diff --git a/day01-hard/main.scm b/day01-hard/main.scm
index 87ee9a0..7894972 100755
--- a/day01-hard/main.scm
+++ b/day01-hard/main.scm
@@ -21,12 +21,12 @@
 
 (define (id value) value)
 (define (is-not value) (lambda (x) (not (equal? x value))))
-(define is-not-empty (lambda (x) (not (null? x))))
+(define (is-not-empty value) (not (null? value)))
 
 (define (prepend first-value) (lambda (rest) (cons first-value rest)))
 
-(define Y (lambda (f) (f (lambda (x) ((Y f) x)))))
-(define Y2 (lambda (f) (f (lambda (x y) ((Y2 f) x y)))))
+(define (Y f) (f (lambda (x) ((Y f) x))))
+(define (Y2 f) (f (lambda (x y) ((Y2 f) x y))))
 
 (define (reduce-right reducer initial) (Y
   (lambda (f) (lambda (values)
@@ -42,7 +42,7 @@
     right)
   left))
 
-;=============== starts-with ======================
+;=============== flat ======================
 (define flat (reduce-right concat '()))
 
 (assert-eq "flat test 1 failed"