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Formal Models of Computation

This text delves into the execution of Haskell programs, specifically the power function implemented using recursion. We explore how functional programs execute mathematical operations step by step, illustrating the recursive nature of functions such as power. By examining the evaluation of the power function, we can see how base cases and recursive calls unfold in the computational model, unveiling the principles behind functional programming in Haskell.

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Formal Models of Computation

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  1. Formal Models of Computation Running Haskell Programs – power

  2. How functional programs work… We have seen simple programs such as Let’s now see how they are executed Given the program above, we get the following: But how? power x 0 = 1 power x (n+1) = x * (power x n) power 2 3 8 formal models of computation

  3. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3 formal models of computation

  4. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) 3matches(n+1), assigning 2 to n power 23 formal models of computation

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

  6. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  2 * (power 2 2) formal models of computation

  7. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  2 * (power 2 2) 2matches(n+1), assigning 1 to n formal models of computation

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

  9. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  2 * (2 * (power 2 1)) formal models of computation

  10. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  2 * (2 * (power 2 1)) 1matches(n+1), assigning 0 to n formal models of computation

  11. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  2 * (2 * (2 * (power 2 0))) formal models of computation

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

  13. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  2 * (2 * (2 * (power 2 0))) formal models of computation

  14. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  2 * (2 * (2 * (1))) formal models of computation

  15. How functional programs work… Execution: power x 0 = 1 power x (n+1) = x * (power x n) power 2 3  8 formal models of computation

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