NAME
Muldis::D::Core::Relation - Muldis D generic relational operators
VERSION
This document is Muldis::D::Core::Relation version 0.128.0.
PREFACE
This document is part of the Muldis D language specification, whose root document is Muldis::D; you should read that root document before you read this one, which provides subservient details. Moreover, you should read the Muldis::D::Core document before this current document, as that forms its own tree beneath a root document branch.
DESCRIPTION
This document describes essentially all of the core Muldis D generic relational operators (for generic relations).
This documentation is pending.
GENERIC RELATIONAL FUNCTIONS WITH SINGLE INPUT RELATION
These functions are applicable to mainly relation types, but are generic in that they typically work with any relation types.
sys.std.Core.Relation.D0C0
function sys.std.Core.Relation.D0C0 (Relation <--) {...}
This named-value selector function results in the only zero-attribute, zero-tuple Relation value, which is known by the special name Relation:D0C0, aka D0C0. Note that The Third Manifesto also refers to this value by the special shorthand name TABLE_DUM.
sys.std.Core.Relation.D0C1
function sys.std.Core.Relation.D0C1 (Relation <--) {...}
This named-value selector function results in the only zero-attribute, single-tuple Relation value, which is known by the special name Relation:D0C1, aka D0C1. Note that The Third Manifesto also refers to this value by the special shorthand name TABLE_DEE.
sys.std.Core.Relation.degree
function sys.std.Core.Relation.degree (NNInt <-- $topic : Relation) {...}
This function results in the degree of its argument (that is, the count of attributes it has).
sys.std.Core.Relation.is_nullary
function sys.std.Core.Relation.is_nullary (Bool <-- $topic : Relation) {...}
This function results in Bool:True iff its argument has a degree of zero (that is, it has zero attributes), and Bool:False otherwise. By definition, the only 2 relation values for which this function would result in Bool:True are the values Relation:D0C[0|1].
sys.std.Core.Relation.is_not_nullary
function sys.std.Core.Relation.is_not_nullary (Bool <-- $topic : Relation) {...}
This function is exactly the same as sys.std.Core.Relation.is_nullary except that it results in the opposite boolean value when given the same argument.
sys.std.Core.Relation.has_attrs
function sys.std.Core.Relation.has_attrs (Bool <-- $topic : Relation, $attr_names : set_of.Name) {...}
This function results in Bool:True iff, for every one of the attribute names specified by its attr_names argument, its topic argument has an attribute with that name; otherwise it results in Bool:False. As a trivial case, this function's result is Bool:True if attr_names is empty.
sys.std.Core.Relation.attr_names
function sys.std.Core.Relation.attr_names (set_of.Name <-- $topic : Relation) {...}
This function results in the set of the names of the attributes of its argument.
sys.std.Core.Relation.cardinality
function sys.std.Core.Relation.cardinality (NNInt <-- $topic : Relation) {...}
This function results in the cardinality of its argument (that is, the count of tuples its body has). Note that this operation is also known as count or r#.
sys.std.Core.Relation.count
function sys.std.Core.Relation.count (NNInt <-- $topic : Relation) {...}
This function is an alias for sys.std.Core.Relation.cardinality.
sys.std.Core.Relation.is_empty
function sys.std.Core.Relation.is_empty (Bool <-- $topic : Relation) {...}
This function results in Bool:True iff its argument has a cardinality of zero (that is, it has zero tuples), and Bool:False otherwise. Note that if you are using a Maybe to represent a sparse data item, analogously to a SQL nullable context, then testing the Maybe with is_empty is analogous to testing a SQL nullable with is null.
sys.std.Core.Relation.is_not_empty
function sys.std.Core.Relation.is_not_empty (Bool <-- $topic : Relation) {...}
This function is exactly the same as sys.std.Core.Relation.is_empty except that it results in the opposite boolean value when given the same argument. And following the analogy with is_empty, is_not_empty is analogous to SQL's is not null.
sys.std.Core.Relation.has_member
function sys.std.Core.Relation.has_member (Bool <-- $r : Relation, $t : Tuple) {...}
This function results in Bool:True iff its t argument matches a tuple of its r argument (that is, iff conceptually t is a member of r), and Bool:False otherwise. This function will warn if its 2 arguments' common-named attributes have declared types that are incompatible as per is_identical. Note that this operation is also known as r∋ or r-has.
sys.std.Core.Relation.has_not_member
function sys.std.Core.Relation.has_not_member (Bool <-- $r : Relation, $t : Tuple) {...}
This function is exactly the same as sys.std.Core.Relation.has_member except that it results in the opposite boolean value when given the same arguments. Note that this operation is also known as r∌ or r-!has or r-not-has.
sys.std.Core.Relation.tuple_is_member
function sys.std.Core.Relation.tuple_is_member (Bool <-- $t : Tuple, $r : Relation) {...}
This function is an alias for sys.std.Core.Relation.has_member. This function results in Bool:True iff its t argument matches a tuple of its r argument (that is, iff conceptually t is a member of r), and Bool:False otherwise. Note that this operation is also known as ∈r or in-r.
sys.std.Core.Relation.tuple_is_not_member
function sys.std.Core.Relation.tuple_is_not_member (Bool <-- $t : Tuple, $r : Relation) {...}
This function is an alias for sys.std.Core.Relation.has_not_member. This function is exactly the same as sys.std.Core.Relation.tuple_is_member except that it results in the opposite boolean value when given the same arguments. Note that this operation is also known as ¬in;r or !in-r or not-in-r.
