Set::Relation - Relation data type for Perl
This document describes Set::Relation version 0.13.0 for Perl 5.
use Set::Relation::V2; sub relation { return Set::Relation::V2->new( @_ ); } my $r1 = relation( [ [ 'x', 'y' ], [ [ 4, 7 ], [ 3, 2 ], ] ] ); my $r2 = relation( [ { 'y' => 5, 'z' => 6 }, { 'y' => 2, 'z' => 1 }, { 'y' => 2, 'z' => 4 }, ] ); my $r3 = $r1->join( $r2 ); my $r3_as_nfmt_perl = $r3->members(); my $r3_as_ofmt_perl = $r3->members( 1 ); # Then $r3_as_nfmt_perl contains: # [ # { 'x' => 3, 'y' => 2, 'z' => 1 }, # { 'x' => 3, 'y' => 2, 'z' => 4 }, # ] # And $r3_as_ofmt_perl contains: # [ [ 'x', 'y', 'z' ], [ # [ 3, 2, 1 ], # [ 3, 2, 4 ], # ] ]
This documentation is pending.
Set::Relation provides a simple Perl-native facility for an application to organize and process information using the relational model of data, without having to employ a separate DBMS, and without having to employ a whole separate sub-/language (such as Muldis::D::RefEng does). Rather, it is integrated a lot more into the Perl way of doing things, and you use it much like a Perl array or hash, or like some other third-party Set:: modules available for Perl. This module defines a Perl 5 object role that represents a Muldis D relation value, whose methods implement all the Muldis D relational operators. Or more specifically, it defines several such roles (immutable and mutable variants) and there are several bundled implementing Perl 5 classes.
WARNING: This module is still experimental and may change in incompatible ways between releases. While the module is considered feature complete, and is fully documented, and a review of its code makes it look correct, most features have in fact not yet been tested in running code and so might actually be broken. This module might in fact work for you now, but it is officially alpha quality. Please use it with caution.
If you want to help out with this module's development, generally the most helpful thing you can do to start out is to flesh out the test suite. I suggest looking at the test suites of other Set:: modules as well as various database related modules as inspiration or a source for copying.
That being said, Set::Relation is several years out of date on its tracking of the Muldis D language, so there is limited value in spending a lot of time on it before Muldis::D::RefEng has nailed the spec down.
Loosely speaking, a Set::Relation object is a wrapper over a set of hash refs, where all the hash refs in the set have the same number of elements and the same set of hash keys; so in this context, a Perl hash ref and a Set::Relation object correspond to the relational model concepts of a tuple and a relation, respectively. A relation is analogous to a SQL row-set but that the columns and rows are not ordered, and there are no duplicate column names or duplicate rows. Set::Relation provides all the normal operators of other Set:: classes, such as 'is_subset', 'union', 'diff' etc, but it also provides operators like 'join', 'quotient', 'projection', 'group', 'summary', 'semijoin', 'restriction', 'semidiff', 'tclose', 'outer_join' etc.
Note, you can model a whole relational database by having a hash ref whose keys are akin to SQL table names and whose values are Set::Relation objects.
The name Set::Relation was chosen because it seems the most descriptive. A 'relation' is a value, same as an integer or an array is a value, and a relation can do everything a generic set can do plus more. The Set:: namespace is used to reduce confusion amongst other concepts of the word 'relation', as some people think it means 'compare'; Set:: illustrates that this class' objects are functionally set-like collection values.
Set::Relation is intended to be used in production environments (except for the fact it is mostly untested at the moment). It has been developed according to a rigorously thought out API and behaviour specification, and it should be easy to learn, to install and use, and to extend. It is expected to be maintained and supported by the original author over the long term, either standalone or by the author providing an effective migration path to a suitable replacement.
At the same time, the primary design goal of Set::Relation is to be simple.
Set::Relation focuses on providing all the operators of the relational model of data to Perl developers in as concise a manner as is possible while focusing on correctness of behaviour above all else, and also focusing on ease of understanding and maintainability, since generally a developer's time is the most valuable resource for us to conserve.
Despite initial design efforts to help Set::Relation's execution (CPU, RAM, etc) performance, this module is still assumed to be very un-optimized for its conceptually low level task of data crunching. It generally applies the same internal representation and algorithms regardless of the actual structure or meaning of the data, and regardless of the amount of data.
This module is still assumed to be considerably, perhaps an order or three of magnitude, slower than a hand-rolled task-specific solution. If your primary concern is execution performance, you will most likely not want to use Set::Relation but rather hand-code what it does specifically for your task with your specific data, or alternately employ some other dependency to do the work for you (or even, if necessary, write the task in C).
Set::Relation is best used in situations where you either want to just get some correct solution up and working quickly (conserving developer time), such as because it is a prototype or proof of concept, or where your data set is relatively small (so Set::Relation's overhead cost is less noticeable), or where your task is one that is less time sensitive like a batch process where a longer execution time isn't harmful.
Some specific suggested uses for Set::Relation are:
Use it to simplify some kinds of batch processing data from flat files such as CSV text files; a Set::Relation object can be used to store the content of one source file, and then the relational operators can be used to easily join or filter the file contents against each other, and eventually reports or other results be produced.
Use it when gathering and pre-processing data that needs to end up in a SQL database for longer term use. If you generate your INSERT SQL from Set::Relation objects then those objects can help you do it all in a batch up front, and Set::Relation can help you test for duplicates or various kinds of dirty data that might violate database constraints. So it is less likely that you would need to connect to your SQL database interactively to test your data against it before insertion, and it is more likely you can just talk to it once when your single batch of SQL INSERTs is ready to go.
Various DBMS wrappers, ORMs, persistence tools, etc can use Set::Relation objects internally or as part of their API to represent database row sets. Wrappers that like to do some database-like work internally, such as associating parent and child row sets, or testing key constraints, or various other tasks can use Set::Relation to do some of their work for them, making development and maintenance of said tools easier. Note that in general this would fall under the "small data set" use category since a large number of applications, particularly web apps, just access or display from one to a hundred rows at a time.
Since it represents row-sets and provides all the relational operators, with a focus on correctness, Set::Relation should be useful in helping to test all sorts of other code intended to work with databases, particularly code that is a wrapper for a database, as a basis for comparison to whether the other code is having correct behaviour or not. For example, it could help test that code which generates and runs SQL is producing the correct results with various inputs and scenarios.
Set::Relation should be helpful in teaching the relational model to people, helping them to know what is really going on conceptually with different operations, without being distracted by a lot of ancillary matters, and without being distracted by limitations of various DBMSs that may not expose the whole relational model or may do it incorrectly. It provides something students can experiment with right now.
Set::Relation is complementary to the things you do with Perl's built-in Array and Hash types, including 'map' and 'grep' operations. It is useful when you want to do miscellaneous combining or filtering of lists of data against other lists, particularly multi-dimensional ones, or helping in summarizing lists of data for reports. Maybe helping with some tasks that are easier in Perl 6 than in Perl 5, when you're using Perl 5.
Of course, like any generic tool, Set::Relation should be widely applicable in many different situations.
Now, another situation where you may not want to use Set::Relation is when its sibling project Muldis::D::RefEng would serve you better. In contrast to Set::Relation, which is standalone and intended to integrate closely with Perl, Muldis::D::RefEng implements a whole programming language distinct from Perl, Muldis D, and presents a superior environment at large for working with the relational model of data; you use it sort of like how you use DBI to talk to a SQL DBMS, as a separate thing walled off from Perl. The benefits of using Muldis::D::RefEng over Set::Relation are multiple, including much better performance and scalability, and that it can directly persist data as you'd expect a DBMS to do, as well as provide easy access to many other relational model features like stronger typing and arbitrary database constraints, and nested transactions, as well as access to full powered DBMS engines like PostgreSQL and Oracle and SQLite (though you don't have to use those and Muldis::D::RefEng can be used purely implemented in Perl).
That all said, Set::Relation is actually implemented and works today, while Muldis::D::RefEng is still under construction and you can't use it yet.
That brings out another important reason why Set::Relation exists now; it also serves as a proof of concept for a main part of Muldis D and Muldis::D::RefEng, or for a so-called "truly relational DBMSs" in general. It demonstrates ideal features and behaviour for relational operators, in a functioning form that users can experiment with right now. Set::Relation is also meant to serve as inspiration for similar projects, and better illustrate features that would be nice for modern programming languages to have built-in, same as they have collection types like ordered and associative arrays and one-dimensional sets and bags built-in. It is reasonable for standard equipment to not just be plain set operators but the other relational model operators too, such as relational join.
