Add polynomial-mermaid module

Basics for generating mermaid definitions for PolyMaps

README.md

@@ -16,19 +16,41 @@ Based on the polynomial functors described in [Niu and Spivak](https://topos.sit
 #### `polynomial`
 
 The `polynomial` library provides the following implementation of poly:
- - objects: built-in ADTs representing `Monomial`, `Binomial`, `Trinomial` functors
+ - objects: built-in ADTs representing `Monomial`, `Binomial`, `Trinomial`, and `Store` functors
  - morphisms: `PolyMap`, a natural transformation between polynomial functors
- - products: `Tensor`, a type match on functors, yielding their Day convolution
+ - products: `Tensor`, a type match on functors, yielding a parallel product
 
 ```scala
-import polynomial.`object`.Monomial
+import polynomial.`object`.{Binomial, Monomial, Store}
 import polynomial.morphism.~>
 import polynomial.product.⊗
 
-type Plant[Y]      = Monomial[(Byte, Byte => Char), Char, Y]
-type Controller[Y] = Monomial[Char, Byte => Char, Y]
-type System[Y]     = Monomial[Byte, Byte => Char, Y]
+type `2y²`             = Store[Boolean, _]
+type `2y⁵¹²`           = Monomial[(Byte, Boolean), Boolean, _]
+type `y² + 2y`         = Binomial[Boolean, Unit, Unit, Boolean, _]
+type `y² + 2y → 2y⁵¹²` = (`y² + 2y` ~> `2y⁵¹²`)[_]
+type `4y⁴`             = (`2y²` ⊗ `2y²`)[_]
+```
+
+#### `polynomial-mermaid`
+
+Certain lenses lend themselves to graphical interpretation:
+
+```scala
+import polynomial.`object`.{Store, Monomial}
+import polynomial.mermaid.Mermaid
+import polynomial.morphism.~>
+
+type P[Y] = (Store[Int, _] ~> Monomial[Char, Unit, _])[Y]
+
+println(s"${summon[Mermaid[P]].showSpecific}")
+// ```mermaid
+// graph LR;
+//   A[Char]:::hidden-->|Char|S[Int]-->|Unit|B[Unit]:::hidden;
+// ```
+```
 
-type ω[Y] = ((Plant ⊗ Controller) ~> System)[Y]
+```mermaid
+graph LR;
+  A[Char]:::hidden-->|Char|S[java.lang.String]-->|Unit|B[Unit]:::hidden;
 ```
-<small>(Note: example adapted from the poly book, by [Niu and Spivak](https://topos.site/poly-book.pdf))</small>

build.sbt

@@ -35,6 +35,11 @@ lazy val poly = crossProject(JSPlatform, JVMPlatform, NativePlatform)
     )
   )
 
+lazy val mermaid = crossProject(JSPlatform, JVMPlatform, NativePlatform)
+  .in(file("modules/mermaid"))
+  .settings(name := "polynomial-mermaid")
+  .dependsOn(poly)
+
 lazy val docs = project.in(file("docs/gitignored"))
   .settings(
     mdocOut := file("."),
@@ -44,6 +49,6 @@ lazy val docs = project.in(file("docs/gitignored"))
       "VERSION" -> version.value.takeWhile(_ != '+'),
     )
   )
-  .dependsOn(poly.jvm)
+  .dependsOn(poly.jvm, mermaid.jvm)
   .enablePlugins(MdocPlugin)
   .enablePlugins(NoPublishPlugin)

docs/readme.md

@@ -16,19 +16,40 @@ Based on the polynomial functors described in [Niu and Spivak](https://topos.sit
 #### `polynomial`
 
