7 files changed, 104 insertions, 54 deletions
diff --git a/doc/refman/Micromega.tex b/doc/refman/Micromega.tex
index 1efed6ef76..4daf98f87a 100644
--- a/doc/refman/Micromega.tex
+++ b/doc/refman/Micromega.tex
@@ -4,16 +4,19 @@
 
  
 \asection{Short description of the tactics}
-\tacindex{psatz}  \tacindex{lra} 
+\tacindex{psatz}  \tacindex{lra} \tacindex{lia}  \tacindex{nia} \tacindex{nra} 
 \label{sec:psatz-hurry}
 The {\tt Psatz} module ({\tt Require Import Psatz.}) gives access to
 several tactics for solving arithmetic goals over {\tt Z}, {\tt Q}, and
 {\tt R}:\footnote{Support for {\tt nat} and {\tt N} is obtained by
-  pre-processing the goal with the {\tt zify} tactic.}
+  pre-processing the goal with the {\tt zify} tactic.}.
+It also possible to get the tactics for integers by a {\tt Require Import Lia}, rationals {\tt Require Import Lqa} 
+and reals {\tt Require Import Lra}.
 \begin{itemize}
 \item {\tt lia} is a decision procedure for linear integer arithmetic (see Section~\ref{sec:lia});
 \item {\tt nia} is an incomplete proof procedure for integer non-linear arithmetic (see Section~\ref{sec:nia});
-\item {\tt lra} is a decision procedure for linear (real or rational) arithmetic goals (see Section~\ref{sec:lra});
+\item {\tt lra} is a decision procedure for linear (real or rational) arithmetic  (see Section~\ref{sec:lra});
+\item {\tt nra} is an incomplete proof procedure for non-linear (real or rational) arithmetic  (see Section~\ref{sec:nra});
 \item {\tt psatz D n} where {\tt D} is {\tt Z} or {\tt Q} or {\tt R}, and
   {\tt n} is an optional integer limiting the proof search depth is is an
   incomplete proof procedure for non-linear arithmetic. It is based on
@@ -114,36 +117,6 @@ The deductive power of {\tt lra} is the combined deductive power of {\tt ring\_s
 %
 There is also an overlap with the {\tt field} tactic {\emph e.g.}, {\tt x = 10 * x / 10} is solved by {\tt lra}.
 
-\asection{{\tt psatz}: a proof procedure for non-linear arithmetic}
-\label{sec:psatz}
-The {\tt psatz} tactic explores the $\mathit{Cone}$ by increasing degrees -- hence the depth parameter $n$.
-In theory, such a proof search is complete -- if the goal is provable the search eventually stops.
-Unfortunately, the external oracle is using numeric (approximate) optimization techniques that might miss a
-refutation. 
-
-To illustrate the working of the tactic, consider we wish to prove the following Coq goal.
-\begin{coq_eval}
-Require Import ZArith Psatz.
-Open Scope Z_scope.
-\end{coq_eval}
-\begin{coq_example*}
-Goal forall x, -x^2 >= 0 -> x - 1 >= 0 -> False.
-\end{coq_example*}
-\begin{coq_eval}
-intro x; psatz Z 2.
-\end{coq_eval}
-Such a goal is solved by {\tt intro x; psatz Z 2}. The oracle returns the
-cone expression $2 \times (\mathbf{x-1}) + (\mathbf{x-1}) \times
-(\mathbf{x-1}) + \mathbf{-x^2}$ (polynomial hypotheses are printed in
-bold). By construction, this expression belongs to $\mathit{Cone}(\{-x^2,
-x -1\})$. Moreover, by running {\tt ring} we obtain $-1$. By
-Theorem~\ref{thm:psatz}, the goal is valid.
-%
-
-%% \paragraph{The {\tt sos} tactic} -- where {\tt sos} stands for \emph{sum of squares} -- tries to prove that a
-%% single polynomial $p$ is positive by expressing it as a sum of squares \emph{i.e.,} $\sum_{i\in S} p_i^2$.
-%% This amounts to searching for $p$ in the cone without generators \emph{i.e.}, $Cone(\{\})$.
-%
 
 \asection{{\tt lia}: a tactic for linear integer arithmetic}
 \tacindex{lia}
@@ -219,22 +192,61 @@ Our current oracle tries to find an expression $e$ with a small range $[c_1,c_2]
 We generate $c_2 - c_1$ subgoals which contexts are enriched with an equation $e = i$ for $i \in [c_1,c_2]$ and
 recursively search for a proof.
 
