[docs/lang0] nat-even-odd.scm -- by wrap and Y -- instead of direct r…

…ecursion

TODO.md

@@ -1,5 +1,4 @@
-[docs/lang0] remove `(fix)`
-[docs/lang0] remove `(fixpoint)`
+[docs/lang0] remove `(fix)` & `(fixpoint)`
 [docs/lang0] 用中文重新整理 lambda encoding 相关的知识，形成一本书。
 [docs/lang0] 用中文重新整理 lambda encoding 和 self type 相关的知识。
 [lang0] 支持直接递归函数与相互递归函数，不能判断等价的地方就不判断。

docs/lang0/examples/nat-even-odd.scm

@@ -1,22 +1,25 @@
 (import "./boolean.scm" true false if and or not)
 (import "./nat-church.scm" zero add1 sub1 zero?)
 (import "./nat-church.scm" one two three four)
+(import "./fix.scm" Y)
 
-(define (even? n)
-  (if (zero? n) true
-      (if (zero? (sub1 n)) false
-          (even? (sub1 (sub1 n))))))
+(define even?-wrap
+  (lambda (even?)
+    (lambda (n)
+      (if (zero? n) true
+          (if (zero? (sub1 n)) false
+              (even? (sub1 (sub1 n))))))))
 
-(define (odd? n)
-  (if (zero? n) false
-      (if (zero? (sub1 n)) true
-          (odd? (sub1 (sub1 n))))))
+(define even? (Y even?-wrap))
 
-even?
-odd?
+(define odd?-wrap
+  (lambda (odd?)
+    (lambda (n)
+      (if (zero? n) false
+          (if (zero? (sub1 n)) true
+              (odd? (sub1 (sub1 n))))))))
 
-(assert-equal even? even?)
-(assert-equal odd? odd?)
+(define odd? (Y odd?-wrap))
 
 (assert-equal
   (even? zero)