CS 11 Ocaml track lecture 2 Today comments algebraic data types more pattern matching records polymorphic types ocaml libraries exception handling Previously ocaml interactive interpreter compiling standalone programs basic data types and operators let expressions if expressions functions pattern matching higher order functions tail recursion Comments Comments start with and end with can be nested No single line comments This is a comment This is a nested comment Algebraic data types AKA union types Idea want a new data type that can be any one of several different things Extremely useful makes it easy to define complex data types Pattern matching automatically works with the structure of these types Example 1 Example type card Spade Heart Diamond Club type is a keyword card is the name of the type you re defining Spade Heart Diamond and Club are type constructors also instances of type card type names must start with lower case letter constructors must start with upper case letter Pattern matching let string of card c match c with Spade Spade Heart Heart Diamond Diamond Club Club means or conceptually N B first is optional Example 2 type number generic numbers Zero Integer of int Real of float let float of number n match n with Zero 0 0 Integer i float of int i Real f f Example 2 alternate type number generic numbers Zero note leading Integer of int Real of float let float of number n match n with Zero 0 0 note leading Integer i float of int i Real f f Aside the function keyword let float of number function Zero 0 0 Integer i float of int i Real f f Used for pattern matching with a oneargument function Just a shortcut Contrast fun keyword doesn t match patterns Example 2 let add n1 n2 add generic numbers match n1 n2 with Zero n fall through to next case n Zero n Integer i1 Integer i2 Integer i1 i2 Integer i Real r fall through Real r Integer i Real r float of int i Real r1 Real r2 Real r1 r2 Example 3 Abstract integer type type integer recursive data type Zero Succ of integer NOTE Can t re use a constructor name here Zero in the same module Example 3 let rec add x y match x with Zero y Succ x Succ add x y Recall when defining a recursive function need to use let rec Defining your own operators In ocaml can define your own operators Note that surrounding operator with makes it into a function int int int fun Here is the function version of the operator Defining your own operators Want a operator for our new integers let rec x y match x with Zero y Succ x Succ x y Recall when defining a recursive function need to use let rec New operators can only use non alphanumeric characters except for some built in ones Defining your own operators Why is this broken let rec x y match x with Zero Zero Succ Zero y Succ x y x y Defining your own operators Correct version let rec x y match x with Zero Zero Succ Zero y Succ x y x y Records A record bundles together different pieces of data with possibly different types Like a tuple with a name for each position in the tuple type named point name string x float y float Creating records name foo x 10 0 y 20 0 named point name foo x 10 y 20 NOTE Type inference correctly determines that the above expression is a named point Can also write this as x 10 0 name foo y 20 0 the fields don t have to be in any order However you can t leave out any of the field names Using records let add points p1 p2 match p1 p2 with name n1 x x1 y y1 name n2 x x2 y y2 name n1 n2 x x1 x2 y y1 y2 The pattern let add points p1 p2 match p1 p2 with name n1 x x1 y y1 name x x2 y y2 name n1 x x1 x2 y y1 y2 in patterns means don t care ignores value in that position Polymorphic types Consider this function let rec list length lst match lst with 0 h t 1 list length t What s the type of list length val list length a list int fun Polymorphic types What s the type of list length val list length a list int fun This is a polymorphic type Same type for lists of ints lists of floats etc list length 1 2 3 4 5 5 list length foo bar baz 3 However list elements must all be of same type How do we define a type like that Polymorphic types Let s define our own list type type a our list Nil Cons of a a our list a says that this is a polymorphic type Note tuple types are printed with e g 10 foo int string 10 foo Polymorphic types Let s use our new type let rec list length our lst match our lst with Nil 0 Cons h t 1 list length t Note on the libraries There is a library function called List length Lives in the List module Documented on www ocaml org web site You should browse through the standard libraries Pervasives built in List Array Hashtbl Printf Note on the libraries You don t have to have an import statement to use library functions List length 1 2 3 4 5 int 5 If you don t want to type List all the time you can do open List but I recommend against it Exception handling Ocaml includes a simple and effective exception handling system ML language one of the first ones in which exception handling was incorporated New keywords raise try with exception Example let rec find x lst match lst with raise Failure not found h t if x h then x else find xt val find a a list a fun Example find 1 1 2 3 4 5 int 1 find 0 1 2 3 4 5 Exception Failure not found Failure not found exn Failure not found exception Exceptions have type exn Like an extensible union type Can add new constructors using the exception keyword exception Bad of string exception Bad of string Recall constructor must have first letter capitalized raise Raise exceptions using the keyword raise raise Bad this is really whacked Exception Bad this is really whacked try with 1 Catch exceptions in a try with statement try raise Bad this is really whacked with Bad s s string this is really whacked try with 2 Catching multiple exceptions try raise Bad this is really whacked with e match e with Bad s s whatever string this is really whacked try with 3 Catching multiple exceptions alternate way try raise Bad this is really whacked with Bad s s Failure f f whatever string this is really whacked try with 4 Slight variation try raise Bad this is really whacked with Bad s s Failure f f whatever …