Note: Assistance is appreciated in making Set::Relation perform better, such that some of its present-day caveats can disappear, keeping in mind its general design goals. But generally first we will need to have a complete test suite to confirm correct behaviour, and correct any outstanding API issues, and preferably also a benchmark suite. That way, when the likely extensive changes are made for performance, we can actually measure their effect and know we didn't break the behaviour. Also if the behaviour/API is nailed first, then new benchmarks we make along the way will be backwards compatible with previous baseline versions. But keep in mind that only some kinds of improvements are suitable; some others may be inordinately complex and may better be relegated to Muldis::D::RefEng or other overlapping solutions instead; the distinction can be discussed case-by-case as solutions are proposed.
The relational model of data fundamentally involves values as being immutable and distinct values having distinct identities, and the type of a value is part of its identity.
The relational model has 3 kinds of types and values, called scalar types/values, tuple types/values, and relation types/values; the 3 are all mutually disjoint and no value in one kind can be identical to a value in another. A Set::Relation-doing class treats the objects of all Set::Relation-doing classes as relation values, it treats ordinary un-blessed Perl hash-refs as tuple values, and it treats all other Perl values (and Perl undef) as scalar values.
This documentation section outlines how Set::Relation considers every kind of Perl value in regards to its value identity, which has a large role to play in the semantics of Set::Relation's routines. Since a tuple is a set of zero or more distinctly named attribute values and a relation is a set of zero or more distinct-valued tuples having the same set of attribute names, matters of whether 2 Perl values are considered duplicates or not depends on this concept of identity.
A tuple/relation attribute name is exactly the same as a Perl Hash key; it is a defined non-reference case/everything-sensitive character string of zero or more characters.
Two tuples/Perl-Hashes are considered identical iff they are of the same degree (same number of elements), have the same keys, and have corresponding values that individually are considered identical.
Two relation/Set::Relation objects are considered identical iff they are of the same degree (same number of attributes), have the same attribute names, are of the same cardinality (same number of tuples), and every tuple in one corresponds to a distinct tuple in the other, individually considered identical. Other object attributes of a Set::Relation object such as keys/key-constraints or member identity caches have no bearing on the value identity of a Set::Relation.
Two Perl undefined values are considered identical to each other, and distinct from all defined values.
Two defined non-reference Perl values are considered identical iff their string representations are identical; either is distinct from Perl undef and from all reference/blessed Perl values.
Two non-blessed reference non-Hash Perl values are considered identical to each other iff they stringify to the same string representations, meaning essentially if they are the very same reference / have the same memory address; either is distinct from any blessed reference or non-reference or Hash-ref Perl value.
Two blessed reference / Perl object non-Set::Relation Perl values are considered identical to each other iff they both are blessed into the same Perl class and they both stringify to the same string representations, meaning generally that either they are the very same reference or their class overloads stringification (in which case we treat their class as a value type); either is distinct from any non-blessed Perl value or Set::Relation object.
Loosely speaking, a Set::Relation-doing class treats the objects of all Set::Relation-doing classes, and Perl Hash-refs and non-reference or undefined Perl values, as being of value types, that compare on their actual values, while treating all other Perl reference or blessed values as being reference types, that compare on their memory addresses. Value types can't be mutated while the containers that the reference values point to can be mutated. If you want some other class' object treated as a value type, make it overload stringification (or an alternate/additional convention can be devised like Set::Relation's own 'which' convention). If you want a Hash-ref/tuple or Set::Relation object to be treated as a reference type, then pass it around using another layer of reference indirection, such as by adding a scalar-ref up front.
Note: Were this Perl 6, we would basically just use the standard WHICH method or === comparison operator to determine identity; but Perl 5 doesn't have that so we do the aforementioned instead.
WHICH
===
Set::Relation explicitly supports implementations that want to give users the option of trading away specified guarantees of correctness for their user-visible behaviour in exchange for better performance (by letting the implementation be lazier), when an approximation is good enough for the users' purposes. But Set::Relation requires that implementations fully guarantee correctness (insomuch as they reasonably have the power to do so) for their user-visible behaviour by default, and only trade this for laziness when users explicitly request the trade. Of course, implementations can always be internally lazy as they see fit where it doesn't impact their externally observable semantics, so the trading feature under discussion here is only about behaviour that users can see.
For example, some Set::Relation routines have the optional boolean parameter $allow_dup_tuples which, when explicitly given a true argument, tells the implementation it may save itself the work of comparing tuples with each other to test their uniqueness, and so multiple instances of the same tuple value may be treated in user-visible ways as being distinct when they logically aren't. For example, if users construct a Set::Relation-doing object using a list of tuples that contains duplicates, then by default that object's cardinality method will only result in a count of distinct tuples, and that object's body method will only result in a list containing distinct tuples, because a relation is logically a set of tuples not a multiset; but if a true $allow_dup_tuples argument is given to either method, then the result may include duplicates as if the class were implementing a multiset rather than a set. Similarly, internal duplicates can arise out of none in many other situations than object construction, such as from a relational union or projection. Note that because Perl closures in general are not pure and so might have different results or side-effects from repeated invocations with the same arguments, the $allow_dup_tuples parameter is also present on methods like restriction and extension.
$allow_dup_tuples
cardinality
body
restriction
extension
It is important to realize that even when users explicitly waive a need for correctness, the implementation may choose to ignore them and give the fully correct answers anyway. Trade-off options should not be construed as having a guarantee to not do the normal behaviour, and in particular a true $allow_dup_tuples argument will not guarantee consistent logical multiset behaviour.
It is an design decision feature of Set::Relation that flags like $allow_dup_tuples are only available directly on the methods where they would take effect just on specific invocations, and are not available as object attributes. This is to prevent action at a distance, where one spot in code requesting less accuracy doesn't also cause other spots in code using the same objects to also get less accuracy. And so you may have to use said flag explicitly multiple times to get continuous such laziness through the lifecycle of an object or chain of derived objects.
This module defines both the Set::Relation role and the Set::Relation::Mutable role, the latter of which composes the former; objects of a class composing just Set::Relation are guaranteed to never mutate; objects also/instead composing the latter may some times mutate.
Now, while a relation value is conceptually immutable, the Set::Relation::Mutable role allows you to mutate a Set::Relation::Mutable object under some circumstances as a convenience to users, in a similar manner to how you can mutate a Perl Hash or Array by inserting or deleting its elements. By default, a newly created Set::Relation::Mutable object is mutable, that is its identity is said to not be frozen; but when you perform certain operations with one, it will become immutable, gaining a frozen identity, and this change can not be reversed, though you can clone said object to get an un-frozen duplicate.
You can make a Set::Relation::Mutable object immutable explicitly by invoking its freeze_identity method. This change may also happen implicitly, with those happenings being implementation-dependent. For example, invoking an object's which method may freeze the object. Or for another example, if another Set::Relation::Mutable object is constructed that is given the first object as a tuple attribute value; this could be done rather than cloning the input object under the assumption that most of the time you wouldn't want to mutate the input object afterwards, for efficiency. These details are subject to change.
freeze_identity
which
Note: See also the "Appropriate Uses For Set::Relation" section above.
The matters of performance can differ significantly depending on the implementation class, so see each of their corresponding documentation sections for details: Set::Relation::V1, Set::Relation::V2.
The interface of Set::Relation is entirely object-oriented; you use it by creating objects from its member classes (or more specifically, of implementing classes that compose its member roles) and then invoking methods on those objects. All of their attributes are private, so you must use accessor methods.
The usual way that Set::Relation indicates a failure is to throw an exception; most often this is due to invalid input. If an invoked routine simply returns, you can assume that it has succeeded, even if the return value is undefined.
A Set::Relation object represents a single relation value. For any class composing this role, its objects guarantee that their value will never mutate following object construction, unless that class also composes the Set::Relation::Mutable role.
