Equations 1.0beta released!
Release 1.0beta of Equations is available, as source and
through opam
(package coqequations.1.0~beta
).
We are pleased to announce release 1.0beta of the Equations
package. Equations is a function definition plugin for Coq (supporting
Coq 8.6 currently), that allows the definition of functions by
dependent patternmatching and (wellfounded) recursion and compiles
them into core terms. This version of Equations is based on a new
simplification engine for the dependent equalities appearing in dependent
eliminations that is also usable as a separate tactic, providing an
axiomfree variant of dependent destruction
. The main features of
Equations include:

Dependent patternmatching in the style of Agda/Epigram, with inaccessible patterns,
with
andwhere
clauses. The use of the K axiom or a proof of K is configurable. 
Support for wellfounded recursion using
by rec
annotations, and automatic derivation of the subterm relation for inductive families. 
Automatic generation of the defining equations as rewrite rules for every definition.

Automatic generation of the unfolding lemma for wellfounded definitions (requiring only functional extensionality).

Automatic derivation of the graph of the function and its elimination principle. In case the automation fails to prove these principles, the user is asked to provide a proof.

A new
dependent elimination
tactic based on the same splitting tree compilation scheme that can advantageously replacedependent destruction
and sometimesinversion
as well. Theas
clause ofdependent elimination
allows to specify exactly the patterns and naming of new variables needed for an elimination. 
A set of
Derive
commands for automatic derivation of constructions from an inductive type: its signature, noconfusion property, wellfounded subterm relation and decidable equality proof.
The current system has known limitations we will address (see FAQ), but is already usable for developping nontoy programs and proofs (see examples). Documentation is available on the website. We are seeking and welcoming feedback from you on the usage of these tools!
– Matthieu Sozeau and Cyprien Mangin