-\asection{{\tt nia}: a proof procedure for non-linear integer arithmetic}
-\tacindex{nia}
-\label{sec:nia}
-The {\tt nia} tactic is an {\emph experimental} proof procedure for non-linear  integer arithmetic.
+
+\asection{{\tt nra}: a proof procedure for non-linear arithmetic}
+\tacindex{nra}
+\label{sec:nra}
+The {\tt nra} tactic is an {\emph experimental} proof procedure for non-linear arithmetic.
 %
 The tactic performs a limited amount of non-linear reasoning before running the
-linear prover of {\tt lia}.
+linear prover of {\tt lra}.
 This pre-processing does the following:
 \begin{itemize}
 \item If the context contains an arithmetic expression of the form $e[x^2]$ where $x$ is a
   monomial, the context is enriched with $x^2\ge 0$;
 \item For all pairs of hypotheses $e_1\ge 0$, $e_2 \ge 0$, the context is enriched with $e_1 \times e_2 \ge 0$.
 \end{itemize}
-After pre-processing, the linear prover of {\tt lia} searches for a proof
+After this pre-processing, the linear prover of {\tt lra} searches for a proof
 by abstracting monomials by variables.
 
+\asection{{\tt nia}: a proof procedure for non-linear integer arithmetic}
+\tacindex{nia}
+\label{sec:nia}
+The {\tt nia} tactic is a proof procedure for non-linear  integer arithmetic.
+%
+It performs a pre-processing similar to {\tt nra}. The obtained goal is solved using the linear integer prover {\tt lia}.
+
+\asection{{\tt psatz}: a proof procedure for non-linear arithmetic}
+\label{sec:psatz}
+The {\tt psatz} tactic explores the $\mathit{Cone}$ by increasing degrees -- hence the depth parameter $n$.
+In theory, such a proof search is complete -- if the goal is provable the search eventually stops.
+Unfortunately, the external oracle is using numeric (approximate) optimization techniques that might miss a
+refutation. 
+
+To illustrate the working of the tactic, consider we wish to prove the following Coq goal.
+\begin{coq_eval}
+Require Import ZArith Psatz.
+Open Scope Z_scope.
+\end{coq_eval}
+\begin{coq_example*}
+Goal forall x, -x^2 >= 0 -> x - 1 >= 0 -> False.
+\end{coq_example*}
+\begin{coq_eval}
+intro x; psatz Z 2.
+\end{coq_eval}
+Such a goal is solved by {\tt intro x; psatz Z 2}. The oracle returns the
+cone expression $2 \times (\mathbf{x-1}) + (\mathbf{x-1}) \times
+(\mathbf{x-1}) + \mathbf{-x^2}$ (polynomial hypotheses are printed in
+bold). By construction, this expression belongs to $\mathit{Cone}(\{-x^2,
+x -1\})$. Moreover, by running {\tt ring} we obtain $-1$. By
+Theorem~\ref{thm:psatz}, the goal is valid.
+%
+
+%% \paragraph{The {\tt sos} tactic} -- where {\tt sos} stands for \emph{sum of squares} -- tries to prove that a
+%% single polynomial $p$ is positive by expressing it as a sum of squares \emph{i.e.,} $\sum_{i\in S} p_i^2$.
+%% This amounts to searching for $p$ in the cone without generators \emph{i.e.}, $Cone(\{\})$.
+%
+
 
 
 %%% Local Variables: 
diff --git a/doc/refman/RefMan-ltac.tex b/doc/refman/RefMan-ltac.tex
index 0433a0f2e4..587f4e5cb3 100644
--- a/doc/refman/RefMan-ltac.tex
+++ b/doc/refman/RefMan-ltac.tex
@@ -1168,7 +1168,7 @@ using the syntax:
 \end{quote}
 A previous definition of {\qualid} must exist in the environment.
 The new definition will always be used instead of the old one and
-it goes accross module boundaries.
+it goes across module boundaries.
 
