Safe Haskell	None
Language	GHC2024

Free.Agent.Hyper

Description

The hypergraph generators for posts and agents (stage 3 of endgame-path).

A hypergraph category lets wires fork and merge. At the stream level the generators are copyP (fork: duplicate a stream) and mergeP (merge: append two streams); braidP swaps the two middle blocks — the permutation whose block-versus-wire confusion was the bug this library family grew out of. With append as merge the bialgebra law holds for streams of posts exactly:

copyP (mergeP (xs, ys)) == merge2 (braidP (copy2 (xs, ys)))
  -- both sides are (xs ++ ys, xs ++ ys)

At the agent level, both is the merge of two agents — the join of the extension semilattice, dual to sequencing: both agents see the same input (copy), their outputs are appended (merge). This is the combinator form of graph overlay / a two-seat roster.

Semantics on record

Merge is bag semantics: 'both a a' double-posts. Idempotence is name-keyed, not structural — seat registries dedupe by name; streams do not dedupe at all. Bag at the wire, set at the name.

Synopsis

copyP :: [a] -> ([a], [a])
copy2 :: ([a], [b]) -> (([a], [a]), ([b], [b]))
mergeP :: ([a], [a]) -> [a]
merge2 :: (([a], [a]), ([a], [a])) -> ([a], [a])
braidP :: ((a, b), (c, d)) -> ((a, c), (b, d))
silent :: System (->) () (Mono a [b])
both :: System (->) s1 (Mono a [b]) -> System (->) s2 (Mono a [b]) -> System (->) (s1, s2) (Mono a [b])

Documentation

copyP :: [a] -> ([a], [a]) Source #

Fork: duplicate a stream.

copy2 :: ([a], [b]) -> (([a], [a]), ([b], [b])) Source #

Fork two streams at once (block-level).

mergeP :: ([a], [a]) -> [a] Source #

Merge: append two streams. Bag semantics — no deduplication.

merge2 :: (([a], [a]), ([a], [a])) -> ([a], [a]) Source #

Merge two stream-pairs componentwise: each inner pair is appended. This is mergeP ⊗ mergeP, the merge half of the bialgebra.

braidP :: ((a, b), (c, d)) -> ((a, c), (b, d)) Source #

Swap the two middle blocks: ((a,b),(c,d)) → ((a,c),(b,d)).

silent :: System (->) () (Mono a [b]) Source #

The silent agent: emits nothing. Additive zero for both.

both :: System (->) s1 (Mono a [b]) -> System (->) s2 (Mono a [b]) -> System (->) (s1, s2) (Mono a [b]) Source #

Merge two bundle-output agents: both see the same input, outputs are appended in left-then-right order. The state is the pair.

Laws (oracle-pinned): commutative up to output bag; silent is a zero on either side; not idempotent — both a a double-posts (bag at the wire).