The term expressive in the question shall bear the same meaning as in the following sentence:
A Turing Machine is as expressive as Lambda Calculus.
While learning Haskell, I had noticed that there are 2 ways to achieve the same effect, namely Pattern Matching and Case Expression. For example,
-- Pattern Matching
not True = False
not False = True
-- Case Expression
not x = case x of True -> False
False -> True
I am also fully aware that Pattern Matching is actually a form of syntax sugar that will be compiled into Case Expression.
Therefore, we can be very sure that every Pattern Matching expression can be converted to Case Expression.
So, this is my question: Is the following statement true?
Every Case Expression can be re-written using Pattern Matching.
Regardless of the truthiness of the statement above, I would be glad if you could provide a formal proof to support your answer.
The motivation that drove me to seek answer for this question is because I'm currently designing my own language, which I wish to have as less feature as possible, but not too minimal like Lambda Calculus which only have 3 features.