Codish Lexicon

is — a binary relation that returns whether two objects are identical by their refs.   distinct: eq, identity   aka: equivalence relation, is same as, is same, same   mentioned: in place ✍

eq — equal to.   a binary relation that notes whether two objects are mutually equivalent.   opposite: ne   is: binary relation   distinct: is   aka: equal, equals, equivalence relation, is same as, is same, same   mentioned: dict, idempotent, nxor, radix64, unique ✍

identity — a value for the second param of a binary function that causes the function to always return its first parameter.   examples: unit for mul and div, zero for add and sub.   distinct: id, is, ref ✍

equivalence relation — concept: a binary relation that returns whether two values are equivalent for some notion of equivalence, like having the same value (eq), identical ref (is), some common attribute, or maping to the same value with a transitive function, like len.   see: eq, is   aka: same   mentioned: group, unique ✍

is same as — see: eq, is ✍

is same — see: eq, is ✍

same — see: eq, is   see: equivalence relation ✍

binary relation — concept: a binary function that returns whether the parameters have a given relationship (source to target), useful for map and for constructing graphs.   is: binary function, relation   distinct: boolean function   includes: eq, ne, lt, gt, le, ge   distinct: transitive function   classes: eq, ge, gt, le, lt, ne, transitive relation   related: relation   mentioned: equivalence relation, inherits, is, judge, normal, orthogonal, skew ✍

whether — indicates a boolean expression, particularly that a function returns a boolean expression.   related: if, iff ✍

objects — mentioned: is ✍

ref — reference.   a representation of a integer that identifies the location of an object in memory.   a reference may be an opaque object, meaning that having a reference does not necessarily imply knowledge of the underlying integer value.   references may be strong or weak for purpose of garbage collection, and may imply the location of supplementary data like a reference counter or class annotations.   distinct: pointer   perl: [class]: find out the type of thing being referenced†   distinct: cursor, identity   related: deref   aka: reference ✍

in place — concept: to statefully modify an object, such that the returned object is the modified parameter or context object.   mentioned: extend, push, unshift ✍

ne — not equal.   ne(a, b) is equivalent to not(eq(a, b)).   logical xor.   is: binary relation   opposite: eq   mentioned: ordinal ✍

equal — see: eq ✍

equals — see: eq ✍

dict — an unordered linear collection (particularly a set) of items that expresses a relation of keys (domain) to values (range).   in systems where dict inherits bag, it overrides the hash and eq attr functions.   is: collection, bag   attrs: keys, values, items, update, complete   related: item, key, value   distinct: object   perl: hash   seuss: a saque of items.   python: dict() -> new empty dictionary.; dict(mapping) -> new dictionary initialized from a mapping object's (key, value) pairs.† ✍

idempotent — (1.) of unary functions, converging on a return value when reapplied, as when the returned value of one application is passed back as a parameter.   a unary function, f, is idempotent iff f(x) eq f(f(x)).   (1.a.) an attribute of a unary function that denotes whether the function is idempotent for all values in its domain.   (2.) of binary functions, returning the same value when that value is passed to both parameters.   a value is idempotent for a binary function iff f(x, x) eq x.   a binary function, g, is idempotent iff f(x, x) eq x for all x in its domain.   (2.a.) a binary function that returns whether a particular value is idempotent for a given binary function, meaning f(x, x) eq x.   (2.b.) an attribute of a binary function that denotes whether the function is idempotent for all values in the domain of both parameters.   classes: abs, absolute, normal   related: stateful ✍

nxor — logical exclusive not or.   see: eq is equivalent for the domain of booleans.   related: nxor2   opposite: xor ✍

Truth Table

	X	Y	X nxor Y
0	false	false	true
1	false	true	false
2	true	false	false
3	true	true	true

radix64 — a number of radix 64, the number of characters in the set of digits followed by lower and upper case letters followed by two punctuation marks, and including the equal sign for "padding" since not all streams of bytes are divisible evenly into the 6-bit digits of radix 64 numbers.   latin: quattuorsexagenary   aka: base64 ✍

unique — an unordered collection of unique values. uniqueness is determined by a given equivalence relation, albeit equality by default.   implementations: hash array   distinct: set   aka: array unique   related: uniq   mentioned: children, graph, intersection, linear collection, power, put, que, union ✍

id — identifier.   see: key   python: id(object) -> integer Return the identity of an object. This is guaranteed to be unique among simultaneously existing objects. (it's the object's memory address).†   distinct: identity ✍

value — data of any class.   see: def, variable   aka: datum   related: dict ✍

param — a variable received by a function when it's called.   distinct: argument   distinct: arg   aka: parameter ✍

binary function — concept: a function that takes two parameters.   is: function   classes: binary relation   distinct: boolean function   mentioned: idempotent, identity ✍

unit — returns the multiplicative identity of a class, object, or group. this is a value that when multiplied by any value of a particular class, returns the same value. for numbers, strings, and most other values, this is the value of one (1). for a matrix, this is a square matrix with unit 1's along the diagonal and zero 0's elsewhere.   related: zero, unary   related: div, mul   mentioned: dec, inc, product ✍

identity: x mul x.class.unit = x

mul — multiply.   oppostie: div   is: multiplicative, stateless   related: unit   related: and, product   aka: array product   opposite: div   mentioned: complexity function, identity, linear logarithmic time, linear time, neg, non polynomial time, reciprocal ✍

