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1 files changed, 130 insertions, 152 deletions
diff --git a/doc/refman/RefMan-ext.tex b/doc/refman/RefMan-ext.tex
index 939fc87a6e..713f344cbe 100644
--- a/doc/refman/RefMan-ext.tex
+++ b/doc/refman/RefMan-ext.tex
@@ -38,21 +38,19 @@ construction allows defining ``signatures''.
\end{figure}
\noindent In the expression
-
-\smallskip
-{\tt Record} {\ident} {\params} \texttt{:}
- {\sort} := {\ident$_0$} \verb+{+
- {\ident$_1$} \binders$_1$ \texttt{:} {\term$_1$};
- \dots
- {\ident$_n$} \binders$_n$ \texttt{:} {\term$_n$} \verb+}+.
-\smallskip
-
+\begin{quote}
+{\tt Record {\ident} {\params} : {\sort} := {\ident$_0$} \{ \\
+ {\ident$_1$} \binders$_1$ : {\term$_1$} ; ... ; \\
+ {\ident$_n$} \binders$_n$ : {\term$_n$} \}.}
+\end{quote}
\noindent the identifier {\ident} is the name of the defined record
and {\sort} is its type. The identifier {\ident$_0$} is the name of
its constructor. If {\ident$_0$} is omitted, the default name {\tt
-Build\_{\ident}} is used. If {\sort} is omitted, the default sort is ``{\Type}''.
-The identifiers {\ident$_1$}, ..,
-{\ident$_n$} are the names of fields and {\tt forall} \binders$_1${\tt ,} {\term$_1$}, ..., {\tt forall} \binders$_n${\tt ,} {\term$_n$}
+Build\_{\ident}} is used.
+If {\sort} is omitted, the default sort is {\Type}.
+The identifiers {\ident$_1$}, \dots, {\ident$_n$} are the names of
+fields and {\tt forall {\binders$_1$}, {\term$_1$}}, \dots,
+{\tt forall {\binders$_n$}, {\term$_n$}}
their respective types. Remark that the type of {\ident$_i$} may
depend on the previous {\ident$_j$} (for $j<i$). Thus the order of the
fields is important. Finally, {\params} are the parameters of the
@@ -82,26 +80,15 @@ Record Rat : Set := mkRat
forall x y z:nat, (x * y) = top /\ (x * z) = bottom -> x = 1}.
\end{coq_example}
-Remark here that the field
-\verb+Rat_cond+ depends on the field \verb+bottom+.
-
-%Let us now see the work done by the {\tt Record} macro.
-%First the macro generates an inductive definition
-%with just one constructor:
-%
-%\medskip
-%\noindent
-%{\tt Inductive {\ident} \zeroone{\binders} : {\sort} := \\
-%\mbox{}\hspace{0.4cm} {\ident$_0$} : forall ({\ident$_1$}:{\term$_1$}) ..
-%({\ident$_n$}:{\term$_n$}), {\ident} {\rm\sl params}.}
-%\medskip
+Remark here that the field \verb+Rat_bottom_cond+ depends
+on the field \verb+bottom+ and \verb+Rat_irred_cond+ depends
+on both \verb+top+ and \verb+bottom+.
Let us now see the work done by the {\tt Record} macro. First the
macro generates a variant type definition with just one constructor:
\begin{quote}
-{\tt Variant {\ident} {\params} :{\sort} :=} \\
-\qquad {\tt
- {\ident$_0$} ({\ident$_1$}:{\term$_1$}) .. ({\ident$_n$}:{\term$_n$}).}
+{\tt Variant {\ident} {\params} : {\sort} := \\
+ {\ident$_0$} ({\ident$_1$} : {\term$_1$}) ... ({\ident$_n$} : {\term$_n$}).}
\end{quote}
To build an object of type {\ident}, one should provide the
constructor {\ident$_0$} with $n$ terms filling the fields of
@@ -109,28 +96,9 @@ the record.
As an example, let us define the rational $1/2$:
\begin{coq_example*}
-Require Import Arith.
Theorem one_two_irred :
forall x y z:nat, x * y = 1 /\ x * z = 2 -> x = 1.
-\end{coq_example*}
-\begin{coq_eval}
-Lemma mult_m_n_eq_m_1 : forall m n:nat, m * n = 1 -> m = 1.
-destruct m; trivial.
-intros; apply f_equal with (f := S).
-destruct m; trivial.
-destruct n; simpl in H.
- rewrite <- mult_n_O in H.
- discriminate.
