RiX Array Generators

Array generator chains are parsed into a GeneratorChain with a seed and an ordered operator list, then lowered to GENERATOR IR. The runtime compiles that IR into a cached incremental sequence producer.

Canonical operators

  • |+ n — primary arithmetic source.
  • |* n — primary geometric source.
  • |: f — primary one-based index source; calls f(index, self).
  • |> f — primary newest-first history source when no source precedes it; otherwise a per-candidate transformation.
  • |? p — filter with p(value, sourceIndex, self).
  • |; n / |; p — eager count or predicate termination.
  • |^ n / |^ p — lazy count or predicate termination.

The removed |^: spelling is reserved and rejected by the parser.

Runtime rules

A chain has one primary source. Explicit seeds initialize that source and then travel through downstream transforms and filters. Rejected candidates still advance upstream source state. Numeric limits count accepted output values, including accepted seeds. Predicate termination includes the triggering value.

History placeholders are newest-first: _1 is the most recent source value, _2 the second most recent, and so on. Missing history is an error.

[2, |+2, |; 5]                         ## [2,4,6,8,10]
[|: (i) -> i^2, |; 5]                  ## [1,4,9,16,25]
[1,1, |> F(_2,_1), |; 7]               ## Fibonacci
[2 |+3 |> (x)->x^2 |? (x)->x%2==0 |;5]

Without |; or |^, a chain with a source is lazy and unbounded. A chain containing only seeds/transforms/filters is finite. Lazy sequences cache emitted values, support positive indexing and bounded slicing, and preserve laziness through map/filter pipes.

Generator iteration limits are runtime safety limits, not semantic output limits. Exhaustion throws a diagnostic; it never returns silently truncated output.

Lazy sequences can be traversed with Iterator(). The iterator owns the cursor while the sequence continues to own generation state and its shared cache. A new cursor begins at index zero; Next(step) moves before returning, and Peek(offset) reads without moving. See methods-guide.md for the complete API.

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