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Diffstat (limited to 'doc/refman/RefMan-cic.tex')
-rw-r--r-- | doc/refman/RefMan-cic.tex | 12 |
1 files changed, 8 insertions, 4 deletions
diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex index b9c17d814..fdd272581 100644 --- a/doc/refman/RefMan-cic.tex +++ b/doc/refman/RefMan-cic.tex @@ -79,8 +79,8 @@ An algebraic universe $u$ is either a variable (a qualified identifier with a number) or a successor of an algebraic universe (an expression $u+1$), or an upper bound of algebraic universes (an expression $max(u_1,...,u_n)$), or the base universe (the expression -$0$) which corresponds, in the arity of sort-polymorphic inductive -types (see Section \ref{Sort-polymorphism-inductive}), +$0$) which corresponds, in the arity of template polymorphic inductive +types (see Section \ref{Template-polymorphism}), to the predicative sort {\Set}. A graph of constraints between the universe variables is maintained globally. To ensure the existence of a mapping of the universes to the positive integers, the graph of @@ -977,8 +977,8 @@ Inductive exType (P:Type->Prop) : Type := %is recursive or not. We shall write the type $(x:_R T)C$ if it is %a recursive argument and $(x:_P T)C$ if the argument is not recursive. -\paragraph[Sort-polymorphism of inductive types.]{Sort-polymorphism of inductive types.\index{Sort-polymorphism of inductive types}} -\label{Sort-polymorphism-inductive} +\paragraph[Template polymorphism.]{Template polymorphism.\index{Template polymorphism}} +\label{Template-polymorphism} Inductive types declared in {\Type} are polymorphic over their arguments in {\Type}. @@ -1120,6 +1120,10 @@ Check (fun (A:Prop) (B:Set) => prod A B). Check (fun (A:Type) (B:Prop) => prod A B). \end{coq_example} +\Rem Template polymorphism used to be called ``sort-polymorphism of +inductive types'' before universe polymorphism (see +Chapter~\ref{Universes-full}) was introduced. + \subsection{Destructors} The specification of inductive definitions with arities and constructors is quite natural. But we still have to say how to use an |