- rewrite <- plus_n_Sm in H.
- discriminate.
-Qed.
-
-intros x y z [H1 H2].
- apply mult_m_n_eq_m_1 with (n := y); trivial.
-\end{coq_eval}
-\ldots
-\begin{coq_example*}
-Qed.
+Admitted.
\end{coq_example*}
\begin{coq_example}
Definition half := mkRat true 1 2 (O_S 1) one_two_irred.
@@ -139,80 +107,6 @@ Definition half := mkRat true 1 2 (O_S 1) one_two_irred.
Check half.
\end{coq_example}
-The macro generates also, when it is possible, the projection
-functions for destructuring an object of type {\ident}. These
-projection functions have the same name that the corresponding
-fields. If a field is named ``\verb=_='' then no projection is built
-for it. In our example:
-
-\begin{coq_example}
-Eval compute in half.(top).
-Eval compute in half.(bottom).
-Eval compute in half.(Rat_bottom_cond).
-\end{coq_example}
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-
-Records defined with the {\tt Record} keyword are not allowed to be
-recursive (references to the record's name in the type of its field
-raises an error). To define recursive records, one can use the {\tt
- Inductive} and {\tt CoInductive} keywords, resulting in an inductive
-or co-inductive record. A \emph{caveat}, however, is that records
-cannot appear in mutually inductive (or co-inductive) definitions.
-Induction schemes are automatically generated for inductive records.
-Automatic generation of induction schemes for non-recursive records
-defined with the {\tt Record} keyword can be activated with the
-{\tt Nonrecursive Elimination Schemes} option
-(see~\ref{set-nonrecursive-elimination-schemes}).
-
-\begin{Warnings}
-\item {\tt {\ident$_i$} cannot be defined.}
-
- It can happen that the definition of a projection is impossible.
- This message is followed by an explanation of this impossibility.
- There may be three reasons:
- \begin{enumerate}
- \item The name {\ident$_i$} already exists in the environment (see
- Section~\ref{Axiom}).
- \item The body of {\ident$_i$} uses an incorrect elimination for
- {\ident} (see Sections~\ref{Fixpoint} and~\ref{Caseexpr}).
- \item The type of the projections {\ident$_i$} depends on previous
- projections which themselves could not be defined.
- \end{enumerate}
-\end{Warnings}
-
-\begin{ErrMsgs}
-
-\item \errindex{Records declared with the keyword Record or Structure cannot be recursive.}
-
- The record name {\ident} appears in the type of its fields, but uses
- the keyword {\tt Record}. Use the keyword {\tt Inductive} or {\tt
- CoInductive} instead.
-\item \errindex{Cannot handle mutually (co)inductive records.}
-
- Records cannot be defined as part of mutually inductive (or
- co-inductive) definitions, whether with records only or mixed with
- standard definitions.
-\item During the definition of the one-constructor inductive
- definition, all the errors of inductive definitions, as described in
- Section~\ref{gal-Inductive-Definitions}, may also occur.
-
-\end{ErrMsgs}
-
-\SeeAlso Coercions and records in Section~\ref{Coercions-and-records}
-of the chapter devoted to coercions.
-
-\Rem {\tt Structure} is a synonym of the keyword {\tt Record}.
-
-\Rem Creation of an object of record type can be done by calling {\ident$_0$}
-and passing arguments in the correct order.
-
-\begin{coq_example}
-Record point := { x : nat; y : nat }.
-Definition a := Build_point 5 3.
-\end{coq_example}
-
\begin{figure}[t]
\begin{centerframe}
\begin{tabular}{lcl}
@@ -226,15 +120,17 @@ Definition a := Build_point 5 3.
\label{fig:fieldsyntax}
\end{figure}
-A syntax is available for creating objects by using named fields, as
+Alternatively, the following syntax allows creating objects by using named fields, as
shown on Figure~\ref{fig:fieldsyntax}. The
fields do not have to be in any particular order, nor do they have to be all
present if the missing ones can be inferred or prompted for (see
Section~\ref{Program}).
\begin{coq_example}
-Definition b := {| x := 5; y := 3 |}.
-Definition c := {| y := 3; x := 5 |}.
+Definition half' :=
+ {| sign := true;
+ Rat_bottom_cond := O_S 1;
+ Rat_irred_cond := one_two_irred |}.
\end{coq_example}
This syntax can be disabled globally for printing by
@@ -256,23 +152,52 @@ This syntax can also be used for pattern matching.
\begin{coq_example}
Eval compute in (
- match b with
- | {| y := S n |} => n
+ match half with
+ | {| sign := true; top := n |} => n
| _ => 0
end).
