of working with Coq, we (the authors of this proposal and their colleagues) have found this pattern, which holds across multiple programming languages, to be the exception rather than the rule in Coq!
This turns performant proof engineering, and especially performant proof automation engineering, from a straightforward science into an arcane form of wizardry.

By presenting in detail a sampling of examples, we propose a defense of the thesis:
Performance bottlenecks in proof automation almost always result from inefficiencies in parts of the system which are conceptually distant from the theorem being proven.%
Said another way, \emph{debugging, understanding, and fixing performance bottlenecks in automated proofs almost always requires extensive knowledge of the proof engine, and almost never requires any domain-specific knowledge of the theorem being proven}.
Further, there is no clear direction of improvement:
We know of no systematic proposal, nor even folklore among experts, of what primitives and performance characteristics are sufficient for a performant proof engine.

We hope to start a discussion on the obvious corollary of this thesis: \emph{This should not be!}

Our presentation, we hope, will serve as a call for a POPLMark for Proof Engines, a call for designing and implementing a %n adequate
proof engine for \emph{scalable performant modular proof automation}.
  url = {https://jasongross.github.io/papers/2022-superlinear-slowness-coq-workshop-draft.pdf}
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