[lo_zamoyski]

> Programming languages were designed to do useful stuff. They can't do this without hardware. There are always concerns of practicality.

Programming languages are formalisms, and formalisms predate machines that simulate them, even if programming languages only really took off with machinery able to simulate them. You can simulate a programming language entirely with pen and paper if you wanted (tedious, but possible; the lambda calculus was entirely theoretical when when conceived). Regardless, while the utility of programming languages is related to there being machines that can simulate them, the distinction remains.

> NAND gates are computationally atomic

They're an implementation detail of the hardware being used. There is no necessarily relation between a language and a NAND gate. It is not as if, by dissecting a language, you will discover a bunch of NAND gates bounding around underneath. A language doesn't reduce to NAND gate operations. It just so happens that NAND gates are incredibly useful for implementation and simulation. You can implement a fully mechanical computer, or a water computer, if you wanted, even if it isn't very practical.

Software is a mental construct that hardware can simulate.