Compositional Computational Reflection

Malecha, Gregory; Chlipala, Adam; Braibant, Thomas

doi:10.1007/978-3-319-08970-6_24

Cited by 15 publications

(7 citation statements)

References 21 publications

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“…Proofs by reflection has been intensively studied [5,16], but without anything similar to the type-safe reflection that we have presented here. If we leave the ground of nice mathematical structures, one can decide to work with arbitrary rewriting rules, but in the general case there isn't a complete decision procedure for such systems, because there is usually no normal form.…”

Section: Related Workmentioning

confidence: 99%

Automatically Proving Equivalence by Type-Safe Reflection

Slama

Brady

2017

Lecture Notes in Computer Science

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Abstract. One difficulty with reasoning and programming with dependent types is that proof obligations arise naturally once programs become even moderately sized. For example, implementing an adder for binary numbers indexed over their natural number equivalents naturally leads to proof obligations for equalities of expressions over natural numbers. The need for these equality proofs comes, in intensional type theories, from the fact that the propositional equality enables us to prove as equal terms that are not judgementally equal, which means that the typechecker can't always obtain equalities by reduction. As far as possible, we would like to solve such proof obligations automatically. In this paper, we show one way to automate these proofs by reflection in the dependently typed programming language Idris. We show how defining reflected terms indexed by the original Idris expression allows us to construct and manipulate proofs. We build a hierarchy of tactics for proving equivalences in semigroups, monoids, commutative monoids, groups, commutative groups, semi-rings and rings. We also show how each tactic reuses those from simpler structures, thus avoiding duplication of code and proofs.

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Section: Related Workmentioning

confidence: 99%

Automatically Proving Equivalence by Type-Safe Reflection

Slama

Brady

2017

Lecture Notes in Computer Science

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“…Recent work by Malecha et al (2014) restricts the use of reflection to reflective hints. Hints are lemmas reflected into an inductive datatype, similar to what the reflection mechanism of Agda does, packed together with a proof of soundness.…”

Section: Typechecked Tactics Through Reflectionmentioning

confidence: 99%

Mtac: A monad for typed tactic programming in Coq

et al. 2015

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Effective support for custom proof automation is essential for large-scale interactive proof development. However, existing languages for automation via tactics either (a) provide no way to specify the behavior of tactics within the base logic of the accompanying theorem prover, or (b) rely on advanced type-theoretic machinery that is not easily integrated into established theorem provers.We present Mtac, a lightweight but powerful extension to Coq that supports dependently typed tactic programming. Mtac tactics have access to all the features of ordinary Coq programming, as well as a new set of typed tactical primitives. We avoid the need to touch the trusted kernel typechecker of Coq by encapsulating uses of these new tactical primitives in a monad, and instrumenting Coq so that it executes monadic tactics during type inference.

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“…Figure 9 shows an excerpt from a real Coq source file, ending in the full code to prove that invariants are never violated. The proof is almost entirely automated, appealing to the separationlogic proof procedures that Bedrock provides [25]. This level of automation persists in verifications of more featureful client code, and it represents a qualitative improvement to the ease of building on verified systems libraries, compared to past work.…”

Section: A Thread-library Component Stackmentioning

confidence: 99%

From Network Interface to Multithreaded Web Applications

Chlipala

2015

Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Many verifications of realistic software systems are monolithic, in the sense that they define single global invariants over complete system state. More modular proof techniques promise to support reuse of component proofs and even reduce the effort required to verify one concrete system, just as modularity simplifies standard software development. This paper reports on one case study applying modular proof techniques in the Coq proof assistant. To our knowledge, it is the first modular verification certifying a system that combines infrastructure with an application of interest to end users. We assume a nonblocking API for managing TCP networking streams, and on top of that we work our way up to certifying multithreaded, database-backed Web applications. Key verified components include a cooperative threading library and an implementation of a domain-specific language for XML processing. We have deployed our case-study system on mobile robots, where it interfaces with off-the-shelf components for sensing, actuation, and control.

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Compositional Computational Reflection

Cited by 15 publications

References 21 publications

Automatically Proving Equivalence by Type-Safe Reflection

Automatically Proving Equivalence by Type-Safe Reflection

Mtac: A monad for typed tactic programming in Coq

From Network Interface to Multithreaded Web Applications

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