% This file was created automatically from record.msk. % DO NOT EDIT! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %A record.msk GAP documentation Martin Schoenert %A Alexander Hulpke %% %A @(#)$Id: record.msk,v 1.14 2002/10/01 15:03:08 gap Exp $ %% %Y (C) 1998 School Math and Comp. Sci., University of St. Andrews, Scotland %Y Copyright (C) 2002 The GAP Group %% \Chapter{Records} \index{type!records} *Records* are next to lists the most important way to collect objects together. A record is a collection of *components*. Each component has a unique *name*, which is an identifier that distinguishes this component, and a *value*, which is an object of arbitrary type. We often abbreviate *value of a component* to *element*. We also say that a record *contains* its elements. You can access and change the elements of a record using its name. Record literals are written by writing down the components in order between ``{`rec('}'' and ``{`)'}'', and separating them by commas ``{`,'}''. Each component consists of the name, the assignment operator `:=', and the value. The *empty record*, i.e., the record with no components, is written as `rec()'. \beginexample gap> rec( a := 1, b := "2" ); # a record with two components rec( a := 1, b := "2" ) gap> rec( a := 1, b := rec( c := 2 ) ); # record may contain records rec( a := 1, b := rec( c := 2 ) ) \endexample We may use the `Display' function to illustrate the hierarchy of the record components. \beginexample gap> Display( last ); rec( a := 1, b := rec( c := 2 ) ) \endexample Records usually contain elements of various types, i.e., they are usually not homogeneous like lists. \>IsRecord( <obj> ) C \>IsRecordCollection( <obj> ) C \>IsRecordCollColl( <obj> ) C \index{test!for records} \beginexample gap> IsRecord( rec( a := 1, b := 2 ) ); true gap> IsRecord( IsRecord ); false \endexample \>RecNames( <rec> ) A returns a list of strings corresponding to the names of the record components of the record <rec>. \beginexample gap> r := rec( a := 1, b := 2 );; gap> RecNames( r ); [ "a", "b" ] \endexample Note that you cannot use the string result in the ordinary way to access or change a record component. You must use the `<rec>.(<name>)' construct (see "Accessing Record Elements" and "Record Assignment"). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Accessing Record Elements} \index{accessing!record elements} \>`<rec>.<name>'{record!component access} O The above construct evaluates to the value of the record component with the name <name> in the record <rec>. Note that the <name> is not evaluated, i.e. it is taken literal. \beginexample gap> r := rec( a := 1, b := 2 );; gap> r.a; 1 gap> r.b; 2 \endexample \>`<rec>.(<name>)'{record!component variable} O This construct is similar to the above construct. The difference is that the second operand <name> is evaluated. It must evaluate to a string or an integer otherwise an error is signalled. The construct then evaluates to the element of the record <rec> whose name is, as a string, equal to <name>. \beginexample gap> old := rec( a := 1, b := 2 );; gap> new := rec(); rec( ) gap> for i in RecNames( old ) do > new.(i) := old.(i); > od; gap> Display( new ); rec( a := 1, b := 2 ) \endexample %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Record Assignment} \index{assignment!to a record} \>`<rec>.<name> := <obj>'{record!component assignment} O The record assignment assigns the object <obj>, which may be an object of arbitrary type, to the record component with the name <name>, which must be an identifier, of the record <rec>. That means that accessing the element with name <name> of the record <rec> will return <obj> after this assignment. If the record <rec> has no component with the name <name>, the record is automatically extended to make room for the new component. \beginexample gap> r := rec( a := 1, b := 2 );; gap> r.a := 10;; gap> Display( r ); rec( a := 10, b := 2 ) gap> r.c := 3;; gap> Display( r ); rec( a := 10, b := 2, c := 3 ) \endexample Note that assigning to a record changes the record. The function `IsBound' can be used to test if a record has a component with a certain name, the function `Unbind' (see "Unbind") can be used to remove a component with a certain name again. \beginexample gap> IsBound(r.a); true gap> IsBound(r.d); false gap> Unbind(r.b); gap> Display( r ); rec( a := 10, c := 3 ) \endexample \>`<rec>.