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