reduction

Module nu.core.reduction.

Reduction atoms: Python's stream-to-scalar builtins.

Maps Python's builtins that fold an iterable down to one value onto Nu Reductions (a ScalarQuery with a stream child - they bridge the REFUSED cell of the cardinality matrix by naming the fold). Pure compute over the source.

Builtins covered (Python -> Nu):

• sum -> Sum, min -> Min, max -> Max
• any -> AnyOf, all -> AllOf
• len over a stream -> Count

Plus the structural folds Python reaches for without a single builtin name - First / Last / Collect - the native ways to take the head, the tail, or the whole drain of a stream.

functools.reduce is stdlib, not a bare builtin, so a generic Reduce is core-adjacent (borderline). It is deferred to nustd, not declared here: core stays the 1:1 map of native builtins.

Every atom is EVALUABLE: each Reduction defines compile (sync) and acompile (async) returning a thunk that drains its stream child to a scalar, with EMPTY / INVALID sentinel propagation.

Sorts: all ScalarQuery / Reduction (Q-scalar over Q-stream).

AllOf

True if every item in its stream child is truthy (all).

AllOf(stream)

Path nu.core.AllOf. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

True or False. INVALID if a sentinel is met before a falsy item.

Notes

• Short-circuits on the first falsy item; the rest of the stream is never drained.
• An empty stream yields True, Python's all rule for no items.

Example

nu.run(nu.AllOf(nu.Iter([1, 1, 1])))[0]

True

AnyOf

True if any item in its stream child is truthy (any).

AnyOf(stream)

Path nu.core.AnyOf. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

True or False. INVALID if a sentinel is met before a truthy item.

Notes

• Short-circuits on the first truthy item; the rest of the stream is never drained.
• An empty stream yields False, Python's any rule for no items.

Example

nu.run(nu.AnyOf(nu.Iter([0, 0, 1])))[0]

True

Collect

Drains its stream child into one list value.

Collect(stream)

Path nu.core.Collect. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

A list of every item, in order. Empty list for an empty stream. INVALID if any item is EMPTY or INVALID.

Notes

• The one reduction with no single Python builtin behind it; it names the structural "materialize the stream" fold.

Example

nu.run(nu.Collect(nu.Iter([1, 2, 3])))[0]

[1, 2, 3]

Count

The number of items in its stream child (len over a stream).

Count(stream)

Path nu.core.Count. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

The count. 0 for an empty stream. INVALID if any item is EMPTY or INVALID.

Notes

• Drains the whole stream to count it; there is no shortcut.

Example

nu.run(nu.Count(nu.Iter([1, 2, 3])))[0]

3

First

The first item of its stream child.

First(stream)

Path nu.core.First. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

The first item. EMPTY if the stream is empty, INVALID if that first item is EMPTY or INVALID.

Notes

• Pulls exactly one item and stops; the rest of the stream is never touched.

Example

nu.run(nu.First(nu.Iter([1, 2, 3])))[0]

1

Last

The last item of its stream child.

Last(stream)

Path nu.core.Last. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

The last item. EMPTY if the stream is empty, INVALID if any item is EMPTY or INVALID.

Notes

• Drains the whole stream to find the last item; there is no shortcut from the tail.

Example

nu.run(nu.Last(nu.Iter([1, 2, 3])))[0]

3

Max

The largest item in its stream child (max).

Max(stream)

Path nu.core.Max. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

The largest item. EMPTY if the stream is empty, INVALID if any item is EMPTY or INVALID.

Notes

• Buffers every item before comparing, since finding a maximum needs the whole set; nothing shortcuts.
• An empty stream yields EMPTY, not an error, unlike Python's max which raises.

Example

nu.run(nu.Max(nu.Iter([3, 1, 2])))[0]

3

Min

The smallest item in its stream child (min).

Min(stream)

Path nu.core.Min. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

The smallest item. EMPTY if the stream is empty, INVALID if any item is EMPTY or INVALID.

Notes

• Buffers every item before comparing, since finding a minimum needs the whole set; nothing shortcuts.
• An empty stream yields EMPTY, not an error, unlike Python's min which raises.

Example

nu.run(nu.Min(nu.Iter([3, 1, 2])))[0]

1

Sum

The sum of every item in its stream child (sum).

Sum(stream)

Path nu.core.Sum. Kind Reduction, sort reduction, cardinality scalar. Arity 1 (1 required).

Arguments

Yields

The sum. INVALID if any item is EMPTY or INVALID.

Notes

• Folds from 0, the additive identity, so an empty stream yields 0 rather than EMPTY.
• The fold stops at the first EMPTY or INVALID item it drains.

Example

nu.run(nu.Sum(nu.Iter([1, 2, 3])))[0]

6