 The `polynomial` library provides the following implementation of poly:
- - objects: built-in ADTs representing `Monomial`, `Binomial`, `Trinomial` functors
+ - objects: built-in ADTs representing `Monomial`, `Binomial`, `Trinomial`, and `Store` functors
  - morphisms: `PolyMap`, a natural transformation between polynomial functors
- - products: `Tensor`, a type match on functors, yielding their Day convolution
+ - products: `Tensor`, a type match on functors, yielding a parallel product
 
 ```scala mdoc
-import polynomial.`object`.Monomial
+import polynomial.`object`.{Binomial, Monomial, Store}
 import polynomial.morphism.~>
 import polynomial.product.⊗
 
-type Plant[Y]      = Monomial[(Byte, Byte => Char), Char, Y]
-type Controller[Y] = Monomial[Char, Byte => Char, Y]
-type System[Y]     = Monomial[Byte, Byte => Char, Y]
+type `2y²`             = Store[Boolean, _]
+type `2y⁵¹²`           = Monomial[(Byte, Boolean), Boolean, _]
+type `y² + 2y`         = Binomial[Boolean, Unit, Unit, Boolean, _]
+type `y² + 2y → 2y⁵¹²` = (`y² + 2y` ~> `2y⁵¹²`)[_]
+type `4y⁴`             = (`2y²` ⊗ `2y²`)[_]
+```
+
+#### `polynomial-mermaid`
+
+```scala mdoc:reset
+import polynomial.`object`.{Store, Monomial}
+import polynomial.mermaid.Mermaid
+import polynomial.morphism.~>
+
+type P[Y] = (Store[Int, _] ~> Monomial[Char, Unit, _])[Y]
 
-type ω[Y] = ((Plant ⊗ Controller) ~> System)[Y]
+println(s"${summon[Mermaid[P]].showSpecific}")
 ```
-<small>(Note: example adapted from the poly book, by [Niu and Spivak](https://topos.site/poly-book.pdf))</small>
+
+```scala mdoc:reset:passthrough
+import polynomial.`object`.{Store, Monomial}
+import polynomial.mermaid.Mermaid
+import polynomial.morphism.~>
+
+type P[Y] = (Store[String, _] ~> Monomial[Char, Unit, _])[Y]
+
+println(s"${summon[Mermaid[P]].showSpecific}")
+```

modules/mermaid/shared/src/main/scala/polynomial/mermaid/Mermaid.scala

@@ -0,0 +1,49 @@
+package polynomial.mermaid
+
+import polynomial.morphism.PolyMap
+import polynomial.`object`.{Monomial, Store}
+import scala.reflect.ClassTag
+
+trait Mermaid[P[_]]:
+    def showGeneric: String
+    def showSpecific: String
+
+object Mermaid:
+
+  given moore[S, A, B](using
+    S: ClassTag[S],
+    A: ClassTag[A],
+    B: ClassTag[B]
+  ): Mermaid[PolyMap[Store[S, _], Monomial[A, B, _], _]] =
+    new Mermaid[PolyMap[Store[S, _], Monomial[A, B, _], _]]:
+
+      def showGeneric: String =
+        s"""|```mermaid
+            |graph LR;
+            |  A:::hidden-->|A|S-->|B|B:::hidden;
+            |```""".stripMargin
+
+      def showSpecific: String =
+        s"""|```mermaid
+            |graph LR;
+            |  A[${A.toString}]:::hidden-->|${A.toString}|S[${S.toString}]-->|${B.toString}|B[${B.toString}]:::hidden;
+            |```""".stripMargin
+
+  given mealy[S, A, B](using
+    S: ClassTag[S],
+    A: ClassTag[A],
+    B: ClassTag[B]
+  ): Mermaid[PolyMap[Store[S, _], Monomial[A, A => B, _], _]] =
+    new Mermaid[PolyMap[Store[S, _], Monomial[A, A => B, _], _]]:
+
+      def showGeneric: String =
+        s"""|```mermaid
+            |graph LR;
+            |  A:::hidden-->|A|S-->|B|B:::hidden;
+            |```""".stripMargin
+
+      def showSpecific: String =
+        s"""|```mermaid
+            |graph LR;
+            |  A[${A.toString}]:::hidden-->|${A.toString}|S[${S.toString}]-->|${A.toString} => ${B.toString}|B[${A.toString} => ${B.toString}]:::hidden;
+            |```""".stripMargin