plurigrid/asi/cats-focus-monad

// 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

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)

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

cats-focus-monad (0) ⊕ cats-effect (+1) ⊕ validation (-1) = 0 ✓

# 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"
)