Heapcon WarmUp MeetUp - 16 October 2025

Data & Behaviour = Information (Algebra of the Business)

• Data (examples/api.kt): Commands, Events, State
• Behaviour (examples/domain.kt): Exhaustive pattern matching on data

Overview

This project encodes information systems as composable algebraic structures using pure Kotlin functions.

It unifies two classical architectural styles:

• 🏛️ State-stored systems — store current state directly
• 🌀 Event-sourced systems — store past events and reconstruct state from them

Both are captured under a single algebraic model — the System type.

decide       : Command × State → Sequence<Event>
evolve       : State × Event   → State
initialState : ()              → State

data class System<Command, State, Event>(
    val decide: (Command, State) -> Sequence<Event>,
    val evolve: (State, Event) -> State,
    val initialState: () -> State
)

Convert between representations easily:

val system: System<C, S, E> = ...

val stateStored: StateStoredSystem<C, S> = system.asStateStoredSystem()
val eventSourced: EventSourcedSystem<C, E> = system.asEventSourcedSystem()

Algebraic View

Concept	Mathematical Structure	Notes
mapCommand	Contravariant Functor	Maps input command types
mapEvent	Profunctor (dimap)	Contravariant in input events, covariant in output
mapState	Profunctor (dimap)	Contravariant in input state, covariant in output
combine	Monoidal Product	Combines two systems into a product system
emptySystem	Monoidal Identity	Represents the “no-op” system (System<Nothing?, Unit, Nothing?>)

📚 Learn More - fmodel.fraktalio.com