The Constitution and Sharia Law would be very compatible.
Basically, the Constitution is an abstract that gives the basic framework for our nation.
And Sharia Law would inact the "Rights" that the Constitution guarantees for all Americans.
Again, where does the quran encourage liberty, equal justice and the pursuit of hapiness? If it isn't in there they are not compatible.
paraphrasing
freedom of speech vs no one can speak against islam or their diety mohammed
the right to bear arms vs islam will cut your arm/hand off
the gov't can't move in your house vs we can tell you how to dress inside your house
protection from unreasonalbe searches vs if you are not muslim this does not apply to you
don't have to witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation. vs if you are not muslim this does not apply to you, "muslims" have the right to take whatever belongs to a person of another religion (as long as you kill the male household member, first).
right to a speedy and public trial, by an impartial jury vs if you are not muslim this does not apply to you
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people. vs if you are not muslim this does not apply to you
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Can you show where this would be different, sunni? did you join islam to be part of the 'legion' (you read the Bible, you should know what that means)?