More type mystery

[Marc Petit-Huguenin]

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With these static methods:

static<T> UnaryOperator<UnaryOperator<T>> ZERO() { return p -> x -> x; }
static<T> UnaryOperator<UnaryOperator<T>> ONE() { return p -> x -> p.apply(x); }
static<T> Function<T,UnaryOperator<T>> TRUE() { return x -> y -> x; }
static<T> Function<T,UnaryOperator<T>> FALSE() { return x -> y -> y; }
static<T>
Function<UnaryOperator<UnaryOperator<Function<T,UnaryOperator<T>>>>,Function<T,UnaryOperator<T>>>
IS_ZERO() { return n -> n.apply(x -> FALSE()).apply(TRUE()); }
static<T>
Function<UnaryOperator<UnaryOperator<Function<T,UnaryOperator<T>>>>,Function<T,UnaryOperator<T>>>
              IS_ZERO(Class<T> t) { return n -> n.apply(x ->
FALSE()).apply(TRUE()); }
static boolean toBoolean(Function<Boolean,UnaryOperator<Boolean>> f) { return
f.apply(true).apply(false); }


Why is this not compiling:

System.out.println(toBoolean(IS_ZERO().apply(ZERO())));
System.out.println(toBoolean(IS_ZERO().apply(ONE())));

Test.java:18: error: method toBoolean in class Test cannot be applied to given
types;
                System.out.println(toBoolean(IS_ZERO().apply(ZERO())));
                                   ^
  required: Function<Boolean,UnaryOperator<Boolean>>
  found: Function<Object,UnaryOperator<Object>>
  reason: argument mismatch; Function<Object,UnaryOperator<Object>> cannot be
converted to Function<Boolean,UnaryOperator<Boolean>>
Test.java:19: error: method toBoolean in class Test cannot be applied to given
types;
                System.out.println(toBoolean(IS_ZERO().apply(ONE())));
                                   ^
  required: Function<Boolean,UnaryOperator<Boolean>>
  found: Function<Object,UnaryOperator<Object>>
  reason: argument mismatch; Function<Object,UnaryOperator<Object>> cannot be
converted to Function<Boolean,UnaryOperator<Boolean>>
2 errors

But this works fine:

Function<UnaryOperator<UnaryOperator<Function<Boolean,UnaryOperator<Boolean>>>>,Function<Boolean,
                    UnaryOperator<Boolean>>> IZ = IS_ZERO();
System.out.println(toBoolean(IZ.apply(ZERO())));
System.out.println(toBoolean(IZ.apply(ONE())));

And this works fine:

System.out.println(toBoolean(IS_ZERO(Boolean.class).apply(ZERO())));
System.out.println(toBoolean(IS_ZERO(Boolean.class).apply(ONE())));


Thanks.

- -- 
Marc Petit-Huguenin
Email: marc at petit-huguenin.org
Blog: http://blog.marc.petit-huguenin.org
Profile: http://www.linkedin.com/in/petithug
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