Define probability monad by using simulacrum.

build.sbt

@@ -1,6 +1,6 @@
 import Dependencies._
 
-scalacOptions += "-Ypartial-unification"
+scalacOptions ++= Seq("-Ypartial-unification", "-Ymacro-annotations")
 
 lazy val commonSettings = Seq(
   organization := "com.github.sdual",
@@ -9,6 +9,9 @@ lazy val commonSettings = Seq(
 )
 
 lazy val root = (project in file("."))
+  .settings(
+    name := "stanz"
+  )
   .aggregate(
     prototype,
     example
@@ -17,8 +20,8 @@ lazy val root = (project in file("."))
 lazy val core = (project in file("core"))
   .settings(
     commonSettings,
-    name                := "stanz",
-    libraryDependencies ++= stanzCommonDependencies,
+    name                := "core",
+    libraryDependencies ++= stanzCoreDependencies,
   )
 
 lazy val prototype = (project in file("prototype"))

core/src/main/scala/com/github/sdual/stanz/distribution/Distribution.scala

@@ -0,0 +1,16 @@
+package com.github.sdual.stanz.distribution
+
+import simulacrum.typeclass
+
+import scala.util.Random
+
+@typeclass trait Distribution[A] {
+  //def sample(dist: Distribution[A])(random: Random): A
+}
+
+object Distribution {
+  case class Point[P](value: P) extends Distribution[P]
+  case class FlatMap[P0, P1](dist: Distribution[P0], f: P0 => Distribution[P1]) extends Distribution[P1]
+  case class Primitive[P](fa: PrimitiveDistribution[P]) extends Distribution[P]
+  case class Conditional[P](dist: Distribution[P], likelihood: P => Probability) extends Distribution[P]
+}

core/src/main/scala/com/github/sdual/stanz/distribution/PrimitiveDistribution.scala

@@ -0,0 +1,5 @@
+package com.github.sdual.stanz.distribution
+
+trait PrimitiveDistribution[P] {
+
+}

core/src/main/scala/com/github/sdual/stanz/distribution/package.scala

@@ -0,0 +1,5 @@
+package com.github.sdual.stanz
+
+package object distribution {
+  type Probability = Double
+}

core/src/main/scala/com/github/sdual/stanz/typeclass/Applicative.scala

@@ -0,0 +1,8 @@
+package com.github.sdual.stanz.typeclass
+
+import simulacrum.typeclass
+
+@typeclass trait Applicative[F[_]] extends Functor[F] {
+  def pure[A](a: => A): F[A]
+  def ap[A, B](fa: => F[A])(f: => F[A => B]): F[B]
+}

core/src/main/scala/com/github/sdual/stanz/typeclass/Functor.scala

@@ -0,0 +1,7 @@
+package com.github.sdual.stanz.typeclass
+
+import simulacrum.typeclass
+
+@typeclass trait Functor[F[_]] {
+  def map[A, B](fa: F[A])(f: A => B): F[B]
+}

core/src/main/scala/com/github/sdual/stanz/typeclass/Monad.scala

@@ -0,0 +1,8 @@
+package com.github.sdual.stanz.typeclass
+
+import simulacrum.typeclass
+
+@typeclass trait Monad[F[_]] extends Applicative[F] {
+  def point[A](a: => A): F[A] = pure(a)
+  def flatMap[A, B](fa: F[A])(f: A => F[B]): F[B]
+}

core/src/main/scala/com/github/sdual/stanz/typeclass/Sampleable.scala

@@ -0,0 +1,9 @@
+package com.github.sdual.stanz.typeclass
+
+import simulacrum.typeclass
+
+import scala.util.Random
+
+@typeclass trait Sampleable[F[_]] {
+  def sample[A](fa: F[A])(random: Random): A
+}

project/Dependencies.scala

@@ -5,7 +5,7 @@ object Dependencies {
   val scalaTest         = "org.scalatest"      %% "scalatest"    % "3.0.5"
   val scalaMock         = "org.scalamock"      %% "scalamock"    % "4.1.0"
   val apacheCommonsMath = "org.apache.commons" % "commons-math3" % "3.6.1"
-  val cats              = "org.typelevel"      %% "cats-core"    % "2.0.0"
+  val simulacrum        =  "org.typelevel"     %% "simulacrum"   % "1.0.0"
 
   val stanzCommonDependencies = Seq(
     apacheCommonsMath,
@@ -14,7 +14,7 @@ object Dependencies {
   )
 
   val stanzCoreDependencies = Seq(
-    cats
+    simulacrum
   ) ++ stanzCommonDependencies
 
 }