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/**
 * Defines an equivalence between types A and B.
 * 
 * Let ~_A be an equivalence relation on A, and ~_B be an equivalence relation
 * on B.
 *
 * Let [a] denote the equivalence class of a in A ({a' | a ~_A a'}), and [b] 
 * denote the equivalence class of b in B ({b' | b ~_B b'}).
 *
 * Let `f: {[a] | a in A} -> {[b] | b in B]`, 'g: {[b] | b in B} -> {[a] | a in A}' 

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// ####### If you use a more generic lens you can transform types along the way.
case class Lens[S, A](get: S => A, set: (S, A) => S)
case class Prism[S, A](get: S => Option[A], unget: A => S) extends (A => S) {
  def apply(a: A): S = unget(a)
  
  def unapply(s: S): Option[A] = get(s)
}

// ####### Sum type

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[error] /Users/John/Documents/github/slamdata/slamengine/src/main/scala/slamdata/engine/physical/mongodb/planner.scala:468: type mismatch;
[error]  found   : slamdata.engine.analysis.fixplate.PhaseE[slamdata.engine.LogicalPlan2,slamdata.engine.PlannerError,Option[slamdata.engine.physical.mongodb.BsonField],Option[slamdata.engine.physical.mongodb.Selector]]
[error]     (which expands to)  slamdata.engine.analysis.fixplate.PhaseM[[X]scalaz.\/[slamdata.engine.PlannerError,X],slamdata.engine.LogicalPlan2,Option[slamdata.engine.physical.mongodb.BsonField],Option[slamdata.engine.physical.mongodb.Selector]]
[error]  required: slamdata.engine.analysis.fixplate.PhaseM[EitherE,slamdata.engine.LogicalPlan2,Option[slamdata.engine.physical.mongodb.BsonField],?]
[error]   val AllPhases = (FieldPhase[Unit]).fork(SelectorPhase, ExprPhase) >>> PipelinePhase

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[error]  found   : (slamdata.engine.analysis.fixplate.Term[[b]slamdata.engine.analysis.fixplate.Ann[slamdata.engine.LogicalPlan,A(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply),b]], slamdata.engine.analysis.fixplate.Term[[b]slamdata.engine.analysis.fixplate.Ann[slamdata.engine.LogicalPlan,A(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply),b]], slamdata.engine.LogicalPlan.JoinType, slamdata.engine.LogicalPlan.JoinRel, slamdata.engine.analysis.fixplate.Term[[b]slamdata.engine.analysis.fixplate.Ann[slamdata.engine.LogicalPlan,A(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply)(in method apply),b]], slamdata.engine.analysis.fixplate.Term[[b]slamdata.engine.analysis.fixplate.Ann[slamdata.engine.LogicalPlan,A(in method apply)(in method apply)(in method apply)(in method app

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  def scan[F[_], A, B](b: B, p: Process[F, A])(f: (B, A) => B): Process[F, B] = {
    import Process._

    def scan0(b: B, p: Process[F, A]) = scan(b, p)(f)

    p match {
      case h @ Halt(e) => h

      case await : Await[F, Any, A] => 
        Process.await[F, Any, B](await.req)( 

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implicit class AnyOps[A](value: A) {
  def ?: [B](left: Option[B]): A \/ B = left.map(\/-(_)).getOrElse(-\/(value))
}

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  import scalaz._
  import Scalaz._

  object cogroup {
    import \&/._

    sealed trait Instr[A] {
      def emit: List[A]
    }
    case class ConsumeLeft [A](emit: List[A]) extends Instr[A]

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module Main where 

import Debug.Trace
import Prelude (flip, const, id, ($), (+), (<<<), show)

type Tuple a b = forall z. (a -> b -> z) -> z

mkTuple :: forall a b. a -> b -> Tuple a b
mkTuple a b = \f -> f a b

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-- booleans as a partition on a set
type Bool a = a -> Either a a

true' :: forall a. Bool a
true' = Right

false' :: forall a. Bool a
false' = Left

not' :: forall a. Bool a -> Bool a

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  reify :: forall eff. ComponentClass (FileSystemTreeProps eff) FileSystemTreeState
  reify = createClass spec 
    { displayName = "FileSystemTree"
    , getInitialState = \_ -> pure {collapsed: true}
    , render = \this -> case this.props.files of
      (FileType {"type" = "file", name = n})                           -> pure $ D.div {}
                                                                          [D.span {}
                                                                            [ dataFileIcon
                                                                            , D.rawText n
                                                                            ]