Set::Relation
Set::Relation::Mutable
This is currently the only routine declared by Set::Relation that you invoke off of the class name; currently you invoke all other routines off of a Set::Relation object.
multi submethod new of Set::Relation (Array|Set::Relation|Str :$members, Array|Str :$keys?)
multi submethod new of Set::Relation (Array|Set::Relation|Str $members)
multi submethod new of Set::Relation ()
This constructor submethod creates and returns a new Set::Relation object, representing a single relation value, that is initialized primarily using the multi-dimensional Perl data structure given in its $members argument, which defines the member attributes and tuples of the new relation. The allowed formats of a $members argument mostly are those defined by the Muldis D language dialect HDMD_Perl5_STD for a Relation value literal node payload, except that attribute values are just ordinary Perl values and not HDMD_Perl5_STD value literal nodes. Examples are:
$members
Relation
sub relation { return $sr_class_name->new( @_ ); } # Zero attrs + zero tuples. my $r1 = relation( [] ); # 3 attrs + zero tuples. my $r2 = relation( [ 'x', 'y', 'z' ] ); # Zero attrs + 1 tuple my $r3 = relation( [ {} ] ); # Named attributes format: 3 attrs + 1 tuple. my $r4 = relation( [ { 'login_name' => 'hartmark', 'login_pass' => 'letmein', 'is_special' => 1, }, ] ); # Ordered attributes format: 2 attrs + 1 tuple. my $r5 = relation( [ [ 'name', 'age' ], [ [ 'Michelle', 17 ], ] ] );
However, Set::Relation also supports a few additional, trivial formats for $members, as illustrated here:
# The default value of a Set::Relation has zero attrs + zero tuples. my $r6 = relation(); # One way to clone a relation object. my $r7 = relation( $r5 ); # Abbreviated way to specify 1 attr + zero tuples. my $r8 = relation( 'value' );
If the optional argument $keys is defined, then it defines one or more explicit candidate keys (or unique key constraints) for the relation value, all of which $members must satisfy or else new will fail; if $keys is not defined, then by default the new relation has a single implicit candidate key ranging over all of its attributes. The canonical format of a $keys argument is a Perl Array of 0..N Perl Array of 0..N Perl Str, where each inner Array defines a single key and each Str defines one of the relation's attributes that the key ranges over. Examples are:
$keys
new
# No explicit keys (just an implicit key over all attributes). my $rI = relation( members => [ 'x', 'y', 'z' ], keys => [] ); # Explicit nullary key (over 0 attrs; rel may have just 0..1 tuples). my $rN = relation( members => [ 'x', 'y', 'z' ], keys => [ [] ] ); # Explicit unary key (over 1 attribute). my $rU = relation( members => [ 'x', 'y', 'z' ], keys => [ [ 'z' ] ] ); # Explicit binary key (over 2 attributes). my $rB = relation( members => [ 'x', 'y', 'z' ], keys => [ [ 'x', 'z' ] ] ); # Explicit ternary key (over 3 attributes). my $rT = relation( members => [ 'x', 'y', 'z' ], keys => [ [ 'x', 'y', 'z' ] ] ); # Explicit unary key plus explicit binary key. my $rUB = relation( members => [ 'x', 'y', 'z' ], keys => [ [ 'x' ], [ 'y', 'z' ] ] ); # Pair of explicit binary keys. my $rBB = relation( members => [ 'x', 'y', 'z' ], keys => [ [ 'x', 'y' ], [ 'y', 'z' ] ] );
Alternately, $keys may be either a Perl Array of 1..N Perl Str, that defines a single key over N attributes, or $keys may be a Perl Str, that defines a single key over a single attribute. Examples are:
# Explicit unary key (over 1 attribute). my $rU2 = relation( members => [ 'x', 'y', 'z' ], keys => 'x' ); my $rU3 = relation( members => [ 'x', 'y', 'z' ], keys => [ 'y' ] ); # Explicit binary key (over 2 attributes). my $rB2 = relation( members => [ 'x', 'y', 'z' ], keys => [ 'x', 'y' ] );
Note that if any explicit key is a superkey of another, that is, the set of attributes that the former ranges over is a proper superset of those that the latter ranges over, then the superkey will be silently eliminated since it is completely redundant; similarly, if any explicit key is the nullary key, then it is the only key.
Note that any explicit key given to new is only a constraint as far as the initial value of the new Set::Relation object is concerned. Any subsequent mutation of the object by insert, if the object is mutable, is allowed to invalidate any prior-existing keys. So 'keys' is simply a reflection of explicitly tested for candidate keys that are still known to be valid. Note: it is possible in the future that subsequent feature additions can permit these keys to also act as constraints against future mutations.
insert
These Set::Relation object methods are mainly about extracting object attributes, essentially the reverse process of an object constructor.
method export_for_new of Hash ($self: Bool|Array $want_ord_attrs?, Bool $allow_dup_tuples?)
This method results in a Perl Hash value whose Hash keys and values you can give as argument names and values to new such that the latter would result in a clone of this method's invocant. In other words, export_for_new is the inverse function to new. If this method's $want_ord_attrs argument is missing or false, then the exported attributes and tuples are in named attributes format; if that argument is true, they are in ordered attributes format. If $want_ord_attrs is a Perl Array then it is assumed to contain a list of attribute names matching those of the invocant, and so it is specifying what order the attributes should be in the result; otherwise if $want_ord_attrs is the Perl string value 1, then the result will have its attributes ordered alphabetically by attribute name (see the heading method docs for why that is the case). If this method's $allow_dup_tuples argument is true, then the result may have duplicate tuples; otherwise (the default), all result tuples are unique.
export_for_new
$want_ord_attrs
1
heading
method which of Str ($self:)
This method results in a character string representation of the invocant's value identity. The identity value result of this method is essentially a serialization of all the invocant's attribute names and tuple values, all of which are encoded and sorted in such a way that any 2 Set::Relation values having the same attributes and tuples are guaranteed to have the same value identity, and any 2 with different attributes or tuples are guaranteed to have different ones. This method is analogous to the special WHICH method of Perl 6 and lets you treat Set::Relation as a "value type". That all being said, currently the details of the serialization format are implementation dependent, and it is assumed that an application will exclusively use a single Set::Relation implementation in any situations where code external to a Set::Relation-doing class is invoking which (code inside said classes will do conversions as needed).
method members of Array ($self: Bool|Array $want_ord_attrs?, Bool $allow_dup_tuples?)
This method results in a Perl Array value as per the 'members' element of the Hash that export_for_new would result in with the same invocant and with the same arguments.
method heading of Array ($self:)
This method results in a Perl Array value whose elements are the attribute names of the invocant. The attribute names are sorted alphabetically so that if this method's result is used together with the result of invoking body on the same invocant with a non-Array but true valued $want_ord_attrs then the default order of the ordered attributes resulting from body matches the default order resulting from heading; in contrast, if body was invoked to return attributes in named format, it doesn't matter what order heading returns their names in. This method is currently an alias for the attr_names functional method.
attr_names
method body of Array ($self: Bool|Array $want_ord_attrs?, Bool $allow_dup_tuples?)
This method results in a Perl Array value whose elements are the tuples of the invocant. Each tuple is either a Perl Hash or a Perl Array depending on the value of the $want_ord_attrs, like with the members method; similarly $allow_dup_tuples affects the result as with members.
members
method slice of Array ($self: Array|Str $attr_names, Bool $want_ord_attrs?, Bool $allow_dup_tuples?)
This method is like body except that the result has just a subset of the attributes of the invocant, those named by $attr_names. Unlike using projection followed by body to do this, any duplicate subtuples are retained in the result of slice. Each result subtuple is either a Perl Hash or a Perl Array depending on the value of the $want_ord_attrs, like with body, except that $want_ord_attrs may only be a Bool here; when that argument is true, the exported attributes are in the same order as specified in $attr_names. If this method's $allow_dup_tuples argument is false (the default), then the result is guaranteed to have the same number of elements as the cardinality of $self; otherwise, the result may have more elements.
$attr_names
projection
slice
$self
method attr of Array ($self: Str $name, Bool $allow_dup_tuples?)
This method is like slice except that the result has exactly one of the invocant's attributes, the one named by $name, and each result element is that attribute value directly, not a single-element tuple. This method is expected to see a lot of use in relation summarizing operations, for extracting the input values for reduction or aggregate operators.
$name
method keys of Array ($self:)
This method results in a Perl Array value as per the 'keys' element of the Hash that export_for_new would result in with the same invocant; the result format is the canonical one for the $keys parameter of new.
These Set::Relation object methods are pure functional, each one whose execution results in a value and each one not mutating anything or having any side-effects; the sole exception to the latter is that some may mutate certain internals of some existing Set::Relation objects in ways that don't affect their value identity, such as by creating indexes to speed up current and future operations with said objects.
