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+---
+language: Standard ML
+contributors:
+ - ["Simon Shine", "http://shine.eu.org/"]
+lang: en-en
+---
+
+Standard ML is a functional programming language with type inference and some
+side-effects. Some of the hard parts of learning Standard ML are: Recursion,
+pattern matching, type inference (guessing the right types but never allowing
+implicit type conversion). If you have an imperative background, not being able
+to update variables can feel severely inhibiting.
+
+```
+(* Comments in Standard ML begin with (* and end with *). Comments can be
+ nested which means that all (* tags must end with a *) tag. This comment
+ contains two nested comments. *)
+
+(* A Standard ML program consists of declarations, e.g. value declarations: *)
+val rent = 1200
+val phone_no = 5551337
+val pi = 3.14159
+val negative_number = ~15 (* Yeah, unary minus is a so-called 'tilde' *)
+
+(* And just as importantly, functions: *)
+fun is_large(x : int) = if x > 37 then true else false
+
+(* Floating-point numbers are called "reals". *)
+val tau = 2.0 * pi (* You can multiply reals *)
+val twice_rent = 2 * rent (* You can multiply ints *)
+(* val meh = 1.25 * 10 *) (* But you can't multiply an int and a real *)
+
+(* +, - and * are overloaded so they work for both int and real. *)
+(* The same cannot be said for division which has separate operators: *)
+val real_division = 14.0 / 4.0 (* gives 3.5 *)
+val int_division = 14 div 4 (* gives 3, rounding down *)
+val int_remainder = 14 mod 4 (* gives 2, since 3*4 = 12 *)
+
+(* ~ is actually sometimes a function (e.g. when put in front of variables) *)
+val negative_rent = ~(rent) (* Would also have worked if rent were a "real" *)
+
+(* There are also booleans and boolean operators *)
+val got_milk = true
+val got_bread = false
+val has_breakfast = got_milk andalso got_bread (* Yes, it's called andalso *)
+val has_something = got_milk orelse got_bread (* Yes, it's called orelse *)
+val is_sad = not(has_something) (* not is a function *)
+
+(* Many values can be compared using equality operators: = and <> *)
+val pays_same_rent = (rent = 1300) (* false *)
+val is_wrong_phone_no = (phone_no <> 5551337) (* false *)
+
+(* The operator <> is what most other languages call != *)
+
+
+(* Actually, most of the parentheses above are unnecessary. Here are some
+ different ways to say some of the things mentioned above: *)
+fun is_large x = x > 37 (* The parens above were necessary because of ': int' *)
+val is_sad = not has_something
+val pays_same_rent = rent = 1300 (* Looks confusing, but works *)
+val is_wrong_phone_no = phone_no <> 5551337
+val negative_rent = ~rent (* ~ rent (notice the space) would also work *)
+
+(* Parens are mostly necessary when grouping things: *)
+val some_answer = is_large (5 + 5) (* Without parens, this would break! *)
+(* val some_answer = is_large 5 + 5 *) (* Read as: (is_large 5) + 5. Bad! *)
+
+
+(* Besides booleans, ints and reals, Standard ML also has chars and strings: *)
+val foo = "Hello, World!\n" (* The \n is the escape sequence for linebreaks *)
+val one_letter = #"a" (* That funky syntax is just one character, a *)
+
+val combined = "Hello " ^ "there, " ^ "fellow!\n" (* Concatenate strings *)
+
+val _ = print foo (* You can print things. We are not interested in the *)
+val _ = print combined (* result of this computation, so we throw it away. *)
+(* val _ = print one_letter *) (* Only strings can be printed this way *)
+
+
+val bar = [ #"H", #"e", #"l", #"l", #"o" ] (* SML also has lists! *)
+(* val _ = print bar *) (* Lists are unfortunately not the same as strings *)
+
+(* Fortunately they can be converted. String is a library and implode and size
+ are functions available in that library that take strings as argument. *)
+val bob = String.implode bar (* gives "Hello" *)
+val bob_char_count = String.size bob (* gives 5 *)
+val _ = print (bob ^ "\n") (* For good measure, add a linebreak *)
+
+(* You can have lists of any kind *)
+val numbers = [1, 3, 3, 7, 229, 230, 248] (* : int list *)
+val names = [ "Fred", "Jane", "Alice" ] (* : string list *)
+val groups = [ [ "Alice", "Bob" ],
+ [ "Huey", "Dewey", "Louie" ],
+ [ "Bonnie", "Clyde" ] ] (* : string list list *)
+
+val number_count = List.length numbers (* gives 7 *)
+
+(* You can put single values in front of lists of the same kind *)
+val more_numbers = 13 :: numbers (* gives [13, 1, 3, 3, 7, ...] *)
+val more_groups = ["Batman","Superman"] :: groups
+
+(* Lists of the same kind can be appended using the @ ("append") operator *)