(<name>) := <obj>'{record!component variable assignment} O This construct is similar to the above construct. The difference is that the second operand <name> is evaluated. It must evaluate to a string or an integer otherwise an error is signalled. The construct then assigns <obj> to the record component of the record <rec> whose name is, as a string, equal to <name>. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Identical Records} With the record assignment (see "Record Assignment") it is possible to change a record. This section describes the semantic consequences of this fact which are essentially the same as for lists (see~"Identical Lists"). \begintt r := rec( a := 1 ); r := rec( a := 1, b := 2 ); \endtt The second assignment does not change the first record, instead it assigns a new record to the variable `r'. On the other hand, in the following example the record is changed by the second assignment. \begintt r := rec( a := 1 ); r.b := 2; \endtt To understand the difference first think of a variable as a name for an object. The important point is that a record can have several names at the same time. An assignment `<var> := <record>' means in this interpretation that <var> is a name for the object <record>. At the end of the following example `r2' still has the value `rec( a := 1 )' as this record has not been changed and nothing else has been assigned to `r2'. \begintt r1 := rec( a := 1 ); r2 := r1; r1 := rec( a := 1, b := 2 ); \endtt But after the following example the record for which `r2' is a name has been changed and thus the value of `r2' is now `rec( a := 1, b := 2 )'. \begintt r1 := rec( a := 1 ); r2 := r1; r1.b := 2; \endtt We shall say that two records are *identical* if changing one of them by a record assignment also changes the other one. This is slightly incorrect, because if *two* records are identical, there are actually only two names for *one* record. However, the correct usage would be very awkward and would only add to the confusion. Note that two identical records must be equal, because there is only one records with two different names. Thus identity is an equivalence relation that is a refinement of equality. Let us now consider under which circumstances two records are identical. If you enter a record literal then the record denoted by this literal is a new record that is not identical to any other record. Thus in the following example `r1' and `r2' are not identical, though they are equal of course. \begintt r1 := rec( a := 1 ); r2 := rec( a := 1 ); \endtt Also in the following example, no records in the list `l' are identical. \begintt l := []; for i in [1..10] do l[i] := rec( a := 1 ); od; \endtt If you assign a record to a variable no new record is created. Thus the record value of the variable on the left hand side and the record on the right hand side of the assignment are identical. So in the following example `r1' and `r2' are identical records. \begintt r1 := rec( a := 1 ); r2 := r1; \endtt If you pass a record as argument, the old record and the argument of the function are identical. Also if you return a record from a function, the old record and the value of the function call are identical. So in the following example `r1' and `r2' are identical record \begintt r1 := rec( a := 1 ); f := function ( r ) return r; end; r2 := f( r1 ); \endtt The functions `StructuralCopy' and `ShallowCopy' (see "StructuralCopy" and "ShallowCopy") accept a record and return a new record that is equal to the old record but that is *not* identical to the old record. The difference between `StructuralCopy' and `ShallowCopy' is that in the case of `ShallowCopy' the corresponding components of the new and the old records will be identical, whereas in the case of `StructuralCopy' they will only be equal. So in the following example `r1' and `r2' are not identical records. \begintt r1 := rec( a := 1 ); r2 := Copy( r1 ); \endtt If you change a record it keeps its identity. Thus if two records are identical and you change one of them, you also change the other, and they are still identical afterwards. On the other hand, two records that are not identical will never become identical if you change one of them. So in the following example both `r1' and `r2' are changed, and are still identical. \begintt r1 := rec( a := 1 ); r2 := r1; r1.b := 2; \endtt %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Comparisons of Records} \>`<rec1> = <rec2>'{equality!of records} O \>`<rec1> \<> <rec2>'{inequality!of records} O Two records are considered equal, if for each component of one record the other record has a component of the same name with an equal value and vice versa. \beginexample gap> rec( a := 1, b := 2 ) = rec( b := 2, a := 1 ); true gap> rec( a := 1, b := 2 ) = rec( a := 2, b := 1 ); false gap> rec( a := 1 ) = rec( a := 1, b := 2 ); false gap> rec( a := 1 ) = 1; false \endexample \>`<rec1> \< <rec2>'{ordering!of records} O \>`<rec1> \<= <rec2>'{ordering!of records} O To compare records we imagine that the components of both records are sorted according to their names. Then the records are compared lexicographically with unbound elements considered smaller than anything else. Precisely one record <rec1> is considered less than another record <rec2> if <rec2> has a component with name <name2> and either <rec1> has no component with this name or `<rec1>.