Trait MonoidalMerge 

pub trait MonoidalMerge<P: HKT3Unbound> {
    // Required method
    fn merge<A, B, C, F>(
        pa: P::Type<A, A, A>,
        pb: P::Type<B, B, B>,
        f: F,
    ) -> P::Type<C, C, C>
       where A: Satisfies<P::Constraint>,
             B: Satisfies<P::Constraint>,
             C: Satisfies<P::Constraint>,
             F: FnMut(A, B) -> C;
}

The MonoidalMerge trait models the “fusion” or “interaction” of two contexts to produce a third.

Category Theory

Restricted to the diagonal $D(A) = P\langle A, A, A\rangle$, merge is liftA2 — the structure map of a lax monoidal functor $$ D(A) \otimes D(B) \to D(A \otimes B) $$ (McBride & Paterson 2008 §7; related to Day convolution).

Naming history

This trait was previously named Promonad. In the categorical literature a promonad is a monad in the bicategory of profunctors — equivalently an identity-on-objects functor (Loregian, (Co)end Calculus, §5.2; Jacobs, Heunen & Hasuo, Categorical semantics for arrows, JFP 19, 2009) — which this trait is not. It was renamed to say what it is; the former fuse operation (whose result type C was structurally undetermined — no lawful implementation existed for value-carrying carriers) was removed in the same change. See openspec/notes/causal-algebra/haft-formalization-deviations.md, D3/P-1.

Law (Informal)

Binaturality of merge: merge(fmap(pa, p), fmap(pb, q), h) == merge(pa, pb, |x, y| h(p(x), q(y))) — mapping the inputs first equals merging with the composed combiner. Machine-checked in lean/DeepCausalityFormal/Haft/MonoidalMerge.lean. Laws are stated for pure functions; a stateful FnMut closure voids them.

Use Cases

• Tensor Contraction: Merging a Vector $u$ and a Dual Vector $v^*$ to produce a Scalar.
• Quantum Entanglement: Combining Qubit A and Qubit B into an Entangled Pair C.
• Force Calculation: Combining Current $J$ and Magnetic Field $B$ to produce Force $F$.

Required Methods

fn merge<A, B, C, F>( pa: P::Type<A, A, A>, pb: P::Type<B, B, B>, f: F, ) -> P::Type<C, C, C>

where A: Satisfies<P::Constraint>, B: Satisfies<P::Constraint>, C: Satisfies<P::Constraint>, F: FnMut(A, B) -> C,

Merges two contexts into a third.

Arguments

• pa: The first context (Input A).
• pb: The second context (Input B).
• f: A function to combine the inner values $A$ and $B$ into $C$.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors

impl MonoidalMerge<Tuple3Witness> for Tuple3Witness