Langage to declare a circuit board
There are a bunch (dozens) of common formats for netlists. 

Netlists describe the logical connections between component pins, and are logically equivalent to a schematic (minus any notes and other information such as rules that is communicated in the schematic- many of which are actually required to create an optimal PCB from the schematic). 

Drawing a good human-readable schematic is an art form. As far as I know nobody has put in the effort it would take into trying to create excellent schematics automatically. I don't see that it would be impossible - there are a number of general rules, and machine learning could suck up all the many examples (assuming it knew which ones were atrocious) and learn from them. 

It's possible to create a PCB without a schematic- the schematic is just for humans to understand, but the netlist does not necessarily contain information on how to handle power connections, differential pairs, controlled impedance conductors, guard rings, shields, parts that need to be close  and so on. If you've ever seen a PCB laid out by a dolt that doesn't understand electrics you will understand- 150mm (6") conductors run to a clock crystal etc. When you start laying out a PCB you usually see the parts (which have to be 'placed' ) and a rat's next of connections that represents the netlist graphically. 

Generally auto-placement and schematics (I've seen a few examples of machine generated schematics) are the hardest for automation. Autorouting is useful in some cases, though humans still tend to do better, so far, with machine assistance that enforces pre-determined rules such as clearances by net, trace width by net, etc.