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Diffstat (limited to 'doc/refman/RefMan-syn.tex')
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diff --git a/doc/refman/RefMan-syn.tex b/doc/refman/RefMan-syn.tex index ecaf82806e..084317776b 100644 --- a/doc/refman/RefMan-syn.tex +++ b/doc/refman/RefMan-syn.tex @@ -13,7 +13,7 @@ described in Section~\ref{scopes}. were present for a while in {\Coq} are no longer available from {\Coq} version 8.0. The underlying AST structure is also no longer available. The functionalities of the command {\tt Syntactic Definition} are -still available, see Section~\ref{Abbreviations}. +still available; see Section~\ref{Abbreviations}. \section[Notations]{Notations\label{Notation} \comindex{Notation}} @@ -35,8 +35,8 @@ The expression \texttt{(and A B)} is the abbreviated term and the string \verb="A /\ B"= (called a {\em notation}) tells how it is symbolically written. -A notation is always surrounded by double quotes (excepted when the -abbreviation is a single identifier, see \ref{Abbreviations}). The +A notation is always surrounded by double quotes (except when the +abbreviation is a single identifier; see \ref{Abbreviations}). The notation is composed of {\em tokens} separated by spaces. Identifiers in the string (such as \texttt{A} and \texttt{B}) are the {\em parameters} of the notation. They must occur at least once each in the @@ -68,7 +68,7 @@ declaration of the notation. \subsection[Precedences and associativity]{Precedences and associativity\index{Precedences} \index{Associativity}} -Mixing different symbolic notations in a same text may cause serious +Mixing different symbolic notations in the same text may cause serious parsing ambiguity. To deal with the ambiguity of notations, {\Coq} uses precedence levels ranging from 0 to 100 (plus one extra level numbered 200) and associativity rules. @@ -88,8 +88,8 @@ precedence level to each notation, knowing that a lower level binds more than a higher level. Hence the level for disjunction must be higher than the level for conjunction. -Since connectives are the less tight articulation points of a text, it -is reasonable to choose levels not so far from the higher level which +Since connectives are not tight articulation points of a text, it +is reasonable to choose levels not so far from the highest level which is 100, for example 85 for disjunction and 80 for conjunction\footnote{which are the levels effectively chosen in the current implementation of {\Coq}}. @@ -102,10 +102,10 @@ even consider that the expression is not well-formed and that parentheses are mandatory (this is a ``no associativity'')\footnote{ {\Coq} accepts notations declared as no associative but the parser on which {\Coq} is built, namely {\camlpppp}, currently does not implement the -no-associativity and replace it by a left associativity; hence it is +no-associativity and replaces it by a left associativity; hence it is the same for {\Coq}: no-associativity is in fact left associativity}. We don't know of a special convention of the associativity of -disjunction and conjunction, let's apply for instance a right +disjunction and conjunction, so let's apply for instance a right associativity (which is the choice of {\Coq}). Precedence levels and associativity rules of notations have to be @@ -701,11 +701,11 @@ Notation}. % Introduction An {\em interpretation scope} is a set of notations for terms with -their interpretation. Interpretation scopes provides with a weak, -purely syntactical form of notations overloading: a same notation, for -instance the infix symbol \verb=+= can be used to denote distinct -definitions of an additive operator. Depending on which interpretation -scopes is currently open, the interpretation is different. +their interpretation. Interpretation scopes provide a weak, +purely syntactical form of notation overloading: the same notation, for +instance the infix symbol \verb=+=, can be used to denote distinct +definitions of the additive operator. Depending on which interpretation +scope is currently open, the interpretation is different. Interpretation scopes can include an interpretation for numerals and strings. However, this is only made possible at the {\ocaml} level. @@ -889,7 +889,8 @@ statically. For instance, if {\tt f} is a polymorphic function of type recognized as an argument to be interpreted in scope {\scope}. \comindex{Bind Scope} -More generally, any {\class} (see Chapter~\ref{Coercions-full}) can be +\label{bindscope} +More generally, any coercion {\class} (see Chapter~\ref{Coercions-full}) can be bound to an interpretation scope. The command to do it is \begin{quote} {\tt Bind Scope} {\scope} \texttt{with} {\class} @@ -908,7 +909,7 @@ Open Scope nat_scope. (* Define + on the nat as the default for + *) Check (fun x y1 y2 z t => P _ (x + t) ((f _ (y1 + y2) + z))). \end{coq_example} -\Rem The scope {\tt type\_scope} has also a local effect on +\Rem The scopes {\tt type\_scope} and {\tt function\_scope} also have a local effect on interpretation. See the next section. \SeeAlso The command to show the scopes bound to the arguments of a @@ -940,10 +941,21 @@ Check # @@%mybool #. The scope {\tt type\_scope} has a special status. It is a primitive interpretation scope which is temporarily activated each time a -subterm of an expression is expected to be a type. This includes goals -and statements, types of binders, domain and codomain of implication, -codomain of products, and more generally any type argument of a -declared or defined constant. +subterm of an expression is expected to be a type. It is delimited by +the key {\tt type}, and bound to the coercion class {\tt Sortclass}. It is also +used in certain situations where an expression is statically known to +be a type, including the conclusion and the type of hypotheses within +an {\tt Ltac} goal match (see Section~\ref{ltac-match-goal}) +the statement of a