sys.std.Core.Relation.has_key
function sys.std.Core.Relation.has_key (Bool <-- $topic : Relation, $attr_names : set_of.Name) {...}
This function results in Bool:True iff its topic argument has a (unique) key over the subset of its attributes whose names are specified by its attr_names argument; otherwise it results in Bool:False. This function will fail if topic does not have all of the attributes named by attr_names. As a trivial case, this function's result is Bool:True if topic is empty.
sys.std.Core.Relation.empty
function sys.std.Core.Relation.empty (Relation <-- $topic : Relation) {...}
This function results in the empty relation of the same heading of its argument, that is having the same degree and attribute names; it has zero tuples.
sys.std.Core.Relation.insertion
function sys.std.Core.Relation.insertion (Relation <-- $r : Relation, $t : Tuple) {...}
This function results in a Relation that is the relational union of r and a relation whose sole tuple is t; that is, conceptually the result is t inserted into r. As a trivial case, if t already exists in r, then the result is just r.
sys.std.Core.Relation.disjoint_ins
function sys.std.Core.Relation.disjoint_ins (Relation <-- $r : Relation, $t : Tuple) {...}
This function is exactly the same as sys.std.Core.Relation.insertion except that it will fail if t already exists in r.
sys.std.Core.Relation.deletion
function sys.std.Core.Relation.deletion (Relation <-- $r : Relation, $t : Tuple) {...}
This function results in a Relation that is the relational difference from r of a relation whose sole tuple is t; that is, conceptually the result is t deleted from r. As a trivial case, if t already doesn't exist in r, then the result is just r.
sys.std.Core.Relation.rename
function sys.std.Core.Relation.rename (Relation <-- $topic : Relation, $map : AttrRenameMap) {...}
This function is the same as sys.std.Core.Tuple.rename but that it operates on and results in a Relation rather than a Tuple. Note that this operation is also known as @{<-}.
sys.std.Core.Relation.projection
function sys.std.Core.Relation.projection (Relation <-- $topic : Relation, $attr_names : set_of.Name) {...}
This function is the same as sys.std.Core.Tuple.projection but that it operates on and results in a Relation rather than a Tuple. But note that the result relation will have fewer tuples than topic if any topic tuples were non-distinct for just the projected attributes. Note that this operation is also known as @{}.
sys.std.Core.Relation.cmpl_proj
function sys.std.Core.Relation.cmpl_proj (Relation <-- $topic : Relation, $attr_names : set_of.Name) {...}
This function is the same as sys.std.Core.Tuple.cmpl_proj but that it operates on and results in a Relation rather than a Tuple. Note that this operation is also known as @{!}.
sys.std.Core.Relation.wrap
function sys.std.Core.Relation.wrap (Relation <-- $topic : Relation, $outer : Name, $inner : set_of.Name) {...}
This function is the same as sys.std.Core.Tuple.wrap but that it operates on and results in a Relation rather than a Tuple, where each of its member tuples was transformed as per sys.std.Core.Tuple.wrap. The result relation has the same cardinality as topic. Note that this operation is also known as @{%<-}.
sys.std.Core.Relation.cmpl_wrap
function sys.std.Core.Relation.cmpl_wrap (Relation <-- $topic : Relation, $outer : Name, $cmpl_inner : set_of.Name) {...}
This function is the same as sys.std.Core.Tuple.cmpl_wrap but that it operates on and results in a Relation rather than a Tuple, where each of its member tuples was transformed as per sys.std.Core.Tuple.cmpl_wrap. Note that this operation is also known as @{%<-!}.
sys.std.Core.Relation.unwrap
function sys.std.Core.Relation.unwrap (Relation <-- $topic : Relation, $inner : set_of.Name, $outer : Name) {...}
This function is the inverse of sys.std.Core.Relation.wrap as sys.std.Core.Tuple.unwrap is to sys.std.Core.Tuple.wrap. But unlike the simplest concept of a Tuple variant of unwrap, this current function requires the extra inner argument to prevent ambiguity in the general case where topic might have zero tuples, because in that situation the most-specific-type of topic{outer} would be Empty, and the names of the attributes to add to topic in place of topic{outer} are not known. This function will fail if topic has at least 1 tuple and inner does not match the names of the attributes of topic{outer}. This function will fail with a non-DHRelation valued topic unless, for every tuple of topic, the attribute specified by outer is valued with a tuple of the same degree and heading (attribute names); this failure is because there would be no consistent set of attribute names to extend topic with (a problem that would never happen by definition with a deeply homogeneous relation topic). Note that this operation is also known as @{<-%}.
sys.std.Core.Relation.group
function sys.std.Core.Relation.group (Relation <-- $topic : Relation, $outer : Name, $inner : set_of.Name) {...}
This function is similar to sys.std.Core.Relation.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 function 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 function supports the new attribute having the same name as an old one being grouped into it. This function 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 @{@<-}.
sys.std.Core.Relation.cmpl_group
function sys.std.Core.Relation.cmpl_group (Relation <-- $topic : Relation, $outer : Name, $group_per : set_of.Name) {...}
This function 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 @{@<-!}.
sys.std.Core.Relation.ungroup
function sys.std.Core.Relation.ungroup (Relation <-- $topic : Relation, $inner : set_of.Name, $outer : Name) {...}
This function is the inverse of sys.std.Core.Relation.group as sys.std.Core.Relation.unwrap is to sys.std.Core.Relation.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 function will fail if outer specifies any attribute name that topic doesn't have, or if an attribute of topic{outer} has the same name as another topic attribute. This function will fail with a non-DHRelation valued topic unless, for every tuple of topic, the attribute specified by outer is valued with a relation of the same degree and heading (attribute names); this failure is because there would be no consistent set of attribute names to extend topic with (a problem that would never happen by definition with a deeply homogeneous relation topic). Note that this operation is also known as unnest or @{<-@}.
