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 that both behaviors are coupled together is a bug in Coq.
• The behavior of Program is tweaked: Unset Transparent Obligations, Obligation Tactic := idtac, Add Search Blacklist "_obligation_". See 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. After that, Coq-std++ has been part of the Iris project, 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.