Smart contracts in a public ledger system are a predicate-- Bitcoin's creator understood this. They take input-- about the transaction, and perhaps the chain-- and they accept or reject the update to the system. The network of thousands of nodes all around the world doesn't give a darn about the particulars of the computation, they care only that it was accepted. The transaction is free to provide arbitrary side information to help it make its decision.

Deciding if an arbitrarily complex condition was met doesn't require a turing complete language or what not-- the verification of a is in P not NP.

In Bitcoin Script, we do use straight up 'computation' to answer these questions; because that is the simplest thing to do, and for trivial rule sets, acceptably efficient. But when we think about complex rule-- having thousands and thousands of computers all around the world replicate the exact same computation becomes obviously ludicrous, it just doesn't scale.

Fortunately, we're not limited to the non-scalablity-- and non-privacy-- of making the public network repeat computation just to verify it. All we have to do is reconize that computation wasn't what we were doing from the very beginning, verification was!