--- name: juvix-intents description: Juvix intent-centric language for Anoma with Geb compilation and GF(3) typed resources version: 1.0.0 --- # Juvix Intents (+1) > Intent-centric language compiling to Geb categorical semantics **Trit**: +1 (PLUS - generative) **Compiles to**: Geb → Vampir → ZK proofs ## Overview Juvix is Anoma's **intent-centric programming language**: ``` Juvix Source → Core → Geb Morphisms → Vampir IR → ZK Circuit ↑ ↑ ↑ ↑ Types Normalize Categorify Arithmetize ``` ## Obstruction Types ```juvix module Obstruction; -- GF(3) trit type type GF3 := Minus | Ergodic | Plus; -- Trit arithmetic (mod 3) add : GF3 -> GF3 -> GF3 add Minus Minus := Plus -- (-1) + (-1) = +1 (mod 3) add Minus Ergodic := Minus -- (-1) + 0 = -1 add Minus Plus := Ergodic -- (-1) + (+1) = 0 add Ergodic x := x -- 0 + x = x add Plus Minus := Ergodic -- (+1) + (-1) = 0 add Plus Ergodic := Plus -- (+1) + 0 = +1 add Plus Plus := Minus; -- (+1) + (+1) = -1 (mod 3) -- Obstruction from Bumpus decomposition failure type Obstruction := mkObstruction { sexp : ByteArray; -- S-expression witness trit : GF3; -- Triadic charge h1Class : Nat; -- Cohomology class (>0 = obstruction) treewidth : Nat; -- Exceeded threshold color : Word64; -- Gay.jl deterministic color seed : Word64 -- SplitMix64 seed }; -- Check if decomposition failed isObstruction : Obstruction -> Bool isObstruction obs := h1Class obs > 0; -- VCG externality payment vcgExternality : Obstruction -> Nat vcgExternality obs := let baseCost := 1000000 -- 0.001 APT multiplier := 10000 -- 100% in (h1Class obs) * baseCost * multiplier / 10000; ``` ## Intent Types ```juvix module Intent; import Obstruction; -- Resource type (what can be nullified/committed) type Resource := | ObstructionRes Obstruction | TokenRes Token | ReceiptRes ChainId ByteArray; -- Intent: preference over state transitions type Intent := mkIntent { owner : Address; nullify : List Resource; -- Resources to consume commit : List Resource; -- Resources to produce constraints : List Constraint }; -- Constraint on intent satisfaction type Constraint := | VcgPayment Nat -- Minimum VCG payment | GF3Balance -- Sum of trits must be 0 (mod 3) | SpectralGap Float; -- Minimum spectral gap preserved -- Cross-chain pass intent passObstruction : Address -> Obstruction -> ChainId -> Intent passObstruction owner obs target := mkIntent { owner := owner; nullify := [ObstructionRes obs]; commit := [ReceiptRes target (hash obs)]; constraints := [VcgPayment (vcgExternality obs), GF3Balance] }; ``` ## Compilation to Geb ```juvix module GebCompile; import Intent; import Geb; -- Compile intent to Geb morphism compileIntent : Intent -> Geb.Morphism compileIntent intent := -- Intent = pair of (nullify, commit) -- Nullify: inject-left to void (consume) -- Commit: inject-right from void (produce) Geb.pair (compileNullify (nullify intent)) (compileCommit (commit intent)); -- Compile nullification compileNullify : List Resource -> Geb.Morphism compileNullify [] := Geb.terminal Geb.so1 compileNullify (r :: rs) := Geb.pair (Geb.injectLeft (compileResource r) Geb.so0) (compileNullify rs); -- Compile commitment compileCommit : List Resource -> Geb.Morphism compileCommit [] := Geb.init Geb.so0 compileCommit (r :: rs) := Geb.pair (Geb.injectRight Geb.so0 (compileResource r)) (compileCommit rs); -- Resource to Geb type compileResource : Resource -> Geb.Object compileResource (ObstructionRes obs) := Geb.prod (Geb.prod Geb.so1 Geb.so1) -- (sexp, trit) (Geb.prod Geb.so1 Geb.so1); -- (h1Class, color) compileResource (TokenRes tok) := Geb.so1; compileResource (ReceiptRes _ _) := Geb.so1; ``` ## Free Monad for Obstruction Game ```juvix module ObstructionMonad; import Obstruction; -- Functor for obstruction game type ObstructionF (a : Type) := | NoObstruction a -- Decomposition succeeded | WithObstruction Obstruction a; -- Decomposition failed → H¹ ≠ 0 -- Free monad type Free (f : Type -> Type) (a : Type) := | Pure a | Roll (f (Free f a)); -- Obstruction monad = Free ObstructionF ObstructionMonad : Type -> Type ObstructionMonad := Free ObstructionF; -- Attempt decomposition (creates obstruction if tw > threshold) attemptDecomposition : ByteArray -> Nat -> Word64 -> ObstructionMonad Unit attemptDecomposition sexp tw seed := if tw <= 3 then Pure unit else let h1 := tw - 3 trit := toGF3 ((seed `xor` (natToWord64 tw)) `mod` 3) color := gayColor seed tw obs := mkObstruction sexp trit h1 tw color seed in Roll (WithObstruction obs (Pure unit)); -- Bind preserves spectral gap bind : ObstructionMonad a -> (a -> ObstructionMonad b) -> ObstructionMonad b bind (Pure a) k := k a bind (Roll (NoObstruction rest)) k := Roll (NoObstruction (bind rest k)) bind (Roll (WithObstruction obs rest)) k := Roll (WithObstruction obs (bind rest k)); ``` ## Spectral Gap Tracking ```juvix module SpectralMonad; -- Monad that tracks spectral gap through composition type SpectralFree (f : Type -> Type) (a : Type) := mkSpectralFree { computation : Free f a; spectralGap : Float }; -- Bind propagates minimum gap bindSpectral : SpectralFree f a -> (a -> SpectralFree f b) -> SpectralFree f b bindSpectral sf k := let result := bind (computation sf) (\a -> computation (k a)) newGap := min (spectralGap sf) (gapOf result) in mkSpectralFree result newGap; -- Ramanujan bound for d=3 ramanujanBound : Float ramanujanBound := 3.0 - 2.0 * sqrt 2.0; -- ≈ 0.172 -- Check if spectral gap preserved gapPreserved : SpectralFree f a -> Bool gapPreserved sf := spectralGap sf >= ramanujanBound; ``` ## GF(3) Type-Level Conservation ```juvix module GF3Types; -- Type-level GF(3) for compile-time conservation type Trit := T_Minus | T_Ergodic | T_Plus; -- Type-level addition (mod 3) type family TritAdd (a : Trit) (b : Trit) : Trit where TritAdd T_Minus T_Plus := T_Ergodic TritAdd T_Plus T_Minus := T_Ergodic TritAdd T_Ergodic x := x TritAdd x T_Ergodic := x TritAdd T_Plus T_Plus := T_Minus TritAdd T_Minus T_Minus := T_Plus; -- Typed resource with trit charge type TResource (t : Trit) := mkTResource { payload : Resource; trit : GF3 -- Runtime trit must match type-level }; -- Balanced transaction: trits sum to 0 type BalancedTx := forall (a b c : Trit). TritAdd a (TritAdd b c) == T_Ergodic => Triple (TResource a) (TResource b) (TResource c); ``` ## CLI Commands ```bash # Compile Juvix to Geb juvix compile intent.juvix --target geb # Type check with GF(3) verification juvix typecheck --gf3-check module.juvix # Generate Vampir circuit juvix compile intent.juvix --target vampir # Run obstruction monad juvix eval "attemptDecomposition sexp 5 0x42" # Verify spectral gap preservation juvix verify --spectral-gap intent.juvix ``` ## GF(3) Triads ``` juvix-intents (+1) ⊗ anoma-intents (0) ⊗ solver-fee (-1) = 0 ✓ └─ Compiles DSL └─ Routes └─ Extracts fee juvix-intents (+1) ⊗ geb (+1) ⊗ sheaf-cohomology (-1) = 1 ✗ (need -1) → Add intent-sink (-1): juvix (+1) ⊗ geb (+1) ⊗ intent-sink (-1) ⊗ sheaf (-1) ... juvix-intents (+1) ⊗ open-games (0) ⊗ ramanujan-expander (-1) = 0 ✓ └─ Type-level gap └─ Coordinates └─ Validates bound ``` ## Integration with Obstruction Hot Potato ```juvix -- Full hot potato game in Juvix module HotPotato; import Obstruction; import Intent; import ObstructionMonad; -- Player state type Player := mkPlayer { address : Address; stake : Nat; obstructions : List Obstruction; alive : Bool }; -- Game action type Action := | AttemptDecomposition ByteArray Nat | PassObstruction Address Nat | EndRound; -- Game monad: State + Obstruction effects type GameMonad := StateT (List Player) ObstructionMonad; -- Execute action executeAction : Action -> GameMonad Unit executeAction (AttemptDecomposition sexp tw) := do obs <- lift (attemptDecomposition sexp tw (currentSeed ())) when (isObstruction obs) (addObstructionToPlayer obs) executeAction (PassObstruction target idx) := do player <- getCurrentPlayer obs <- getObstruction player idx vcg <- pure (vcgExternality obs) transferPayment player target vcg moveObstruction player target idx executeAction EndRound := do players <- get deadPlayers <- filterM hasNegativeUtility players mapM_ slashStake deadPlayers verifyGF3Conservation; ``` ## References - **anoma/juvix** - https://github.com/anoma/juvix (504 stars) - **anoma/geb** - Categorical compilation target - **Juvix docs** - https://docs.juvix.org - **Bumpus arXiv:2402.00206** - Decomposition theory - **Roughgarden CS364A** - VCG mechanism --- **Trit**: +1 (PLUS - generative) **Key Property**: Intent DSL with type-level GF(3) conservation ## Scientific Skill Interleaving This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem: ### Graph Theory - **networkx** [○] via bicomodule - Universal graph hub ### Bibliography References - `general`: 734 citations in bib.duckdb ## Cat# Integration This skill maps to **Cat# = Comod(P)** as a bicomodule in the equipment structure: ``` Trit: 0 (ERGODIC) Home: Prof Poly Op: ⊗ Kan Role: Adj Color: #26D826 ``` ### GF(3) Naturality The skill participates in triads satisfying: ``` (-1) + (0) + (+1) ≡ 0 (mod 3) ``` This ensures compositional coherence in the Cat# equipment structure.