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PAD Sequence Documentation

The PAD sequence subsystem is a powerful mathematical sequence generation and manipulation engine. It provides over 80 sequence types, sequence storage and retrieval, and a rich set of transformation operations.

Quick Example

{fibonacci rows=10}{$fibonacci} {/fibonacci}

Output: 1 1 2 3 5 8 13 21 34 55

Documents

File	Description
SEQUENCES.md	Sequence types - all 80+ available sequences and how to generate them
ACTIONS.md	Sequence actions - transformations, aggregations, and operations
EXPLAIN.md	Technical internals - how the sequence subsystem works
PAD.md	Framework integration - sequence implementation details

Key Features

80+ Sequence Types: Fibonacci, prime, triangular, Lucas, Catalan, and many more
Storage & Retrieval: Store sequences with push, retrieve with pull
Transformations: reverse, sort, shuffle, dedup
Selection: first, last, slice, shift, pop
Aggregations: sum, average, minimum, maximum, count
Multi-sequence: append, merge, intersection, difference
OEIS Integration: Fetch any sequence from the Online Encyclopedia of Integer Sequences

Getting Started

Generate a simple range:

{sequence '1..10', name='n'}{$n} {/sequence}

Store and transform:

{sequence '1..10', push='nums'}
{resume reverse}
{pull:nums}{$sequence} {/pull:nums}

Aggregate values:

{sequence '1..100', push='nums'}
Sum: {pull:nums sum}{$sequence}{/pull:nums}

Options for Sequence Tags

Option	Description
`rows`	Limit number of elements
`name`	Variable name for current value
`push`	Store sequence with this name
`minimal`	Minimum value (for random)
`maximal`	Maximum value (for random)
`increment`	Step increment
`unique`	Ensure unique values

Notes

Sequences are lazily evaluated where possible
Use push to store sequences for later transformation
Use {resume} to apply transformations to the last pushed sequence
Use {pull:name} to iterate over a stored sequence
The @ symbol represents the current value in eval expressions

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