+val guest_list = [ "Mom", "Dad" ] @ [ "Aunt", "Uncle" ]
+
+(* This could have been done with the :: operator (pronounced "cons") *)
+val guest_list = "Mom" :: "Dad" :: [ "Aunt", "Uncle" ]
+
+(* If you have many lists of the same kind, you can concatenate them all *)
+val everyone = List.concat groups (* [ "Alice", "Bob", "Huey", ... ] *)
+
+(* A list can contain any (finite) amount of values *)
+val lots = [ 5, 5, 5, 6, 4, 5, 6, 5, 4, 5, 7, 3 ] (* still just an int list *)
+
+(* Lists can only contain one kind of thing... *)
+(* val bad_list = [ 1, "Hello", 3.14159 ] : ??? list *)
+
+
+(* Tuples, on the other hand, can contain a fixed number of different things *)
+val person1 = ("Simon", 28, 3.14159) (* : string * int * real *)
+
+(* You can even have tuples inside lists and lists inside tuples *)
+val likes = [ ("Alice", "ice cream"),
+ ("Bob", "hot dogs"),
+ ("Bob", "Alice") ] (* : (string * string) list *)
+
+val mixup = [ ("Alice", 39),
+ ("Bob", 37),
+ ("Eve", 41) ] (* : (string * int) list *)
+
+val good_bad_stuff =
+ (["ice cream", "hot dogs", "chocolate"],
+ ["liver", "paying the rent" ]) (* string list * string list *)
+
+
+(* Functions! *)
+fun add_them (a, b) = a + b (* A simple function that adds two numbers *)
+val test_it = add_them (3, 4) (* gives 7 *)
+
+(* Larger functions are usually broken into several lines for readability *)
+fun thermometer temp =
+ if temp < 37
+ then "Cold"
+ else if temp > 37
+ then "Warm"
+ else "Normal"
+
+val test_thermo = thermometer 40 (* gives "Warm" *)
+
+(* if-sentences are actually expressions and not statements/declarations.
+ A function body can only contain one expression. There are some tricks
+ for making a function do more than just one thing, though. *)
+
+(* A function can call itself as part of its result (recursion!) *)
+fun fibonacci n =
+ if n = 0 then 0 else (* Base case *)
+ if n = 1 then 1 else (* Base case *)
+ fibonacci (n - 1) + fibonacci (n - 2) (* Recursive case *)
+
+(* Sometimes recursion is best understood by evaluating a function by hand:
+
+ fibonacci 4
+ ~> fibonacci (4 - 1) + fibonacci (4 - 2)
+ ~> fibonacci 3 + fibonacci 2
+ ~> (fibonacci (3 - 1) + fibonacci (3 - 2)) + fibonacci 2
+ ~> (fibonacci 2 + fibonacci 1) + fibonacci 2
+ ~> ((fibonacci (2 - 1) + fibonacci (2 - 2)) + fibonacci 1) + fibonacci 2
+ ~> ((fibonacci 1 + fibonacci 0) + fibonacci 1) + fibonacci 2
+ ~> ((1 + fibonacci 0) + fibonacci 1) + fibonacci 2
+ ~> ((1 + 0) + fibonacci 1) + fibonacci 2
+ ~> (1 + fibonacci 1) + fibonacci 2
+ ~> (1 + 1) + fibonacci 2
+ ~> 2 + fibonacci 2
+ ~> 2 + (fibonacci (2 - 1) + fibonacci (2 - 2))
+ ~> 2 + (fibonacci (2 - 1) + fibonacci (2 - 2))
+ ~> 2 + (fibonacci 1 + fibonacci 0)
+ ~> 2 + (1 + fibonacci 0)
+ ~> 2 + (1 + 0)
+ ~> 2 + 1
+ ~> 3 which is the 4th Fibonacci number, according to this definition
+
+ *)
+
+(* A function cannot change the variables it can refer to. It can only
+ temporarily shadow them with new variables that have the same names. In this
+ sense, variables are really constants and only behave like variables when
+ dealing with recursion. For this reason, variables are also called value
+ bindings. An example of this: *)
+
+val x = 42
+fun answer(question) =
+ if question = "What is the meaning of life, the universe and everything?"
+ then x
+ else raise Fail "I'm an exception. Also, I don't know what the answer is."
+val x = 43
+val hmm = answer "What is the meaning of life, the universe and everything?"
+(* Now, hmm has the value 42. This is because the function answer refers to
+ the copy of x that was visible before its own function definition. *)
+
+
+(* Functions can take several arguments by taking one tuples as argument: *)
+fun solve2 (a : real, b : real, c : real) =
+ ( Math.sqrt (~b + Math.sqrt(b * b - 4.0*a*c) / (2.0 * a),
+ Math.sqrt (~b - Math.sqrt(b * b - 4.0*a*c) / (2.0 * a) )
+
+(* Sometimes, the same computation is carried out several times. It makes sense
+ to save and re-use the result the first time. We can use "let-bindings": *)
+fun solve2 (a : real, b : real, c : real) =
+ let val discr = b * b - 4.0*a*c
+ val sqr = Math.sqrt d
+ val denom = 2.0 * a
+ in (~b + sq / denom,
+ ~b - sq / denom) end
+
+
+(* Pattern matching is a funky part of functional programming. It is an
+ alternative to if-sentences. The fibonacci function can be rewritten: *)
+fun fibonacci 0 = 0 (* Base case *)
+ | fibonacci 1 = 1 (* Base case *)
+ | fibonacci n = fibonacci (n - 1) + fibonacci (n - 2) (* Recursive case *)
+
+(* Pattern matching is also possible on composite types like tuples and lists.