\end{coq_example}
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
+The macro generates also, when it is possible, the projection
+functions for destructuring an object of type {\ident}. These
+projection functions are given the names of the corresponding
+fields. If a field is named ``\verb=_='' then no projection is built
+for it. In our example:
+
+\begin{coq_example}
+Eval compute in top half.
+Eval compute in bottom half.
+Eval compute in Rat_bottom_cond half.
+\end{coq_example}
+
+An alternative syntax for projections based on a dot notation is
+available:
+
+\begin{coq_example}
+Eval compute in half.(top).
+\end{coq_example}
-\Rem A syntax for projections based on a dot notation is
-available. The command to activate it is
+It can be activated for printing with the command
\optindex{Printing Projections}
\begin{quote}
{\tt Set Printing Projections.}
\end{quote}
+\begin{coq_example}
+Set Printing Projections.
+Check top half.
+\end{coq_example}
+
+The corresponding grammar rules are given in Figure~\ref{fig:projsyntax}.
+When {\qualid} denotes a projection, the syntax {\tt
+ {\term}.({\qualid})} is equivalent to {\qualid~\term}, the syntax
+{\term}{\tt .(}{\qualid}~{\termarg}$_1$ {\ldots} {\termarg}$_n${\tt )} to
+{\qualid~{\termarg}$_1$ {\ldots} {\termarg}$_n$~\term}, and the syntax
+{\term}{\tt .(@}{\qualid}~{\term}$_1$~\ldots~{\term}$_n${\tt )} to
+{@\qualid~{\term}$_1$ {\ldots} {\term}$_n$~\term}. In each case, {\term}
+is the object projected and the other arguments are the parameters of
+the inductive type.
+
\begin{figure}[t]
\begin{centerframe}
\begin{tabular}{lcl}
@@ -285,18 +210,66 @@ available. The command to activate it is
\label{fig:projsyntax}
\end{figure}
-The corresponding grammar rules are given Figure~\ref{fig:projsyntax}.
-When {\qualid} denotes a projection, the syntax {\tt
- {\term}.({\qualid})} is equivalent to {\qualid~\term}, the syntax
-{\term}{\tt .(}{\qualid}~{\termarg}$_1$ {\ldots} {\termarg}$_n${\tt )} to
-{\qualid~{\termarg}$_1$ {\ldots} {\termarg}$_n$~\term}, and the syntax
-{\term}{\tt .(@}{\qualid}~{\term}$_1$~\ldots~{\term}$_n${\tt )} to
-{@\qualid~{\term}$_1$ {\ldots} {\term}$_n$~\term}. In each case, {\term}
-is the object projected and the other arguments are the parameters of
-the inductive type.
+\begin{coq_eval}
+Reset Initial.
+\end{coq_eval}
+
+\begin{Remarks}
+
+\item Records defined with the {\tt Record} keyword are not allowed to be
+recursive (references to the record's name in the type of its field
+raises an error). To define recursive records, one can use the {\tt
+Inductive} and {\tt CoInductive} keywords, resulting in an inductive
+or co-inductive record.
+A \emph{caveat}, however, is that records
+cannot appear in mutually inductive (or co-inductive) definitions.
+
+\item Induction schemes are automatically generated for inductive records.
+Automatic generation of induction schemes for non-recursive records
+defined with the {\tt Record} keyword can be activated with the
+{\tt Nonrecursive Elimination Schemes} option
+(see~\ref{set-nonrecursive-elimination-schemes}).
+
+\item {\tt Structure} is a synonym of the keyword {\tt Record}.
-To deactivate the printing of projections, use
-{\tt Unset Printing Projections}.
+\end{Remarks}
+
+\begin{Warnings}
+\item {\tt {\ident$_i$} cannot be defined.}
+
+ It can happen that the definition of a projection is impossible.
+ This message is followed by an explanation of this impossibility.
+ There may be three reasons:
+ \begin{enumerate}
+ \item The name {\ident$_i$} already exists in the environment (see
+ Section~\ref{Axiom}).
+ \item The body of {\ident$_i$} uses an incorrect elimination for
+ {\ident} (see Sections~\ref{Fixpoint} and~\ref{Caseexpr}).
+ \item The type of the projections {\ident$_i$} depends on previous
+ projections which themselves could not be defined.
