NAME

Muldis::D::Outdated::Ext::Counted - Muldis D extension for count-sensitive relational operators

VERSION

This document is Muldis::D::Outdated::Ext::Counted version 0.148.2.

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.

DESCRIPTION

Muldis D has a mandatory core set of system-defined (eternally available) entities, which is referred to as the Muldis D core or the core; they are the minimal entities that all Muldis D implementations need to provide; they are mutually self-describing and are either used to bootstrap the language or they constitute a reasonable minimum level of functionality for a practically useable industrial-strength (and fully TTM-conforming) programming language; any entities outside the core, called Muldis D extensions, are non-mandatory and are defined in terms of the core or each other, but the reverse isn't true.

This current Counted document describes the system-defined Muldis D Counted Extension, which consists of relational operators that are sensitive to special relation attributes that store count metadata as if the relation conceptually was a bag of tuples rather than a set of tuples. This extension doesn't introduce any new data types, and its operators all range over ordinary relations. The operators do not assume that their argument relations have attributes of any particular names, including that count-containing attributes have any particular names; rather, each operator is told what attributes to treat as special by taking extra explicit parameters specifying their names. The operators are all short-hands for generic relational operators either in the language core or in other language extensions. The Muldis D Counted Extension differs from the Muldis D Bag Extension in that the latter deals just with Bag binary relations with specific attribute names while the former works with any relations at all.

This current document does not describe the polymorphic operators that all types, or some types including core types, have defined over them; said operators are defined once for all types in Muldis::D::Outdated::Core.

This documentation is pending.

GENERIC RELATIONAL FUNCTIONS THAT MAINTAIN COUNT ATTRIBUTES

Every one of these functions that takes a count_attr_name argument is expecting that each of any other applicable arguments will have an attribute whose name matches that given in count_attr_name and that the type of this attribute is PInt; said functions will fail if these conditions aren't met. For brevity, this documentation will hereafter refer to the attribute named in count_attr_name as tcount, and moreafter it will refer to the collection of all attributes except tcount as tattrs.

sys.std.Counted.add_count_attr

function add_count_attr (Relation <-- topic : Relation, count_attr_name : Name) {...}

This function is a shorthand for sys.std.Core.Relation.static_exten that adds to topic a single tcount attribute whose value for all tuples is 1. This function conceptually converts a set of tuples into a bag of tuples, of multiplicity 1 per tuple.

sys.std.Counted.remove_count_attr

function remove_count_attr (Relation <-- topic : Relation, count_attr_name : Name) {...}

This function is a shorthand for sys.std.Core.Relation.cmpl_proj that removes from topic the single tcount attribute. This function conceptually converts a bag of tuples into a set of tuples, elimimating all duplicates.

sys.std.Counted.counted_cardinality

function counted_cardinality (NNInt <-- topic : Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.cardinality but that it accounts for the greater-than-one conceptual multiplicity of tuples in its topic argument; it results in the sum of the tcount attribute of its topic argument.

sys.std.Counted.counted_has_member

function counted_has_member (Bool <-- r : Relation, t : Tuple, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.has_member except that t must have one fewer attribute than r does, specifically tcount (and otherwise they must have the same headings).

sys.std.Counted.counted_has_not_member

function counted_has_not_member (Bool <-- r : Relation, t : Tuple, count_attr_name : Name) {...}

This function is exactly the same as sys.std.Counted.counted_has_member except that it results in the opposite boolean value when given the same arguments.

sys.std.Counted.counted_insertion

function counted_insertion (Relation <-- r : Relation, t : Tuple, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.insertion as per counted_has_member but that its result differs depending on whether t already exists in r; if it does, then no new tuple is added, but the tcount attribute for the matching tuple is incremented by 1; if it does not, then a new tuple is added where its tattrs is t and its tcount is 1. Actually this function differs in another way, such that it is semantically the single-tuple case of sys.std.Counted.counted_union_sum, and is not the single-tuple case of sys.std.Counted.counted_union (which is the direct analogy to set union).

sys.std.Counted.counted_deletion

function counted_deletion (Relation <-- r : Relation, t : Tuple, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.deletion as per counted_has_member but that its result differs depending on what the tcount for any tuple matching t that already exists in r is; if the tcount is greater than 1, then it is decremented by 1; if it is equal to 1, then the tuple whose tattrs is t is deleted.

sys.std.Counted.counted_projection

function counted_projection (Relation <-- topic : Relation, attr_names : set_of.Name, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.projection except that the counted_cardinality of the result is guaranteed to be the same as that of topic rather than possibly less. The topic argument must have a tcount attribute and attr_names must not specify that attribute; the result has the just attributes of topic named by attr_names plus the tcount attribute.

sys.std.Counted.counted_cmpl_proj

function counted_cmpl_proj (Relation <-- topic : Relation, attr_names : set_of.Name, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.cmpl_proj except that the counted_cardinality of the result is guaranteed to be the same as that of topic rather than possibly less. The topic argument must have a tcount attribute and attr_names must not specify that attribute; the result has the just the attributes of topic not named by attr_names including the tcount attribute.