sys.std.Core.Relation.power_set
function sys.std.Core.Relation.power_set (set_of.Relation <-- $topic : Relation) {...}
This function results in the power set of its argument. The result is a Set whose sole attribute is Relation-typed (its type is nominally the same as that of the argument) and which has a tuple for every distinct subset of tuples in the argument. The cardinality of the result is equal to 2 raised to the power of the cardinality of the argument (which may easily lead to a very large result, so use this function with care). Note that the N-adic relational union of the power set of some relation is that relation; the N-adic intersection of any power set is the empty relation.
sys.std.Core.Relation.tclose
function sys.std.Core.Relation.tclose (Relation <-- $topic : Relation) {...}
This function results in the transitive closure of its argument. The argument must be a binary relation whose attributes are both of the same type, and the result is a relation having the same heading and a body which is a superset of the argument's tuples. Assuming that the argument represents all of the node pairs in a directed graph that have an arc between them, and so each argument 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 function 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).
sys.std.Core.Relation.restriction
function sys.std.Core.Relation.restriction (Relation <-- $topic : Relation, $func : ValFiltCFuncNC) {...}
This function results in the relational restriction of its topic argument as determined by applying the value-filter function named 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 function named by func results in Bool:True when passed the tuple as its topic argument. As a trivial case, if func is defined to unconditionally result in Bool:True, then this function results simply in topic; or, for an unconditional Bool:False, this function results in the empty relation with the same heading. Note that this operation is also known as where. See also the sys.std.Core.Relation.semijoin function, which is a simpler-syntax alternative for sys.std.Core.Relation.restriction in its typical usage where restrictions are composed simply of anded or ored tests for attribute value equality.
sys.std.Core.Relation.restr_and_cmpl
function sys.std.Core.Relation.restr_and_cmpl (Tuple <-- $topic : Relation, $func : ValFiltCFuncNC) {...}
This function performs a 2-way partitioning of all the tuples of topic and results in a binary tuple whose attribute values are each relations that have the same heading as topic and complementary subsets of its tuples; the 2 result attributes have the names pass and fail, and their values are what sys.std.Core.Relation.restriction and sys.std.Core.Relation.cmpl_restr, respectively, would result in when given the same arguments.
sys.std.Core.Relation.cmpl_restr
function sys.std.Core.Relation.cmpl_restr (Relation <-- $topic : Relation, $func : ValFiltCFuncNC) {...}
This function is the same as restriction but that it results in the complementary subset of tuples of topic when given the same arguments. See also the sys.std.Core.Relation.semidiff function. Note that this operation is also known as !where or not-where.
sys.std.Core.Relation.classification
function sys.std.Core.Relation.classification (Relation <-- $topic : Relation, $func : ValMapCFuncNC, $class_attr_name : Name, $group_attr_name : Name) {...}
This function conceptually is to sys.std.Core.Relation.restriction what sys.std.Core.Relation.group is to sys.std.Core.Relation.semijoin. It classifies the tuples of topic into N groups using the value-map function named by func, such that any distinct tuples are in a common group if the function named by func results in the same value when given either of those tuples as its topic argument. This function 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 function 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.
sys.std.Core.Relation.extension
function sys.std.Core.Relation.extension (Relation <-- $topic : Relation, $attr_names : set_of.Name, $func : ValMapCFuncNC) {...}
This function results in the relational extension of its topic argument as determined by applying the Tuple-resulting value-map function named 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 function named by func results in a second tuple when passed the first tuple as its topic argument; 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 function 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 function 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.
sys.std.Core.Relation.static_exten
function sys.std.Core.Relation.static_exten (Relation <-- $topic : Relation, $attrs : Tuple) {...}
This function is a simpler-syntax alternative to both sys.std.Core.Relation.extension and sys.std.Core.Relation.product in the typical scenario of extending a relation, given in the topic argument, 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.
sys.std.Core.Relation.map
function sys.std.Core.Relation.map (Relation <-- $topic : Relation, $result_attr_names : set_of.Name, $func : ValMapCFuncNC) {...}
This function 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 function results in a relation each of whose tuples is the result of applying, to each of the tuples of its topic argument, the Tuple-resulting value-map function named 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 function results simply in topic; or, if func is defined to have a static result, then this function'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 function 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.
sys.std.Core.Relation.summary
function sys.std.Core.Relation.summary (Relation <-- $topic : Relation, $group_per : set_of.Name, $summ_attr_names : set_of.Name, $summ_func : ValMapCFuncNC) {...}
This function 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 argument. This function 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 function applies the Tuple-resulting value-map function named in its summ_func argument; for each post-group main relation tuple, the function named in summ_func results in a second tuple when the first tuple is its topic argument; the topic argument has the 2 attribute names summarize and per, which are valued with the relation-valued attribute and tuple-valued attribute, respectively. As per a function that extension applies, the function named by 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 function 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 function 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.
sys.std.Core.Relation.cardinality_per_group
function sys.std.Core.Relation.cardinality_per_group (Relation <-- $topic : Relation, $count_attr_name : Name, $group_per : set_of.Name) {...}
This function 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 PInt). Note that this operation is also known as @{#@<-!}.
