cse321, programming languages and compilers 1 6/21/2015 standard ml in this course we will use an...

Cse321, Programming Languages and Compilers

104/18/23

Standard ML• In this course we will use an

implementation of the language Standard ML

• Notes by Riccardo Pucella, about programming in ML • http://www.cs.cornell.edu/riccardo/smlnj.html

• The SML/NJ Homepage has lots of useful information: http://www.smlnj.org//

• You can get a version to install on your own machine there.

I will use the version 110.57 of SML. Earlier versions probably will work as well. I don’t foresee any problems with other versions, but if you want to use the identical version that I use in class then this is the one.

204/18/23

Characteristics of SML

• Applicative style – input output description of problem.

• First class functions – pass as parameters

– return as value of a function

– store in data-structures

• Less Importantly:– Automatic memory management (G.C. no new or malloc)

– Use of a strong type system which uses type inference, i.e. no declarations but still strongly typed.

304/18/23

Syntactic Elements

• Identifiers start with a letter followed by digits or other letters or primes or underscores.– Valid Examples: a a3 a’b aF

– Invalid Examples: 12A

• Identifiers can also be constructed with a sequence of operators like: !@#$%^&*+~

• Reserved words include– fun val datatype if then else– if of let in end type

404/18/23

Interacting

• The normal style for interaction is to start SML, and then type definitions into the window.

• Types of commands– 4 + 5;– val x = 34;– fun f x = x + 1;

• Here are two commands you might find useful.

val pwd = OS.FileSys.getDir;val cd = OS.FileSys.chDir;

• To load a file that has a sml program type

Use “file.sml”;

504/18/23

The SML Read-Typecheck-Eval-Print Loop

Standard ML of New Jersey v110.57 [built: Mon Nov 21 21:46:28 2005]-- 3+5;val it = 8 : int-- print "Hi there\n";Hi thereval it = () : unit-- val x = 22;val x = 22 : int-- x+ 5;val it = 27 : int--val pwd = OS.FileSys.getDir;-val pwd = fn : unit -> string

- val cd = OS.FileSys.chDir;val cd = fn : string -> unit-

Note the semicolon when you’re ready to evaluate.

Otherwise commands can spread across several

lines.

604/18/23

Evaluation vs. Declaration evaluation- 5;val it = 5 : int- 3+4;val it = 7 : int

declaration- val it = 7 : int- val tim = 5 : int

evaluation- tim + 7;val it = 12 : int

declaration- fun plusone x = x + 1;val plusone = fn : int -> int

704/18/23

Bindings and environments, and scope:val x = 12;fun f x = x + 2;fun g y = x + 2;

• fun bindings are just like val bindings

val f = (fn x => x + 2);

• But NOT RECURSIVE PROGRAMS! why?

fun plus x y = if x = 0 then y else 1 + (plus (x-1) y); val rec plus = fn x => fn y => if x = 0 then y else 1 + (plus (x-1) y);

804/18/23

Functions• Functions are usually defined in Files and

loaded into to SML. Example:– use “lect01.sml”

• Functions on numbers– Type of numbers: Int and Real

– Conversion functions: floor, ceiling, trunc, round

• Functions on Booleans– Relational operators

< > <= >= == !=

– Combinators

andalso orelse

• Examples- 5 > 7

- 1==4

904/18/23

Finding type of functions- length

val it = fn : 'a list -> int

- op @;

val it = fn : 'a list * 'a list -> 'a list

- rev;

val it = fn : 'a list -> 'a list

- op +;

val it = fn : int * int -> int

1004/18/23

Functions• Defined by writing equations (sometimes more than

1)• By Declaration: fun plusone x = x+1;

• By Lambda expression: fn x => x + 1– These are anonymous functions, and are probably new to you. Don’t let

them scare you.