sys.std.Counted.counted_reduction

function counted_reduction (Tuple <-- topic : Relation, func : ValRedPFuncNC, identity : Tuple, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.reduction except that func is invoked extra times, where both its v1 and v2 arguments might be different instances of the same tattrs tuple having >= 2 multiplicity. This function's topic argument has a tcount attribute while its identity argument does not, and both the result tuple of func and its v1 and v2 arguments don't have the tcount attribute either.

sys.std.Counted.counted_map

function counted_map (Relation <-- topic : Relation, result_attr_names : set_of.Name, func : ValMapPFuncNC, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.map except that the counted_cardinality of the result is guaranteed to be the same as that of topic rather than possibly less. The topic argument must have a tcount attribute and result_attr_names must not specify that attribute; the result has the attributes named in result_attr_names plus the tcount attribute. Both the result tuple of func and its topic argument don't have the tcount attribute.

sys.std.Counted.counted_is_subset

function counted_is_subset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.is_subset but that it accounts for the greater-than-one multiplicity of tattrs in its topic and other arguments, both of which have a tcount attribute; this function returns Bool:True iff the multiplicity of each topic value is less than or equal to the multiplicity of its counterpart other value.

sys.std.Counted.counted_is_not_subset

function counted_is_not_subset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.is_not_subset as per counted_is_subset.

sys.std.Counted.counted_is_superset

function counted_is_superset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is an alias for sys.std.Counted.counted_is_subset except that it transposes the topic and other arguments. This function is like sys.std.Core.Relation.is_superset but that it accounts for the greater-than-one multiplicity of tattrs in its topic and other arguments, both of which have a tcount attribute; this function returns Bool:True iff the multiplicity of each topic value is greater than or equal to the multiplicity of its counterpart other value.

sys.std.Counted.counted_is_not_superset

function counted_is_not_superset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is an alias for sys.std.Counted.counted_is_not_subset except that it transposes the topic and other arguments. This function is like sys.std.Core.Relation.is_not_superset as per counted_is_superset.

sys.std.Counted.counted_is_proper_subset

function counted_is_proper_subset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.is_proper_subset as per counted_is_subset. TODO: What is its definition?

sys.std.Counted.counted_is_not_proper_subset

function counted_is_not_proper_subset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.is_not_proper_subset as per counted_is_subset. TODO: What is its definition?

sys.std.Counted.counted_is_proper_superset

function counted_is_proper_superset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is an alias for sys.std.Counted.counted_is_proper_subset except that it transposes the topic and other arguments. This function is like sys.std.Core.Relation.is_proper_superset as per counted_is_superset.

sys.std.Counted.counted_is_not_proper_superset

function counted_is_not_proper_superset (Bool <-- topic : Relation, other : Relation, count_attr_name : Name) {...}

This function is an alias for sys.std.Counted.counted_is_not_proper_subset except that it transposes the topic and other arguments. This function is like sys.std.Core.Relation.is_not_proper_superset as per counted_is_superset.

sys.std.Counted.counted_union

function counted_union (Relation <-- topic : set_of.Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.union but that it just looks at the tattrs attributes of its argument elements when determining what element tuples correspond; then for each tuple in the result, its tcount attribute value is the maximum of the tcount attribute values of its corresponding input element tuples.

sys.std.Counted.counted_union_sum

function counted_union_sum (Relation <-- topic : bag_of.Relation, count_attr_name : Name) {...}

This function is like sys.std.Counted.counted_union but that for each pair of argument elements being unioned, the output tcount value is the sum of the input tcount values rather than being the maximum of the inputs. This function is the nearest Muldis D analogy to the SQL "UNION ALL" operation, versus sys.std.Core.Relation.union which is the nearest analogy to "UNION DISTINCT".

sys.std.Counted.counted_intersection

function counted_intersection (Relation <-- topic : set_of.Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.intersection as counted_union is like sys.std.Core.Relation.union; the minimum of tcount attribute values is used rather than the maximum.

sys.std.Counted.counted_diff

function counted_diff (Relation <-- source : Relation, filter : Relation, count_attr_name : Name) {...}

This function is like sys.std.Core.Relation.diff as counted_union is like sys.std.Core.Relation.union; for corresponding input tuples, the result only has a tuple with the same tattrs if the tcount of the source tuple is greater than the tcount of the filter tuple, and the tcount of the result tuple is the difference of those two.

sys.std.Counted.counted_substitution

function counted_substitution (Relation <-- topic : Relation, attr_names : set_of.Name, func : ValMapPFuncNC, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.substitution except that the counted_cardinality of the result is guaranteed to be the same as that of topic rather than possibly less. The topic argument must have a tcount attribute and attr_names must not specify that attribute.

sys.std.Counted.counted_static_subst

function counted_static_subst (Relation <-- topic : Relation, attrs : Tuple, count_attr_name : Name) {...}

This function is the same as sys.std.Core.Relation.static_subst except that the counted_cardinality of the result is guaranteed to be the same as that of topic rather than possibly less. The topic argument must have a tcount attribute and attrs must not have that attribute.

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 © 2002-2011, 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.

cpanm Muldis::D::Outdated::Ext::Counted

perl -MCPAN -e shell
install Muldis::D::Outdated::Ext::Counted