These methods each have a single Set::Relation object as input, which is the invocant. Some of them also result in a Set::Relation object while others do not.
method degree of UInt ($topic:)
This functional method results in the degree of its invocant (that is, the count of attributes it has).
method is_nullary of Bool ($topic:)
This functional method results in true iff its invocant has a degree of zero (that is, it has zero attributes), and false otherwise.
method has_attrs of Bool ($topic: Array|Str $attr_names)
This functional method results in true iff, for every one of the attribute names specified by its argument, its invocant has an attribute with that name; otherwise it results in false. As a trivial case, this method's result is true if its argument is empty. Note that has_attrs has a side-effect in that subsequent calls to keys will include the key tested for with has_attrs if the latter had returned true, assuming an intermediate call to insert hadn't invalidated that.
has_attrs
keys
method attr_names of Array ($topic:)
This functional method results in the set of the names of the attributes of its invocant. This method is currently an alias for the heading accessor method.
method cardinality of UInt ($topic: Bool $allow_dup_tuples?)
This functional method results in the cardinality of its invocant (that is, the count of tuples its body has). If this method's $allow_dup_tuples argument is false (the default), then the result is guaranteed to only count the number of distinct tuples of $topic; otherwise, the result may be higher, unless the invocant is empty, in which case the result is still exactly zero. Note that this operation is also known as count or #.
$topic
#
method count of UInt ($topic: Bool $allow_dup_tuples?)
This functional method is an alias for cardinality.
method is_empty of Bool ($topic:)
This functional method results in true iff its invocant has a cardinality of zero (that is, it has zero tuples), and false otherwise.
method has_member of Bool ($r: Array|Hash $t)
This functional method results in true iff all of the tuples of its $t argument match tuples of its invocant (that is, iff conceptually $t is a member of $r), and false otherwise. Note that this operation is also known as @∋ or holds.
$t
$r
@∋
holds
method has_key of Bool ($topic: Array|Str $attr_names)
This functional method results in true iff its invocant has a (unique) key over the subset of its attributes whose names are specified by its argument; otherwise it results in false. This function will fail if its invocant does not have all of the attributes named by its argument. As a trivial case, this function's result is true if its invocant is empty.
method empty of Set::Relation ($topic:)
This functional method results in the empty relation of the same heading of its invocant, that is having the same degree and attribute names; it has zero tuples.
method insertion of Set::Relation ($r: Array|Hash $t)
This functional method results in a relation that is the relational union of $r and a relation whose tuples are $t; that is, conceptually the result is $t inserted into $r. As a trivial case, if all of $t already exist in $r, then the result is just $r.
method deletion of Set::Relation ($r: Array|Hash $t)
This functional method results in a relation that is the relational difference from $r of a relation whose tuples are $t; that is, conceptually the result is $t deleted from $r. As a trivial case, if all of $t already doesn't exist in $r, then the result is just $r.
method rename of Set::Relation ($topic: Hash $map)
This functional method results in a relation value that is the same as its $topic invocant but that some of its attributes have different names. Each element of the Hash argument $map specifies how to rename one $topic attribute, with the element's Hash key and Hash value representing the new and old names of a $topic attribute, respectively. As a trivial case, this method's result is $topic if $map has no elements. This method supports renaming attributes to each others' names. This method will fail if $map specifies any old names that $topic doesn't have, or any new names that are the same as $topic attributes that aren't being renamed. Note that this operation is also known as {<-}.
$map
{<-}
method projection of Set::Relation ($topic: Array|Str $attr_names)
This functional method results in the relational projection of its $topic invocant that has just the subset of attributes of $topic which are named in its $attr_names argument. As a trivial case, this method's result is $topic if $attr_names lists all attributes of $topic; or, it is a nullary relation if $attr_names is empty. This method will fail if $attr_names specifies any attribute names that $topic doesn't have. Note that this operation is also known as {}.
{}
method cmpl_proj of Set::Relation ($topic: Array|Str $attr_names)
This functional method is the same as projection but that it results in the complementary subset of attributes of its invocant when given the same argument. Note that this operation is also known as {!}.
{!}
method wrap of Set::Relation ($topic: Str $outer, Array|Str $inner)
This functional method results in a relation value that is the same as its $topic invocant but that, for each of its member tuples, some of its attributes have been wrapped up into a new tuple-typed attribute, which exists in place of the original attributes. The $inner argument specifies which $topic attributes are to be removed and wrapped up, and the $outer argument specifies the name of their replacement attribute. The result relation has the same cardinality as $topic. As a trivial case, if $inner is empty, then the result has all the same attributes as before plus a new tuple-typed attribute of degree zero; or, if $inner lists all attributes of $topic, then for each of its member tuples TT, the result tuple TR has a single attribute whose value is the same as TT. This method supports the new attribute having the same name as an old one being wrapped into it. This method will fail if $inner specifies any attribute names that $topic doesn't have, or if $outer is the same as a $topic attribute that isn't being wrapped. Note that this operation is also known as {%<-}.
$inner
$outer
TT
TR
{%<-}
method cmpl_wrap of Set::Relation ($topic: Str $outer, Array|Str $cmpl_inner)
This functional method is the same as wrap but that it wraps the complementary subset of attributes of $topic to those specified by $cmpl_inner. Note that this operation is also known as {%<-!}.
wrap
$cmpl_inner
{%<-!}
method unwrap of Set::Relation ($topic: Array|Str $inner, Str $outer)
This functional method is the inverse of wrap, such that it will unwrap a tuple-type attribute into its member attributes. This method will fail if $outer specifies any attribute name that $topic doesn't have, or if $topic{$outer} does not have a same-heading tuple value for every tuple of $topic (because then there would be no consistent set of attribute names to extend $topic with), or if an attribute of $topic{$outer} has the same name as another $topic attribute. Now, unwrap requires the extra $inner argument to prevent ambiguity in the general case where $topic might have zero tuples, because in that situation the names of the attributes to add to $topic in place of $topic{$outer} can not be determined from $topic{$outer}. This method will fail if $topic has at least 1 tuple and $inner does not match the names of the attributes of $topic{$outer} for every tuple of $topic. Note that this operation is also known as {<-%}.
$topic{$outer}
unwrap
{<-%}
method group of Set::Relation ($topic: Str $outer, Array|Str $inner)
This functional method is similar to wrap but that the $topic attribute-wrapping transformations result in new relation-typed attributes rather than new tuple-typed attributes, and moreover multiple $topic tuples may be combined into fewer tuples whose new relation-typed attributes have multiple tuples. This method takes a relation of N tuples and divides the tuples into M groups where all the tuples in a group have the same values in the attributes which aren't being grouped (and distinct values in the attributes that are being grouped); it then results in a new relation of M tuples where the new relation-valued attribute of the result has the tuples of the M groups. A grouped relation contains all of the information in the original relation, but it has less redundancy due to redundant non-grouped attributes now just being represented in one tuple per the multiple tuples whose grouped attributes had them in common. A relation having relation-valued attributes like this is a common way to group so-called child tuples under their parents. As a trivial case, if $inner is empty, then the result has all the same tuples and attributes as before plus a new relation-typed attribute of degree zero whose value per tuple is of cardinality one; or, if $inner lists all attributes of $topic, then the result has a single tuple of a single attribute whose value is the same as $topic (except that the result has zero tuples when $topic does). This method supports the new attribute having the same name as an old one being grouped into it. This method will fail if $inner specifies any attribute names that $topic doesn't have, or if $outer is the same as $topic attributes that aren't being grouped. Note that this operation is also known as nest or {@<-}.
{@<-}
method cmpl_group of Set::Relation ($topic: Str $outer, Array|Str $group_per)
This functional method is the same as group but that it groups the complementary subset of attributes of $topic to those specified by $group_per. Note that this operation is also known as {@<-!}.
group
$group_per
{@<-!}
method ungroup of Set::Relation ($topic: Array|Str $inner, Str $outer)
This functional method is the inverse of group as unwrap is to wrap; it will ungroup a relation-type attribute into its member attributes and tuples. A relation can be first grouped and then that result ungrouped to produce the original relation, with no data loss. However, the ungroup of a relation on a relation-valued attribute will lose the information in any outer relation tuples whose inner relation value has zero tuples; a group on this result won't bring them back. This method will fail if $outer specifies any attribute name that $topic doesn't have, or if $topic{$outer} does not have a same-heading relation value for every tuple of $topic (because then there would be no consistent set of attribute names to extend $topic with), or if an attribute of $topic{$outer} has the same name as another $topic attribute. Note that this operation is also known as unnest or {<-@}.
{<-@}
method tclose of Set::Relation ($topic:)
This functional method results in the transitive closure of its invocant. The invocant must be a binary relation whose attributes are both of the same type (for whatever concept of "type" you want to have), and the result is a relation having the same heading and a body which is a superset of the invocant's tuples. Assuming that the invocant represents all of the node pairs in a directed graph that have an arc between them, and so each invocant tuple represents an arc, tclose will determine all of the node pairs in that graph which have a path between them (a recursive operation), so each tuple of the result represents a path. The result is a superset since all arcs are also complete paths. The tclose method is intended to support recursive queries, such as in connection with the "part explosion problem" (the problem of finding all components, at all levels, of some specified part).
tclose
method restriction of Set::Relation ($topic: Callable $func, Bool $allow_dup_tuples?)
This functional method results in the relational restriction of its $topic invocant as determined by applying the Bool-resulting zero-parameter Perl subroutine reference given in its $func argument. The result relation has the same heading as $topic, and its body contains the subset of $topic tuples where, for each tuple, the subroutine given in $func results in true when the tuple is its $_ topic. As a trivial case, if $func is defined to unconditionally result in true, then this method results simply in $topic; or, for an unconditional false, this method results in the empty relation with the same heading. Note that this operation is also known as where. See also the semijoin method, which is a simpler-syntax alternative for restriction in its typical usage where restrictions are composed simply of anded or ored tests for attribute value equality. If this method's $allow_dup_tuples argument is false (the default), then $func is guaranteed to be invoked just once per distinct tuple of $topic; otherwise it might be multiple invoked.
$func
$_
semijoin
method restr_and_cmpl of Array ($topic: Callable $func, Bool $allow_dup_tuples?)
This functional method performs a 2-way partitioning of all the tuples of $topic and results in a 2-element Perl Array whose element values are each Set::Relation objects that have the same heading as $topic and complementary subsets of its tuples; the first and second elements are what restriction and cmpl_restr, respectively, would result in when having the same invocant and arguments.
cmpl_restr
method cmpl_restr of Set::Relation ($topic: Callable $func, Bool $allow_dup_tuples?)
This functional method is the same as restriction but that it results in the complementary subset of tuples of $topic when given the same invocant and arguments. See also the semidiff method.
semidiff
method classification of Set::Relation ($topic: Callable $func, Str $class_attr_name, Str $group_attr_name, Bool $allow_dup_tuples?)
This functional method conceptually is to restriction what group is to semijoin. It classifies the tuples of $topic into N groups using the zero-parameter Perl subroutine reference given in $func, such that any distinct tuples are in a common group if the subroutine given in $func results in the same value when given either of those tuples as its $_ topic. This method conceptually is a short-hand for first extending $topic with a new attribute whose name is given in $class_attr_name, whose value per tuple is determined from $topic using $func, and then grouping that result relation on all of its original attributes, with the post-group RVA having the name given in $group_attr_name; the result of classification is a binary relation whose 2 attributes have the names given in $class_attr_name and $group_attr_name. This method is intended for use when you want to partition a relation's tuples into an arbitrary number of groups using arbitrary criteria, in contrast with restriction where you are dividing into exactly 2 groups (and returning one) using arbitrary criteria. If this method's $allow_dup_tuples argument is false (the default), then $func is guaranteed to be invoked just once per distinct tuple of $topic; otherwise it might be multiple invoked.
$class_attr_name
$group_attr_name
classification
method extension of Set::Relation ($topic: Array|Str $attr_names, Callable $func, Bool $allow_dup_tuples?)
This functional method results in the relational extension of its topic invocant as determined by applying the tuple/Hash-resulting zero-parameter Perl subroutine reference given in its $func argument. The result relation has a heading that is a superset of that of $topic, and its body contains the same number of tuples, with all attribute values of $topic retained, and possibly extra present, determined as follows; for each $topic tuple, the subroutine given in $func results in a second tuple when the first tuple is its $_ topic; the first and second tuples must have no attribute names in common, and the result tuple is derived by joining (cross-product) the tuples together. As a trivial case, if $func is defined to unconditionally result in the degree-zero tuple, then this method results simply in $topic. Now, extension requires the extra $attr_names argument to prevent ambiguity in the general case where $topic might have zero tuples, because in that situation, $func would never be invoked, and the names of the attributes to add to $topic are not known (we don't generally assume that extension can reverse-engineer $func to see what attributes it would have resulted in). This method will fail if $topic has at least 1 tuple and the result of $func does not have matching attribute names to those named by $attr_names. If this method's $allow_dup_tuples argument is false (the default), then $func is guaranteed to be invoked just once per distinct tuple of $topic; otherwise it might be multiple invoked.
topic
method static_exten of Set::Relation ($topic: Hash $attrs)
This functional method is a simpler-syntax alternative to both extension and product in the typical scenario of extending a relation, given in the $topic invocant, such that every tuple has mutually identical values for each of the new attributes; the new attribute names and common values are given in the $attrs argument.
product
$attrs
method map of Set::Relation ($topic: Array|Str $result_attr_names, Callable $func, Bool $allow_dup_tuples?)
This functional method provides a convenient one-place generalization of per-tuple transformations that otherwise might require the chaining of up to a half-dozen other operators like projection, extension, and rename. This method results in a relation each of whose tuples is the result of applying, to each of the tuples of its $topic invocant, the tuple/Hash-resulting zero-parameter Perl subroutine reference given in its $func argument. There is no restriction on what attributes the result tuple of $func may have (except that all tuples from $func must have compatible headings); this tuple from $func would completely replace the original tuple from $topic. The result relation has a cardinality that is the same as that of $topic, unless the result of $func was redundant tuples, in which case the result has appropriately fewer tuples. As a trivial case, if $func is defined to unconditionally result in the same tuple as its own $topic argument, then this method results simply in $topic; or, if $func is defined to have a static result, then this method's result will have just 0..1 tuples. Now, map requires the extra $result_attr_names argument to prevent ambiguity in the general case where $topic might have zero tuples, because in that situation, $func would never be invoked, and the names of the attributes of the result are not known (we don't generally assume that map can reverse-engineer $func to see what attributes it would have resulted in). This method will fail if $topic has at least 1 tuple and the result of $func does not have matching attribute names to those named by $result_attr_names. If this method's $allow_dup_tuples argument is false (the default), then $func is guaranteed to be invoked just once per distinct tuple of $topic; otherwise it might be multiple invoked.
map
$result_attr_names
method summary of Set::Relation ($topic: Array|Str $group_per, Array|Str $summ_attr_names, Callable $summ_func, Bool $allow_dup_tuples?)
This functional method provides a convenient context for using aggregate functions to derive a per-group summary relation, which is its result, from another relation, which is its $topic invocant. This method first performs a cmpl_group on $topic using $group_per to specify which attributes get grouped into a new relation-valued attribute and which don't; those that don't instead get wrapped into a tuple-valued attribute. Then, per binary tuple in the main relation, this method applies the tuple/Hash-resulting zero-parameter Perl subroutine reference given in its $summ_func argument; for each post-group main relation tuple, the subroutine given in $summ_func results in a second tuple when the first tuple is its $_ topic; the $_ tuple has the 2 attribute names summarize and per, which are valued with the relation-valued attribute and tuple-valued attribute, respectively. As per a subroutine that extension applies, the subroutine given in $summ_func effectively takes a whole post-grouping input tuple and results in a partial tuple that would be joined by summary with the per tuple to get the result tuple; the applied subroutine would directly invoke any N-adic / aggregate operators, and extract their inputs from (or calculate) summarize as it sees fit. Note that summary is not intended to be used to summarize an entire $topic relation at once (except by chance of it resolving to 1 group); you should instead invoke your summarize-all $summ_func directly, or inline it, rather than by way of summary, especially if you want a single-tuple result on an empty $topic (which summary) won't do. Now, summary requires the extra $summ_attr_names argument to prevent ambiguity in the general case where $topic might have zero tuples, because in that situation, $summ_func would never be invoked, and the names of the attributes to add to per are not known (we don't generally assume that summary can reverse-engineer $summ_func to see what attributes it would have resulted in). This method will fail if $topic has at least 1 tuple and the result of $summ_func does not have matching attribute names to those named by $summ_attr_names. If this method's $allow_dup_tuples argument is false (the default), then $summ_func is guaranteed to be invoked just once per distinct post-group tuple; otherwise it might be multiple invoked.
cmpl_group
$summ_func
summarize
per
summary
$summ_attr_names
method cardinality_per_group of Set::Relation ($topic: Str $count_attr_name, Array|Str $group_per, Bool $allow_dup_tuples?)
