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How to transform the key and value of a each entry set of a Map using Java 8?

I have a Map<String, String> that I want to transform to a Map<Type1,Type2> using Java streams.

This is what I tried but I think I am getting the syntax wrong:

myMap.entrySet()
.stream()
.collect(Collectors.toMap(e -> Type1::new Type1(e.getKey()), e -> Type2::new Type2(e.getValue))));

Also tried

myMap.entrySet()
    .stream()
    .collect(Collectors.toMap(new Type1(Map.Entry::getKey), new Type2(Map.Entry::getValue));

But I just keep running compile errors. How do I do this transform?

It looks like what you really want is

 myMap.entrySet()
     .stream()
     .collect(Collectors.toMap(
         e -> new Type1(e.getKey()), e -> new Type2(e.getValue())));

though I admit it's honestly difficult to tell.

myMap.entrySet().stream()
     .map(entry -> new AbstractMap.SimpleEntry(new Type1(entry.getKey()), new Type2(entry.getValue()))
     .collect(Collectors.toMap(Map.Entry::getKey, Map.Entry::getValue))

https://docs.oracle.com/javase/7/docs/api/java/util/AbstractMap.SimpleEntry.html

Or more elegantly:

myMap.entrySet().stream()
     .map(this::getEntry)
     .collect(Collectors.toMap(Map.Entry::getKey, Map.Entry::getValue));

private Map.Entry<Type1, Type2> getEntry(Map.Entry<String, String> entry) { 
     return new AbstractMap.SimpleEntry(new Type1(entry.getKey()), new Type2(entry.getValue());
}

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