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Introduction to ML - Part 2

Introduction to ML - Part 2. Kenny Zhu. What is next?. ML has a rich set of structured values Tuples: (17, true, “stuff”) Records: {name = “george”, age = 35} Lists: 3::4::5::nil or [3,4]@[5] Datatypes Functions And more! We put things together in a more complex program. An interpreter.

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Introduction to ML - Part 2

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  1. Introduction to ML - Part 2 Kenny Zhu

  2. What is next? • ML has a rich set of structured values • Tuples: (17, true, “stuff”) • Records: {name = “george”, age = 35} • Lists: 3::4::5::nil or [3,4]@[5] • Datatypes • Functions • And more! • We put things together in a more complex program

  3. An interpreter • Interpreters are usually implemented as a series of transformers: lexing/ parsing evaluate print stream of characters abstract syntax abstract value stream of characters

  4. A little language (LL) • An arithmetic expression e is • a boolean value • an if statement (if e1 then e2 else e3) • an integer • an add operation • a test for zero (isZero e)

  5. LL abstract syntax in ML datatype term = Bool of bool | If of term * term * term | Num of int | Add of term * term | IsZero of term -- constructors are capitalized -- constructors can take a single argument of a particular type type of a tuple another eg: string * char vertical bar separates alternatives

  6. LL abstract syntax in ML Add Add (Num 2, Num 3) represents the expression “2 + 3” Num Num 2 3

  7. LL abstract syntax in ML If If (Bool true, Num 0, Add (Num 2, Num 3)) represents “if true then 0 else 2 + 3” Add Bool Num true Num Num 0 3 2

  8. Function declarations function name function parameter fun isValue t = case t of Num n => true | Bool b => true | _ => false default pattern matches anything

  9. What is the type of the parameter t? Of the function? function name function parameter fun isValue t = case t of Num n => true | Bool b => true | _ => false default pattern matches anything

  10. What is the type of the parameter t? Of the function? fun isValue (t:term) : bool = case t of Num n => true | Bool b => true | _ => false val isValue : term -> bool ML does type inference => you need not annotate functions yourself (but it can be helpful)

  11. A type error fun isValue t = case t of Num _ => 1 | _ => false ex.sml:22.3-24.15 Error: types of rules don't agree [literal] earlier rule(s): term -> int this rule: term -> bool in rule: _ => false

  12. A type error Actually, ML may give you several errors in a row: ex.sml:22.3-25.15 Error: types of rules don't agree [literal] earlier rule(s): term -> int this rule: term -> bool in rule: Num t2 => true ex.sml:22.3-25.15 Error: types of rules don't agree [literal] earlier rule(s): term -> int this rule: term -> bool in rule: _ => false

  13. A very subtle error fun isValue t = case t of num => true | _ => false The code above type checks. But when we test it, the function always returns “true.” What has gone wrong?

  14. A very subtle error fun isValue t = case t of num => true | _ => false The code above type checks. But when we test it, the function always returns “true.” What has gone wrong? -- num is not capitalized (and has no argument) -- ML treats it like a variable pattern (matches anything!)

  15. Exceptions exception Error of string fun debug s : unit = raise (Error s)

  16. Exceptions exception Error of string fun debug s : unit = raise (Error s) in SML interpreter: - debug "hello"; uncaught exception Error raised at: ex.sml:15.28-15.35

  17. Evaluator fun isValue t = ... exception NoRule fun eval t = case t of Bool _ | Num _ => t | ...

  18. Evaluator ... fun eval t = case t of Bool _ | Num _ => t | If(t1,t2,t3) => let val v = eval t1 in case v of Bool b => if b then (eval t2) else (eval t3) | _ => raise NoRule end let statement for remembering temporary results

  19. Evaluator exception NoRule fun eval1 t = case t of Bool _ | Num _ => ... | ... | Add (t1,t2) => case (eval v1, eval v2) of (Num n1, Num n2) => Num (n1 + n2) | (_,_) => raise NoRule

  20. Finishing the Evaluator fun eval1 t = case t of ... | ... | Add (t1,t2) => ... | IsZero t => ... be sure your case is exhaustive

  21. Finishing the Evaluator fun eval1 t = case t of ... | ... | Add (t1,t2) => ... What if we forgot a case?

  22. Finishing the Evaluator fun eval1 t = case t of ... | ... | Add (t1,t2) => ... What if we forgot a case? ex.sml:25.2-35.12 Warning: match nonexhaustive (Bool _ | Zero) => ... If (t1,t2,t3) => ... Add (t1,t2) => ...

  23. Demo • Managing the source files for the interpreter

  24. More on lists: Map fun map f l = case l of nil => [] l x :: l => (f x) :: (map f l) applies the function f to every element in the list - fun add1 x = x + 1; - map add1 [1,2,3]; > val it = [2,3,4] : int list

  25. More on lists: Fold fun fold f init l = case l of nil => init | x :: l => f (x, fold f init l) applies function f (x, y) on the elements of l and the result from previous application recursively - fun sum (x, y) = x + y; - foldr sum 0 [1,2,3,4]; val it = 10 : int

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