sys.std.Core.Relation.count_per_group
function sys.std.Core.Relation.count_per_group (Relation <-- $topic : Relation, $count_attr_name : Name, $group_per : set_of.Name) {...}
This function is an alias for sys.std.Core.Relation.cardinality_per_group.
sys.std.Core.Relation.reduction
function sys.std.Core.Relation.reduction (Tuple <-- $topic : Relation, $func : ValRedCFuncNC, $identity : Tuple) {...}
This function is a generic reduction operator that recursively takes each pair of tuples in topic and applies an argument-specified tuple value-resulting value-reduction function (which is both commutative and associative) to the pair until just one input tuple is left, which is the result. The value-reduction function to apply is named in the func argument, and that function must have 2 parameters named v1 and v2, which take the 2 input tuples for an invocation. If topic has zero tuples, then reduction results in the tuple given in identity. Note that identity may be changed to take a function name rather than a value, for consistency with func. This function will fail|warn if the |declared headings of identity and topic aren't compatible.
GENERIC RELATIONAL FUNCTIONS WITH MULTIPLE INPUT RELATIONS
These functions are applicable to mainly relation types, but are generic in that they typically work with any relation types.
sys.std.Core.Relation.is_subset
function sys.std.Core.Relation.is_subset (Bool <-- $topic : Relation, $other : Relation) {...}
This function results in Bool:True iff the set of tuples comprising topic is a subset of the set of tuples comprising other, and Bool:False otherwise. This function will warn if the input relations common-named attributes have declared types that are incompatible as per is_identical. Note that this operation is also known as ⊆ or sub.
sys.std.Core.Relation.is_not_subset
function sys.std.Core.Relation.is_not_subset (Bool <-- $topic : Relation, $other : Relation) {...}
This function is exactly the same as sys.std.Core.Relation.is_subset except that it results in the opposite boolean value when given the same arguments. Note that this operation is also known as ⊈ or !sub or not-sub.
sys.std.Core.Relation.is_superset
function sys.std.Core.Relation.is_superset (Bool <-- $topic : Relation, $other : Relation) {...}
This function is an alias for sys.std.Core.Relation.is_subset except that it transposes the topic and other arguments. This function results in Bool:True iff the set of tuples comprising topic is a superset of the set of tuples comprising other, and Bool:False otherwise. Note that this operation is also known as ⊇ or super.
sys.std.Core.Relation.is_not_superset
function sys.std.Core.Relation.is_not_superset (Bool <-- $topic : Relation, $other : Relation) {...}
This function is an alias for sys.std.Core.Relation.is_not_subset except that it transposes the topic and other arguments. This function is exactly the same as sys.std.Core.Relation.is_superset except that it results in the opposite boolean value when given the same arguments. Note that this operation is also known as ⊉ or !super or not-super.
sys.std.Core.Relation.is_proper_subset
function sys.std.Core.Relation.is_proper_subset (Bool <-- $topic : Relation, $other : Relation) {...}
This function is exactly the same as sys.std.Core.Relation.is_subset except that it results in Bool:False if its 2 arguments are identical. Note that this operation is also known as ⊂ or psub.
sys.std.Core.Relation.is_not_proper_subset
function sys.std.Core.Relation.is_not_proper_subset (Bool <-- $topic : Relation, $other : Relation) {...}
This function is exactly the same as sys.std.Core.Relation.is_proper_subset except that it results in the opposite boolean value when given the same arguments. Note that this operation is also known as ⊄ or !psub or not-psub.
sys.std.Core.Relation.is_proper_superset
function sys.std.Core.Relation.is_proper_superset (Bool <-- $topic : Relation, $other : Relation) {...}
This function is an alias for sys.std.Core.Relation.is_proper_subset except that it transposes the topic and other arguments. This function is exactly the same as sys.std.Core.Relation.is_superset except that it results in Bool:False if its 2 arguments are identical. Note that this operation is also known as ⊃ or psuper.
sys.std.Core.Relation.is_not_proper_superset
function sys.std.Core.Relation.is_not_proper_superset (Bool <-- $topic : Relation, $other : Relation) {...}
This function is an alias for sys.std.Core.Relation.is_not_proper_subset except that it transposes the topic and other arguments. This function is exactly the same as sys.std.Core.Relation.is_proper_superset except that it results in the opposite boolean value when given the same arguments. Note that this operation is also known as ⊅ or !psuper or not-psuper.
sys.std.Core.Relation.is_disjoint
function sys.std.Core.Relation.is_disjoint (Bool <-- $topic : Relation, $other : Relation) {...}
This symmetric function results in Bool:True iff the set of tuples comprising each of its 2 arguments are mutually disjoint, that is, iff the intersection of the 2 arguments is empty; it results in Bool:False otherwise.
sys.std.Core.Relation.is_not_disjoint
function sys.std.Core.Relation.is_not_disjoint (Bool <-- $topic : Relation, $other : Relation) {...}
This symmetric function is exactly the same as sys.std.Core.Relation.is_disjoint except that it results in the opposite boolean value when given the same arguments.
sys.std.Core.Relation.union
function sys.std.Core.Relation.union (Relation <-- $topic : set_of.Relation) {...}
This function results in the relational union/inclusive-or of the N element values of its argument; 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 inputs, and its body contains every tuple that is in any of the input relations. If topic has zero values, then this function will fail. Note that, conceptually union does have an identity value which could be this function's result when topic has zero values, which is the empty relation with the same heading, which is the per-distinct-heading identity value for relational union; however, since a topic with zero values wouldn't know the heading / attribute names for the result relation in question, it seems the best alternative is to require invoking code to work around the limitation somehow, which might mean it will supply the identity value explicitly as an extra topic element. Note that this operation is also known as ∪.
