Codish Lexicon

abs — absolute value.   returns the positive reflection of negative integers, returning positive numbers as they were.   a transitive function that maps integers into the natural number line.   distinct: absolute   is: stateless, idempotent   related: neg   python: abs(number) -> number Return the absolute value of the argument.†   perl: [number]: absolute value function†   php: absolute value &dagger.   distinct: pos   related: positive ✍

neg — arithmetic negation.   number: mul -1.   integer: returns the two's complement, which means to not2 then add 1.   distinct: not, not2, negative   related: abs, negative   mentioned: scalar, signed ✍

positive — a unary boolean function that returns whether a value is ge zero.   opposite: negative   related: abs   distinct: pos   is: sign   mentioned: cardinality, integer, natural, signed, true, uint, whole ✍

stateless — an attribute of a function that connotes that a function will always return the same result for given input.   opposite: stateful   classes: abs, absolute, add, div, first, mul, pad, reversed, slice, sub   mentioned: expression, getset, transitive ✍

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 ✍

absolute — returns the fully qualified path for a given path and the cwd.   is: stateless, idempotent   distinct: abs, normal, canonical ✍

pos — temporal: position.   distinct: positive, abs, index, key   perl: [regex]: find or set the offset for the last/next m//g search†   php: alias of current() &dagger.   see: index   aka: position   mentioned: remove, shift, time, unshift ✍

negative — a unary boolean function that returns whether a value is lt zero.   opposite: positive   related: neg   distinct: neg   is: sign   mentioned: abs, false, integer, signed, uint ✍

integer — pertains to number values that are positive, negative, and zero, but have no mantissa.   integers have arbitrary magnitude.   distinct: int   distinct: natural, whole   mentioned: abs, bitwise, genericity, pointer, rational, real, ref ✍

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 ✍

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 ✍

natural — pertains to number values that are positive or zero.   natural numbers have arbitrary magnitude.   distinct: integer, whole, uint   mentioned: abs, binary, digit, unsigned ✍

number — concept: a whole, natural, integer, real, or complex numeric value.   a transitive function that returns the corresponding number, usually limited to a subset of the real domain like int or float. ✍

not — logical negation.   related: not2   distinct: neg   mentioned: nand, nand2, nor, nor2, nxor, nxor2, signed ✍

	X	not X
0	false	true
1	true	false

not2 — bitwise not.   is: bitwise   distinct: neg   related: not ✍

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 ✍

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 ✍

scalar — pertains to 1-dimensional, non-negative values.   related: linear, planar, spatial, temporal   perl: force a scalar context†   aka: planar   mentioned: hash, lapse, vector ✍

signed — pertains: integers that use their big bit to represent whether the int is positive or negative. negative integers are usually stored in "two's complement" form, meaning that, neg can be calculated with not and adding 1.   opposite: unsigned   is: int   related: sign   mentioned: int16, int32, int64 ✍

identity: neg(x) eq (not(x) add 1)

sign — related: signed   classes: positive, negative ✍

unary — describes functions that take one parameter.   related: unit   mentioned: boolean function, negative, positive, transitive function, transitive, unary function ✍

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 ✍

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

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 ✍

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

cardinality — math: size, magnitude, length, thus cardinality values are in the domain of zero and positive real numbers.   see: cardinal, length ✍

true — a boolean value that corresponds to all things positive or affirmative.   a non-zero value.   aka: yes, nonzero   python: bool(x) -> bool Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.†   mentioned: bit, cond, if, truthy ✍

uint — a magnitude-limited natural number.   an unsigned int, meaning the most significant bit, the big end, does not represent whether the int is positive or negative, but rather adds another bit of precision.   distinct: natural, whole ✍

whole — pertains to number values that are positive, but not zero.   distinct: natural, integer, uint   mentioned: digit ✍

stateful — an attribute of a function that indicates that a function may not always return the same result for given input because the result depends on state like an input stream or scope values.   opposite: stateless   related: idempotent   see: state   classes: complete, getset, reverse, update   mentioned: closure, count, in place, statement ✍

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

first — returns the first element of a linear collection.   is: stateless   opposite: last   related: pop   seuss: opposite: forst   pertains: ordered   mentioned: chain, head, heap array, index, peek, queue, shift, tip ✍

pad — pad a numeric string with a particular character, "0" by default, on either the left or right side or into the "center" or distributed among the interpolated spaces as in justify, by default left, so that the resultant string has a given minimum length.   is: stateless   related: sprintf   related: center   aka: zfill ✍

example: pad("1", 3) eq "001"

example: pad("1", 3, " ") eq " 1"

reversed — returns the reversed form of an iterable.   is: stateless   distinct: reverse   opposite: reversed   python: reversed(sequence) -> reverse iterator over values of the sequence Return a reverse iterator.†   aka: array reverse   mentioned: ed, next ✍

slice — returns the corresponding values for a given range of indicies (indexy).   is: stateless   python: slice([start,] stop[, step]) Create a slice object. This is used for extended slicing (e.g. a[0:10:2]).†   aka: array slice   mentioned: indices ✍

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 ✍

expression — an element of a program's syntax, typically used to express stateless computation through function application (apply), including algebraic operators.   aka: term   mentioned: destructure, eval, heap array, literal, lvalue, return, statement, whether ✍

getset — dict: get the value for a given key, beforehand setting the value for the key to a default if no key exists yet.   is: stateful   distinct: get with a default value is stateless as it does not modify the object when it returns the default value.   pertains: collection ✍

transitive — going consistently from a source to a target, as a directed edge in a graph or as a stateless unary function.   see: transitive function, transitive relation   mentioned: ancestors, descendants ✍

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 ✍

unary function — a unary function is a function that takes 1 parameter.   mentioned: idempotent ✍

return — a statement that stops the execution within a function, sending the cursor of execution to the function that applyed the current function, and providing a value for the apply expression.   perl: [control flow]: get out of a function early†   php: If called from within a function, the return() statement immediately ends execution of the current function, and returns its argument as the value of the function call. return() will also end the execution of an eval() statement or script file. &dagger.   mentioned: cut, empty, frame, group, higher order function, idempotent, iteration, whether ✍

application — see: apply   mentioned: frame, idempotent ✍

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

iff — if and only if.   related: if   related: whether   mentioned: idempotent ✍

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 ✍

attr — an attribute of an object.   a setable and getable value associated with a symbol or name in an object.   in some languages, attributes are either private, protected, or public.   distinct: item   python: property   c++: member   aka: member, property   related: pair ✍

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

function — related: scope, frame, closure   includes: apply   classes: binary function, boolean function ✍

all — returns whether all values froma given iterable are true.   short circuits on the first falsy value.   related: any, every   python: all(iterable) -> bool Return True if bool(x) is True for all values x in the iterable.†   aka: intersection   pertains: iterable   mentioned: idempotent ✍