# Verified Calculations

@inproceedings{Leino2013VerifiedC, title={Verified Calculations}, author={K. Rustan M. Leino and Nadia Polikarpova}, booktitle={VSTTE}, year={2013} }

Calculational proofs--proofs by stepwise formula manipulation--are praised for their rigor, readability, and elegance. [... ] Key Result The examples show that calculational proofs in Dafny compare favorably, in terms of readability and conciseness, with arguments written in other styles and proof languages. Expand

## 32 Citations

Automating Theorem Proving with SMT

- Computer ScienceITP
- 2013

To show that proof tools rooted in SMT are growing up, this paper presents a series of examples that illustrate how theorems are expressed and proved using the SMT-based program verifier Dafny.

Automated Theorem Prover Assisted Program Calculations

- Computer ScienceIFM
- 2014

An automated theorem provers assisted program and formula transformation rules, which when coupled with the ability to extract context of a subformula, help in shortening and simplifying the derivations.

Untangling mechanized proofs

- Computer ScienceSLE
- 2020

A compiler that interleaves Coq’s output with the original proof script to produce interactive webpages that are complete, self-contained presentations of Coq proofs; and a new literate programming toolkit that allows authors to switch seamlessly between prose- and code-oriented views of the same sources, by translating back and forth between reStructuredText documents and literate Coq source files.

Theorem proving for all: equational reasoning in liquid Haskell (functional pearl)

- Computer ScienceProceedings of the 11th ACM SIGPLAN International Symposium on Haskell
- 2018

Concretely, this article shows how the equational proofs and derivations from Graham's textbook can be recast as proofs in Haskell (spoiler: they look essentially the same).

Theorem proving for all: equational reasoning in liquid Haskell (functional pearl)

- Computer ScienceHaskell@ICFP
- 2018

Concretely, this article shows how the equational proofs and derivations from Graham's textbook can be recast as proofs in Haskell (spoiler: they look essentially the same).

Functional Pearl: Theorem Proving for All (Equational Reasoning in Liquid Haskell)

- Computer ScienceArXiv
- 2018

Concretely, this article shows how the equational proofs and derivations from Graham's textbook can be recast as proofs in Haskell (spoiler: they look essentially the same).

Refinement reflection: complete verification with SMT

- Computer ScienceProc. ACM Program. Lang.
- 2018

Refinement Reflection is introduced, a new framework for building SMT-based deductive verifiers, and a proof-search algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning.

Towards Verified Handwritten Calculational Proofs - (Short Paper)

- Computer Science, MathematicsITP
- 2018

This paper presents the implementation of a proof-of-concept prototype that can formally verify handwritten calculational proofs without the need to learn the specific syntax of theorem provers.

Refinement Reflection (or, how to turn your favorite language into a proof assistant using SMT)

- Computer ScienceArXiv
- 2016

The approach is implemented in the Liquid Haskell system, thereby converting Haskell into an interactive proof assistant that is used to verify a variety of properties ranging from arithmetic properties of higher order, recursive functions to the Monoid, Applicative, Functor and Monad type class laws.

Some Ideas for Program Verifier Tactics

- Computer ScienceArXiv
- 2014

This work develops "tactics" as a form of program refactoring called DTacs, which enables users to encode common proof patterns as special programs called "tACTics" in an interactive theorem prover.

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