NAME
Muldis::D::Core::Ordered - Muldis D generic ordered-sensitive operators
VERSION
This document is Muldis::D::Core::Ordered version 0.143.0.
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 ordered-sensitive operators, essentially all the generic ones that a typical programming language should have.
This documentation is pending.
VIRTUAL FUNCTIONS FOR THE ORDERED MIXIN TYPE
Rather than having a whole set of virtual functions for the Ordered mixin, such as before/after/min/max/between/etc, we have just the one order for each ordered type to implement, and then all the other ordered-sensitive routines (before/etc) just wrap the virtual order.
sys.std.Core.Ordered.order
function order (Order <-- topic@ : Ordered, other@ : Ordered, misc_args? : Tuple, is_reverse_order? : Bool) {...}
This virtual (total) order-determination function results in Order:Same iff its topic and other arguments are exactly the same value, and otherwise it results in Order:Increase if the value of the other argument is considered to be an increase (as defined by the implementing function) over the value of the topic argument, and otherwise it results in Order:Decrease as the reverse of the last condition would be true. This function will fail if its topic and other arguments are not values of a common ordered type for which an order-determination function is defined that explicitly implements this function. Note that order-determination functions are considered the only fundamental order-sensitive operators, and all others are defined over them. This function also has a Tuple-typed third parameter, named misc_args, which carries optional customization details for the order-determination algorithm; this permits the function to implement a choice between multiple (typically similar) ordering algorithms rather than just one, which reduces the number of functions needed for supporting that choice; if the algorithm is not customizable, then a tuple argument would be of degree zero. This function also has a Bool-typed fourth parameter, named is_reverse_order; a Bool:False argument means the function's algorithm operates as normal when given any particular 3 other arguments (meaning a sorting operation based on it will place elements in ascending order), while a Bool:True argument means the function's algorithm operates in reverse, so the function results in the reverse Order value it would have otherwise when given the same 3 other arguments (meaning a sorting operation based on it will place elements in descending order). The misc_args and is_reverse_order parameters are optional and default to the zero-attribute tuple and Bool:False, respectively, if no explicit arguments are given to them.
VIRTUAL FUNCTIONS FOR THE ORDINAL MIXIN TYPE
Conceivably, the Ordinal mixin could come with functions like first or last, since such are common practice for ordinal types in other languages or contexts, to complement the pred and succ functions, providing the basis to take an Ordinal type and enumerate all of its values. However, that common practice is generally based in contexts where all ordinal types are finite, such as a "32 bit integer" type. In Muldis D, there is no requirement for an Ordinal-composing type to be finite, and at least 1 system-defined ordinal type, Int, is instead unlimited, and there is no concept of a first or last Int that can be counted from. Therefore, Ordinal has no first or last, and if you want to enumerate an ordinal type's values, the canonical means to do so is to start with that type's default value instead, which the system-defined default function provides; starting with the default value, you can reach all values of any ordinal Muldis D type eventually, enumerating your way to them in sequence using either pred to go earlier and succ to go later, for any arbitrary distance along the ordinal type's value line. In the future, if a finite-ordinal mixin type is deemed useful and is created, then actual "first" and "last" functions could be made for it.
sys.std.Core.Ordered.Ordinal.pred
function pred (Ordinal <-- topic@ : Ordinal) {...}
This virtual function results in the value that precedes its argument, iff the argument has a preceding value according to the Ordinal-composing type of the argument; otherwise, this virtual function results in the singleton value -Inf (negative infinity), which can be tested for to know you've run out of values. Note that this operation is also known as --.
sys.std.Core.Ordered.Ordinal.succ
function succ (Ordinal <-- topic@ : Ordinal) {...}
This virtual function results in the value that succeeds its argument, iff the argument has a succeeding value according to the Ordinal-composing type of the argument; otherwise, this virtual function results in the singleton value Inf (positive infinity), which can be tested for to know you've run out of values. Note that this operation is also known as ++.
GENERIC ORDERED-SENSITIVE FUNCTIONS FOR ALL DATA TYPES
These are 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.
Each of these functions is a wrapper over the order-determination function named sys.std.Core.Ordered.order when the latter function is curried by a misc_args argument of Tuple:D0 and by a calling-function-specific is_reverse_order argument value.
sys.std.Core.Ordered.is_before
function is_before (Bool <-- topic : Ordered, other : Ordered) {...}
This function results in Bool:True iff sys.std.Core.Ordered.order would result in Order:Increase when given the same corresponding 2 arguments plus an is_reverse_order argument of Bool:False, and Bool:False otherwise. Note that this operation is also known as less than or <.
sys.std.Core.Ordered.is_after
function is_after (Bool <-- topic : Ordered, other : Ordered) {...}
This function is an alias for sys.std.Core.Ordered.is_before except that it transposes the topic and other arguments. This function results in Bool:True iff sys.std.Core.Ordered.order would result in Order:Decrease when given the same corresponding 2 arguments plus an is_reverse_order argument of Bool:False, and Bool:False otherwise. Note that this operation is also known as greater than or >.
sys.std.Core.Ordered.is_before_or_same
function is_before_or_same (Bool <-- topic : Ordered, other : Ordered) {...}
This function is exactly the same as sys.std.Core.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.Core.Ordered.is_after_or_same
function is_after_or_same (Bool <-- topic : Ordered, other : Ordered) {...}
This function is an alias for sys.std.Core.Ordered.is_before_or_same except that it transposes the topic and other arguments. This function is exactly the same as sys.std.Core.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.Core.Ordered.min
function min (Ordered <-- topic : set_of.Ordered) {...}
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 min results in the singleton value Inf (positive infinity), which is the identity value for min.
sys.std.Core.Ordered.max
function max (Ordered <-- topic : set_of.Ordered) {...}
This function is exactly the same as sys.std.Core.Ordered.min except that it results in the maximum input element value rather than the minimum one, and that max's identity value is -Inf (negative infinity).
sys.std.Core.Ordered.minmax
function minmax (Tuple <-- topic : set_of.Ordered) {...}
This function results in a binary tuple whose attribute names are min and max and whose respective attribute values are what sys.std.Core.Ordered.min and sys.std.Core.Ordered.max would result in when given the same arguments.
VIRTUAL UPDATERS FOR THE ORDINAL MIXIN TYPE
sys.std.Core.Ordered.Ordinal.assign_pred
updater assign_pred (&topic@ : Ordinal) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Ordered.Ordinal.pred function with the same argument, and then assigning the result of that function to its argument. Note that this operation is also known as :=--.
sys.std.Core.Ordered.Ordinal.assign_succ
updater assign_succ (&topic@ : Ordinal) {...}
This update operator is a short-hand for first invoking the sys.std.Core.Ordered.Ordinal.succ function with the same argument, and then assigning the result of that function to its argument. Note that this operation is also known as :=++.
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.