• Application by juxtaposition (no parenthesis needed)• plusone 8 • (fn x => x + 1) 8

• Functions of more than 1 argument:• tuples• currying

1104/18/23

Multi Argument functions: Tuples

• fun evenprod (x,y) = even(x * y);

• Conditional Expressions: If

• fun minpair (x,y) = if x < y then x else y;

1204/18/23

Multi Argument functions: By Currying

fun f a b c = a + b + c + 1;

• has type

val f = fn : int -> int -> int -> int

• READ AS: int -> (int -> (int -> int))

• Be sure you understand the difference between the two styles.

• fun evenprod (x,y) = even(x * y);– (int * int) -> bool

• fun evenprod’ x y = even(x * y);– int -> int -> bool

1304/18/23

Pattern Matching Definitions:

fun and true false = false

| and true true = true

| and false false = false

| and false true = false;

• (ORDER MATTERS)

• Variables in Patterns:

fun and true true = true

| and x y = false

Note that “and” has more than

1 equation.

1404/18/23

Rules for patterns:

• Patterns has only Constructors, (true, false, :: ) variables (x, y, z) , and constants (3, “red”).

• All the patterns (on the left) should have

compatible types

• The cases should be exhaustive

• There should be no ambiguity as to which case applies. (Ordering fixes ambiguity if there is any)

1504/18/23

Lists in ML

• Constant lists

• [3,6,8]

• ["red", "yellow", ""]

• []

1604/18/23

Construction of lists

• The Empty List

• The "Cons" (op :: ) Constructor

4::[3,7];

val it = [4,3,7] : int list

• Concatenation

[3,4] @ [6,7,8]

val it = [3,4,6,7,8] : int list

1704/18/23

Taking Lists Apart? hd [1,2,3]

? tl [1,2,3]

[2, 3]

? List.take (2,[1,2,3])

? List.drop (2,[1,2,3])

1804/18/23

Libraries

• There are lots of predefined types and functions in SML when it starts up.

• You can find out about them at:http://www.smlnj.org//basis/pages/top-level-chapter.html

• Many more can be found in the other libraries.– http://www.standardml.org/Basis/manpages.html

• Libraries are encapsulated in Structures which are classified by Signatures (a list of what is in the structure).

1904/18/23

Peeking inside a Structure

• To see what is inside a Structure you can open it.

• This is somewhat of a hack, but it is useful.Standard ML of New Jersey v110.57 [built: Mon Nov 21 21:46:28 2005]- signature S = INTEGER;signature INTEGER = sig eqtype int val precision : Int31.int option val minInt : int option val maxInt : int option val ~ : int -> int val + : int * int -> int val - : int * int -> int val * : int * int -> int val div : int * int -> int val mod : int * int -> int val quot : int * int -> int val rem : int * int -> int . . .end

2004/18/23

fun lastone x = hd (rev x)fun prefix x = rev (tl (rev x))

In Class Exercise 1• Define prefix and lastone in terms of head tail and reverse.

• First make a file “S01code.sml”• Start sml• Change directory to where the file resides• Load the file ( use “S01code.sml” )• Test the function

Standard ML of New Jersey v110.57 - K;- val cd = OS.FileSys.chDir;val cd = fn : string -> unit- cd "D:/work/sheard/courses/PsuCs321/web/notes";- use "S01code.sml";[opening S01code.sml]val lastone = fn : 'a list -> 'aval prefix = fn : 'a list -> 'a listval it = () : unit- lastone [1,2,3,4];val it = 4 : int

2104/18/23

In Class Exercise 2• define map and filter functions

– mymap f [1,2,3] = [f 1, f 2, f 3]– filter even [1,2,3,4,5] = [2,4]

fun mymap f [] = []

| mymap f (x::xs) = (f x)::(mymap f xs);

fun filter p [] = []

| filter p (x::xs) =

if (p x) then x::(filter p xs) else (filter p xs);

• Sample Session

- mymap plusone [2,3,4]

[3, 4, 5]

- myfilter even [1,2,3,4,5,6]

[2, 4, 6]

2204/18/23

Case expressions

val ex1 =

case [1,2,3] of

[] => 0

| (1::xs) => if null xs

then 1

else 2

| (x::xs) => 3;

Clauses separated

by “|”

Keyword of

Clauses can span multiple

The semicolon ends the “val ex1 = ” declaration not the

case exp.

