diff --git a/Pantograph/Delate.lean b/Pantograph/Delate.lean
index 38d8bda..ad923aa 100644
--- a/Pantograph/Delate.lean
+++ b/Pantograph/Delate.lean
@@ -12,24 +12,56 @@ open Lean
 
 namespace Pantograph
 
-structure ProjectionApplication where
-  projector: Name
-  numParams: Nat
-  inner: Expr
+inductive Projection where
+  -- Normal field case
+  | field (projector : Name) (numParams : Nat)
+  -- Singular inductive case
+  | singular (recursor : Name) (numParams : Nat) (numFields : Nat)
+
+/-- Converts a `.proj` expression to a form suitable for exporting/transpilation -/
+@[export pantograph_analyze_projection]
+def analyzeProjection (env: Environment) (e: Expr): Projection :=
+  let (typeName, idx, _) := match e with
+    | .proj typeName idx struct => (typeName, idx, struct)
+    | _ => panic! "Argument must be proj"
+  if (getStructureInfo? env typeName).isSome then
+    let ctor := getStructureCtor env typeName
+    let fieldName := getStructureFields env typeName |>.get! idx
+    let projector := getProjFnForField? env typeName fieldName |>.get!
+    .field projector ctor.numParams
+  else
+    let recursor := mkRecOnName typeName
+    let ctor := getStructureCtor env typeName
+    .singular recursor ctor.numParams ctor.numFields
+
+def anonymousLevel : Level := .mvar ⟨.anonymous⟩
 
 @[export pantograph_expr_proj_to_app]
-def exprProjToApp (env: Environment) (e: Expr): ProjectionApplication :=
-  let (typeName, idx, inner) := match e with
-    | .proj typeName idx inner => (typeName, idx, inner)
-    | _ => panic! "Argument must be proj"
-  let ctor := getStructureCtor env typeName
-  let fieldName := getStructureFields env typeName |>.get! idx
-  let projector := getProjFnForField? env typeName fieldName |>.get!
-  {
-    projector,
-    numParams := ctor.numParams,
-    inner,
-  }
+def exprProjToApp (env: Environment) (e: Expr): Expr :=
+  let anon : Expr := .mvar ⟨.anonymous⟩
+  match analyzeProjection env e with
+  | .field projector numParams =>
+    let info := match env.find? projector with
+      | .some info => info
+      | _ => panic! "Illegal projector"
+    let callee := .const projector $ List.replicate info.numLevelParams anonymousLevel
+    let args := (List.replicate numParams anon) ++ [e.projExpr!]
+    mkAppN callee args.toArray
+  | .singular recursor numParams numFields =>
+    let info := match env.find? recursor with
+      | .some info => info
+      | _ => panic! "Illegal recursor"
+    let callee := .const recursor $ List.replicate info.numLevelParams anonymousLevel
+    let typeArgs := List.replicate numParams anon
+    -- Motive type can be inferred directly
+    let motive := .lam .anonymous anon anon .default
+    let major := e.projExpr!
+    -- Generate a lambda of `numFields` parameters, and returns the `e.projIdx!` one.
+    let induct := List.foldl
+      (λ acc _ => .lam .anonymous anon acc .default)
+      (.bvar $ (numFields - e.projIdx! - 1))
+      (List.range numFields)
+    mkAppN callee (typeArgs ++ [motive, major, induct]).toArray
 
 def _root_.Lean.Name.isAuxLemma (n : Lean.Name) : Bool := n matches .num (.str _ "_auxLemma") _
 
@@ -288,7 +320,6 @@ partial def serializeSortLevel (level: Level) : String :=
   | _, .zero => s!"{k}"
   | _, _ => s!"(+ {u_str} {k})"
 
-
 /--
  Completely serializes an expression tree. Json not used due to compactness
 
@@ -375,12 +406,17 @@ partial def serializeExpressionSexp (expr: Expr) : MetaM String := do
       -- NOTE: Equivalent to expr itself, but mdata influences the prettyprinter
       -- It may become necessary to incorporate the metadata.
       self inner
-    | .proj _ _ _ => do
+    | .proj typeName idx inner => do
       let env ← getEnv
-      let projApp := exprProjToApp env e
-      let autos := String.intercalate " " (List.replicate projApp.numParams "_")
-      let inner ← self projApp.inner
-      pure s!"((:c {projApp.projector}) {autos} {inner})"
+      match analyzeProjection env e with
+      | .field projector numParams =>
+        let autos := String.intercalate " " (List.replicate numParams "_")
+        let inner' ← self inner
+        pure s!"((:c {projector}) {autos} {inner'})"
+      | .singular _ _ _ =>
+        let typeName' := serializeName typeName (sanitize := false)
+        let e' ← self e
+        pure s!"(:proj {typeName'} {idx} {e'})"
   -- Elides all unhygenic names
   binderInfoSexp : Lean.BinderInfo → String
     | .default => ""
diff --git a/Test/Delate.lean b/Test/Delate.lean
index 013be73..517a394 100644
--- a/Test/Delate.lean
+++ b/Test/Delate.lean
@@ -96,6 +96,23 @@ def test_instance (env: Environment): IO LSpec.TestSeq :=
     let _expr := (← runTermElabMInMeta <| elabTerm s) |>.toOption |>.get!
     return LSpec.TestSeq.done
 
+def test_projection_prod (env: Environment) : IO LSpec.TestSeq:= runTest do
+  let struct := .app (.bvar 1) (.bvar 0)
+  let expr := .proj `Prod 1 struct
+  let .field projector numParams := analyzeProjection env expr |
+    fail "`Prod has fields"
+  checkEq "projector" projector `Prod.snd
+  checkEq "numParams" numParams 2
+
+def test_projection_exists (env: Environment) : IO LSpec.TestSeq:= runTest do
+  let struct := .app (.bvar 1) (.bvar 0)
+  let expr := .proj `Exists 1 struct
+  let .singular recursor numParams numFields := analyzeProjection env expr |
+    fail "`Exists has no projectors"
+  checkEq "recursor" recursor `Exists.recOn
+  checkEq "numParams" numParams 2
+  checkEq "numFields" numFields 2
+
 def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
   [
     ("serializeName", do pure test_serializeName),
@@ -104,6 +121,8 @@ def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
     ("Sexp from elaborated expr", test_sexp_of_elab env),
     ("Sexp from expr", test_sexp_of_expr env),
     ("Instance", test_instance env),
+    ("Projection Prod", test_projection_prod env),
+    ("Projection Exists", test_projection_exists env),
   ]
 
 end Pantograph.Test.Delate