<name2> \< <rec2>.<name2>' and for each component of <rec1> with name `<name1> \< <name2>' <rec2> has a component with this name and `<rec1>.<name1> = <rec2>.<name1>'. \beginexample gap> rec( a := 1, b := 2 ) < rec( b := 2, a := 1 ); # they are equal false gap> rec( a := 1 ) < rec( a := 1, b := 2 ); # unbound is less than 2 true gap> # note in the following examples that the `a' elements are compared first gap> rec( a := 1, b := 2 ) < rec( a := 2, b := 0 ); # 1 is less than 2 true gap> rec( a := 1 ) < rec( a := 0, b := 2 ); # 0 is less than 1 false gap> rec( b := 1 ) < rec( b := 0, a := 2 ); # unbound is less than 2 true \endexample %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{IsBound and Unbind for Records} \){\fmark `IsBound( <rec>.<name> )'} O `IsBound' returns `true' if the record <rec> has a component with the name <name> (which must be an identifier) and `false' otherwise. <rec> must evaluate to a record, otherwise an error is signalled. \beginexample gap> r := rec( a := 1, b := 2 );; gap> IsBound( r.a ); true gap> IsBound( r.c ); false \endexample \){\fmark `Unbind( <rec>.<name> )'} O `Unbind' deletes the component with the name <name> in the record <rec>. That is, after execution of `Unbind', <rec> no longer has a record component with this name. Note that it is not an error to unbind a nonexisting record component. <rec> must evaluate to a record, otherwise an error is signalled. \beginexample gap> r := rec( a := 1, b := 2 );; gap> Unbind( r.a ); r; rec( b := 2 ) gap> Unbind( r.c ); r; rec( b := 2 ) \endexample Note that `IsBound' and `Unbind' are special in that they do not evaluate their argument, otherwise `IsBound' would always signal an error when it is supposed to return `false' and there would be no way to tell `Unbind' which component to remove. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{Record Access Operations} Internally, record accesses are done using the operations listed in this section. For the records implemented in the kernel, kernel methods are provided for all these operations but otherwise it is possible to install methods for these operations for any object. This permits objects to simulate record behavior. To save memory, records do not store a list of all component names, but only numbers identifying the components. There numbers are called *RNams*. {\GAP} keeps a list of all RNams that are used and provides functions to translate RNams to strings that give the component names and vice versa. \>NameRNam(<nr>) F returns a string representing the component name corresponding to the RNam <nr>. \>RNamObj(<str>) F \>RNamObj(<int>) F returns a number (the RNam) corresponding to the string <str>. It is also possible to pass a positive integer <int> in which case the decimal expansion of <int> is used as a string. %notest \beginexample gap> NameRNam(798); "BravaisSupergroups" gap> RNamObj("blubberflutsch"); 2075 gap> NameRNam(last); "blubberflutsch" \endexample The correspondence between Strings and RNams is not predetermined ab initio, but RNams are assigned to component names dynamically on a ``first come, first serve'' basis. Therefore, depending on the version of the library you are using and on the assignments done so far, the *same* component name may be represented by *different* RNams in different runs of {\GAP}. The following operations are called for record accesses to arbitrary objects. If applicable methods are installed, they are called when the object is accessed as a record. \> `\\.(<obj>,<rnam>)'{record component!operation} O \> `IsBound\\.(<obj>,<rnam>)'{record boundness test!operation} O \> `\\.\\:\\=(<obj>,<rnam>)'{record assignment!operation} O \> `Unbind\\.(<obj>,<rnam>)'{record unbind!operation} O These operations implement component access, test for element boundness, component assignment and removal of the component represented by the RNam <rnam>. The component identifier <rnam> is always declared as `IsPosInt'.