1. Introduction to ML You will be responsible for learning ML on your own. Today I will cover some basics Read Robert Harper’s notes on “an introduction to ML” See course webpage for pointers and info about how to get the software

2. Intro to ML Highlights Functional Language Functions are pervasive: First-class values Storable, arguments, results, nested Strongly-typed language Every expression has a type Certain errors cannot occur Polymorphic types provide flexibility Flexible Module System Abstract Types Higher-order modules (functors)

3. Interactive Language Type in expressions Evaluate and print type and result Statically Scoped Language Compile-time resolution of values Call-by-value language f(e) High-level programming features Data types Pattern matching Exceptions Mutable data discouraged

4. Preliminaries Read – Eval – Print – Loop - 3 + 2; > 5: int - it + 7; > 12 : int - it – 3; > 9 : int - 4 + true; Type clash in : 3 + true Looking for a : intType I have found a : boolError - 3 div 0 Failure : Div- run-time error

5. Basic Values - (); > () : unit=> like “void” in c (sort of) => the uninteresting value/type - true; > : bool - False; > : bool - if it then 3+2 else 7;always necessary > 7 : int - false and also loop_Forever; > False : booland also, or else short-circuit eval

6. Basic Values Integers -3 + 2j > 5:int - 3 + (if not true then 5 else 7); > 10 : intNo division between expressions and statements Strings - “Dave” ^ “ “ ^ “Walker”; > “Dave Walker”:string - size “foo”; > 3 : int Reals - 3.14; > 3.14 : real

7. Structured Values Tuples - (true, 17, “Stuff”); > (true, 17, “Stuff”) : bool * int * string - (if 3 < 2 then “x” else “y”, false); >(“y”, false) : string * bool Records -{name = “Dave”, ssn = 332177} >_____________ : {name = string, ssn : int} -#name it ; >“Dave” : string -#1 (true, False); -true : bool

8. Parametric Polymorphism Functions like compose work on objects of many different types In ML, we write compose: (‘a -> ‘b) -> (‘c -> ‘a) -> type variables are written with ‘ (‘c -> ‘b) compose not : compose not not : compose (op + 1) not : compose (fn x => x) :

9. What is the type of compose? Fun compose = Fn f => (fn g => Fn x => f (g x)) T3 Compose : T2 -> (T2 -> (T5 -> T6) : T2 -> (( T7 -> T8) -> (T5 -> T6)) : (T9 -> TA) -> (T7 -> T9) -> (T7 -> TA) : (‘a -> ‘b) -> (‘c -> ‘a) -> (‘a -> ‘c) Compose (fn x => x + 1) (fn y => y * 3)7;

10. Declarations -val x = 4 * 5;Declare new name x and bind it to value >val x = 20 : int -val y = x + 1; >val y = 21 : int -val x = x + y;reuse name >val x = 41 : int -x; >41 : int static scoping -y; local declaration >21 : intscope -(let val x = 10 in (x + x, y + x) and, x); >((20, 31), 41) : (int * int) * int

11. Functions (the good stuff) - not;functions are values >Not = fn : bool -> bool we can’t write out a function so ML just says this -not true;function application is a space >False : bool -fun twice x = 2 * x >Val twice = fn : int -> int -fun fact x = if x = 0 then 1 else (fact (x-1)) * x -fact (twice (twice 3));

12. functions - fn s => x ^ “!”;an anonymous function like writing >Fn : string -> string-3 -val exclaim = rather than - val x = 3; fn : => s ^ “!” >… -val compose = fn f => fn g => fn x => f(g x); >… - ((compose twice) twice) 3; >12 -four = compose twice twice >… -four 7; >…