div — divide.   opposite: mul   is: multiplicative, stateless   related: reciprocal, unit   mentioned: atan, identity, radix64 ✍

zero — returns the arithmetic identity of a class, object, or group. this is a value that when added to any value of a particular class returns the same value. for numbers, this is the value of zero (0). for any collection class, this is an empty collection. for a string, this is a null string, "". for a tuple, this is the nuple.   related: unit   related: add, false, sub ✍

identity: x add x.class.zero = x

add — returns the result of adding values arithmetically.   opposite: sub   is: arithmetic, stateless   related: zero   python: set: Add an element to a set. This has no effect if the element is already present.†   related: bale, or, sum   aka: concat, merge, plus   distinct: extend   mentioned: complexity function, end, identity, magnitude, neg, non polynomial time, signed ✍

sub — calculates a difference of the latter from the former.   opposite: add   commute: diff   distinct: subscript   is: arithmetic, stateless   related: zero   perl: [control flow]: declare a subroutine, possibly anonymously; see: [function]†   mentioned: identity ✍

equivalent — mentioned: equivalence relation, normal ✍

map — a function that returns the respective values for an linear collection of keys and a transitive function.   commute: each   python: map(function, sequence[, sequence, ...]) -> list Return a list of the results of applying the function to the items of the argument sequence(s). If more than one sequence is given, the function is called with an argument list consisting of the corresponding item of each sequence, substituting None for missing values when not all sequences have the same length. If the function is None, return a list of the items of the sequence (or a list of tuples if more than one sequence).†   perl: [list]: apply a change to a list to get back a new list with the changes†   aka: array map   pertains: iterable   related: pair   mentioned: abs, binary relation, enumerate, equivalence relation, font, zip with ✍

transitive function — concept: a unary function that consistently returns the corresponding value in a range for a given key in a domain.   distinct: relation, binary relation, transitive relation ✍

len — the number of values in a collection, even unordered collections.   distinct: size, width, count   aka: length   pertains: collection   python: len(object) -> integer Return the number of items of a sequence or mapping.† ✍

group — a collection of equivalent objects for a given equivalence relation.   a function that groups values into bags keyed by the results of a transitive function on each value. the returned object is a dict of sets.   aka: equivalence class   distinct: class   pertains: iterable   mentioned: duck, genericity, interface, unit, zero ✍

relation — a "finitary relation".   a function of a particular number of arguments that returns whether the arguments have a particular relationship.   related: binary relation, transitive relation   distinct: transitive function   classes: binary relation   aka: mapping   mentioned: bound, complexity function, dict, each, range, ternary relation ✍

ge — greater than or equal to.   gt(a, b) is equivalent to not(lt(a, b)).   is: binary relation   invsere: lt   aka: gte   inverse: lt   mentioned: long, positive ✍

gt — greater than.   gt(a, b) is equivalent to not(le(a, b)).   is: transitive relation, binary relation   inverse: le   aka: larger   related: max   distinct: more   mentioned: great, greater ✍

le — less than or equal to.   le(a, b) is equivalent to or(eq(a, b), lt(a, b)). or may short circuit the lt apply.   is: binary relation   inverse: gt   aka: lte   mentioned: short ✍

lt — less than.   is: transitive relation, binary relation   inverse: ge   related: min   aka: smaller   mentioned: le, less, negative ✍

transitive relation — concept: a binary relation that returns whether there is an edge from the former to the latter for a particular acyclic graph.   is: binary relation   includes: lt, gt   classes: ancestor, gt, lt   related: relation   distinct: transitive function   mentioned: descendant, domain, pertains, stable, transitive ✍

boolean function — a unary function that returns whether a value passes or fails a particular criterion or condition.   is: function   distinct: binary function   distinct: binary relation   mentioned: empty, filter, negative, positive ✍

source — a place to acquire values.   opposite: target   mentioned: binary relation, complete, message, stream, transitive, update ✍

target — a place to put values.   opposite: source   aka: dest, destination   mentioned: binary relation, complete, message, stream, transitive, update ✍

graph — a unique of nodes and edges among those nodes.   graphs can be directed or undirected.   graphs can be cyclic or acyclic.   some graphs are trees.   distinct: chart ✍

inherits — a binary relation that returns whether a child class inherits a parent class.   see: inherit   aka: is a, is instance, isa   mentioned: beget ✍

judge — a binary relation that returns whether the former is closer than the latter to a particular bound.   mentioned: bounder ✍

normal — file system: returns the one equivalent path that does not include parent ("..") and self (".") path components.   is: idempotent   distinct: canonical, absolute   geometry: a binary relation between a line and a plane that returns whether the line is perpendicular with every intersecting line in the plane.   distinct: perpendicular, orthogonal ✍

orthogonal — a binary relation between two lines that denotes that a point moving along one line, projected on the other line, would not move.   all perpendicular lines are orthogonal.   some skew lines are orthogonal but not perpendicular.   distinct: normal, perpendicular   mentioned: axis ✍

skew — a binary relation between two lines that denotes that they are do not share a plane (non-co-planar), are not parallel, and do not intersect.   mentioned: orthogonal ✍