sys.std.Core.Relation.disjoint_union
function sys.std.Core.Relation.disjoint_union (Relation <-- $topic : set_of.Relation) {...}
This function is exactly the same as sys.std.Core.Relation.union except that it will fail if any 2 input values have a tuple in common.
sys.std.Core.Relation.exclusion
function sys.std.Core.Relation.exclusion (Relation <-- $topic : bag_of.Relation) {...}
This function results in the relational exclusion/exclusive-or of the N element values of its argument; 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 inputs, and its body contains every tuple that is in just an odd number of the input relations. Matters concerning a topic with zero values are as per sys.std.Core.Relation.union; this function will fail when given such, and the per-distinct-heading identity value for relational exclusion is the same as for relational union. Note that this operation is also known as symmetric difference or ∆.
sys.std.Core.Relation.symmetric_diff
function sys.std.Core.Relation.symmetric_diff (Relation <-- $topic : bag_of.Relation) {...}
This function is an alias for sys.std.Core.Relation.exclusion.
sys.std.Core.Relation.intersection
function sys.std.Core.Relation.intersection (Relation <-- $topic : set_of.Relation) {...}
This function results in the relational intersection/and of the N element values of its argument; 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 inputs, and its body contains only the tuples that are in every one of the input relations. If topic has zero values, then this function will fail. Note that, conceptually intersection does have an identity value which could be this function's result when topic has zero values, which is the universal relation with the same heading (that is, the relation having all the tuples that could ever exist in a relation with that heading), which is the per-distinct-heading identity value for relational intersection; however, since a topic with zero values wouldn't know the heading / attribute names for the result relation in question (and even if they were, more information on attribute types would be needed to produce said universal relation, and even then it might be infinite or impossibly large), it seems the best alternative is to require invoking code to work around the limitation somehow, which might mean it will supply the identity value explicitly as an extra topic element. Note that this intersection operator is conceptually a special case of join, applicable when the headings of the inputs are the same, and the other will produce the same result as this when given the same inputs, but with the exception that intersection has a different identity value when given zero inputs. Note that this operation is also known as ∩.
sys.std.Core.Relation.diff
function sys.std.Core.Relation.diff (Relation <-- $source : Relation, $filter : Relation) {...}
This function results in the relational difference when its filter argument is subtracted from its source argument. The result relation has the same heading as both of its arguments, and its body contains only the tuples that are in source and are not in filter. This function will warn if the input relations common-named attributes have declared types that are incompatible as per is_identical. Note that this difference 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 ∖.
sys.std.Core.Relation.semidiff
function sys.std.Core.Relation.semidiff (Relation <-- $source : Relation, $filter : Relation) {...}
This function 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 ⊿.
sys.std.Core.Relation.antijoin
function sys.std.Core.Relation.antijoin (Relation <-- $source : Relation, $filter : Relation) {...}
This function is an alias for sys.std.Core.Relation.semidiff.
sys.std.Core.Relation.semijoin_and_diff
function sys.std.Core.Relation.semijoin_and_diff (Tuple <-- $source : Relation, $filter : Relation) {...}
This function performs a 2-way partitioning of all the tuples of source and results in a binary tuple whose attribute values are each relations that have the same heading as source and complementary subsets of its tuples; the 2 result attributes have the names pass and fail, and their values are what sys.std.Core.Relation.semijoin and sys.std.Core.Relation.semidiff, respectively, would result in when given the same arguments.
sys.std.Core.Relation.semijoin
function sys.std.Core.Relation.semijoin (Relation <-- $source : Relation, $filter : Relation) {...}
This function results in the relational semijoin of its source and filter arguments. 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 its 2 arguments, and then performing a relational projection on all of the attributes that just source has. This function will fail|warn any time that join would fail|warn on the same 2 input relations. Note that this operation is also known as matching or ⋉.
sys.std.Core.Relation.join
function sys.std.Core.Relation.join (Relation <-- $topic? : set_of.Relation) {...}
This function results in the relational join of the N element values of its argument; 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 inputs, 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. If topic has zero values, then join results in the nullary relation with one tuple, which is the identity value for relational join. As a trivial case, if any input relation has zero tuples, then the function'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. This function will warn if any input relations have attributes with common names where their declared types are incompatible as per is_identical. Note that this operation is also known as natural inner join or ⋈.
sys.std.Core.Relation.product
function sys.std.Core.Relation.product (Relation <-- $topic? : set_of.Relation) {...}
This function results in the relational cartesian/cross product of the N element values of its argument; 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 ×.
sys.std.Core.Relation.quotient
function sys.std.Core.Relation.quotient (Relation <-- $dividend : Relation, $divisor : Relation) {...}
This function results in the quotient when its dividend argument 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 ÷.
sys.std.Core.Relation.composition
function sys.std.Core.Relation.composition (Relation <-- $topic : Relation, $other : Relation) {...}
This symmetric function results in the relational composition of its 2 arguments. It is conceptually a short-hand for first doing an ordinary relational join between its 2 arguments, 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 2 arguments. This function will fail|warn any time that join would fail|warn on the same 2 input relations.
sys.std.Core.Relation.join_with_group
function sys.std.Core.Relation.join_with_group (Relation <-- $primary : Relation, $secondary : Relation, $group_attr : Name) {...}
This function is a short-hand for first taking a (natural inner) join of its primary and secondary arguments, 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 function will fail if group_attr is the same name as any source attribute that wasn't grouped. This function 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.
