fa'ai'ai

valsi

fa'ai'ai

type

experimental cmavo

creator

krtisfranks

time entered

Sun Sep 8 05:20:25 2019  

English

Definition #71498 - Preferred

 

selma'o

VUhU

definition

mekso k-ary operator, for natural k and 1 < k < 5: ordered input MATH

$(f, g, S, m)$

(f, g, S, m) where f and g are functions, S is a set of positive integers or "ro" (="all"), and m is 0 or 1 (as a toggle); output is a function equivalent to the function f as applied to an input ordered tuple with g applied to the entries/terms with indices in S (or to all entries/terms if S="ro") if m = 0, or g left-composed with the same if m = 1.

notes

S="ro" is default case (making this operator binary or ternary); S must be a set or "ro" (no bare integers); m = 0 is the default case (making this operator binary or ternary); use "mau'au" and "zai'ai" in order to quote f and g each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form MATH

$(x_1, x_2, x_3, ..., x_n, ...)$

(x₁, x₂, x₃,..., x_n,...); thus, notationally, a concrete output of this function, as applied to the aforementioned concrete input tuple, is of form (fa'ai'ai MATH

$(f, g, S, m))(x_1, x_2, ..., x_n, ...)$

(f, g, S, m))(x₁, x₂,..., x_n,...). For example, maintaining this notation, if S="ro" and m = 0, then the output is MATH

$f(g(x_1), g(x_2), ..., g(x_n), ...)$

f (g(x₁), g(x₂),..., g(x_n),...); if S = Set(1, 3, 23) and m = 0, then the output is MATH

$f(g(x_1), x_2, g(x_3), x_4, x_5, ..., x_<a class="undefined" href="../dict/21?bg=1;langidarg=2">21</a>, x_<a class="undefined" href="../dict/22?bg=1;langidarg=2">22</a>, g(x_<a class="undefined" href="../dict/23?bg=1;langidarg=2">23</a>), x_<a class="undefined" href="../dict/24?bg=1;langidarg=2">24</a>, x_<a class="undefined" href="../dict/25?bg=1;langidarg=2">25</a>, ..., x_n, ...)$

f (g(x₁), x₂, g(x₃), x₄, x₅,..., x₂₁, x₂₂, g(x₂₃), x₂₄, x₂₅,..., x_n,...); vel sim. If h is the function output by this expression when m = 0, then for the same inputs (ignoring m), goh is the function output by the same expression but with m = 1. Obviously, in order to be meaningful, the output of each step along the way must be defined. If S is the empty set and g is defined, then the output is just the function f if m = 0. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when S or m is omitted (as being equal to the default "ro" or 0 resp.).

gloss words

• extended functional composition

created by

krtisfranks

vote information

1

time

Sun Sep 8 06:07:04 2019

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