 If preceded by the keyword {\tt Local} the tactic definition will not
 be exported outside the current module.
@@ -1287,7 +1287,7 @@ Prints the profile
 Prints a profile for all tactics that start with {\qstring}. Append a period (.) to the string if you only want exactly that name.
 
 \begin{quote}
-{\tt Reset Profile}.
+{\tt Reset Ltac Profile}.
 \end{quote}
 Resets the profile, that is, deletes all accumulated information
 
diff --git a/doc/refman/RefMan-oth.tex b/doc/refman/RefMan-oth.tex
index 6a8bda35d6..919e7b5cdc 100644
--- a/doc/refman/RefMan-oth.tex
+++ b/doc/refman/RefMan-oth.tex
@@ -87,7 +87,7 @@ is restored when the current \emph{section} ends.
 \item {\tt Global Unset {\rm\sl flag}.\comindex{Global Unset}}\\
 This command switches {\rm\sl flag} off.  The original state of
 {\rm\sl flag} is \emph{not} restored at the end of the module. Additionally,
-if set in a file, {\rm\sl flag} is switched on when the file is
+if set in a file, {\rm\sl flag} is switched off when the file is
 {\tt Require}-d.
 \end{Variants}
 
diff --git a/doc/refman/RefMan-syn.tex b/doc/refman/RefMan-syn.tex
index e91480ded3..92107b750b 100644
--- a/doc/refman/RefMan-syn.tex
+++ b/doc/refman/RefMan-syn.tex
@@ -589,6 +589,14 @@ Notation "[| t * ( x , y , .. , z ) ; ( a , b , .. , c )  * u |]" :=
   (t at level 39).
 \end{coq_example*}
 
+Recursive patterns can occur several times on the right-hand side.
+Here is an example:
+
+\begin{coq_example*}
+Notation "[> a , .. , b <]" :=
+  (cons a .. (cons b nil) .., cons b .. (cons a nil) ..).
+\end{coq_example*}
+
 Notations with recursive patterns can be reserved like standard
 notations, they can also be declared within interpretation scopes (see
 section \ref{scopes}).
@@ -634,7 +642,16 @@ empty. Here is an example of recursive notation with closed binders:
 \begin{coq_example*}
 Notation "'mylet' f x .. y :=  t 'in' u":=
   (let f := fun x => .. (fun y => t) .. in u)
-  (x closed binder, y closed binder, at level 200, right associativity).
+  (at level 200, x closed binder, y closed binder, right associativity).
+\end{coq_example*}
+
+A recursive pattern for binders can be used in position of a recursive
+pattern for terms. Here is an example:
+
+\begin{coq_example*}
+Notation ``'FUNAPP' x .. y , f'' :=
+  (fun x => .. (fun y => (.. (f x) ..) y ) ..)
+  (at level 200, x binder, y binder, right associativity).
 \end{coq_example*}
 
 \subsection{Summary}
diff --git a/doc/refman/RefMan-tac.tex b/doc/refman/RefMan-tac.tex
index 0e4435cf39..c5fd40bf15 100644
--- a/doc/refman/RefMan-tac.tex
+++ b/doc/refman/RefMan-tac.tex
@@ -1491,10 +1491,10 @@ the local context.
 \tacindex{contradiction}
 
 This tactic applies to any goal. The {\tt contradiction} tactic
-attempts to find in the current context (after all {\tt intros}) one
-hypothesis that is equivalent to {\tt False}. It permits to prune
-irrelevant cases. This tactic is a macro for the tactics sequence
-{\tt intros; elimtype False; assumption}.
+attempts to find in the current context (after all {\tt intros}) an
+hypothesis that is equivalent to an empty inductive type (e.g. {\tt
+  False}), to the negation of a singleton inductive type (e.g. {\tt
+  True} or {\tt x=x}), or two contradictory hypotheses.
 
 \begin{ErrMsgs}
 \item \errindex{No such assumption}
@@ -2280,6 +2280,15 @@ hypothesis.
 
 \end{Variants}
 
+\optindex{Structural Injection}
+
+It is possible to ensure that \texttt{injection {\term}} erases the
+original hypothesis and leaves the generated equalities in the context
+rather than putting them as antecedents of the current goal, as if
+giving \texttt{injection {\term} as} (with an empty list of names). To
+obtain this behavior, the option {\tt Set Structural Injection} must
+be activated. This option is off by default.
+
 \subsection{\tt inversion \ident}
 \tacindex{inversion}
 
@@ -3033,8 +3042,10 @@ $\beta$ (reduction of functional application), $\delta$ (unfolding of
 transparent constants, see \ref{Transparent}), $\iota$ (reduction of
 pattern-matching over a constructed term, and unfolding of {\tt fix}
 and {\tt cofix} expressions) and $\zeta$ (contraction of local
-definitions), the flag are either {\tt beta}, {\tt delta}, {\tt iota}
-or {\tt zeta}. The {\tt delta} flag itself can be refined into {\tt
+definitions), the flags are either {\tt beta}, {\tt delta},
+{\tt match}, {\tt fix}, {\tt cofix}, {\tt iota} or {\tt zeta}.
+The {\tt iota} flag is a shorthand for {\tt match}, {\tt fix} and {\tt cofix}.
+The {\tt delta} flag itself can be refined into {\tt
 delta [\qualid$_1$\ldots\qualid$_k$]} or {\tt delta
 -[\qualid$_1$\ldots\qualid$_k$]}, restricting in the first case the
 constants to unfold to the constants listed, and restricting in the
@@ -3282,6 +3293,16 @@ reduced to \texttt{S t}.
 
 \end{Variants}
 
+\begin{quote}
+\optindex{Refolding Reduction}
+{\tt Refolding Reduction}
+\end{quote}
+
+This option (off by default) controls the use of the refolding strategy
+of {\tt cbn} while doing reductions in unification, type inference and
+tactic applications. It can result in expensive unifications, as
+refolding currently uses a potentially exponential heuristic.
+
 \subsection{\tt unfold \qualid}
 \tacindex{unfold}
 \label{unfold}
diff --git a/doc/refman/RefMan-uti.tex b/doc/refman/RefMan-uti.tex
index c282083b5c..9962ce9961 100644
--- a/doc/refman/RefMan-uti.tex
+++ b/doc/refman/RefMan-uti.tex
@@ -102,7 +102,7 @@ generator using for instance the command:
 
 This command generates a file \texttt{Makefile} that can be used to
 compile all the sources of the current project. It follows the
-syntax described by the output of \texttt{\% coq\_makefile ----help}.
+syntax described by the output of \texttt{\% coq\_makefile -{}-help}.
 Once the \texttt{Makefile} file has been generated a first time, it
 can be used by the \texttt{make} command to compile part or all of
 the project. Note that once it has been generated once, as soon as
@@ -112,8 +112,8 @@ automatically regenerated by an invocation of \texttt{make}.
 The following command generates a minimal example of
 \texttt{\_CoqProject} file:
 \begin{quotation}
-\texttt{\% \{ echo '-R .} \textit{MyFancyLib} \texttt{' ; find . -name
-  '*.v' -print \} > \_CoqProject}
+\texttt{\% ( echo "-R .\ }\textit{MyFancyLib}\texttt{" ; find .\ -name
+  "*.v" -print ) > \_CoqProject}
 \end{quotation}
 when executed at the root of the directory containing the
 project. Here the \texttt{\_CoqProject} lists all the \texttt{.v} files
@@ -251,7 +251,7 @@ to the \Coq\ toplevel or conversely from the \Coq\ toplevel to some
 files.
 
 {\ProofGeneral} is developed and distributed independently of the
-system \Coq. It is freely available at \verb!proofgeneral.inf.ed.ac.uk!.
+system \Coq. It is freely available at \verb!https://proofgeneral.github.io/!.
 
 
 \section[Module specification]{Module specification\label{gallina}\ttindex{gallina}}
diff --git a/doc/refman/biblio.bib b/doc/refman/biblio.bib
index 70ee1f41f0..e69725838e 100644
--- a/doc/refman/biblio.bib
+++ b/doc/refman/biblio.bib
@@ -1199,7 +1199,7 @@ Decomposition}},
 @Misc{ProofGeneral,
   author      = {David Aspinall},
   title       = {Proof General},
-  note        = {\url{http://proofgeneral.inf.ed.ac.uk/}}
+  note        = {\url{https://proofgeneral.github.io/}}
 }
 
 @Book{CoqArt,