2304/18/23

Using case in fun definition• The case expression uses patterns

fun length(y) =

case y of

[] => 0

| (x :: xs) => 1 + (length xs)

• In the pattern: (x :: xs)– x, stands for the hd(y)

– xs, stands for the tl(y)

2404/18/23

More about patterns• Patterns can be nested• Patterns can have wild-cards

fun double y =

case y of

(a :: (b :: [])) => true

| _ => false

• Special syntax for list Patterns

fun exactlytwo x =

Case x of

[] => false

| [x] => false

| [x,y] => true

| (x:xs) => false;

These features can be used in “fun”

declarations with multiple clauses as

well as in “case” expressions!

2504/18/23

Let expressions

• Let expressions allow programmers to make local declaration for both values and functions.

val ex2 =

let val x = 34

fun f x = x - 3

in f x - 4 end;

Multiple declarations allowed, both “val” and

“fun”, no separators necessary

The scope of the new declarations is the

expression between the key words “in” and “end”

2604/18/23

Exceptions

exception Error of string;

fun error s = raise (Error s);

fun ex3 b =

(if b then error "true branch"

else "false branch")

handle Error message => message

| other => raise other;

A new exception is declared, it carries a string as error information. Exceptions

can carry any kind of data.

Exceptions can be raised, to short-circuit normal

evaluation.

Main computation

returns a string

Handler also returns a stringA handler, like a “case” has multiple clauses, each can

handle a different kind of error. Note “|” separating clauses.

Keyword handle

2704/18/23

Syntax of “case” vs “handle”• “case” is before the computation being

analyzed

case (revonto (g x) 4) of

[] => true

| (x:xs) => false

• “handle” is after the computation that might fail

(compute (g y) (length zs))

handle Error s => g s

| BadLevel n => n+1

| other => raise other

2804/18/23

Review

• Case, let, and exceptions are rich constructs in ML.

• Case allows pattern matching without defining a new function.

• Let allows us to introduce local bindings. It allows us to introduce more than 1 binding.

• Exceptions allow non-standard control. The key operations on exceptions are “raise” and “handle”– Handle is like a “case” in that it can have several clause, separated

by “|”, the first that matches “wins”

2904/18/23

Introducing new kinds of data• Objects of an inductive type are allocated in

the heap.

• The abstract interface is to use constructor (functions) rather than malloc

• This provides some level of type checking, and abstraction.

• Constructor functions automatically defined. No need to define like constructors in Java

• Two kinds of constructors. Constants like nil ([]), and functions like cons (::).

3004/18/23

Constant Constructors• Constant constructors are constant

• Can be allocated once at compile-time.

• Like constant pointers that never change.

• The nil constructor [] for lists is an example.

3104/18/23

Constructor Functions• Constructor functions allocate in the heap.• Each constructor may allocate a different

amount of memory• If we had to do this in C we might write

list cons (void * hd, list tl){ list Block = (list) malloc (sizeof (struct listStruct)); Block->Tag = consTag; Block->Data.consData.hd = hd; Block->Data.consData.tl = tl; return (Block);};

• In ML this is done automatically.

3204/18/23

Introducing new data and constructors

datatype Tree = Tip | Node of Tree * int * Tree;

val tree1 = Node(Node(Tip,4,Tip) ,7 ,Node(Tip,10,Tip));

Constant constructor, contains no data

Constructor function. Contains 3 fields. The function Node takes a triple with 3

components. The “of” keyword is used for constructor functions

3304/18/23

Pattern Matching functions

fun sum Tip = 0

| sum (Node(x,n,y)) = n + sum x + sum y;

• using binary search tree invariant

fun search n Tip = false

| search n (Node(x,m,y)) =

if n=m

then true

else if (n < m) then search n x

else search n y;

Two constructors, two clauses

The bar “|” separates clauses

3404/18/23

Searching Trees.fun search n Tip = false

| search n (Node(x,m,y)) =

if n=m then true

else if (n < m) then search n x else search n y;

