Christopher Boone, the narrator of Mark Haddon's bestselling novel The Curious Incident of the Dog in the Night-Time, has a penchant for facts. The 15-year-old's story, which begins with the mysterious murder of his neighbour's dog, is peppered with maths problems, science and – because he has Asperger's syndrome and finds messy human emotions incomprehensible – dispassionate observations about the behaviour of the adults around him. All of which makes him a difficult character to put on stage.

I meet the team behind the production at the National Theatre in London. If Marianne Elliott, who is directing Curious Incident there, was feeling anxious before she sat down to talk with me, Haddon and playwright Simon Stephens, the men are not reassuring her. "On some level, everyone will disagree with what we've done," says Stephens, who adapted the story for the stage. "Thanks for that," says Elliott. "You're not staging it literally," Haddon adds. "No one's going to say, 'That's the wrong furniture.'"

That might be because there isn't any. In a corner of Elliott's rehearsal room sits a model showing Bunny Christie's set design; the stage is empty but for a neatly geometric pattern of lines crisscrossing the floor. Haddon admits that this could cause trouble. "I got two sets of letters from readers of the book. One, almost entirely positive, came from people who had someone like Christopher in their family; and an odd set came from people who disagreed with the science and maths and got cross about facts. The press office will be inundated with letters from viewers who are, shall we say, slightly on the spectrum themselves, who find the lack of literalism annoying."

Elliott knows how hard it is to live up to audience anticipation: Michael Morpurgo's War Horse may not have been particularly well known when she worked with Tom Morris and Handspring Puppet Company to stage it at the National in 2007; but five years on, it has become a multi-award-winning international franchise. "I've been through all sorts of different psychological feelings about War Horse," she says. "You're aware that there is a very particular expectation of people coming to see it, and a weight on you to deliver certain things."

Haddon regards her with quiet amusement. If he has ever fretted about living up to his reputation, you wouldn't guess it from his CV, which weaves from children's books (self-illustrated) and TV drama to adults' novels, poetry and, in 2010, his first play, Polar Bears. He asked Stephens to adapt Curious Incident for the stage, not because a theatre had commissioned it, but to satisfy his own curiosity. Ever since the novel was published in 2003, Haddon's agent has been fending off offers, including two people who wanted to turn it into a Broadway musical (an idea Stephens finds hilarious) because Haddon didn't believe it could work on stage. But he liked the idea of "bringing it to life again", and was a fan of Stephens' plays because, he says (to Stephens' evident embarrassment), "You manage to inhabit characters completely yet I recognise your voice in the work."

What's fascinating about Stephens' script is how forthrightly it faces up to the problem of being an adaptation. The novel itself is framed as a book Christopher has written, and on stage we see his teacher, Siobhan, reading from that book; later, she asks him if he would be willing to work with his schoolmates to turn it into a play. The irony, says Stephens, is that "Christopher sees stories as lies, and theatre as dishonest. But it's through the lie that you find the greater truth. That's why you need to expose the mechanics of it."

This exposing, argues Haddon, is the hallmark of all thought-provoking art. "Really good paintings are never just of stuff: they're about how you look at stuff. All half-decent books are about how you read other people, how you get between the lines. And there's hardly a good play in the world that doesn't have some reference to play-acting in it, whether it's a play-within-a-play, or how you act in the drawing room to cover up your secrets."

For Stephens, this point finds echoes in Haddon's work, from his Agent Z children's books to his latest novel, The Red House. . "There is an insistent interrogation of the dignity of reading and writing," he says. "Again and again, Mark returns to characters who are in some kind of crisis, and in that crisis they either learn to make sense of themselves through what they read – or, in the case of Christopher, through what he writes and the process of reading his own book. When I teach playwrights, I always ask the same question: what is the difference between humans and other animals? A very simple answer would be: we read."

Stephens thinks he has gained much from adapting the novel. "Having to put text on stage is good exercise. I just think it made me a better writer: it nourished me intellectually." He doesn't think of himself as a writer, he says, but a "wroughter: the 'wright' in playwright comes from to wrought rather than to write". Writing adaptations is a better means of honing his craft than writing for TV or film would be, he argues. And these ideas of nourishment and honing are becoming more important to him as he gets older. At 41, he is brutally aware how few British playwrights manage to sustain their careers into their 50s and beyond.

Curious Incident also offered Stephens a welcome respite from the more challenging narratives pouring from his imagination. He worked on it in between 2009's Punk Rock, which depicted a shooting in an English private school (and featured a character who shared an obsession with science and some social inadequacy with Haddon's Christopher); and Wastwater in 2011, an oblique study of corrosive relationships between people, and between humankind and the planet. Curious Incident was written at the same time as Three Kingdoms; thrillingly and controversially staged in London earlier this year, this looked at the porn industry and female trafficking. "Those are three really savage plays," admits Stephens. "At the heart of them is a brutality and a darkness. So it was such a joy to go back into the book."

When accepting Haddon's offer, Stephens said he didn't want to approach a theatre until he had finished a workable draft. Nonetheless, he quickly settled on Elliott as the ideal director: "I thought there was a very happy marriage of sensibilities between the book and Marianne." Elliott agrees: "The reason I'm attracted to things like Curious Incident is because Christopher feels like the world is very confusing and he doesn't have a voice. That's definitely how I felt when I was growing up."

Elliott was 27 before she decided to become a theatre director; that was 18 years ago, but she is still drawn to work in which there is "a protagonist – usually female – who finds the world utterly confusing. They don't have a voice in it. That's why I'm a director: because other people can say it better than I can."

As he was producing the first draft, Stephens was also talking to physical theatre company Frantic Assembly about the possibility of writing a play for them – and their fluid, dance-driven style affected how he saw Curious Incident on stage. Sure enough, when I visit the rehearsal room, Frantic's Scott Graham and Steven Hoggett are there too, choreographing a scene in which Christopher (played by Luke Treadaway) struggles to deal with the London underground. "I can't write plays just imagining an entirely fictional world," says Stephens. "I write best when I know the stage I'm writing for. If I know the director, so much the better – and if I know the actor, that's magic."

Stephens talks eloquently about his love of collaboration. Yet it's clear that the key relationship for him here is with Haddon. The pair met a few years ago when they were both on attachment at the National. "We hung out and were grumpy men talking about music," he says. "The great thing about doing this is getting to know Mark."

"Regardless of me," says Elliott.

"It's basically a bromance," agrees Haddon, "with a play attached."