It's both. It's the lambda calculus and the turing machine. It's useful to understand both the way that the machine works, down the the assembly level, and if

It's both. It's the lambda calculus and the turing machine. It's useful to understand both the way that the machine works, down the the assembly level, and if possible below, since it lets you write code that fits the way the hardware works well. It's useful to understand the symbolic side, since it lets you reason about algorithms, and write code that fits the way mathematics work. You can't get away from either.