• val ex4 = search 3 tree1;• search 3 (Node(Node(Tip,4,Tip),7,Node(Tip,10,Tip)))• search 3 (Node (Tip,4,Tip))• search 3 Tip• false

• val ex5 = search 10 tree1;• search 10 (Node(Node(Tip,4,Tip),7,Node(Tip,10,Tip)))• search 10 (Node (Tip,10,Tip))• true

3504/18/23

Expressions

datatype Exp

= Const of int

| Add of Exp * Exp

| Mult of Exp * Exp

| Sub of Exp * Exp;

val exp1 = Add(Const 4,Const 3); (* 4+3 *)

val exp2 = Mult(exp1,exp1); (* (4+3)*(4+3) *)

Mult(Add(Const 4,Const 3)

, Add(Const 4,Const 3));

3604/18/23

Pattern matching functions

fun ExpValue (Const n) = n

| ExpValue (Add(x,y))

= ExpValue x + ExpValue y

| ExpValue (Mult(x,y))

= ExpValue x * ExpValue y

| ExpValue (Sub(x,y))

= ExpValue x - ExpValue y;

3704/18/23

More SML

• In SML we use library functions all the time.– Int.toString– List.exists

• The list library functions are particularly useful.– These library functions often take a function as an argument– List.map : ('a -> 'b) -> 'a list -> 'b list– List.find : ('a -> bool) -> 'a list -> 'a option– List.filter : ('a -> bool) -> 'a list -> 'a list– List.exists : ('a -> bool) -> 'a list -> bool– List.all : ('a -> bool) -> 'a list -> bool– List.foldr : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b

• It is worth studying these functions closely

3804/18/23

List.map captures a pattern

• Add one to every element of a list– fun addone [] = []– | addone (x::xs) = (x + 1) :: addone xs

addone [2,3,4] val it = [3,4,5] : int list

• Turn a list of ints into a list of strings– fun stringy [] = []– | stringy (x::xs) = (Int.toString x) :: stringy xs

stringy [2,5,9] val it = ["2","5","9"]:string list

• Negate every element of a list– fun negL [] = []– | negL (x::xs) = (not x) :: negL xs

negL [true,3 > 4] val it = [false,true] : bool list

3904/18/23

Patternfun addone [] = [] | addone (x::xs) = (x + 1) :: addone xsfun stringy [] = [] | stringy (x::xs) = (Int.toString x) :: stringy xsfun negL [] = [] | negL (x::xs) = (not x) :: negL xs

fun map f [] = [] | map f (x::xs) = (f x) :: (map f xs)

val ex1 = map (fn x => (x+1)) [2,3,4];val ex1 = [3,4,5] : int list

val ex2 = map Int.toString [2,5,7];val ex2 = ["2","5","7"] : string list

val ex3 = map not [true, 3 > 4];val ex3 = [false,true] : bool list

4004/18/23

Anonymous functions• Study: (fn x => (x+1))

– It is an anonymous function. A function without a name.– It has one parameter “x”– It adds one to its parameter, and returns the result.

(fn x => (x+1)) 4;val it = 5 : int

• Any non-recursive function can be written anonymously.– (fn x => x = 5)

» Tests if its parameter is equal to 5map (fn x => x=5) [1,4,5,3,5];val it = [false,false,true,false,true] : bool list

– (fn x => fn y => (x,y))» Has two parameters» Returns a pair

– (fn (x,y) => (not y, x+3))» What is the type of this function?

4104/18/23

List.find

• Used for searching a list.– List.find : ('a -> bool) -> 'a list -> 'a option

• Uses a function as a parameter to determine if the search is successful.