FUNCTIONS FOR RELATIONAL RANKING AND QUOTAS
These additional functions are specific to supporting ranking and quotas.
sys.std.Core.Relation.rank
function sys.std.Core.Relation.rank (Relation <-- $topic : Relation, $name : Name, $ord_func : OrdDetCFuncNC, $is_reverse_order? : Bool, $first_rank? : NNInt) {...}
This function results in the relational extension of its topic argument by a single NNInt-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 (total) order-determination function named in the ord_func argument when the latter function is curried by the is_reverse_order argument. The order-determination function compares tuples, with each invocation of it getting a topic tuple as each its topic and other arguments. The new attribute of rank's result has the value of the first_rank argument (that defaults to zero if not explicitly given) 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 (as per a (total) order-determination function) and so there is no "dense" / "not dense" distinction (however a partial ordering can be implemented over it). See also the sys.std.Core.Array.Array_from_wrap function, which is the same as sys.std.Core.Relation.rank but that it wraps the source tuples rather than just adding an attribute to them. The main purpose of the first_rank parameter is to support rank being used as a sequence generator to attach non-descriptive id attributes to a set of tuples that are about to be added to a database, where we want to start the sequence larger than the largest id value already in use there; granted, for that purpose the new ids don't have to be ordered, just distinct, but ordering is necessary for this setwise operation to remain deterministic.
sys.std.Core.Relation.rank_by_attr_names
function sys.std.Core.Relation.rank_by_attr_names (Relation <-- $topic : Relation, $name : Name, $order_by : array_of.OrderByName, $is_reverse_order? : Bool, $first_rank? : NNInt) {...}
This function is a short-hand for invoking rank with the function sys.std.Core.Tuple.order_by_attr_names as its ord_func argument after the latter is curried with this function's order_by argument.
sys.std.Core.Relation.limit
function sys.std.Core.Relation.limit (Relation <-- $topic : Relation, $ord_func : OrdDetCFuncNC, $is_reverse_order? : Bool, $rank_interval : sp_interval_of.NNInt) {...}
This function results in the relational restriction of its topic argument as determined by first ranking its tuples as per the rank function (using ord_func and is_reverse_order) and then keeping just those tuples whose rank is included within the interval specified by the rank_interval argument (rank's extra attribute is not kept). The limit function implements a certain kind of quota query where all the result tuples are consecutive in their ranks. It is valid for the lowest and highest rank specified by rank_interval 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 the lowest rank, if any. 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 (but see sys.std.Core.Array.limit_of_Array_from_wrap for an alternative).
sys.std.Core.Relation.limit_by_attr_names
function sys.std.Core.Relation.limit_by_attr_names (Relation <-- $topic : Relation, $order_by : array_of.OrderByName, $is_reverse_order? : Bool, $rank_interval : sp_interval_of.NNInt) {...}
This function is to limit what rank_by_attr_names is to rank.
FUNCTIONS FOR RELATIONAL ATTRIBUTE VALUE SUBSTITUTIONS
These additional functions are specific to supporting substitutions.
sys.std.Core.Relation.substitution
function sys.std.Core.Relation.substitution (Relation <-- $topic : Relation, $attr_names : set_of.Name, $func : ValMapCFuncNC) {...}
This function 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 value-map function named in func must have a heading that is a subset of the heading of topic; corresponding values resulting from the function named 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 function results simply in topic; or, if func is defined to have a static result and it replaces all attributes, then this function'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 function'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 function 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.
sys.std.Core.Relation.static_subst
function sys.std.Core.Relation.static_subst (Relation <-- $topic : Relation, $attrs : Tuple) {...}
This function is a simpler-syntax alternative to sys.std.Core.Relation.substitution in the typical scenario where every tuple of a relation, given in the topic argument, is updated with identical values for the same attributes; the new attribute values are given in the attrs argument.
sys.std.Core.Relation.subst_in_restr
function sys.std.Core.Relation.subst_in_restr (Relation <-- $topic : Relation, $restr_func : ValFiltCFuncNC, $subst_attr_names : set_of.Name, $subst_func : ValMapCFuncNC) {...}
This function 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 function, 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.
sys.std.Core.Relation.static_subst_in_restr
function sys.std.Core.Relation.static_subst_in_restr (Relation <-- $topic : Relation, $restr_func : ValFiltCFuncNC, $subst : Tuple) {...}
This function is to sys.std.Core.Relation.subst_in_restr what sys.std.Core.Relation.static_subst is to sys.std.Core.Relation.substitution. See also the static_subst_in_semijoin function.
sys.std.Core.Relation.subst_in_semijoin
function sys.std.Core.Relation.subst_in_semijoin (Relation <-- $topic : Relation, $restr : Relation, $subst_attr_names : set_of.Name, $subst_func : ValMapCFuncNC) {...}
This function 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.
sys.std.Core.Relation.static_subst_in_semijoin
function sys.std.Core.Relation.static_subst_in_semijoin (Relation <-- $topic : Relation, $restr : Relation, $subst : Tuple) {...}
This function is to sys.std.Core.Relation.subst_in_semijoin what sys.std.Core.Relation.static_subst is to sys.std.Core.Relation.substitution.
