diff --git a/src/lib/lambda/churchPrimitives.ts b/src/lib/lambda/churchPrimitives.ts
index 1b122d6..23396b6 100644
--- a/src/lib/lambda/churchPrimitives.ts
+++ b/src/lib/lambda/churchPrimitives.ts
@@ -1,6 +1,7 @@
 import { equal } from './equality';
 import { parseTerm } from './parser';
 import { cannonize } from './cannonize';
+import { id } from './wellKnownFunctions';
 
 // TODO: do the inverse of these -- generation of church primitives
 
@@ -10,6 +11,10 @@ export function renderAsChurchNumeral(uncannonized) {
   if (expression.type !== 'function') {
     return undefined;
   }
+  // exception: identity fn under beta-eta reduction is church 1
+  if (equal(expression, id)) {
+    return 1;
+  }
   const outerName = expression.argument;
   const inner = expression.body;
   if (inner.type !== 'function') {
diff --git a/src/lib/lambda/normalize.ts b/src/lib/lambda/normalize.ts
index a08e821..b3d9808 100644
--- a/src/lib/lambda/normalize.ts
+++ b/src/lib/lambda/normalize.ts
@@ -1,4 +1,4 @@
-import { bReducable, bReduce } from './operations';
+import { bReducable, bReduce, eReducable, eReduce } from './operations';
 
 // Call by name eval strategy
 // Expression -> Expression (with a depth overflow)
@@ -22,6 +22,9 @@ function leftmostOutermostRedex(expression){
   if(bReducable(expression)) {
     return bReduce(expression);
   }
+  if (eReducable(expression)) {
+    eReduce(expression);
+  }
   if (expression.type === 'function'){
     const res = leftmostOutermostRedex(expression.body);
     if (res === undefined) {
diff --git a/src/lib/lambda/wellKnownFunctions.ts b/src/lib/lambda/wellKnownFunctions.ts
new file mode 100644
index 0000000..1bc9d6e
--- /dev/null
+++ b/src/lib/lambda/wellKnownFunctions.ts
@@ -0,0 +1 @@
+export const id = {"type":"function","argument":"a","body":{"type":"variable","name":"a"}};