Formal Models of Computation

1. Formal Models of Computation Running Haskell Programs - take

2. How functional programs work… take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) Main> take 3 [1..] [1,2,3] • Comments: • [1..] is an infinite data structure • take is built-in in Haskell • If you want to try the definition above, change its name to myTake or something like that… formal models of computation

3. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3[1..] • 3matches(n+1)assigning 2 to n • The infinite list [1..] matches (x:xs), assigning 1 to x and [2..] (aha!) to xs formal models of computation

4. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(take 2 [2..]) formal models of computation

5. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(take 2 [2..]) formal models of computation

6. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(take 2 [2..]) • 2matches(n+1)assigning 1 to n • The infinite list [2..] matches (x:xs), assigning 2 to x and [3..] to xs formal models of computation

7. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(2:(take 1 [3..])) formal models of computation

8. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(2:(take 1 [3..])) formal models of computation

9. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(2:(take 1 [3..])) • 1matches(n+1)assigning 0 to n • The infinite list [3..] matches (x:xs), assigning 3 to x and [4..] to xs formal models of computation

10. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(2:(3:(take 0 [4..]))) formal models of computation

11. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(2:(3:(take 0 [4..]))) formal models of computation

12. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  1:(2:(3:[]))) formal models of computation

13. How functional programs work… Execution: take 0 xs = [] take (n+1) (x:xs) = x:(take n xs) take 3 [1..]  [1,2,3] formal models of computation