• E.g. Is there an even element in a list?List.find even [1,3,5];

val it = NONE : int option

List.find even [1,3,4];

val it = SOME 4 : int option

4204/18/23

List.find and anonymous functions

List.find (fn x => x = "Tim")

["Tom", "Jane"];

val it = NONE : string option

List.find (fn x => even x andalso x>10)

[2,4,5,12];

4304/18/23

List.filter

Filter keeps some elements, and throws away others.– List.filter : ('a -> bool) -> 'a list -> 'a list

It uses a function (p) as a parameter to decide which elements to keep (p x = true), and which to throw away (p x = false)

val ex6 = List.filter even [1,2,3,4,5,6];

val ex6 = [2,4,6] : int list

4404/18/23

List.filter and anonymous functionsval people = [("tim",22),("john",18),("jane",25),("tim",8)];

val ex7 = filter

(fn (nm,age) => nm <> "tim" orelse age>10)

people;

val ex7 =

[("tim",22),("john",18),("jane",25)]

: (string * int) list

4504/18/23

List.exists

• “exists” is like “find” in that it searches a list– but rather than the element that completes the search it is only

interested in if such an element exists.– List.exists : ('a -> bool) -> 'a list -> bool

• Uses a function as a parameter to determine if the search is successful.

val ex8 = List.exists even [2,3,5];

val ex8 = true : bool

• Note that even if only 1 element in the list causes the function to be true, exists returns true.

4604/18/23

List.all

• List.all tests elements in a list for a property. It returns true only if every element has that property.– List.all : ('a -> bool) -> 'a list -> bool

• Uses a function as a parameter to perform the test.

val ex9 = List.all even [2,4,5];

val ex9 = false : bool

• List.exists and List.all are related functions. They are duals.– not(List.all p xs) = List.exists (fn x => not(p x)) xs

4704/18/23

List.foldr captures a pattern

• Add up every element in a list.

fun sum [] = 0

| sum (x::xs) = x + (sum xs);

• Compute the maximum element in a list of natural numbers (Integers >= 0).

fun maximum [] = 0

| maximum (x::xs) = Int.max(x,maximum xs);

• Compute if every element in a list of boolean is true.

fun allTrue [] = true

| allTrue (x::xs) = x andalso (allTrue xs);

4804/18/23

Patternfun sum [] = 0

fun maximum [] = 0

fun foldr acc base [ ] = base

| foldr acc base (x::xs)

= acc(x,foldr acc base xs);

4904/18/23

See the pattern in use.fun sum [] = 0

fun sum xs = foldr (op +) 0 xs;

fun maximum [] = 0

fun maximum xs = foldr Int.max 0 xs;

fun allTrue xs =

foldr (fn (a,b) => a andalso b) true xs;

5004/18/23

Take another lookWhat does this function do?

fun ok [] = false

| ok xs = not(exists (fn ys => xs=ys) (!old))

andalso

not(exists (fn ys => xs=ys) (!worklist))

5104/18/23

The Option Library- open Option;opening Option datatype 'a option = NONE | SOME of 'a exception Option val getOpt : 'a option * 'a -> 'a val isSome : 'a option -> bool val valOf : 'a option -> 'a val filter : ('a -> bool) -> 'a -> 'a option val join : 'a option option -> 'a option val app : ('a -> unit) -> 'a option -> unit val map : ('a -> 'b) -> 'a option -> 'b option val mapPartial : ('a -> 'b option) -> 'a option -> ‘ b option

5204/18/23

Interesting functions that use Options• Int.fromString: string -> int option

Int.fromString "234";

Int.fromString "abc";

• String.extract: string * int * int option -> stringString.extract("abcde",1,SOME 3);

val it = "bcd" : string

String.extract("abcde",1,NONE);

val it = "bcde" : string

5304/18/23

More option functions• List.find: ('a -> bool) -> 'a list -> 'a option

List.find even [1,3,5];

List.find (fn x => x="tim") ["tom","tim","jane"];

val it = SOME "tim" : string option

• List.getItem: 'a list -> ('a * 'a list) option– List.getItem [1,2,3,4];– val it = SOME (1,[2,3,4])

– List.getItem [];– val it = NONE

5404/18/23

Using While Loopsfun ident c cs = let val xs = ref cs val x = ref c val ans = ref [] in while (not(null(!xs)) andalso Char.isAlpha (hd (!xs))) do ( ans := !ans @ [!x] ; x := hd(!xs) ; xs := tl(!xs) ); (Id (String.implode (!ans @ [!x])), !xs)

Don’t forget to test for empty list

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