+ Writing "fun solve2 (a, b, c) = ..." is in fact a pattern match on the one
+ three-tuple solve2 takes as argument. Similarly, but less intuitively, you
+ can match on a list consisting of elements in it (from the beginning of the
+ list only). *)
+fun first_elem (x::xs) = x
+fun second_elem (x::y::xs) = y
+fun evenly_positioned_elems (odd::even::xs) = even::evenly_positioned_elems xs
+ | evenly_positioned_elems [odd] = [] (* Base case: throw away *)
+ | evenly_positioned_elems [] = [] (* Base case *)
+
+
+(* Higher order functions: Functions can take other functions as arguments.
+ Functions are just other kinds of values, and functions don't need names
+ to exist. Functions without names are called "anonymous functions" or
+ lambda expressions or closures (since they also have a lexical scope). *)
+val is_large = (fn x => x > 37)
+val add_them = fn (a,b) => a + b
+val thermometer =
+ fn temp => if temp < 37
+ then "Cold"
+ else if temp > 37
+ then "Warm"
+ else "Normal"
+
+(* The following uses an anonymous function directly and gives "ColdWarm" *)
+val some_result = (fn x => thermometer (x - 5) ^ thermometer (x + 5)) 37
+
+(* Here is a higher-order function that works on lists (a list combinator) *)
+val readings = [ 34, 39, 37, 38, 35, 36, 37, 37, 37 ] (* first an int list *)
+val opinions = List.map thermometer readings (* gives [ "Cold", "Warm", ... ] *)
+
+(* And here is another one for filtering lists *)
+val warm_readings = List.filter is_large readings (* gives [39, 38] *)
+
+(* You can create your own higher-order functions, too. Functions can also take
+ several arguments by "currying" them. Syntax-wise this means adding spaces
+ between function arguments instead of commas and surrounding parentheses. *)
+fun map f [] = []
+ | map f (x::xs) = f(x) :: map f xs
+
+(* map has type ('a -> 'b) -> 'a list -> 'b list and is called polymorphic. *)
+(* 'a is called a type variable. *)
+
+(* Datatypes are useful for creating both simple and complex structures *)
+datatype color = Red | Green | Blue
+
+(* Here is a function that takes one of these as argument *)
+fun say(col) =
+ if col = Red then "You are red!" else
+ if col = Green then "You are green!" else
+ if col = Blue then "You are blue!" else
+ raise Fail "Unknown color"
+
+(* Datatypes are very often used in combination with pattern matching *)
+fun say Red = "You are red!"
+ | say Green = "You are green!"
+ | say Blue = "You are blue!"
+ | _ = raise Fail "Unknown color"
+
+
+(* Here is a binary tree datatype *)
+datatype 'a btree = Leaf of 'a
+ | Node of 'a btree * 'a * 'a btree (* three-arg constructor *)
+
+(* Here is a binary tree *)
+val myTree = Node (Leaf 9, 8, Node (Leaf 3, 5, Leaf 7))
+
+(* Drawing it, it might look something like...
+
+ 8
+ / \
+ leaf -> 9 5
+ / \
+ leaf -> 3 7 <- leaf
+ *)
+
+(* This function counts the sum of all the elements in a tree *)
+fun count (Leaf n) = n
+ | count (Node (leftTree, n, rightTree)) = count leftTree + n + count rightTree
+
+
+(* File I/O! *)
+(* Write a nice poem to a file *)
+fun writePoem(filename) =
+ let val file = TextIO.openOut(filename)
+ val _ = TextIO.output(file, "Roses are red,\nViolets are blue.\n")
+ val _ = TextIO.output(file, "I have a gun.\nGet in the van.\n")
+ in TextIO.closeOut(file) end
+
+(* Read a nice poem from a file into a list of strings *)
+fun readPoem(filename) =
+ let val file = TextIO.openIn filename
+ val poem = TextIO.inputAll file
+ val _ = TextIO.closeIn file
+ in String.tokens (fn c => c = #"\n") poem
+ end
+
+val _ = writePoem "roses.txt"
+val test_poem = readPoem "roses.txt" (* gives [ "Roses are red,",
+ "Violets are blue.",
+ "I have a gun.",
+ "Get in the van." ] *)
+~~~~
+
+## Further learning
+
+* Install an interactive compiler (REPL), for example
+ [http://www.polyml.org/](Poly/ML),
+ [http://mosml.org](Moscow ML) or
+ [http://smlnj.org/](SML/NJ).
+* Follow the Coursera course [Programming Languages](https://www.coursera.org/course/proglang).
+* Get the book *ML for the Working Programmer* by Larry C. Paulson.
+