theorem, the type of +a definition, the type of a binder, the domain and codomain of +implication, the codomain of products, and more generally any type +argument of a declared or defined constant. + +\subsection[The {\tt function\_scope} interpretation scope]{The {\tt function\_scope} interpretation scope\index{function\_scope@\texttt{function\_scope}}} + +The scope {\tt function\_scope} also has a special status. +It is temporarily activated each time the argument of a global reference is +recognized to be a {\tt Funclass instance}, i.e., of type {\tt forall x:A, B} or {\tt A -> B}. \subsection{Interpretation scopes used in the standard library of {\Coq}} @@ -953,38 +965,39 @@ commands {\tt Print Scopes} or {\tt Print Scope {\scope}}. \subsubsection{\tt type\_scope} -This includes infix {\tt *} for product types and infix {\tt +} for -sum types. It is delimited by key {\tt type}. +This scope includes infix {\tt *} for product types and infix {\tt +} for +sum types. It is delimited by key {\tt type}, and bound to the coercion class +{\tt Sortclass}, as described at \ref{bindscope}. \subsubsection{\tt nat\_scope} -This includes the standard arithmetical operators and relations on +This scope includes the standard arithmetical operators and relations on type {\tt nat}. Positive numerals in this scope are mapped to their canonical representent built from {\tt O} and {\tt S}. The scope is -delimited by key {\tt nat}. +delimited by key {\tt nat}, and bound to the type {\tt nat} (see \ref{bindscope}). \subsubsection{\tt N\_scope} -This includes the standard arithmetical operators and relations on +This scope includes the standard arithmetical operators and relations on type {\tt N} (binary natural numbers). It is delimited by key {\tt N} and comes with an interpretation for numerals as closed term of type {\tt Z}. \subsubsection{\tt Z\_scope} -This includes the standard arithmetical operators and relations on +This scope includes the standard arithmetical operators and relations on type {\tt Z} (binary integer numbers). It is delimited by key {\tt Z} and comes with an interpretation for numerals as closed term of type {\tt Z}. \subsubsection{\tt positive\_scope} -This includes the standard arithmetical operators and relations on +This scope includes the standard arithmetical operators and relations on type {\tt positive} (binary strictly positive numbers). It is delimited by key {\tt positive} and comes with an interpretation for numerals as closed term of type {\tt positive}. \subsubsection{\tt Q\_scope} -This includes the standard arithmetical operators and relations on +This scope includes the standard arithmetical operators and relations on type {\tt Q} (rational numbers defined as fractions of an integer and a strictly positive integer modulo the equality of the numerator-denominator cross-product). As for numerals, only $0$ and @@ -993,13 +1006,13 @@ interpretations are $\frac{0}{1}$ and $\frac{1}{1}$ respectively). \subsubsection{\tt Qc\_scope} -This includes the standard arithmetical operators and relations on the +This scope includes the standard arithmetical operators and relations on the type {\tt Qc} of rational numbers defined as the type of irreducible fractions of an integer and a strictly positive integer. \subsubsection{\tt real\_scope} -This includes the standard arithmetical operators and relations on +This scope includes the standard arithmetical operators and relations on type {\tt R} (axiomatic real numbers). It is delimited by key {\tt R} and comes with an interpretation for numerals as term of type {\tt R}. The interpretation is based on the binary decomposition. The @@ -1014,35 +1027,40 @@ those of {\tt R}. \subsubsection{\tt bool\_scope} -This includes notations for the boolean operators. It is -delimited by key {\tt bool}. +This scope includes notations for the boolean operators. It is +delimited by key {\tt bool}, and bound to the type {\tt bool} (see \ref{bindscope}). \subsubsection{\tt list\_scope} -This includes notations for the list operators. It is -delimited by key {\tt list}. +This scope includes notations for the list operators. It is +delimited by key {\tt list}, and bound to the type {\tt list} (see \ref{bindscope}). + +\subsubsection{\tt function\_scope} + +This scope is delimited by the key {\tt function}, and bound to the coercion class {\tt Funclass}, +as described at \ref{bindscope}. \subsubsection{\tt core\_scope} -This includes the notation for pairs. It is delimited by key {\tt core}. +This scope includes the notation for pairs. It is delimited by key {\tt core}. \subsubsection{\tt string\_scope} -This includes notation for strings as elements of the type {\tt +This scope includes notation for strings as elements of the type {\tt string}. Special characters and escaping follow {\Coq} conventions on strings (see Section~\ref{strings}). Especially, there is no convention to visualize non printable characters of a string. The file {\tt String.v} shows an example that contains quotes, a newline -and a beep (i.e. the ascii character of code 7). +and a beep (i.e. the ASCII character of code 7). \subsubsection{\tt char\_scope} -This includes interpretation for all strings of the form -\verb!"!$c$\verb!"! where $c$ is an ascii character, or of the form +This scope includes interpretation for all strings of the form +\verb!"!$c$\verb!"! where $c$ is an ASCII character, or of the form \verb!"!$nnn$\verb!"! where $nnn$ is a three-digits number (possibly with leading 0's), or of the form \verb!""""!. Their respective -denotations are the ascii code of $c$, the decimal ascii code $nnn$, -or the ascii code of the character \verb!"! (i.e. the ascii code +denotations are the ASCII code of $c$, the decimal ASCII code $nnn$, +or the ASCII code of the character \verb!"! (i.e. the ASCII code 34), all of them being represented in the type {\tt ascii}. \subsection{Displaying informations about scopes} |