This functional method is a convenient shorthand for the common use of summary that is just counting the tuples of each group. This function is like cmpl_group but that the single added attribute, rather than an RVA of the grouped $topic attributes, has the cardinality that said RVA would have had. The result's heading consists of the attributes named in $group_per plus the attribute named in $count_attr_name (a positive integer). Note that this operation is also known as {#@<-!}.
$count_attr_name
{#@<-!}
method count_per_group of Set::Relation ($topic: Str $count_attr_name, Array|Str $group_per, Bool $allow_dup_tuples?)
This functional method is an alias for cardinality_per_group.
cardinality_per_group
These methods each have at least 2 Set::Relation objects as input, one of which is the invocant and the other of which is an additional argument. Some of them also result in a Set::Relation object while others do not.
method is_identical of Bool ($topic: Set::Relation $other)
This symmetric functional method results in true iff its invocant and argument are exactly the same value (that is, Set::Relation considers them to have the same value identity), and false otherwise. Note that this operation is also known as is equal or =.
=
method is_subset of Bool ($topic: Set::Relation $other)
This functional method results in true iff the set of tuples comprising $topic is a subset of the set of tuples comprising $other (both must have the same heading regardless), and false otherwise. Note that this operation is also known as ⊆ or {<=}.
$other
⊆
{<=}
method is_superset of Bool ($topic: Set::Relation $other)
This functional method is an alias for is_subset except that it transposes the $topic invocant and $other argument. This functional method results in true iff the set of tuples comprising $topic is a superset of the set of tuples comprising $other (both must have the same heading regardless), and false otherwise. Note that this operation is also known as ⊇ or {>=}.
is_subset
⊇
{>=}
method is_proper_subset of Bool ($topic: Set::Relation $other)
This functional method is exactly the same as is_subset except that it results in false if its invocant and argument are identical. Note that this operation is also known as ⊂ or {<}.
⊂
{<}
method is_proper_superset of Bool ($topic: Set::Relation $other)
This functional method is an alias for is_proper_subset except that it transposes the $topic invocant and $other argument. This functional method is exactly the same as is_superset except that it results in false if its invocant and argument are identical. Note that this operation is also known as ⊃ or {>}.
is_proper_subset
is_superset
⊃
{>}
method is_disjoint of Bool ($topic: Set::Relation $other)
This symmetric functional method results in true iff the set of tuples comprising each of its same-heading invocant and argument are mutually disjoint, that is, iff the intersection of the invocant and argument is empty; it results in false otherwise.
method union of Set::Relation ($topic: Array|Set::Relation $others)
This functional method results in the relational union/inclusive-or of the collective N element values of its same-heading invocant and argument, hereafter referred to as $inputs; it is a reduction operator that recursively takes each pair of input values and relationally unions (which is commutative, associative, and idempotent) them together until just one is left, which is the result. The result relation has the same heading as all of its input relations, and its body contains every tuple that is in any of the input relations. The identity value of relational union is the same-heading empty relation value (having zero tuples). Note that this operation is also known as ∪.
$inputs
∪
method exclusion of Set::Relation ($topic: Array|Set::Relation $others)
This functional method results in the relational exclusion/exclusive-or of the collective N element values of its same-heading invocant and argument, hereafter referred to as $inputs; it is a reduction operator that recursively takes each pair of input values and relationally excludes (which is both commutative and associative) them together until just one is left, which is the result. The result relation has the same heading as all of its input relations, and its body contains every tuple that is in just an odd number of the input relations. The identity value of relational exclusion is the same as for union. Note that this operation is also known as symmetric difference or ∆.
union
∆
method symmetric_diff of Set::Relation ($topic: Array|Set::Relation $others)
This functional method is an alias for exclusion.
exclusion
method intersection of Set::Relation ($topic: Array|Set::Relation $others)
This functional method results in the relational intersection/and of the collective N element values of its same-heading invocant and argument, hereafter referred to as $inputs; it is a reduction operator that recursively takes each pair of input values and relationally intersects (which is commutative, associative, and idempotent) them together until just one is left, which is the result. The result relation has the same heading as all of its input relations, and its body contains only the tuples that are in every one of the input relations. The identity value of relational intersection is the same-heading universal relation value (having all the tuples that could possible exist together in a common relation value with that heading; this is impossibly large to represent in the general case, except perhaps lazily). Note that this intersection method is conceptually a special case of join, applicable when the headings of the inputs are the same, and join will produce the same result as this when given the same inputs, but with the exception that relational intersection has a different identity value for zero inputs than relational join has. Note that this operation is also known as ∩.
intersection
join
∩
method diff of Set::Relation ($source: Set::Relation $filter)
This functional method results in the relational difference when its $filter argument is subtracted from its same-heading $source invocant. The result relation has the same heading as the input relations, and its body contains only the tuples that are in $source and are not in $filter. Note that this diff operator is conceptually a special case of semidiff, applicable when the headings of the inputs are the same. Note that this operation is also known as minus or except or ∖.
$filter
$source
∖
method semidiff of Set::Relation ($source: Set::Relation $filter)
This functional method is the same as semijoin but that it results in the complementary subset of tuples of $source when given the same arguments. Note that this operation is also known as antijoin or anti-semijoin or semiminus or !matching or not-matching or ⊿.
!matching
not-matching
⊿
method antijoin of Set::Relation ($source: Set::Relation $filter)
This functional method is an alias for semidiff.
method semijoin_and_diff of Array ($source: Set::Relation $filter)
This functional method performs a 2-way partitioning of all the tuples of $source and results in a 2-element Perl Array whose element values are each Set::Relation objects that have the same heading as $source and complementary subsets of its tuples; the first and second elements are what semijoin and semidiff, respectively, would result in when having the same invocant and argument.
method semijoin of Set::Relation ($source: Set::Relation $filter)
This functional method results in the relational semijoin of its invocant and argument. The result relation has the same heading as $source, and its body contains the subset of $source tuples that match those of $filter as per join. Note that relational semijoin is conceptually a short-hand for first doing an ordinary relational join between $source and $filter, and then performing a relational projection on all of the attributes that just $source has. Note that this operation is also known as matching or ⋉.
matching
⋉
method join of Set::Relation ($topic: Array|Set::Relation $others)
This functional method results in the relational join (natural inner join) of the collective N element values of its invocant and argument, hereafter referred to as $inputs; it is a reduction operator that recursively takes each pair of input values and relationally joins (which is commutative, associative, and idempotent) them together until just one is left, which is the result. The result relation has a heading that is a union of all of the headings of its input relations, and its body is the result of first pairwise-matching every tuple of each input relation with every tuple of each other input relation, then where each member of a tuple pair has attribute names in common, eliminating pairs where the values of those attributes differ and unioning the remaining said tuple pairs, then eliminating any result tuples that duplicate others. The identity value of relational join is the nullary (zero attribute) relation value having a single tuple. As a trivial case, if any input relation has zero tuples, then the method's result will too; or, if any input is the nullary relation with one tuple, that input can be ignored (see identity value); or, if any 2 inputs have no attribute names in common, then the join of just those 2 is a cartesian product; or, if any 2 inputs have all attribute names in common, then the join of just those 2 is an intersection; or, if for 2 inputs, one's set of attribute names is a proper subset of another's, then the join of just those two is a semijoin with the former filtering the latter. Note that this operation is also known as natural inner join or ⋈.