+ \end{enumerate}
+\end{Warnings}
+
+\begin{ErrMsgs}
+
+\item \errindex{Records declared with the keyword Record or Structure cannot be recursive.}
+
+ The record name {\ident} appears in the type of its fields, but uses
+ the keyword {\tt Record}. Use the keyword {\tt Inductive} or {\tt
+ CoInductive} instead.
+\item \errindex{Cannot handle mutually (co)inductive records.}
+
+ Records cannot be defined as part of mutually inductive (or
+ co-inductive) definitions, whether with records only or mixed with
+ standard definitions.
+\item During the definition of the one-constructor inductive
+ definition, all the errors of inductive definitions, as described in
+ Section~\ref{gal-Inductive-Definitions}, may also occur.
+
+\end{ErrMsgs}
+
+\SeeAlso Coercions and records in Section~\ref{Coercions-and-records}
+of the chapter devoted to coercions.
\subsection{Primitive Projections}
\optindex{Primitive Projections}
@@ -732,20 +705,20 @@ when the {\tt FunInd} library has been loaded via {\tt Require Import FunInd}:
This command can be seen as a generalization of {\tt Fixpoint}. It is actually
a wrapper for several ways of defining a function \emph{and other useful
related objects}, namely: an induction principle that reflects the
-recursive structure of the function (see \ref{FunInduction}), and its
+recursive structure of the function (see \ref{FunInduction}) and its
fixpoint equality.
The meaning of this
declaration is to define a function {\it ident}, similarly to {\tt
Fixpoint}. Like in {\tt Fixpoint}, the decreasing argument must be
-given (unless the function is not recursive), but it must not
-necessary be \emph{structurally} decreasing. The point of the {\tt
+given (unless the function is not recursive), but it might not
+necessarily be \emph{structurally} decreasing. The point of the {\tt
\{\}} annotation is to name the decreasing argument \emph{and} to
describe which kind of decreasing criteria must be used to ensure
termination of recursive calls.
-The {\tt Function} construction enjoys also the {\tt with} extension
+The {\tt Function} construction also enjoys the {\tt with} extension
to define mutually recursive definitions. However, this feature does
-not work for non structural recursive functions. % VRAI??
+not work for non structurally recursive functions. % VRAI??
See the documentation of {\tt functional induction}
(see Section~\ref{FunInduction}) and {\tt Functional Scheme}
@@ -776,7 +749,7 @@ Function plus (n m : nat) {struct n} : nat :=
\end{coq_example*}
\paragraph[Limitations]{Limitations\label{sec:Function-limitations}}
-\term$_0$ must be build as a \emph{pure pattern-matching tree}
+\term$_0$ must be built as a \emph{pure pattern-matching tree}
(\texttt{match...with}) with applications only \emph{at the end} of
each branch.
@@ -803,7 +776,7 @@ For now dependent cases are not treated for non structurally terminating functio
The generation of the graph relation \texttt{(R\_\ident)} used to
compute the induction scheme of \ident\ raised a typing error. Only
- the ident is defined, the induction scheme will not be generated.
+ the ident is defined; the induction scheme will not be generated.
This error happens generally when:
@@ -875,14 +848,14 @@ the following:
being the decreasing argument and \term$_1$ being a function
from type of \ident$_0$ to \texttt{nat} for which value on the
decreasing argument decreases (for the {\tt lt} order on {\tt
- nat}) at each recursive call of \term$_0$, parameters of the
+ nat}) at each recursive call of \term$_0$. Parameters of the
function are bound in \term$_0$;
\item {\tt \{wf} \term$_1$ \ident$_0${\tt\}} with \ident$_0$ being
the decreasing argument and \term$_1$ an ordering relation on
the type of \ident$_0$ (i.e. of type T$_{\ident_0}$
$\to$ T$_{\ident_0}$ $\to$ {\tt Prop}) for which
the decreasing argument decreases at each recursive call of
- \term$_0$. The order must be well founded. parameters of the
+ \term$_0$. The order must be well founded. Parameters of the
function are bound in \term$_0$.
\end{itemize}
@@ -2011,6 +1984,11 @@ Check (fun x y => _) 0 1.
Unset Printing Existential Instances.
\end{coq_eval}
+Existential variables can be named by the user upon creation using
+the syntax {\tt ?[\ident]}. This is useful when the existential
+variable needs to be explicitly handled later in the script (e.g.
+with a named-goal selector, see~\ref{ltac:selector}).
+
\subsection{Explicit displaying of existential instances for pretty-printing
\label{SetPrintingExistentialInstances}
\optindex{Printing Existential Instances}}
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