introduction to ml - part 2
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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 Interpreters are usually implemented as a series of transformers:
stream ofcharacters
abstractsyntax
lexing/parsing
evaluate
abstractvalue
stream ofcharacters
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)
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 tupleanother eg: string * char
vertical barseparates alternatives
LL abstract syntax in ML
Add (Num 2, Num 3)
represents the expression “2 + 3”
Add
Num Num
2 3
LL abstract syntax in ML
If (Bool true, Num 0, Add (Num 2, Num 3))
represents
“if true then 0 else 2 + 3”
Add
Num Num
2 3
true
Bool Num
0
If
Function declarations
fun isValue t = case t of Num n => true | Bool b => true | _ => false
function name function parameter
default pattern matches anything
What is the type of the parameter t? Of the function?
fun isValue t = case t of Num n => true | Bool b => true | _ => false
function name function parameter
default pattern matches anything
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 notannotate functions yourself (but it can be helpful)
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
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 => trueex.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
A very subtle error
fun isValue t = case t of num => true | _ => false
The code above type checks. But whenwe test it, the function always returns “true.”What has gone wrong?
A very subtle error
fun isValue t = case t of num => true | _ => false
The code above type checks. But whenwe 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!)
Exceptions
exception Error of string
fun debug s : unit = raise (Error s)
Exceptions
exception Error of string
fun debug s : unit = raise (Error s)
- debug "hello";
uncaught exception Error raised at: ex.sml:15.28-15.35
in SML interpreter:
Evaluator
fun isValue t = ...
exception NoRule
fun eval t = case t of Bool _ | Num _ => t | ...
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 statementfor rememberingtemporaryresults
Evaluatorexception 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
Finishing the Evaluatorfun eval1 t = case t of ... | ... | Add (t1,t2) => ... | IsZero t => ...
be sure yourcase isexhaustive
Finishing the Evaluatorfun eval1 t = case t of ... | ... | Add (t1,t2) => ... What if we
forgot a case?
Finishing the Evaluator
ex.sml:25.2-35.12 Warning: match nonexhaustive (Bool _ | Zero) => ... If (t1,t2,t3) => ... Add (t1,t2) => ...
fun eval1 t = case t of ... | ... | Add (t1,t2) => ... What if we
forgot a case?
Demo Managing the source files for the interpreter
More on lists: Mapfun 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
More on lists: Foldfun 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