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authorTanaka Akira2019-01-31 16:53:29 +0900
committerTanaka Akira2019-01-31 16:53:29 +0900
commit757084431407d90ee454c06a9e05a978ba4f8663 (patch)
tree61b07d5dad99b9d7f3ce57c1e827dff025d7c9f2
parent631ca702f355cf96a6460682ae2d95bb7a0172b7 (diff)
Use "∀" and "λ" instead of \forall and \lambda.
The former is more succinct and consistent with most of other parts in cic.rst.
-rw-r--r--doc/sphinx/language/cic.rst30
1 files changed, 15 insertions, 15 deletions
diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst
index 26200d3b22..4553546833 100644
--- a/doc/sphinx/language/cic.rst
+++ b/doc/sphinx/language/cic.rst
@@ -331,7 +331,7 @@ following rules.
s \in \Sort
\WTE{\Gamma::(x:T)}{U}{\Prop}
-----------------------------
- \WTEG{\forall~x:T,U}{\Prop}
+ \WTEG{∀~x:T,U}{\Prop}
.. inference:: Prod-Set
@@ -339,25 +339,25 @@ following rules.
s \in \{\Prop, \Set\}
\WTE{\Gamma::(x:T)}{U}{\Set}
----------------------------
- \WTEG{\forall~x:T,U}{\Set}
+ \WTEG{∀~x:T,U}{\Set}
.. inference:: Prod-Type
\WTEG{T}{\Type(i)}
\WTE{\Gamma::(x:T)}{U}{\Type(i)}
--------------------------------
- \WTEG{\forall~x:T,U}{\Type(i)}
+ \WTEG{∀~x:T,U}{\Type(i)}
.. inference:: Lam
- \WTEG{\forall~x:T,U}{s}
+ \WTEG{∀~x:T,U}{s}
\WTE{\Gamma::(x:T)}{t}{U}
------------------------------------
- \WTEG{\lb x:T\mto t}{\forall x:T, U}
+ \WTEG{\lb x:T\mto t}{∀ x:T, U}
.. inference:: App
- \WTEG{t}{\forall~x:U,T}
+ \WTEG{t}{∀~x:U,T}
\WTEG{u}{U}
------------------------------
\WTEG{(t\ u)}{\subst{T}{x}{u}}
@@ -726,8 +726,8 @@ the sort of the inductive type :math:`t` (not to be confused with :math:`\Sort`
.. math::
\ind{1}{[\List:\Set→\Set]}{\left[\begin{array}{rcl}
- \Nil & : & \forall A:\Set,\List~A \\
- \cons & : & \forall A:\Set, A→ \List~A→ \List~A
+ \Nil & : & ∀ A:\Set,\List~A \\
+ \cons & : & ∀ A:\Set, A→ \List~A→ \List~A
\end{array}
\right]}
@@ -771,8 +771,8 @@ the sort of the inductive type :math:`t` (not to be confused with :math:`\Sort`
\odd&:&\nat → \Prop \end{array}\right]}
{\left[\begin{array}{rcl}
\evenO &:& \even~0\\
- \evenS &:& \forall n, \odd~n → \even~(\nS~n)\\
- \oddS &:& \forall n, \even~n → \odd~(\nS~n)
+ \evenS &:& ∀ n, \odd~n → \even~(\nS~n)\\
+ \oddS &:& ∀ n, \even~n → \odd~(\nS~n)
\end{array}\right]}
which corresponds to the result of the |Coq| declaration:
@@ -821,8 +821,8 @@ contains an inductive declaration.
E[Γ] ⊢ \even : \nat→\Prop\\
E[Γ] ⊢ \odd : \nat→\Prop\\
E[Γ] ⊢ \evenO : \even~\nO\\
- E[Γ] ⊢ \evenS : \forall~n:\nat,~\odd~n → \even~(\nS~n)\\
- E[Γ] ⊢ \oddS : \forall~n:\nat,~\even~n → \odd~(\nS~n)
+ E[Γ] ⊢ \evenS : ∀~n:\nat,~\odd~n → \even~(\nS~n)\\
+ E[Γ] ⊢ \oddS : ∀~n:\nat,~\even~n → \odd~(\nS~n)
\end{array}
@@ -1450,7 +1450,7 @@ corresponding to the :math:`c:C` constructor.
.. math::
\begin{array}{ll}
\{c:(I~p_1\ldots p_r\ t_1 \ldots t_p)\}^P &\equiv (P~t_1\ldots ~t_p~c) \\
- \{c:\forall~x:T,C\}^P &\equiv \forall~x:T,\{(c~x):C\}^P
+ \{c:∀~x:T,C\}^P &\equiv ∀~x:T,\{(c~x):C\}^P
\end{array}
We write :math:`\{c\}^P` for :math:`\{c:C\}^P` with :math:`C` the type of :math:`c`.
@@ -1477,9 +1477,9 @@ We write :math:`\{c\}^P` for :math:`\{c:C\}^P` with :math:`C` the type of :math:
:nowrap:
\begin{eqnarray*}
- P & = & \lambda~l~.~P^\prime\\
+ P & = & λ~l~.~P^\prime\\
f_1 & = & t_1\\
- f_2 & = & \lambda~(hd:\nat)~.~\lambda~(tl:\List~\nat)~.~t_2
+ f_2 & = & λ~(hd:\nat)~.~λ~(tl:\List~\nat)~.~t_2
\end{eqnarray*}
According to the definition: