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-rw-r--r--doc/sphinx/addendum/miscellaneous-extensions.rst67
-rw-r--r--doc/sphinx/index.rst1
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diff --git a/doc/sphinx/addendum/miscellaneous-extensions.rst b/doc/sphinx/addendum/miscellaneous-extensions.rst
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+.. include:: ../replaces.rst
+
+.. _miscellaneousextensions:
+
+Miscellaneous extensions
+=======================
+
+:Source: https://coq.inria.fr/distrib/current/refman/miscellaneous.html
+:Converted by: Paul Steckler
+
+.. contents::
+ :local:
+ :depth: 1
+----
+
+Program derivation
+-----------------
+
+|Coq| comes with an extension called ``Derive``, which supports program
+derivation. Typically in the style of Bird and Meertens or derivations
+of program refinements. To use the Derive extension it must first be
+required with ``Require Coq.Derive.Derive``. When the extension is loaded,
+it provides the following command:
+
+.. cmd:: Derive @ident SuchThat @term As @ident
+
+The first `ident` can appear in `term`. This command opens a new proof
+presenting the user with a goal for term in which the name `ident` is
+bound to an existential variable `?x` (formally, there are other goals
+standing for the existential variables but they are shelved, as
+described in Section :ref:`TODO-8.17.4`).
+
+When the proof ends two constants are defined:
+
++ The first one is named using the first `ident` and is defined as the proof of the
+ shelved goal (which is also the value of `?x`). It is always
+ transparent.
++ The second one is named using the second `ident`. It has type `term`, and its body is
+ the proof of the initially visible goal. It is opaque if the proof
+ ends with ``Qed``, and transparent if the proof ends with ``Defined``.
+
+.. example::
+ .. coqtop:: all
+
+ Require Coq.derive.Derive.
+ Require Import Coq.Numbers.Natural.Peano.NPeano.
+
+ Section P.
+
+ Variables (n m k:nat).
+
+ Derive p SuchThat ((k*n)+(k*m) = p) As h.
+ Proof.
+ rewrite <- Nat.mul_add_distr_l.
+ subst p.
+ reflexivity.
+ Qed.
+
+ End P.
+
+ Print p.
+ Check h.
+
+Any property can be used as `term`, not only an equation. In particular,
+it could be an order relation specifying some form of program
+refinement or a non-executable property from which deriving a program
+is convenient.
diff --git a/doc/sphinx/index.rst b/doc/sphinx/index.rst
index 3dd4f8020..db03693ff 100644
--- a/doc/sphinx/index.rst
+++ b/doc/sphinx/index.rst
@@ -55,6 +55,7 @@ Table of contents
addendum/nsatz
addendum/generalized-rewriting
addendum/parallel-proof-processing
+ addendum/miscellaneous-extensions
.. toctree::
:caption: Reference