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| author | Matej Kosik | 2015-11-02 16:58:39 +0100 |
|---|---|---|
| committer | Hugo Herbelin | 2015-12-10 09:35:11 +0100 |
| commit | fdb02e793da45a37355050342109da1be4a49c89 (patch) | |
| tree | fdb7461ca8e1c1961159fee40e9de75f69a82b1a /doc | |
| parent | 10f9c82c38c6eb01e64ab9a8fa233300568c18d4 (diff) | |
TYPOGRAPHY: Examples of "arity" concept(s) were put to a separate \paragraph{...}
Diffstat (limited to 'doc')
| -rw-r--r-- | doc/refman/RefMan-cic.tex | 23 |
1 files changed, 15 insertions, 8 deletions
diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex index deaa1047c8..2fa9c59a86 100644 --- a/doc/refman/RefMan-cic.tex +++ b/doc/refman/RefMan-cic.tex @@ -766,16 +766,23 @@ We restrict ourselves to definitions which satisfy a syntactic criterion of positivity. Before giving the formal rules, we need a few definitions: -\paragraph[Definitions]{Definitions\index{Positivity}\label{Positivity}} - -A type $T$ is an {\em arity of sort $s$}\index{Arity} if it converts +\paragraph[Definition]{Definition\index{Arity}\label{Arity}} +A type $T$ is an {\em arity of sort $s$} if it converts to the sort $s$ or to a product $\forall~x:T,U$ with $U$ an arity -of sort $s$. (For instance $A\ra \Set$ or $\forall~A:\Prop,A\ra -\Prop$ are arities of sort respectively \Set\ and \Prop). -\vskip.5em -\noindent A type $T$ is an {\em arity} if there is a $s\in\Sort$ +of sort $s$. + +\paragraph[Examples]{Examples} +$A\ra \Set$ is an arity of sort $\Set$. +$\forall~A:\Prop,A\ra \Prop$ is an arity of sort \Prop. + +\paragraph[Definition]{Definition} +A type $T$ is an {\em arity} if there is a $s\in\Sort$ such that $T$ is an arity of sort $s$. -\vskip.5em + +\paragraph[Examples]{Examples} +$A\ra \Set$ and $\forall~A:\Prop,A\ra \Prop$ are arities. + +\paragraph[Definition]{Definition\index{Positivity}\label{Positivity}} \noindent A {\em type of constructor of $I$}\index{Type of constructor} is either a term $(I~t_1\ldots ~t_n)$ or $\fa x:T,C$ with $C$ recursively |
