1 / 14

CSE-321 Programming Languages Review

CSE-321 Programming Languages Review. 박성우. POSTECH June 14, 2011. Topics Covered. SML programming Inductive proofs  -Calculus Operational semantics De Bruijn indexes Simply-typed  -calculus Abstract machine Subtyping, Object-orientation (Assignment 7) Recursive type Polymorphism

veta
Download Presentation

CSE-321 Programming Languages Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CSE-321 Programming LanguagesReview 박성우 POSTECH June 14, 2011

  2. Topics Covered • SML programming • Inductive proofs • -Calculus • Operational semantics • De Bruijn indexes • Simply-typed -calculus • Abstract machine • Subtyping, Object-orientation (Assignment 7) • Recursive type • Polymorphism • Type reconstruction, W-algorithm • Compilation (Assignment 8, Part 2)

  3. 321 강의의 범위 • CMU 15-312 Principles of Programming Languages 수준 • http://www.cs.cmu.edu/~rwh/courses/ppl/ • http://www.cs.cmu.edu/~rwh/courses/ppl/schedule.html

  4. Assignments • A1: 26, 95.27 (SML programming 1) • A2: 26, 92.4 (SML programming 2) • A3: 26, 81.54 (SML programming 3) • A4: 25, 89.6 (Implementing -calculus) • A5: 25, 91.4 (Typechecking) • A6: 22, 70.18 (De Bruijn indexes) • A7: 18, 79.17 (Featherweight Java) • A8: ?, ? (Type reconstruction and translation)

  5. 2006 vs. 2007 vs. 2009 vs. 2010 • Assignment 4 (Implementing -calculus) • average 2006: 88.0 • average 2007: 88.57 • average 2009: 90.17 • average 2010: 93.48 • average 2011: 89.6 • Assignment 6 (De Bruijn indexes) • average 2007: 59.13 • average 2009: 56.12 • average 2010: 54.55 • average 2011: 70.18 • Assignment 7 (Featherweight Java) • average 2006: 71.30 • average 2007: 77.71 • average 2009: 68.13 • average 2010: 66.92 • average 2011: 79.17

  6. 절대 평가 • Exam 20% * 2 • Quiz 10% • Assignment 50% • A1, A2, A3: 2.5% • A4: 5% • A5: 5% • A6: 10% • A7: 7.5% • A8 (Part 1): 15% • A8 part 2: Extra 25%

  7. 학점

  8. LICS 2011(Logic in Computer Science) http://www.postech.ac.kr/~gla/cs433/index.html

  9. Paper-and-Pencil Proof

  10. Proof in Coq • Strings of matched parentheses Inductive T : Set := | eps : T | cons : E -> T -> T. Inductive mparen : T -> Prop := ... Inductive lparen : T -> Prop := ... Theorem mparen2lparen : forall s:T, mparen s -> lparen s. Proof. intros s H. induction H. apply Leps. rewrite <- concat_eps. auto using Leps, Lseq. auto using lparenConcat. Qed.

  11. Pythagoras' theorem • Proof Theorem even_is_even_times_even: forall (n : nat), even (n * n) -> even n. Theorem main_thm: forall (n p : nat), n * n = double (p * p) -> p = 0. Definition irrational (x : R) : Prop := forall (p : Z) (q : nat), q <> 0 -> x <> (p / q)%R. Theorem irrational_sqrt_2: irrational (sqrt 2%nat).

  12. Simply-typed -Calculus • Proof of determinism of evaluations Theorem eval_deterministic : forall t t' t'', eval t t' -> eval t t'' -> t' = t''. • Proof of type safety in simply-typed lambda-calculus

  13. 5 4 Four Color Problem • "Every map can be colored with no more than 4 colors." • Proposed in 1852 • Computer-based solution published in 1976 • Formalization of the proof in 1994 • theorem prover Coq

  14. 감사합니다 Life is an exciting adventure... gla@postech.ac.kr

More Related