NoneTrue¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

NoneTrue[list, test]

Gives True if test[e] is True for no element e (True for an empty list). Over an association, tests the values.

Examples (6)¶

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (3)¶

In[1]:= AllTrue[{2, 4, 6}, EvenQ]
Out[1]= True

In[2]:= AnyTrue[{1, 3, 4}, EvenQ]
Out[2]= True

In[3]:= NoneTrue[{1, 3, 5}, EvenQ]
Out[3]= True

Applications (3)¶

No element is even, so True

In[4]:= NoneTrue[{1, 3, 5}, EvenQ]
Out[4]= True

One even element makes it False

In[5]:= NoneTrue[{1, 2, 3}, EvenQ]
Out[5]= False

Nothing exceeds 10

In[6]:= NoneTrue[Range[5], # > 10 &]
Out[6]= True

Implementation notes¶

Algorithm. builtin_none_true is all_any_none_true(res, 2), the mode = 2 case of the quantifier it shares with AllTrue (mode 0) and AnyTrue (mode 1). NoneTrue is the logical complement of AnyTrue: a bool NDArray with an identity-shaped predicate (TrueQ/Identity) scans the raw byte buffer and returns False if any byte is set, True otherwise. The compiled-predicate path pred_quantify, visible-NDArray materialisation, and association-over-values handling are all shared with the siblings.

The fallback walks the elements building and evaluating test[e]; NoneTrue short-circuits to False on the first test[e] that is True. A result that is neither True nor False leaves the whole call unevaluated (return NULL), and a Throw from the test propagates. With no match the result is True, so the empty list gives True.

Data structures. The argument array is borrowed; each test[e] is built, evaluated, read for True/False, and freed. The bool-buffer path reads only the unsigned char NDArray buffer.

Complexity / limits. O(n) tests with early exit; the bool scan is O(n) bytes. An indeterminate predicate value leaves the call unevaluated, matching Wolfram.

Attributes: Protected.

References¶

See also: AllTrue, AnyTrue

Source: src/funcprog.c
Specification: docs/spec/builtins/functional-programming.md
Tests: tests/test_assoc_forms.c
Tests: tests/test_association.c
Tests: tests/test_compile.c
Tests: tests/test_hypergraph.c

Notes & additional examples¶

Notes¶

NoneTrue[list, test] is True exactly when test[e] is True for no element e — the negation of AnyTrue — and short-circuits to False on the first match. Over an association the values are tested. The empty list gives True.

A test[e] that is neither True nor False leaves the whole call unevaluated. Over a boolean packed array with TrueQ or Identity as the test, the check is a single early-exit scan of the raw buffer.