If a cheese sold as pasta-cheese does not melt, is it "cheese"? This might sound like a dumb question:

Back in the day I cooked some pasta for some friends and they bought this cheap grated cheese in the supermarket. I remember my shock because the cheese did not melt no matter how much time we heated it (not with the hot pasta, neither in the microwave nor oven). 

Months later I learned that not all cheeses melt: halloumi, kasseri, manouri, queso blanco, and paneer become a tad creamier, but don't melt the way cheddar, Swiss, and Gruyere do. 

Those made with rennet and not acid, those with higher moister and higher fat are the ones to melt (or melt better). 

But as far as I know, pasta cheese (the cheese used in pasta, it can be parmesan, emmental or even mozarella), are cheeses that might have the melting qualities, to give texture or good looks to the dish (as well as flavour). 

So, is it "right" to sell a "pasta-cheese" which does not melt nor change any physical property (at least visually) when heat is applied?

The cheese's ingredients, translated to english, just in case, are: 


  CHEESE, concentrated DAIRY serum, MILK proteins, dietary fiber (corn dextrine) (4.5%), BUTTER, salt, melting salts(polyphosphates, sodium citrates), modified starch, acidic corrector (citric acid), conservator(potassic sorbate)
That's a processed cheese product. It may be allowed to be called cheese in some places, but that's a matter of product labelling regulations where you happen to be.

The melting is a different issue. I'd expect that product to melt, though possibly not if it has the texture of parmesan - parmesan doesn't really melt on its own though it melts into sauces. And parmesan is commonly served on pasta, so a non-melting (or not really melting) pasta cheese is a thing.