It's also a place that saw continuous violence during Northern Ireland's 30-year sectarian conflict. One of the many political events commemorated in its gigantic street murals is Bloody Sunday when, in 1972, British paratroopers shot dead 13 unarmed civilians. Derry-Londonderry's public art tends to be massive, in your face and shriekingly symbolic; this city was experimenting with creative shock value while 2013's Turner nominees were still children.

Given such a raw background, the fact the exhibition is taking place in Ebrington, a former British military barracks - now (metaphor alert) accessed by the city's new Peace Bridge - is as provocative a statement as any artist could dream up. "How will you REACT?" yell the posters. The subtext is: forget those art critics blathering in London, 1,000 kilometres away on a neighbouring island. Here's a show to engage and challenge a local population that (sometimes literally) takes no hostages.

As a result, it's probably the most interactive Turner Prize exhibition there's ever been. From the moment you enter the first gallery to encounter David Shrigley's , you're no longer simply in viewer mode. A naked man stands surrounded by easels and everyone is invited to do what art students do in their first year: draw a nude. The fact that he's three metres tall, animatronic, blinks noisily, pees (also noisily) into a bucket, and bears as much relation to a real human being as Shrigley's cartoons in newspaper naturally didn't stop an opening-day controversy, on Northern Ireland's evening news, about schoolchildren taking part in the exhibition.

Laure Prouvost's work is in the second gallery. Prouvost, 35, is French but works in London, and was invited by Tate Britain to reflect on the last few years of German artist Kurt Schwitters in England's Lake District. The title comes from Schwitters' girlfriend's constant refrain, "Want tea?" and visitors to the installation sit at a dimly-lit tea-table of misshapen pottery and watch a film about Prouvost's mysterious grandfather who has disappeared through a trapdoor while tunnelling to Africa.

In an adjacent pink-carpeted room, another Prouvost film specially created for Derry-Londonderry is running on a loop. "Please mind your head on entering and leaving ," says a polite sign at the entrance. While it's literally true that you have to duck to enter the womb-like enclosure, the warning could also apply to your sense of reality. Both videos feature Prouvost's whispery, French-accented narration, which makes domesticity seem seductive yet dangerous: behind the flickering gas-flames, packets of crisps, fried eggs and cosy tea-pots, something much darker is lurking.

On the opening night, a line of schoolchildren marched round the gloom bearing trays of wobbly cups and singing, "Wantee, would you like some tea? Wantee, would you like some tea?" while Prouvost's background voiceover grew increasingly panic-stricken. This, unlike Shrigley's nude, caused no controversy. Sex is always going to be more problematic in Ireland, north or south, than hints of violence over tea.

Upstairs, there are six of nominee Lynette Yiadom-Boakye's paintings, each executed in a single day. Two are new pieces; of the others, is owned by Adam Clayton, bassist of Irish rock band U2, and is owned by Tate Britain. In theory, Yiadom-Boakye, who was born in London in 1977 of Ghanaian descent, is creating what most people would consider "proper" art, i.e. portraits in oil on canvas. But her figures don't spring from the formal Western canon of portraiture. They're black men with white slashes of eyes and teeth and no historical context, and the room's lights are deliberately kept low so that you have to approach them, face to face.

And in the last gallery, there's Tino Sehgal - or, to be more accurate, there isn't Tino Sehgal. There's nothing. No visible work of any description sullies the white space. Instead, a few individuals in black T-shirts wait to engage with an unsuspecting public. Sehgal, 37, who lives in Berlin but happened to be born in London (and therefore qualifies for Turner Prize inclusion) is probably best known for his 2012 work at Tate Modern's Turbine Hall, in which visitors and participants were encouraged to engage.

For Derry-Londonderry, he is re-visiting his 2003 work, . Here's how it works. One of the black-T-shirted "interpreters", all of whom are locals trained by a Sehgal assistant, will tell you that he'd like to make an offer: he'll give you £2 (about HK$25) if you have a meaningful discussion about the market economy.

As it happens, the economy is a touchy subject in Northern Ireland. A recent example of public art occurred during June's G8 summit at Lough Erne Resort in County Fermanagh, when deserted shops in the region were given paint jobs to impress presidents Barack Obama and Vladimir Putin as their cavalcades swept past. Unemployment is high, wages are low. Visitors on the first day thought more people would engage with Sehgal's concept than the other three nominees simply because they could do with the money.

What seems more likely is that locals will come because they're curious and they know that the £25,000 top prize, awarded on December 2, is part of the bigger picture of the city's renewal. This Turner Prize isn't about high-end art in slick galleries. Whichever side they're on, Derry-Londonderry people will REACT to it passionately.

"Pretentious nonsense," said one of the policemen on duty outside the barracks. But at least he'd gone inside to have a look. As Eamonn McCann, a social activist and one of the city's best-known commentators, who witnessed Bloody Sunday 40 years ago, said: "You have to think it through for yourself. Most of the people on my street are coming because they want to know what it feels like. I think that Derry will draw more people to this exhibition than London would."