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CSE 130: Spring 2012
Programming Languages
Lecture 2: A Crash Course in ML
Wednesday, April 4, 2012 1 News
On webpage:
- Suggested HW #
- PA #1 (due next Fri 4/13)
Please post questions to Piazza
Today: A crash course in ML contd…
Wednesday, April 4, 2012 2 Recap: ML’s Holy Trinity
1. Programmer enters expression
2. ML checks if expression is “well-typed”
- Using a precise set of rules, ML tries to find a unique
type for the expression meaningful type for the expr
3. ML evaluates expression to compute value
- Of the same “type” found in step 2
Expressions (Syntax) Values (Semantics)
Types
Compile-time
“Static”
Exec-time
“Dynamic”
Complex types: Lists []; (^) [] ’a list
- Unbounded size
- Can have lists of anything (e.g. lists of lists)
- But… [1;2;3]; [1;2;3] int list [“a”;“b”; “c”^“d”]; [“a”;“b”; “cd”] string list [1+1;2+2;3+3;4+4]; [2;4;6;8] int list [(1,“a”^“b”);(3+4,“c”)]; [(1,“ab”);(7,“c”)] (int*string) list [[1];[2;3];[4;5;6]]; (^) [[1];[2;3];[4;5;6]]; (int list) list
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Complex types: Lists
All elements must have same type
[1; “pq”];
Wednesday, April 4, 2012 5 Complex types: Lists List operator “Cons” [1] int list 1::[2;3]; (^) [1;2;3] int list 1::[“b”; “cd”]; “a”::[“b”;“c”]; [“a”;“b”;“c”]^ string list
1::[];
Can only “cons” element to a list of same type Wednesday, April 4, 2012 6 Lists: Construct
[] [] : ’a list [] => []
1::[2;3] [1;2;3]
int list
Cons operator e1=>v1 e2 => v e1::e2 => v1::v e1 : T e2 : T list e1::e2 : T list Nil operator Complex types: Lists List operator “Append” int list [“a”]@[“b”]; (^) [“a”;“b”] string list 1 @ [2;3]; []@[1]; [1] int list
[1;2]@[3;4;5];
Can only append two lists
[1;2;3;4;5]
… of the same type^ [1]^ @^ [“a”;“b”];
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So far, a fancy calculator… … what do we need next? Wednesday, April 4, 2012 13 So far, a fancy calculator…
Branches
Wednesday, April 4, 2012 14 If-then-else expressions
- Then-subexp, Else-subexp must have same type!
- Equals type of resulting expression if 1>2 then [1,2] else [] (^) [] int list if 1<2 then [] else [“a”] (^) [] string list (if 1>2 then [1,2] else [])=(if 1<2 then [] else [“a”]) e1 : bool e2: T e3: T if e1 then e2 else e3 : T If-then-else expressions if (1 < 2) then [1;2] else 5 e1 : bool e2: T e3: T if e1 then e2 else e3 : T if false then [1;2] else 5
- then-subexp, else-subexp must have same type!
- …which is the type of resulting expression
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So far, a fancy calculator…
Variables
Wednesday, April 4, 2012 17 Variables and bindings
let x = e;
“Bind the value of expression e to the variable x”
# let x = 2+2;;
val x : int = 4
Wednesday, April 4, 2012 18
# let x = 2+2;;
val x : int = 4
# let y = x * x * x;;
val y : int = 64
# let z = [x;y;x+y];;
val z : int list = [4;64;68]
Variables and bindings
Later declared expressions can use x
- Most recent “bound” value used for evaluation
let p = a + 1;
Characters 8-9: let p = a + 1 ;; ^ Unbound value a Variables and bindings Undeclared variables (i.e. without a value binding) are not accepted! Catches many bugs due to typos
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Next class: functions, but remember …
Everything is an expression
Everything has a value
Everything has a type
Expression (^) Value Type
A function is a value!
Wednesday, April 4, 2012 25 Complex types: Functions!
fun x -> x+1;; fn
int -> int
Parameter
(formal)
Body
Expr
let inc = fun x -> x+1 ;
val inc : int -> int = fn
inc 0;
val it : int = 1
inc 10;
val it : int = 11 Wednesday, April 4, 2012 26 A Problem
fn
int -> int
Parameter
(formal)
Body
Expr
Functions only have
ONE parameter ?!
How a call (“application”) is evaluated:
- Evaluate argument
- Bind formal to arg value
- Evaluate “Body expr”
fun x -> x+1;;
A Solution: Simultaneous Binding
fun (x,y) -> x bool
Parameter
(formal)
Body
Expr
How a call (“application”) is evaluated:
- Evaluate argument
- Bind formal to arg value
- Evaluate “Body expr”
Functions only have
ONE parameter?
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Another Solution (“Currying”)
fun x -> fun y-> x (int -> bool)
Parameter
(formal)
Body
Expr
Whoa! A function can return a function
let lt = fun x -> fun y -> x < y ;
val lt : int -> int -> bool = fn
let is5Lt = lt 5;
val is5lt : int -> bool = fn;
is5lt 10;
val it : bool = true;
is5lt 2;
val it : bool = false; Wednesday, April 4, 2012 29 And how about…
fun f -> fun x -> not(f x); fn
(’a ->bool) -> (’a -> bool)
Parameter
(formal)
Body
Expr
A function can also take a function argument
let neg = fun f -> fun x -> not (f x);
val lt : int -> int -> bool = fn
let is5gte = neg is5lt;
val is5gte : int -> bool = fn
is5gte 10;
val it : bool = false;
is5gte 2;
val it : bool = true; (…odd, even …) Wednesday, April 4, 2012 30
A shorthand for function binding
# let neg = fun f -> fun x -> not ( f x );
# let neg f x = not ( f x );
val neg : int -> int -> bool = fn
# let is5gte = neg is5lt;
val is5gte : int -> bool = fn;
# is5gte 10;
val it : bool = false;
# is5gte 2;
val it : bool = true;
Put it together: a “filter” function
- let rec filter f xs = match xs with | [] -> [] | (x::xs’)-> if f x then x::(filter f xs’) else (filter f xs’);; val filter : (‘a->bool)->‘a list->‘a lisi) = fn
If arg “matches”
this pattern…
…then use
this Body Expr
let list1 = [1;31;12;4;7;2;10];;
filter is5lt list1 ;;
val it : int list = [31;12;7;10]
filter is5gte list1;;
val it : int list = [1;4;2]
filter even list1;;
val it : int list = [12;4;2;10]
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