⋈
method product of Set::Relation ($topic: Array|Set::Relation $others)
This functional method results in the relational cartesian/cross product of the collective N element values of its invocant and argument, hereafter referred to as $inputs; it is conceptually a special case of join where all input relations have mutually distinct attribute names; unlike join, product will fail if any inputs have attribute names in common. Note that this operation is also known as cartesian join or cross-join or ×.
cross-join
×
method quotient of Set::Relation ($dividend: Set::Relation $divisor)
This functional method results in the quotient when its $dividend invocant is divided by its $divisor argument using relational division. Speaking informally, say the relations $dividend and $divisor are called A and B, and their attribute sets are respectively named {X,Y} and {Y}, then the result relation has a heading composed of attributes {X} (so the result and $divisor headings are both complementary subsets of the $dividend heading); the result has all tuples {X} such that a tuple {X,Y} appears in A for all tuples {Y} appearing in B; that is, A ÷ B is shorthand for A{X} ∖ ((A{X} × B) ∖ A){X}. Note that this operation is also known as divideby or ÷.
$dividend
$divisor
A
B
{X,Y}
{Y}
{X}
A ÷ B
A{X} ∖ ((A{X} × B) ∖ A){X}
÷
method composition of Set::Relation ($topic: Set::Relation $other)
This symmetric functional method results in the relational composition of its invocant and argument. It is conceptually a short-hand for first doing an ordinary relational join between the input relations, and then performing a relational projection on all of the attributes that only one of the arguments has; that is, the result has all of and just the attributes that were not involved in matching the tuples of the inputs.
method join_with_group of Set::Relation ($primary: Set::Relation $secondary, Str $group_attr)
This functional method is a short-hand for first taking a (natural inner) join of its $primary invocant and $secondary argument, and then taking a group on all of the attributes that only the $secondary argument had, such that the attribute resulting from the group has the name $group_attr. The result has 1 tuple for every tuple of $primary where at least 1 matching tuple exists in $secondary. This method will fail if $group_attr is the same name as any source attribute that wasn't grouped. This method is a convenient tool for gathering both parent and child records from a database using a single query while avoiding duplication of the parent record values.
$primary
$secondary
$group_attr
These Set::Relation object methods are pure functional. They are specific to supporting ranking and quotas.
method rank of Set::Relation ($topic: Str $name, Callable $ord_func)
This functional method results in the relational extension of its $topic invocant by a single nonnegative-integer-typed attribute whose name is provided by the $name argument, where the value of the new attribute for each tuple is the rank of that tuple as determined by the Order-resulting zero-parameter Perl subroutine reference given in its $ord_func argument. The subroutine compares tuples, similarly to Perl's built-in sort operator, with each invocation of it having a $_ topic whose value is a binary tuple/Hash with attributes named a and b, each of the latter having a $topic tuple as its value. The new attribute of rank's result has a value of zero for its ranked-first tuple, and each further consecutive ranked tuple has the next larger integer value. Note that rank provides the functionality of SQL's "RANK" feature but that the result of rank is always a total ordering and so there is no "dense" / "not dense" distinction (however a partial ordering can be implemented over it).
$ord_func
sort
a
b
rank
method rank_by_attr_names of Set::Relation ($topic: Str $name, Array|Str $order_by)
This functional method provides a convenient short-hand of rank for the common case of ranking tuples of a relation on a sequential list of its named attributes; it simply takes a $order_by array argument rather than a Perl closure argument, and it ranks each pair of tuples by comparing corresponding attribute values in the order that they are named in $order_by, stopping once a comparison doesn't result in same. Iff $order_by is a Str then it is equivalent to an $order_by that is a single-element Array whose element is that Str; the rest of this documentation assumes that $order_by is simply an Array. Each element of $order_by is either a Str or a 1-3 element Array; in the first case, that is simply the name of the attribute; in the second case, the Array has these 1-3 elements in order: attribute name, "is reverse order" direction indicator, and comparison operator. This method will fail if $order_by contains any non-Str|Array elements, or if it names an attribute that $topic doesn't have. The "is reverse order" direction indicator is a boolean value; if it is false/undefined/missing then ordering on that attribute will be as per usual for the comparator; if it is true then the result is the reverse to what is usual. This method will fail if the comparison operator is defined and is anything other than cmp (string compare semantics) or <=> (numeric compare semantics); if it is undefined then cmp (string) is the default.
$order_by
cmp
<=>
method limit of Set::Relation ($topic: Callable $ord_func, UInt $min_rank, UInt $max_rank)
This functional method results in the relational restriction of its $topic argument as determined by first ranking its tuples as per rank method (using $ord_func) and then keeping just those tuples whose rank is within the inclusive range specified by the $min_rank and $max_rank arguments (rank's extra attribute is not kept). The limit method implements a certain kind of quota query where all the result tuples are consecutive in their ranks. This method will fail if $max_rank is before $min_rank. It is valid for $min_rank or $max_rank to be greater than the maximum rank of the source tuples; in the first case, the result has zero tuples; in the second case, the result has all remaining tuples starting at min_rank. If $topic has any tuples and $min_rank matches the rank of a source tuple, then the result will always have at least 1 tuple. Note that limit provides the functionality of SQL's "LIMIT/OFFSET" feature in combination with "ORDER BY" but that the result tuples of limit do not remain ordered.
$min_rank
$max_rank
limit
min_rank
method limit_by_attr_names of Set::Relation ($topic: Array|Str $order_by, UInt $min_rank, UInt $max_rank)
This functional method is to limit what rank_by_attr_names is to rank.
rank_by_attr_names
These Set::Relation object methods are pure functional. They are specific to supporting substitutions.
method substitution of Set::Relation ($topic: Array|Str $attr_names, Callable $func, Bool $allow_dup_tuples?)
This functional method is similar to extension except that it substitutes values of existing relation attributes rather than adding new attributes. The result relation has the same heading as $topic. The result tuple of the Perl subroutine reference given in $func must have a heading that is a subset of the heading of $topic; corresponding values resulting from the subroutine given in $func will replace the values of the tuples of $topic. The result relation has a cardinality that is the same as that of $topic, unless the result of any substitutions was redundant tuples, in which case the result has appropriately fewer tuples. As a trivial case, if $func is defined to unconditionally result in either the degree-zero tuple or in the same tuple as its own $topic argument, then this method results simply in $topic; or, if $func is defined to have a static result and it replaces all attributes, then this method's result will have just 0..1 tuples. Now, strictly speaking, substitution could conceivably be implemented such that each result from $func is allowed to specify replacement values for different subsets of $topic attributes; however, to improve the method's predictability and ease of implementation over disparate foundations, substitution requires the extra $attr_names argument so that users can specify a consistent subset that $func will update (possibly to itself). This method will fail if $topic has at least 1 tuple and the result of $func does not have matching attribute names to those named by $attr_names. If this method's $allow_dup_tuples argument is false (the default), then $func is guaranteed to be invoked just once per distinct tuple of $topic; otherwise it might be multiple invoked.
substitution
method static_subst of Set::Relation ($topic: Hash $attrs)
This functional method is a simpler-syntax alternative to substitution in the typical scenario where every tuple of a relation, given in the $topic invocant, is updated with identical values for the same attributes; the new attribute values are given in the $attrs argument.
method subst_in_restr of Set::Relation ($topic: Callable $restr_func, Array|Str $subst_attr_names, Callable $subst_func, Bool $allow_dup_tuples?)
This functional method is like substitution except that it only transforms a subset of the tuples of $topic rather than all of them. It is a short-hand for first separating the tuples of $topic into 2 groups where those passed by a relational restriction (defined by $restr_func) are then transformed (defined by $subst_attr_names and $subst_func), then the result of the substitution is unioned with the un-transformed group. See also the subst_in_semijoin method, which is a simpler-syntax alternative for subst_in_restr in its typical usage where restrictions are composed simply of anded or ored tests for attribute value equality.
$restr_func
$subst_attr_names
$subst_func
subst_in_semijoin
subst_in_restr
method static_subst_in_restr of Set::Relation ($topic: Callable $restr_func, Hash $subst, Bool $allow_dup_tuples?)
This functional method is to subst_in_restr what static_subst is to substitution. See also the static_subst_in_semijoin method.
static_subst
static_subst_in_semijoin
method subst_in_semijoin of Set::Relation ($topic: Set::Relation $restr, Array|Str $subst_attr_names, Callable $subst_func, Bool $allow_dup_tuples?)
This functional method is like subst_in_restr except that the subset of the tuples of $topic to be transformed is determined by those matched by a semijoin with $restr rather than those that pass a generic relational restriction.
$restr
method static_subst_in_semijoin of Set::Relation ($topic: Set::Relation $restr, Hash $subst)
This functional method is to subst_in_semijoin what static_subst is to substitution.
