CSE-321 Programming Languages (So Many Topics)

1. CSE-321 Programming Languages(So Many Topics) 박성우 POSTECH May 29, 2006

2. Outline for Today's Lecture • Existential types • Dependent types • Call-by-name and call-by-need • CPS (Continuation-passing style) transformation • Constructive logic • Curry-Howard isomorphism • Module system of Standard ML • -calculus • LF type theory • Twelf for mechanizing proofs

3. List Reversal in TML datatype list = Nil | Cons of (int * list); valrec append = fn Nil => (fn x => Cons (x, Nil)) | Cons (h, t) => (fn x => Cons (h, append t x)); valrec reverse = fn Nil => Nil | Cons (h, t) => append (reverse t) h; val l = Cons (1, Cons (2, Cons (3, Cons (4, Nil)))); val id = fn x => x; id reverse l

4. Data Constructors in TML datatype list = Nil | Consof (int * list); valrec append = fn Nil => (fn x => Cons (x, Nil)) | Cons (h, t) => (fn x => Cons (h, append t x)); valrec reverse = fn Nil => Nil | Cons (h, t) => append (reverse t) h; val l = Cons (1, Cons (2, Cons (3, Cons (4, Nil)))); val id = fn x => x; id reverse l

5. Patterns in TML datatype list = Nil | Consof (int * list); valrec append = fnNil => (fn x => Cons (x, Nil)) | Cons (h, t) => (fn x => Cons (h, append t x)); valrec reverse = fnNil => Nil | Cons (h, t) => append (reverse t) h; val l = Cons (1, Cons (2, Cons (3, Cons (4, Nil)))); val id = fn x => x; id reverse l

6. More Patterns in TML datatype list = Nil | Consof (int * list); valrecappend = fnNil => (fnx => Cons (x, Nil)) | Cons (h, t) => (fnx => Cons (h, append t x)); valrecreverse = fnNil => Nil | Cons (h, t) => append (reverse t) h; vall = Cons (1, Cons (2, Cons (3, Cons (4, Nil)))); valid = fnx => x; id reverse l

7. Patterns val_ = 1; val true = true; val Cons (h, t) = Cons (1, Nil); val (x, y) = (1, ~1); val (x) = 1; val (x : int) = 1;

8. Match Rule : pat => exp datatype list = Nil | Cons of (int * list); valrec append = fnNil => (fn x => Cons (x, Nil)) | Cons (h, t) => (fn x => Cons (h, append t x)); valrec reverse = fnNil => Nil | Cons (h, t) => append (reverse t) h; val l = Cons (1, Cons (2, Cons (3, Cons (4, Nil)))); val id = fnx => x; id reverse l

9. Outline • Patterns in TML V • Syntax of TML • Typing and translation

10. Syntax for TML • scontype  ::= int  |  bool  |  unit • sconpat  ::= num  |  true  |  false  |  () • scon  ::= num  |  true  |  false  |  ()  • op  ::= +  |  -  | *  |  =  |  <> • ty  ::= scontype  |  tycon  |  (ty * ty)  | (ty -> ty)  |  (ty) • pat  ::= _  |  sconpat  |  vid <pat>  |  (pat,pat)  |  (pat)  |  (pat:ty) • num  ::= <integer constants> • tycon  ::= <alphanumeric identifiers> • vid  ::= <alphanumeric identifiers> • conbinding  ::= vid <ofty> • conbind  ::= conbinding <| conbind> • dec  ::= valpat = exp  |  val rec pat = exp  |  datatypetycon = conbind • mrule  ::= pat=>exp • match  ::= mrule <|match> • exp  ::= scon  |  vid  |  (exp,exp)  |  letdecinexpend   | (exp)  |  expexp   |  expopexp   |  (exp : ty) | fn match • dlist  ::= <dec;>* • program  ::= dlistexp

11. Types • scontype  ::= int  |  bool  |  unit • tycon  ::= <alphanumeric identifiers> • ty  ::= scontype  |  tycon  |  (ty * ty)  | (ty -> ty)  |  (ty)

12. Patterns • sconpat  ::= num  |  true  |  false  |  () • vid  ::= <alphanumeric identifiers> • pat  ::= _  |  sconpat  |  vid <pat>  |  (pat, pat)  |  (pat)  |  (pat:ty)

13. Declarations • vid  ::= <alphanumeric identifiers> • conbinding  ::= vid <ofty> • conbind  ::= conbinding <| conbind> • dec  ::= valpat = exp  |  val rec pat = exp  |  datatypetycon = conbind

14. Expressions and Programs • scon  ::= num  |  true  |  false  |  ()  • op  ::= +  |  -  | *  |  =  |  <> • mrule  ::= pat=>exp • match  ::= mrule <|match> • exp  ::= scon  |  vid  |  (exp,exp)  |  letdecinexpend   |(exp)  |  expexp   | expopexp   |  (exp : ty)| fn match • dlist  ::= <dec;>* • program  ::= dlistexp

15. Outline • Patterns in TML V • Syntax of TML V • Typing and translation

16. Monomorphic Typing • No polymoprhic types, i.e., no type variables • every expression has a unique monomorphic type val id = fn x => x; id 1

17. Typing and Translation • Ast.program • source program • Core.programty • program with type annotations • Mach.code • machine code • val tprogram : Ast.program -> Core.programty • val programty2code : Core.programty -> Mach.code

18. 50% of Assignment 8 type venv = (avid, loc) dict type env = venv * int val pat2code : Mach.label * Mach.label * loc -> Core.pat -> Mach.code * venv val exp2code : env * Mach.label -> Core.exp -> Mach.code * Mach.rvalue val dec2code : env * Mach.label -> Core.dec -> Mach.code * env val matchty2code : env * Mach.label -> Core.matchty -> Mach.code

19. The Remaining 49% • Representation for functions • Representation for recursive functions • Context switch • Function arguments and return values ) These questions test your understanding of closures.

20. The Remaining 1% • Representation for pairs • Representation for data constructors • Registers • Heap • Optimizations • 하면서 보내 버리는 시간 • ...

21. Advice on Assignment 8

22. Don't get scared by Parjong's misleading message on the discussion board. 제 목: 허허허.. ㅠ_ㅠ 교수님 HW8.. 도저히.. -_-aa 그 시간에 끝낼 수 있을 거라는 생각이 안드는데요;; • Everyone of you can finish this assignment!

23. Assignment 8 • will be the most fun of all the assignments this course offers. • will be the most rewarding experience you can have in this course. • Discuss with your classmates (not just with your partner) • Start early! • Sample solution: about 600 lines of code • You will write 300 ~ 500 lines of code.