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authorJim Fehrle2020-04-01 13:18:03 -0700
committerJim Fehrle2020-06-08 16:50:53 -0700
commit27d6686f399f40904ff6005a84677907d53c5bbf (patch)
tree5a27b8acdab8ce79b9a7d10685c8979cda82416b /doc/sphinx/addendum
parent6a76e4394876cb08b02d8e7ea185049147f9cd2b (diff)
Convert Ltac chapter to prodn
Diffstat (limited to 'doc/sphinx/addendum')
-rw-r--r--doc/sphinx/addendum/implicit-coercions.rst2
-rw-r--r--doc/sphinx/addendum/ring.rst20
2 files changed, 13 insertions, 9 deletions
diff --git a/doc/sphinx/addendum/implicit-coercions.rst b/doc/sphinx/addendum/implicit-coercions.rst
index 5d257c7370..dafa510ade 100644
--- a/doc/sphinx/addendum/implicit-coercions.rst
+++ b/doc/sphinx/addendum/implicit-coercions.rst
@@ -44,7 +44,7 @@ Formally, the syntax of classes is defined as:
.. prodn::
class ::= Funclass
| Sortclass
- | @smart_qualid
+ | @reference
diff --git a/doc/sphinx/addendum/ring.rst b/doc/sphinx/addendum/ring.rst
index f037fed394..479fa674f5 100644
--- a/doc/sphinx/addendum/ring.rst
+++ b/doc/sphinx/addendum/ring.rst
@@ -102,17 +102,17 @@ forget this paragraph and use the tactic according to your intuition.
Concrete usage in Coq
--------------------------
-.. tacv:: ring
+.. tacn:: ring {? [ {+ @term } ] }
- This tactic solves equations upon polynomial expressions of a ring
+ Solves polynomical equations of a ring
(or semiring) structure. It proceeds by normalizing both sides
of the equation (w.r.t. associativity, commutativity and
distributivity, constant propagation, rewriting of monomials) and
- comparing syntactically the results.
+ syntactically comparing the results.
-.. tacv:: ring_simplify
+.. tacn:: ring_simplify {? [ {+ @term } ] } {+ @term } {? in @ident }
- This tactic applies the normalization procedure described above to
+ Applies the normalization procedure described above to
the given terms. The tactic then replaces all occurrences of the terms
given in the conclusion of the goal by their normal forms. If no term
is given, then the conclusion should be an equation and both
@@ -125,6 +125,10 @@ Concrete usage in Coq
``Require Import ZArithRing`` or simply ``Require Import ZArith``; for |N|, do
``Require Import NArithRing`` or ``Require Import NArith``.
+ All declared field structures can be printed with the :cmd:`Print Rings` command.
+
+ .. cmd:: Print Rings
+ :undocumented:
.. example::
@@ -511,7 +515,7 @@ application of the main correctness theorem to well-chosen arguments.
Dealing with fields
------------------------
-.. tacv:: field
+.. tacn:: field {? [ {+ @term } ] }
This tactic is an extension of the :tacn:`ring` tactic that deals with rational
expressions. Given a rational expression :math:`F = 0`. It first reduces the
@@ -568,7 +572,7 @@ Dealing with fields
Rewriting works with the equality :g:`m = p` only if :g:`p` is a polynomial since
rewriting is handled by the underlying ring tactic.
-.. tacv:: field_simplify
+.. tacn:: field_simplify {? [ {+ @term } ] } {+ @term } {? in @ident }
performs the simplification in the conclusion of the
goal, :math:`F_1 = F_2` becomes :math:`N_1 / D_1 = N_2 / D_2`. A normalization step
@@ -602,7 +606,7 @@ Dealing with fields
assumption :token:`ident` using the
equalities defined by the :token:`term`\s inside the brackets.
-.. tacv:: field_simplify_eq
+.. tacn:: field_simplify_eq {? [ {+ @term } ] } {? in @ident }
performs the simplification in the conclusion of
the goal removing the denominator. :math:`F_1 = F_2` becomes :math:`N_1 D_2 = N_2 D_1`.