FUNCTIONS FOR RELATIONAL OUTER-JOINS
These additional functions are specific to supporting outer-joins.
sys.std.Core.Relation.outer_join_with_group
function sys.std.Core.Relation.outer_join_with_group (Relation <-- $primary : Relation, $secondary : Relation, $group_attr : Name) {...}
This function is the same as sys.std.Core.Relation.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+.
sys.std.Core.Relation.outer_join_with_maybes
function sys.std.Core.Relation.outer_join_with_maybes (Relation <-- $primary : Relation, $secondary : Relation) {...}
This function results in a plain half-outer natural join of its primary and secondary arguments where all the result attributes that come from just secondary are Maybe-typed; for result tuples from matched source tuples, each secondary attribute value is a Single; for result tuples from non-matched primary tuples, each secondary attribute value is Nothing. The outer_join_with_maybes function is Muldis D's answer to the SQL LEFT OUTER JOIN where SQL NULL is implicitly used in result rows that were a non-match.
sys.std.Core.Relation.outer_join_with_defaults
function sys.std.Core.Relation.outer_join_with_defaults (Relation <-- $primary : Relation, $secondary : Relation, $filler : APTypeNC) {...}
This function is the same as sys.std.Core.Relation.outer_join_with_static_exten but that the filler tuple is the default value of the tuple data type whose name is given in the filler argument. This function is a short-hand for invoking outer_join_with_static_exten with the result from invoking sys.std.Core.Universal.default.
sys.std.Core.Relation.outer_join_with_static_exten
function sys.std.Core.Relation.outer_join_with_static_exten (Relation <-- $primary : Relation, $secondary : Relation, $filler : Tuple) {...}
This function is the same as sys.std.Core.Relation.outer_join_with_maybes but that secondary-sourced result attributes are not converted to Maybe; rather, for result tuples from non-matches, the missing values are provided explicitly from the filler argument, which is a tuple whose heading matches the projection of secondary's attributes that aren't in common with primary, and whose body is the specific values to use for those missing attribute values.
sys.std.Core.Relation.outer_join_with_exten
function sys.std.Core.Relation.outer_join_with_exten (Relation <-- $primary : Relation, $secondary : Relation, $exten_func : ValMapCFuncNC) {...}
This function is the same as sys.std.Core.Relation.outer_join_with_static_exten but that the result tuples from non-matches are the result of performing a relational extension on the un-matched primary tuples such that each said result tuple is determined by applying the function named in exten_func to each said primary tuple.
GENERIC UPDATERS FOR RELATION VARIABLES
Updaters That Rename Attributes
sys.std.Core.Relation.assign_rename
updater sys.std.Core.Relation.assign_rename (&$topic : Relation, $map : AttrRenameMap) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.rename function with the same arguments, and then assigning the result of that function to topic. This procedure is analogous to the data-manipulation phase of a SQL ALTER TABLE|VIEW RENAME COLUMN statement; each tuple of map corresponds to a renamed SQL table column.
Updaters That Add Attributes
sys.std.Core.Relation.assign_extension
updater sys.std.Core.Relation.assign_extension (&$topic : Relation, $attr_names : set_of.Name, $func : ValMapCFuncNC) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.extension function with the same arguments, and then assigning the result of that function to topic.
sys.std.Core.Relation.assign_static_exten
updater sys.std.Core.Relation.assign_static_exten (&$topic : Relation, $attrs : Tuple) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.static_exten function with the same arguments, and then assigning the result of that function to topic. This procedure is analogous to the data-manipulation phase of a SQL ALTER TABLE|VIEW ADD COLUMN statement; each attribute of attrs corresponds to an added SQL table column.
Updaters That Remove Attributes
sys.std.Core.Relation.assign_projection
updater sys.std.Core.Relation.assign_projection (&$topic : Relation, $attr_names : set_of.Name) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.projection function with the same arguments, and then assigning the result of that function to topic.
sys.std.Core.Relation.assign_cmpl_proj
updater sys.std.Core.Relation.assign_cmpl_proj (&$topic : Relation, $attr_names : set_of.Name) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.cmpl_proj function with the same arguments, and then assigning the result of that function to topic. This procedure is analogous to the data-manipulation phase of a SQL ALTER TABLE|VIEW DROP COLUMN statement; each attribute named by attr_names corresponds to a dropped SQL table column.
Updaters That Add Tuples
sys.std.Core.Relation.assign_insertion
updater sys.std.Core.Relation.assign_insertion (&$r : Relation, $t : Tuple) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.insertion function with the same arguments, and then assigning the result of that function to r. This updater is analogous to the general case of the single-row SQL "INSERT" statement.
sys.std.Core.Relation.assign_disjoint_ins
updater sys.std.Core.Relation.assign_disjoint_ins (&$r : Relation, $t : Tuple) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.disjoint_ins function with the same arguments, and then assigning the result of that function to r.
sys.std.Core.Relation.assign_union
updater sys.std.Core.Relation.assign_union (&$topic : Relation, $other : Relation) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.union function such that it has 2 input relations from assign_union's 2 arguments, and then assigning the result of that function to topic. Note that this operation is also known as :=union or :=∪. This updater is analogous to the general case of the multiple-row SQL "INSERT" statement.
sys.std.Core.Relation.assign_disjoint_union
updater sys.std.Core.Relation.assign_disjoint_union (&$topic : Relation, $other : Relation) {...}
This update operator is to sys.std.Core.Relation.disjoint_union what the function sys.std.Core.Relation.assign_union is to sys.std.Core.Relation.union.
