1. Programming Paradigms CPSC 449 Week 5 Prepared by : Mona Hosseinkhani, ArashAfshar Winter 2014 Department of Computer Science, University of Calgary

2. Understanding definitions • Alternatives • Evaluate on particular inputs • Using an implementation (e.g. GHCi) • By hand (by performing a line by line calculation) • Argue about how it behaves in general • Example

3. Evaluation on particular inputs

4. Analyze the behavior in general • Find general properties of length • length [x] = 1 • length (xs ++ ys) = length xs + length ys • We could show • This is called Symbolic Evaluation. • Rather than evaluating length at a particular value, we used a variable x. So for all values of x:

5. Understanding definitions • Symbolic evaluation is an important part of the proofs. • But we also need another principle: induction to do most proofs for recursive functions • Note that understanding and describing definitions in imperative languages (e.g. Pascal) is very difficult

6. Program correctness: recall • Test on inputs • Property-based test • Proof

7. Total correctness (proof)

8. Example • No termination

9. Lazy evaluation • Evaluate • Haskell evaluates an expression only if its value is actually needed.

10. Questions hossem@ucalgary.ca

11. Install bmp package for next assignment • http://hackage.haskell.org/package/bmp • $ cabal update • $ cabal install cabal-install • if the last step is successful execute the following • $ cabal install bmp