Introduction to ML

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

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)

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

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 : int Type I have found a : bool Error - 3 div 0 Failure : Div - run-time error

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 : bool and also, or else short-circuit eval

Basic Values Integers -3 + 2j > 5:int - 3 + (if not true then 5 else 7); > 10 : int No division between expressions and statements Strings - “Dave” ^ “ “ ^ “Walker”; > “Dave Walker”:string - size “foo”; > 3 : int Reals - 3.14; > 3.14 : real

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

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) :

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;

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 : int scope - (let val x = 10 in (x + x, y + x) and, x); > ((20, 31), 41) : (int * int) * int

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));

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; > …

Introduction to ML