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

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
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
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
Cse536 Functional Programming 5
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern