# Coq-std++
This project contains an extended "Standard Library" for Coq called coq-std++.
The key features of this library are as follows:
- It provides a great number of definitions and lemmas for common data
structures such as lists, finite maps, finite sets, and finite multisets.
- It uses type classes for common notations (like `∅`, `∪`, and Haskell-style
monad notations) so that these can be overloaded for different data structures.
- It uses type classes to keep track of common properties of types, like it
having decidable equality or being countable or finite.
- Most data structures are represented in canonical ways so that Leibniz
equality can be used as much as possible (for example, for maps we have
`m1 = m2` iff `∀ i, m1 !! i = m2 !! i`). On top of that, the library provides
setoid instances for most types and operations.
- It provides various tactics for common tasks, like an ssreflect inspired
`done` tactic for finishing trivial goals, a simple breadth-first solver
`naive_solver`, an equality simplifier `simplify_eq`, a solver `solve_proper`
for proving compatibility of functions with respect to relations, and a solver
`set_solver` for goals involving set operations.
- It is entirely dependency- and axiom-free.
## Side-effects
Importing std++ has some side effects as the library sets some global options.
Notably:
* `Generalizable All Variables`: This option enables implicit generalization in
arguments of the form `` `{...}`` (i.e., anonymous arguments). Unfortunately, it
also enables implicit generalization in `Instance`. We think that the fact
taht both behaviors are coupled together is a
[bug in Coq](https://github.com/coq/coq/issues/6030).
* The behavior of `Program` is tweaked: `Unset Transparent Obligations`,
`Obligation Tactic := idtac`, `Add Search Blacklist "_obligation_"`. See
[`base.v`](theories/base.v) for further details.
## History
Coq-std++ has originally been developed by Robbert Krebbers as part of his
formalization of the C programming language in his PhD thesis, called
[CH2O](http://robbertkrebbers.nl/thesis.html). After that, Coq-std++ has been
part of the [Iris project](http://iris-project.org), and has continued to be
developed by Robbert Krebbers, Ralf Jung, and Jacques Henri-Jourdan.
## Prerequisites
This version is known to compile with:
- Coq version 8.6 / 8.6.1 / 8.7.0
## Building Instructions
Run `make` to build the full development. Run `make install` to install the library.