Updaters That Remove Tuples
sys.std.Core.Relation.assign_empty
updater sys.std.Core.Relation.assign_empty (&$topic : Relation) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.empty function with the same argument, and then assigning the result of that function to topic. This updater is analogous to the SQL "TRUNCATE" statement.
sys.std.Core.Relation.assign_deletion
updater sys.std.Core.Relation.assign_deletion (&$r : Relation, $t : Tuple) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.deletion function with the same arguments, and then assigning the result of that function to r.
sys.std.Core.Relation.assign_restriction
updater sys.std.Core.Relation.assign_restriction (&$topic : Relation, $func : ValFiltCFuncNC) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.restriction function with the same arguments, and then assigning the result of that function to topic. Note that this operation is also known as :=where.
sys.std.Core.Relation.assign_cmpl_restr
updater sys.std.Core.Relation.assign_cmpl_restr (&$topic : Relation, $func : ValFiltCFuncNC) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.cmpl_restr function with the same arguments, and then assigning the result of that function to topic. Note that this operation is also known as :=!where or :=not-where. This updater is analogous to the general case of the SQL "DELETE" statement.
sys.std.Core.Relation.assign_intersection
updater sys.std.Core.Relation.assign_intersection (&$topic : Relation, $other : Relation) {...}
This update operator is to sys.std.Core.Relation.intersection what the function sys.std.Core.Relation.assign_union is to sys.std.Core.Relation.union. Note that this operation is also known as :=intersect or :=∩.
sys.std.Core.Relation.assign_diff
updater sys.std.Core.Relation.assign_diff (&$source : Relation, $filter : Relation) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.diff function with the same arguments, and then assigning the result of that function to source. Note that this operation is also known as :=minus or :=except or :=∖.
sys.std.Core.Relation.assign_semidiff
updater sys.std.Core.Relation.assign_semidiff (&$source : Relation, $filter : Relation) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.semidiff function with the same arguments, and then assigning the result of that function to source. Note that this operation is also known as :=antijoin or :=semiminus or :=!matching or :=not-matching or :=⊿. This updater is analogous to the common case of the SQL "DELETE" statement where the criteria is simply a set of and-ed and or-ed value equality tests.
sys.std.Core.Relation.assign_antijoin
updater sys.std.Core.Relation.assign_antijoin (&$source : Relation, $filter : Relation) {...}
This update operator is an alias for sys.std.Core.Relation.assign_semidiff.
sys.std.Core.Relation.assign_semijoin
updater sys.std.Core.Relation.assign_semijoin (&$source : Relation, $filter : Relation) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.semijoin function with the same arguments, and then assigning the result of that function to source. Note that this operation is also known as :=semijoin or :=matching or :=⋉.
Updaters That Add and Remove Tuples
sys.std.Core.Relation.assign_exclusion
updater sys.std.Core.Relation.assign_exclusion (&$topic : Relation, $other : Relation) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.exclusion function such that it has 2 input relations from assign_exclusion's 2 arguments, and then assigning the result of that function to topic. Note that this operation is also known as :=exclude or :=symdiff or :=∆.
Updaters That Substitute Tuple Attribute Values
sys.std.Core.Relation.assign_substitution
updater sys.std.Core.Relation.assign_substitution (&$topic : Relation, $attr_names : set_of.Name, $func : ValMapCFuncNC) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.substitution function with the same arguments, and then assigning the result of that function to topic. This updater is analogous to the general case of the unconditional SQL "UPDATE" statement.
sys.std.Core.Relation.assign_static_subst
updater sys.std.Core.Relation.assign_static_subst (&$topic : Relation, $attrs : Tuple) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.static_subst function with the same arguments, and then assigning the result of that function to topic.
sys.std.Core.Relation.assign_subst_in_restr
updater sys.std.Core.Relation.assign_subst_in_restr (&$topic : Relation, $restr_func : ValFiltCFuncNC, $subst_attr_names : set_of.Name, $subst_func : ValMapCFuncNC) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.subst_in_restr function with the same arguments, and then assigning the result of that function to topic. This updater is analogous to the general case of the conditional SQL "UPDATE" statement.
sys.std.Core.Relation.assign_static_subst_in_restr
updater sys.std.Core.Relation.assign_static_subst_in_restr (&$topic : Relation, $restr_func : ValFiltCFuncNC, $subst : Tuple) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.static_subst_in_restr function with the same arguments, and then assigning the result of that function to topic.
sys.std.Core.Relation.assign_subst_in_semijoin
updater sys.std.Core.Relation.assign_subst_in_semijoin (&$topic : Relation, $restr : Relation, $subst_attr_names : set_of.Name, $subst_func : ValMapCFuncNC) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.subst_in_semijoin function with the same arguments, and then assigning the result of that function to topic. This updater is analogous to the common case of the conditional SQL "UPDATE" statement where the criteria is simply a set of and-ed and or-ed value equality tests.
sys.std.Core.Relation.assign_static_subst_in_semijoin
updater sys.std.Core.Relation.assign_static_subst_in_semijoin (&$topic : Relation, $restr : Relation, $subst : Tuple) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Relation.static_subst_in_semijoin function with the same arguments, and then assigning the result of that function to topic.
SEE ALSO
Go to Muldis::D for the majority of distribution-internal references, and Muldis::D::SeeAlso for the majority of distribution-external references.
AUTHOR
Darren Duncan (darren@DarrenDuncan.net)
LICENSE AND COPYRIGHT
This file is part of the formal specification of the Muldis D language.
Muldis D is Copyright © 2002-2010, Muldis Data Systems, Inc.
See the LICENSE AND COPYRIGHT of Muldis::D for details.
TRADEMARK POLICY
The TRADEMARK POLICY in Muldis::D applies to this file too.
ACKNOWLEDGEMENTS
The ACKNOWLEDGEMENTS in Muldis::D apply to this file too.