NAME
Muldis::D::Ext::Ordered - Muldis D extension for generic ordered-sensitive operators
VERSION
This document is Muldis::D::Ext::Ordered version 0.97.0.
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.
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 used to bootstrap the 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 Ordered document describes the system-defined Muldis D Ordered Extension, which consists of generic operators that are sensitive to an ordering of a type's values, and are used for such things as list sorting or quota queries or determining before/after/min/max/between/etc. They can potentially be used with values of any data type as long as said data type has a (total) order-determination function defined for it, and all system-defined conceptually-ordered Muldis D scalar root types do.
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::Core.
This documentation is pending.
SYSTEM-DEFINED ORDER-CONCERNING FUNCTIONS
Each of these functions which has the parameter named func is a wrapper over the order-determination function named in its func argument when the latter function is curried by a calling-function-specific is_reverse_order argument value. For any scalar root type's type-default order function, the argument for func is sys.std.Core.Scalar.order. Each func parameter is optional and defaults to sys.std.Core.Scalar.order if no explicit argument is given to it.
These functions' Interval-typed arguments' min and max attribute values must be of compatible declared types with the wrapped functions' topic and other parameters; otherwise these functions will fail|warn when the wrapped function would. Likewise, any other argument values would be compared to an interval's endpoints must be compatible with them.
sys.std.Ordered.is_before
function sys.std.Ordered.is_before (Bool <-- $topic : Universal, $other : Universal, $func? : OrdDetFuncRef)
This function results in Bool:true iff the wrapped function would result in Order:increase when given the same corresponding 2 arguments plus a is_reverse_order argument of Bool:false, and Bool:false otherwise. Note that this operation is also known as less than or <.
sys.std.Ordered.is_after
function sys.std.Ordered.is_after (Bool <-- $topic : Universal, $other : Universal, $func? : OrdDetFuncRef)
This function is an alias for sys.std.Ordered.is_before except that it transposes the topic and other arguments. This function results in Bool:true iff the wrapped function would result in Order:decrease when given the same corresponding 2 arguments plus a is_reverse_order argument of Bool:false, and Bool:false otherwise. Note that this operation is also known as greater than or >.
sys.std.Ordered.is_before_or_same
function sys.std.Ordered.is_before_or_same (Bool <-- $topic : Universal, $other : Universal, $func? : OrdDetFuncRef)
This function is exactly the same as sys.std.Ordered.is_before except that it results in Bool:true if its 2 primary arguments are identical. Note that this operation is also known as less than or equal to or ≤.
sys.std.Ordered.is_after_or_same
function sys.std.Ordered.is_after_or_same (Bool <-- $topic : Universal, $other : Universal, $func? : OrdDetFuncRef)
This function is an alias for sys.std.Ordered.is_before_or_same except that it transposes the topic and other arguments. This function is exactly the same as sys.std.Ordered.is_after except that it results in Bool:true if its 2 primary arguments are identical. Note that this operation is also known as greater than or equal to or ≥.
sys.std.Ordered.is_member
function sys.std.Ordered.is_member (Bool <-- $value : Universal, $interval : Interval, $func? : OrdDetFuncRef)
This function is an alias for sys.std.Interval.has_member. This function results in Bool:true iff its value argument is included within the interval defined by its interval argument, and Bool:false otherwise. That is, if conceptually the interval represents a set of values, this function tests if value is a member of interval. Note that this operation is also known as I∈ or between, and depending on the combination of excludes_[min|max] attributes of its interval argument, it is alternately also known as one of [≤≤, ≤<, <≤, <<].
sys.std.Ordered.is_not_member
function sys.std.Ordered.is_not_member (Bool <-- $value : Universal, $interval : Interval, $func? : OrdDetFuncRef)
This function is an alias for sys.std.Interval.has_not_member. This function is exactly the same as sys.std.Ordered.is_member except that it results in the opposite boolean value when given the same arguments. Note that this operation is also known as I¬in; or not between, and depending on the combination of excludes_[min|max] attributes of its interval argument, it is alternately also known as one of [!≤≤, !≤<, !<≤, !<<].
sys.std.Ordered.min
function sys.std.Ordered.min (Universal <-- $topic : Set, $func? : OrdDetFuncRef)
This function is a reduction operator that recursively takes each pair of its N input element values and picks the minimum of the 2 (which is commutative, associative, and idempotent) until just one is left, which is the function's result. If topic has zero values, then this function will fail. Note that, conceptually min does have an identity value which could be this function's result when topic has zero values, which is the result type's concept of positive infinity; however, in practice there is little benefit to min supporting this identity value, since the wrapped order-determination function can't supply the value, and also many types' concept of positive infinity is impossible or impractically large to represent, such as with the infinite Text type.
sys.std.Ordered.max
function sys.std.Ordered.max (Universal <-- $topic : Set, $func? : OrdDetFuncRef)
This function is exactly the same as sys.std.Ordered.min except that it results in the maximum input element value rather than the minimum one. (Note that, conceptually max has an identity value which is the result type's concept of negative infinity, but it is unsupported here).
sys.std.Ordered.minmax
function sys.std.Ordered.minmax (Tuple <-- $topic : Set, $func? : OrdDetFuncRef)
This function results in a binary tuple whose attribute names are min and max and whose respective attribute values are what sys.std.Ordered.min and sys.std.Ordered.max would result in when given the same arguments. If topic has zero values, then this function will fail.
sys.std.Ordered.maybe_min
function sys.std.Ordered.maybe_min (Maybe <-- $topic : Set, $func? : OrdDetFuncRef)
This function is exactly the same as sys.std.Ordered.min except that it results in a Maybe of what is otherwise the result type, and that result has zero elements if the argument has zero elements, rather than the function failing.
sys.std.Ordered.maybe_max
function sys.std.Ordered.maybe_max (Maybe <-- $topic : Set, $func? : OrdDetFuncRef)
This function is to sys.std.Ordered.max as sys.std.Ordered.maybe_min is to sys.std.Ordered.min.
sys.std.Ordered.maybe_minmax
function sys.std.Ordered.maybe_minmax (Relation <-- $topic : Set, $func? : OrdDetFuncRef)
This function results in a binary relation whose attribute names are min and max. If topic has zero values then the result has a single tuple whose respective attribute values are what sys.std.Ordered.min and sys.std.Ordered.max would result in when given the same arguments; if topic has zero values, then the result has zero tuples.
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 (perl@DarrenDuncan.net)
LICENSE AND COPYRIGHT
This file is part of the formal specification of the Muldis D language.
Muldis D is Copyright © 2002-2009, 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.