plurigrid Cats Focus + Monad
flatMap that shit
Core Laws
// Monad Laws
pure(a).flatMap(f) === f(a) // Left identity
fa.flatMap(pure) === fa // Right identity
fa.flatMap(f).flatMap(g) === fa.flatMap(a => f(a).flatMap(g)) // Associativity
Focus (Monocle Optics)
import monocle.Focus
import monocle.syntax.all._
case class State(entropy: Long, archive: List[HyDefn])
// Lens into nested structure
val entropyLens = Focus[State](_.entropy)
val archiveLens = Focus[State](_.archive)
// Compose
state.focus(_.archive).modify(_ :+ newDefn)
Monad Composition Pattern
import cats.Monad
import cats.syntax.all._
def godelStep[F[_]: Monad](state: State): F[State] =
for {
entropy <- nextEntropy[F](state.entropy)
hydefn <- generateHyDefn[F](entropy)
proven <- attemptProof[F](hydefn)
newState <- if (proven)
Monad[F].pure(state.focus(_.archive).modify(_ :+ hydefn))
else
Monad[F].pure(state)
} yield newState
GF(3) Trit
cats-focus-monad (0) ⊕ cats-effect (+1) ⊕ validation (-1) = 0 ✓
Commands
# Add to build.sbt
libraryDependencies ++= Seq(
"org.typelevel" %% "cats-core" % "2.13.0",
"dev.optics" %% "monocle-core" % "3.3.0",
"dev.optics" %% "monocle-macro" % "3.3.0"
)
Autopoietic Marginalia
The interaction IS the skill improving itself.
Every use of this skill is an opportunity for worlding:
- MEMORY (-1): Record what was learned
- REMEMBERING (0): Connect patterns to other skills
- WORLDING (+1): Evolve the skill based on use
Add Interaction Exemplars here as the skill is used.
CT lattice atlas
Part of: para-mensch-commons (CT lattice family).