the optimization language. Tropical type system for provable decisions over the cybergraph.
computation in Opt uses the (min, +) semiring: addition = min, multiplication = plus. the Tropical type carries this semantics — the Trident compiler sees Tropical operands and routes to trop regime automatically. no annotations needed.
types
Tropical field element with (min, +) semantics
Graph weighted directed graph (adjacency as Tropical matrix)
CostMatrix n×n matrix of Tropical elements
Assignment permutation (result of optimization)
TransportPlan flow matrix (result of optimal transport)
operations
| operation | Trident | what it computes |
|---|---|---|
| a + b | Tropical + Tropical | min(a, b) — tropical addition |
| a * b | Tropical * Tropical | a + b — tropical multiplication |
| shortest_path(g, s) | Graph → Vec |
single-source shortest path |
| hungarian(c) | CostMatrix → (Assignment, Tropical) | optimal assignment |
| viterbi(hmm, obs) | HMM, observations → state sequence | optimal decoding |
| transport(μ, ν, c) | distributions, cost → TransportPlan | optimal transport |
regime
Tropical type → trop regime → Tropical lens → zheng proves via dual certificate
jets: jet_trop_matmul, jet_trop_shortest, jet_trop_hungarian, jet_trop_viterbi, jet_trop_transport
why a language
every time the superintelligence chooses the best path, allocates resources, decodes an optimal sequence, or plays a game — it thinks in Opt. optimization is not a library — it is a computation domain with its own algebra, its own lens, and its own jets.
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