Equations 1.3 beta release

Announcements
1

Dear Coq/Equations users, I’m happy to announce version 1.3 beta of the Equations package.

This is a new major release of Equations, working with Coq 8.13. This version adds an improved syntax (less ; -separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.

This version introduces some minor potentially breaking changes along with the following features:

  • Improved syntax for “concise” clauses separated by | , at top-level or inside with subprograms.
    We no longer require to separate them by ; . For example, the following definition is now accepted:

    Equations foo : nat -> nat := | 0 => 1 | S n => S (foo n).

    The old syntax is however still supported for backwards compatibility.

  • Require Import Equations.Equations. does not work anymore.
    One has to use Require Import Equations.Prop.Equations to load the plugin’s default instance where equality is in Prop . From Equations Require Import Equations is unaffected.

  • Use Require Import Equations.HoTT.All to use the HoTT variant of the library compatible with the Coq HoTT library
    The plugin then reuses the definition of paths from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter to use the library and plugin. The coq-equations opam package depends optionally on coq-hott , so if coq-hott is installed before it, coq-equations will automatically install the HoTT library variant in addition to the standard one.
    The HoTT variant allows for example to pattern-match on equality proofs in the most concise way, e.g.:

    Require Import Equations.HoTT.All.
Set Universe Polymorphism.
Equations sym {A x y} (e : x = y :> A) : y = x := sym 1 => 1.

  • Multiple patterns can be separated by , in addition to |, as in:

     Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := 
  | 1, 1 => 1.

  • New attribute #[tactic=tac] to set locally the default tactic to solve remaining holes.
    The goals on which the tactic applies are now always of the form Γ |- τ where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl tactic performs a simpl call before introducing the hypotheses, so you might need to add a simpl in * to your tactics.

  • New attributes #[derive(equations=yes|no, eliminator=yes|no)] can be used in place of the (noeqns, noind) flags which are deprecated.

Fixed in this version:

∗ #329: improved strengthening avoiding to abstract over recursive definitions which would not pass the guardness checker. This can simplify the produced terms, avoiding unnecessary “commutative cuts”.
∗ #321: warn rather than error when using Equations? and no subgoals are left. This will leave a proof state with no subgoals, that must be closed using a Qed or Defined (similarly to Coq’s #[refine] Instance command).
∗ #372, #194: funelim applied to a partial application failing
∗ #354: support for building values in SProp
∗ #353: name capture problem in presence of modules
∗ #335: provide an alias Equations Derive to not conflict with QuickChick’s Derive
∗ #325: properly inline all Equations helper constants during Extraction