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authorClément Pit-Claudel2018-05-16 21:24:47 -0400
committerThéo Zimmermann2018-09-20 10:12:55 +0200
commita63bc54bfd697e76182044a8515818fa8f92e849 (patch)
treef1c0b461365586c855e94db7277683dcbe753fea /doc/sphinx/language
parentb627c7242d71c834e7a06353ced967c43598e344 (diff)
[doc] Fix a few LaTeX mistakes
Diffstat (limited to 'doc/sphinx/language')
-rw-r--r--doc/sphinx/language/cic.rst26
1 files changed, 15 insertions, 11 deletions
diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst
index ac0f0f8ea6..13d6e228a6 100644
--- a/doc/sphinx/language/cic.rst
+++ b/doc/sphinx/language/cic.rst
@@ -1010,7 +1010,7 @@ the Type hierarchy.
It is possible to declare the same inductive definition in the
universe :math:`\Type`. The :g:`exType` inductive definition has type
- :math:`(\Type(i)→\Prop)→\Type(j)` with the constraint that the parameter :math:`X` of :math:`\kw{exT_intro}`
+ :math:`(\Type(i)→\Prop)→\Type(j)` with the constraint that the parameter :math:`X` of :math:`\kw{exT}_{\kw{intro}}`
has type :math:`\Type(k)` with :math:`k<j` and :math:`k≤ i`.
.. coqtop:: all
@@ -1264,14 +1264,14 @@ The |Coq| term for this proof
will be written:
.. math::
- \Match~m~\with~(c_1~x_{11} ... x_{1p_1} ) ⇒ f_1 | … | (c_n~x_{n1} ... x_{np_n} ) ⇒ f_n \endkw
+ \Match~m~\with~(c_1~x_{11} ... x_{1p_1} ) ⇒ f_1 | … | (c_n~x_{n1} ... x_{np_n} ) ⇒ f_n \kwend
In this expression, if :math:`m` eventually happens to evaluate to
:math:`(c_i~u_1 … u_{p_i})` then the expression will behave as specified in its :math:`i`-th branch
and it will reduce to :math:`f_i` where the :math:`x_{i1} …x_{ip_i}` are replaced by the
:math:`u_1 … u_{p_i}` according to the ι-reduction.
-Actually, for type checking a :math:`\Match…\with…\endkw` expression we also need
+Actually, for type checking a :math:`\Match…\with…\kwend` expression we also need
to know the predicate P to be proved by case analysis. In the general
case where :math:`I` is an inductively defined :math:`n`-ary relation, :math:`P` is a predicate
over :math:`n+1` arguments: the :math:`n` first ones correspond to the arguments of :math:`I`
@@ -1285,7 +1285,7 @@ using the syntax:
.. math::
\Match~m~\as~x~\In~I~\_~a~\return~P~\with~
(c_1~x_{11} ... x_{1p_1} ) ⇒ f_1 | …
- | (c_n~x_{n1} ... x_{np_n} ) ⇒ f_n~\endkw
+ | (c_n~x_{n1} ... x_{np_n} ) ⇒ f_n~\kwend
The :math:`\as` part can be omitted if either the result type does not depend
on :math:`m` (non-dependent elimination) or :math:`m` is a variable (in this case, :math:`m`
@@ -1471,6 +1471,8 @@ We write :math:`\{c\}^P` for :math:`\{c:C\}^P` with :math:`C` the type of :math:
where
.. math::
+ :nowrap:
+
\begin{eqnarray*}
P & = & \lambda~l~.~P^\prime\\
f_1 & = & t_1\\
@@ -1711,13 +1713,15 @@ for primitive recursive operators. The following reductions are now
possible:
.. math::
- \def\plus{\mathsf{plus}}
- \def\tri{\triangleright_\iota}
- \begin{eqnarray*}
- \plus~(\nS~(\nS~\nO))~(\nS~\nO) & \tri & \nS~(\plus~(\nS~\nO)~(\nS~\nO))\\
- & \tri & \nS~(\nS~(\plus~\nO~(\nS~\nO)))\\
- & \tri & \nS~(\nS~(\nS~\nO))\\
- \end{eqnarray*}
+ :nowrap:
+
+ {\def\plus{\mathsf{plus}}
+ \def\tri{\triangleright_\iota}
+ \begin{eqnarray*}
+ \plus~(\nS~(\nS~\nO))~(\nS~\nO) & \tri & \nS~(\plus~(\nS~\nO)~(\nS~\nO))\\
+ & \tri & \nS~(\nS~(\plus~\nO~(\nS~\nO)))\\
+ & \tri & \nS~(\nS~(\nS~\nO))\\
+ \end{eqnarray*}}
.. _Mutual-induction: