CS 11 Ocaml track: lecture 2Previously...CommentsAlgebraic data typesExample 1Pattern matchingExample 2Example 2 -- alternateAside: the function keywordExample 2Example 3Example 3Defining your own operatorsDefining your own operatorsDefining your own operatorsDefining your own operatorsRecordsCreating recordsUsing recordsThe _ patternPolymorphic typesPolymorphic typesPolymorphic typesPolymorphic typesNote on the librariesNote on the librariesException handlingExampleExampleexceptionraisetry/with (1)try/with (2)try/with (3)try/with (4)Next weekCS 11 Ocaml track: lecture 2 Today: comments algebraic data types more pattern matching records polymorphic types ocaml libraries exception handlingPreviously... ocaml interactive interpreter compiling standalone programs basic data types and operators let expressions, if expressions functions pattern matching higher-order functions tail recursionComments Comments start with (* and end with *) can be nested No single-line comments(* This is a comment. *)(* This isa (* 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 typesExample 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 letterPattern matchinglet string_of_card c =match c with| Spade -> "Spade"| Heart -> "Heart"| Diamond -> "Diamond"| Club -> "Club" | means "or" (conceptually) N.B. first | is optionalExample 2type number = (* generic numbers *)Zero| Integer of int| Real of floatlet float_of_number n =match n withZero -> 0.0| Integer i -> float_of_int i| Real f -> fExample 2 -- alternatetype number = (* generic numbers *)| Zero (* note leading | )| Integer of int| Real of floatlet float_of_number n =match n with| Zero -> 0.0 (* note leading | )| Integer i -> float_of_int i| Real f -> fAside: the function keywordlet float_of_number = functionZero -> 0.0| Integer i -> float_of_int i| Real f -> f Used for pattern matching with a one-argument function Just a shortcut Contrast: fun keyword doesn't match patternsExample 2let add n1 n2 = (* add generic numbers *)match n1, n2 withZero, 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 moduleExample 3let 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 recDefining 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 + operatorDefining 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 tupletype 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 namesUsing recordslet 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 _ patternlet 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 positionPolymorphic 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 polymorphictype Same type for lists of ints, lists of floats, etc.list_length [1;2;3;4;5] Æ 5list_length ["foo"; "bar"; "baz"] Æ 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 tNote 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 PrintfNote 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 doopen 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 exceptionExample# let rec find x lst =match lst with| [] -> raise (Failure "not