Chemical Abstract Machine

Origin. Berry and Boudol (1990). Computation as chemical reaction. Multiset of molecules. Reaction rules. Concurrent, non-deterministic. Foundation for process calculi semantics.

Models. Solution: multiset of molecules. Membrane: scope delimiter. Heating/cooling: structural rearrangement. Reaction: computation step.

Formalism.

Solution: S = M₁, M₂, ..., Mₙ (multiset) Molecules separated by comma. Order irrelevant (commutative).

Membrane: ⟨S⟩: solution in membrane. Scope delimiter.

Structural equivalence (heating/cooling): M, ⟨S⟩ ⇌ ⟨M, S⟩ (molecule crosses membrane) Airlock law.

Reaction rule: M₁, ..., Mₙ → M'₁, ..., M'ₘ Consumes left, produces right.

Chemical law: If S → S' and S ≡ T, T' ≡ S': Then T → T' Reactions work modulo heating/cooling.

Example (λ-calculus): (λx.M), N → M[N/x] Application as reaction.

Concurrency: Multiple reactions can fire simultaneously. Independent molecules react in parallel. Non-determinism: choice of reaction.

Join patterns (Join calculus): x⟨v⟩, y⟨w⟩ → P Synchronization via multi-way join.

Symbols.

Symbol	Unicode	Name	Meaning
,	—	Comma	Multiset union
⟨⟩	—	Membrane	Scope
→	U+2192	Reaction	Computation
⇌	U+21CC	Heating	Structural equiv

Metatheory. Turing complete. Encodes λ-calculus. Concurrent semantics. Join calculus basis.

Applies to. Concurrent programming. Process calculi. Biological modeling. Distributed systems. Chemical computing.

Limitations. Non-determinism hard to control. Debugging complex. Efficiency unclear. Abstract model.