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https://github.com/uwplse/structtact

Coq utility and tactic library.
https://github.com/uwplse/structtact

coq coq-library tactics

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Coq utility and tactic library.

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# StructTact



[![Docker CI][docker-action-shield]][docker-action-link]



[docker-action-shield]: https://github.com/uwplse/StructTact/actions/workflows/docker-action.yml/badge.svg?branch=master

[docker-action-link]: https://github.com/uwplse/StructTact/actions/workflows/docker-action.yml



StructTact is a Coq library of structural tactics as well as lemmas about

lists, finite types, and orders on strings that use the tactics.

The structural tactics enable a style of proof where hypothesis names

are never mentioned. When automatically generated names change during

proof development, structural tactics will still work.



## Meta



- Author(s):

  - Ryan Doenges

  - Karl Palmskog

  - Keith Simmons (initial)

  - James R. Wilcox (initial)

  - Doug Woos (initial)

- License: [BSD 2-Clause "Simplified" license](LICENSE)

- Compatible Coq versions: 8.10 or later

- Additional dependencies: none

- Coq namespace: `StructTact`

- Related publication(s):

  - [Verdi: A Framework for Implementing and Verifying Distributed Systems](https://homes.cs.washington.edu/~mernst/pubs/verify-distsystem-pldi2015.pdf) doi:[10.1145/2737924.2737958](https://doi.org/10.1145/2737924.2737958)



## Building and installation instructions



The easiest way to install StructTact is via

[OPAM](https://opam.ocaml.org/doc/Install.html):

```shell

opam repo add coq-extra-dev https://coq.inria.fr/opam/extra-dev

opam install coq-struct-tact

```



To instead build and install manually, do:

``` shell

git clone https://github.com/uwplse/StructTact.git

cd StructTact

make   # or make -j 

make install

```



## Documentation



StructTact consists mainly of files originally developed as part of

the [Verdi framework][verdi-link], which have here been adapted for easier

reuse in other projects.



### Structural tactics



The structural tactics are found in the file `StructTactics.v`,

and are named by analogy to the structural properties of

simple type systems: weakening, exchange, and contraction.

In the context of proof assistants, these are analogous to the ability to add

new hypotheses in the context, reorder existing hypotheses, and delete

unused hypotheses. Theoretically, Coq inherits these properties from the

underlying type system, but in practice, automatically generated hypothesis

names cause proof scripts to break when the context is adjusted in seemingly

irrelevant ways.



Structural tactics restore these properties at the level of Ltac by enabling a

style of proof where hypothesis names are never mentioned. When automatically

generated names change during proof development, structural tactics still work.



For tactic documentation, see the inline comments in `StructTactics.v`.



### Utility definitions and lemmas



The file `Util.v` collects definitions, lemmas, and tactics about lists, booleans, propositions, and

functions that were useful in other projects. Notably, the following files are exported:



- `BoolUtil.v`: general boolean lemmas, tactics, and definitions

- `PropUtil.v`: general lemmas about propositions and sum types

- `Update.v`: function `update` that modifies a function to return a new value for a specific argument

- `Update2.v`: function `update2` that modifies a function to return a new value for specific pair of arguments

- `ListTactics.v`: tactics operating on contexts with `map`, `NoDup`, and `In`

- `ListUtil.v`: general list lemmas, involving, e.g., `NoDup`, `map`, `filter`, and `firstn`

- `Assoc.v`: association lists with get, set, and delete functions

- `Before.v`: relation `before` capturing when an element appears before another in a list

- `Dedup.v`: function `dedup` remove duplicates from a list using decidable equality

- `FilterMap.v`: function `filterMap` that maps a partial function on a list and ignores failures

- `Nth.v`: relation `Nth` capturing the element at some position in a list

- `Prefix.v`: relation `Prefix` capturing when one list is a prefix of another

- `RemoveAll.v`: function `remove_all` which removes all elements of one list from another; set subtraction

- `Subseq.v`: relation `subseq` capturing when one list is a subsequence of another



### Finite types



The file `Fin.v` contains definitions and lemmas related to `fin n`, a type with `n` elements,

isomorphic to `Fin.t n` from the standard library, but with a slightly different

definition that is more convenient to work with.



The following constructions are defined on `fin`:



- `fin_eq_dec`: decidable equality

- `all_fin n`: list of all elements of `fin n`

- `fin_to_nat`: convert a `fin n` to a `nat`

- `fin_lt`: an ordering on `fin n`, implemented using `fin_to_nat`

- `fin_OT_compat`: legacy `OrderedType` module for `fin n` (for use with `FMap`)

- `fin_OT`: modern `OrderedType` module for `fin n` (for use with `MSet`)

- `fin_of_nat`: convert a `nat` to a `fin n`, when possible



### String orders



The file `StringOrders.v` contains some order relations on strings, in particular a total lexicographic order.



The following modules are defined:



- `string_lex_as_OT_compat`: legacy `OrderedType` module for `string` (for use with `FMap`)

- `string_lex_as_OT`: modern `OrderedType` module for `string` (for use with `MSet`)



[verdi-link]: https://github.com/uwplse/verdi