These Set::Relation object methods are pure functional. They are specific to supporting outer-joins.
method outer_join_with_group of Set::Relation ($primary: Set::Relation $secondary, Str $group_attr)
This functional method is the same as join_with_group except that it results in a half-outer natural join rather than an inner natural join; every tuple of $primary has exactly 1 corresponding tuple in the result, but where there were no matching $secondary tuples, the result attribute named by $group_attr contains zero tuples rather than 1+.
join_with_group
method outer_join_with_undefs of Set::Relation ($primary: Set::Relation $secondary)
This functional method results in a plain half-outer natural join of its $primary invocant and $secondary argument where, for all result tuples coming from a $primary tuple that didn't match a $secondary tuple, the result attributes coming from just $secondary are filled with the Perl undef.
method outer_join_with_static_exten of Set::Relation ($primary: Set::Relation $secondary, Hash $filler)
This functional method is the same as outer_join_with_undefs but that $secondary-sourced result attributes are not filled with the Perl undef; rather, for result tuples from non-matches, the missing values are provided explicitly from the $filler argument, which is a tuple/Hash whose heading matches the projection of $secondary's attributes that aren't in common with $primary, and whose body is the literal values to use for those missing attribute values.
outer_join_with_undefs
$filler
method outer_join_with_exten of Set::Relation ($primary: Set::Relation $secondary, Callable $exten_func, Bool $allow_dup_tuples?)
This functional method is the same as outer_join_with_static_exten but that the result tuples from non-matches are the result of performing a relational extension on the un-matched $primary tuples such that each said result tuple is determined by applying the Perl subroutine given in $exten_func to each said $primary tuple. If this method's $allow_dup_tuples argument is false (the default), then $exten_func is guaranteed to be invoked just once per un-matched tuple of $primary; otherwise it might be multiple invoked.
outer_join_with_static_exten
$exten_func
A Set::Relation::Mutable object is a Set::Relation object that is also allowed to have its value mutate at some times.
multi submethod new of Set::Relation::Mutable (Array|Set::Relation|Str :$members, Array|Str :$keys?, Bool :$has_frozen_identity?)
The Set::Relation::Mutable role extends the new constructor submethod of the Set::Relation role to add the optional named-only parameter $has_frozen_identity; if its argument is true, then the new Set::Relation::Mutable object is made value-immutable once initialized (its identity is frozen); otherwise, if that argument is false or not provided, then the new object is initially mutable (its identity is not frozen).
$has_frozen_identity
method clone of Set::Relation::Mutable ($self:)
This method results in a new Set::Relation::Mutable object that has an exact clone of its invocant's attributes and tuples. The new Set::Relation::Mutable is initially a mutable object; its value identity is not frozen, regardless of whether the invocant is frozen or not.
method has_frozen_identity of Bool ($self:)
This method results in true if the invocant is currently value-immutable, and it results in false otherwise.
method freeze_identity ($self:)
This method causes the invocant to become value-immutable when invoked; it freezes the invocant's value identity. This change is not reversible (an immutable Set::Relation::Mutable object can't be made mutable again), however invoking clone on said object will give you a mutable duplicate.
clone
Invocations of these Set::Relation::Mutable object methods will cause their invocants to mutate. But they do not mutate any of their non-invocant arguments. These methods also result in their invocants post-mutation, for the convenience of users that like to chain method calls.
method evacuate of Set::Relation::Mutable ($topic:)
This mutator method deletes all of the tuples in its invocant relation. For a non-mutating equivalent, see the empty functional method.
empty
method insert of Set::Relation::Mutable ($r: Array|Hash $t)
This mutator method inserts its tuples argument into its invocant relation. For a non-mutating equivalent, see the insertion functional method. Note that insert is allowed to invalidate any currently existing candidate keys of the invocant, in which case, the keys method would no longer list them; those keys are not constraints on future mutations.
insertion
method delete of Set::Relation::Mutable ($r: Array|Hash $t)
This mutator method deletes its tuples argument from its invocant relation. For a non-mutating equivalent, see the deletion functional method.
deletion
This file requires any version of Perl 5.x.y that is at least 5.8.1.
None reported.
The separate all-documentation distribution Muldis::D is the formal definition of the Muldis D language, a portion of which Set::Relation is mainly based on. The Muldis D language in turn has as a primary influence the work of Chris Date (C.J. Date) and Hugh Darwen whose home website is http://www.thethirdmanifesto.com/.
These Perl 5 packages that are in the current distribution are classes that implement the Set::Relation roles: Set::Relation::V1, Set::Relation::V2.
These other Perl 6 packages: Muldis::D::RefEng, Set.
These other Perl 5 packages: Muldis::D::RefEng, Set::Object, Set::Scalar.
The Set::Relation library for Perl 5 does not make explicit attempts in code to enforce privacy of the library's internals, besides not documenting them as part of the public API. (The Set::Relation library for Perl 6 is different.) That said, you should still respect that privacy and just use the public API that Set::Relation provides. If you bypass the public API anyway, as Perl 5 allows, you do so at your own peril.
Darren Duncan (darren@DarrenDuncan.net)
darren@DarrenDuncan.net
Set::Relation is Copyright © 2006-2015, Muldis Data Systems, Inc.
http://www.muldis.com/
Set::Relation is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation (http://www.fsf.org/); either version 3 of the License, or (at your option) any later version. You should have received a copy of the LGPL as part of the Set::Relation distribution, in the files named "LICENSE/LGPL" and "LICENSE/GPL" (the LGPLv3 is defined as the terms of the GPLv3 plus extra permissions); if not, see http://www.gnu.org/licenses/.
If it is not feasible for you to employ Set::Relation subject to the terms of the LGPL, then the copyright holder of Set::Relation can provide you a customized proprietary license, often at no cost, so that it is still possible for you to employ Set::Relation to meet your needs.
Any versions of Set::Relation that you modify and distribute must carry prominent notices stating that you changed the files and the date of any changes, in addition to preserving this original copyright notice and other credits. Set::Relation is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. However, for an additional fee, the copyright holders of Set::Relation can sell you a warranty for it.
While it is by no means required, the copyright holder of Set::Relation would appreciate being informed any time you create a modified version of Set::Relation that you are willing to distribute, because that is a practical way of suggesting improvements to the standard version.
thepler@employees.org
Thanks for proposing significant module design improvements and bug fixes, providing files for the test suite, and giving other constructive input.
Several public email-based forums exist whose main topic is the Muldis D language and its implementations, especially the Muldis::D::RefEng reference implementation, but also the Set::Relation module. They exist so that users of Muldis D or Muldis::D::RefEng can help each other, or so that help coming from the projects' developers can be said once to many people, rather than necessarily to each individually. All of these you can reach via http://mm.darrenduncan.net/mailman/listinfo; go there to manage your subscriptions to, or view the archives of, the following:
muldis-db-announce@mm.darrenduncan.net
This low-volume list is mainly for official announcements from Muldis D language or implementation developers, though developers of related projects can also post their announcements here. This is not a discussion list.
muldis-db-users@mm.darrenduncan.net
This list is for general discussion among people who are using Muldis D or any of its implementations, especially the Muldis::D::RefEng reference implementation. This is the best place to ask for basic help in getting Muldis::D::RefEng installed on your machine or to make it do what you want. If you are in doubt on which list to use, then use this one by default. You could also submit feature requests for Muldis D projects or report perceived bugs here, if you don't want to use CPAN's RT system.
muldis-d-language@mm.darrenduncan.net
This list is mainly for discussion among people who are designing the Muldis D language specification, or who are implementing or adapting Muldis D in some form, or who are writing Muldis D documentation, tests, or examples. It is not the main forum for any Muldis D implementations, nor is it the place for non-implementers to get help in using said.
muldis-db-devel@mm.darrenduncan.net
This list is for discussion among people who are designing or implementing Muldis::D::RefEng, or other Muldis D implementations, or who are writing Muldis::D::RefEng core documentation, tests, or examples. It is not the main forum for the Muldis D language itself, nor is it the place for non-implementers to get help in using said.
An official IRC channel for Muldis D and its implementations is also intended, but not yet started.
Alternately, you can purchase more advanced commercial support for various Muldis D implementations, particularly Muldis::D::RefEng, from its author by way of Muldis Data Systems; see http://www.muldis.com/ for details.
To install Set::Relation, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Set::Relation
CPAN shell
perl -MCPAN -e shell install Set::Relation
For more information on module installation, please visit the detailed CPAN module installation guide.