S10ProofInd - Cse536 Functional Programming Lecture#9 Guest...

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Cse536 Functional Programming 1 10/05/15 Lecture #9, Oct 25, 2004 Guest lecture by Tom Harke Todays Topics Review of Proofs by calculation Structure of Proofs by induction over lists Proofs by induction with case analysis Proofs by structural Induction Proofs by induction over Trees Read Chapter 11 - Proofs by induction Home work assignment #5 See Webpage (this assignment is given on Monday, but you have 10 days) Due Wednesday, Nov. 3 (Day of midterm exam) Mid-Term Exam We need to discuss a midterm exam One possibility » Exam distributed one day » Due in class on next meeting » Honor System – Use only two hours of time. » Notes and use of computer allowed.

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Cse536 Functional Programming 2 10/05/15 Remember, No Class Wednesday Sun Mon Tue Wed Thu Fri Sat Oct 24 26 27 28 29 Makeup Class Tim Sheard Regions 30 31 Nov 1 2 3 Midterm exam 4 5 6 Guest Lect. Tom Harke The Haskell Class System 25 Guest Lect. Tom Harke Proofs about Haskell programs No Class
Cse536 Functional Programming 3 10/05/15 Recall the calculation proof method Substitution of equals for equals. if name: f x = e is a definition or a theorem, then we can replace ( f n) with e[n/x] where ever ( f n ) occurs . name: is the name of the definition or theorem for reference in the proof. e[n/x] means e with all free occurrences of x replaced by n For example consider: comp: (f . g) x = f (g x) Now prove that ((f . g) . h) x = (f . (g . h)) x

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Cse536 Functional Programming 4 10/05/15 Proof by calculation Pick one side of the equation and transform using rule comp: above ((f . g) . h) x = by comp: (left to right) (f . g) (h x) = by comp: (left to right) f (g (h x)) = by comp: (right to left) f ((g . h) x) by comp: (right to left) (f . (g . h)) x
Cse536 Functional Programming 5

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