Sketch out autodiff types

packages/rose/src/ad.rose

@@ -0,0 +1,52 @@
+pub class AD T {
+  type D
+}
+
+instance AD () {
+  type D = ()
+}
+
+instance AD bool {
+  type D = bool
+}
+
+instance AD i32 {
+  type D = i32
+}
+
+instance AD u32 {
+  type D = u32
+}
+
+instance AD i64 {
+  type D = i64
+}
+
+instance AD u64 {
+  type D = u64
+}
+
+instance AD f32 {
+  type D = (f32, f32)
+}
+
+instance AD f64 {
+  type D = (f64, f64)
+}
+
+instance T (AD T) => AD []T {
+  type D = []((AD T).D)
+}
+
+instance A B (AD A) (AD B) => AD (A, B) {
+  type D = ((AD A).D, (AD B).D)
+}
+
+instance A B (AD A) (AD B) => AD (A | B) {
+  type D = (AD A).D | (AD B).D
+}
+
+pub val A B (AD A) (AD B) => linearize : (A -> B) -> (AD A).D -> (AD B).D
+
+pub val A B (AD A) (AD B) =>
+  transpose : ((AD A).D -> (AD B).D) -> (AD A).D -> ((AD B).D, () -> ())