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diff --git a/standard-ml.html.markdown b/standard-ml.html.markdown new file mode 100644 index 00000000..d1a8fc12 --- /dev/null +++ b/standard-ml.html.markdown @@ -0,0 +1,334 @@ +--- +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. + |