From 5cdf3cfc8ddfb9854534fadc1a08019e9c472590 Mon Sep 17 00:00:00 2001 From: Hugo Herbelin Date: Sun, 4 Oct 2015 08:16:54 +0200 Subject: RefMan, ch. 4: Fixing the definition of terms considered in the section. --- doc/refman/RefMan-cic.tex | 19 +++++++++++++------ 1 file changed, 13 insertions(+), 6 deletions(-) diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex index 9d79f7cac3..ef7b99d6a8 100644 --- a/doc/refman/RefMan-cic.tex +++ b/doc/refman/RefMan-cic.tex @@ -176,9 +176,11 @@ in a theory where inductive objects are represented by terms. \subsection{Terms} -Terms are built from variables, constants, constructors, -abstraction, application, local declarations bindings (``let-in'' -expressions) and product. +Terms are built from sorts, variables, constant, +%constructors, inductive types, +abstraction, application, local definitions, +%case analysis, fixpoints, cofixpoints +and products. From a syntactic point of view, types cannot be distinguished from terms, except that they cannot start by an abstraction, and that if a term is @@ -188,9 +190,11 @@ More precisely the language of the {\em Calculus of Inductive Constructions} is built from the following rules: \begin{enumerate} -\item the sorts {\sf Set, Prop, Type} are terms. -\item names for global constants of the environment are terms. -\item variables are terms. +\item the sorts {\Set}, {\Prop}, ${\Type(i)}$ are terms. +\item variables are terms +\item constants are terms. +%\item constructors are terms. +%\item inductive types are terms. \item if $x$ is a variable and $T$, $U$ are terms then $\forall~x:T,U$ ($\kw{forall}~x:T,U$ in \Coq{} concrete syntax) is a term. If $x$ occurs in $U$, $\forall~x:T,U$ reads as {\it ``for all x of type T, @@ -212,6 +216,9 @@ More precisely the language of the {\em Calculus of Inductive term which denotes the term $U$ where the variable $x$ is locally bound to $T$. This stands for the common ``let-in'' construction of functional programs such as ML or Scheme. +%\item case ... +%\item fixpoint ... +%\item cofixpoint ... \end{enumerate} \paragraph{Notations.} Application associates to the left such that -- cgit v1.2.3