SML is a rich enough language that there are often several ways to express things. This page contains miscellaneous tips (ideas not rules) for writing concise SML. The metric that we are interested in here is the number of tokens or words (rather than the number of lines, for example).

Datatypes in Signatures

A seemingly frequent source of repetition in SML is that of datatype definitions in signatures and structures. Actually, it isn’t repetition at all. A datatype specification in a signature, such as,

signature EXP = sig
   datatype exp = Fn of id * exp | App of exp * exp | Var of id

is just a specification of a datatype that may be matched by multiple (albeit identical) datatype declarations. For example, in

structure AnExp : EXP = struct
   datatype exp = Fn of id * exp | App of exp * exp | Var of id

structure AnotherExp : EXP = struct
   datatype exp = Fn of id * exp | App of exp * exp | Var of id

the types AnExp.exp and AnotherExp.exp are two distinct types. If such generativity isn’t desired or needed, you can avoid the repetition:

structure Exp = struct
   datatype exp = Fn of id * exp | App of exp * exp | Var of id

signature EXP = sig
   datatype exp = datatype Exp.exp

structure Exp : EXP = struct
   open Exp

Keep in mind that this isn’t semantically equivalent to the original.

Clausal Function Definitions

The syntax of clausal function definitions is rather repetitive. For example,

fun isSome NONE = false
  | isSome (SOME _) = true

is more verbose than

val isSome =
 fn NONE => false
  | SOME _ => true

For recursive functions the break-even point is one clause higher. For example,

fun fib 0 = 0
  | fib 1 = 1
  | fib n = fib (n-1) + fib (n-2)

isn’t less verbose than

val rec fib =
 fn 0 => 0
  | 1 => 1
  | n => fib (n-1) + fib (n-2)

It is quite often the case that a curried function primarily examines just one of its arguments. Such functions can be written particularly concisely by making the examined argument last. For example, instead of

fun eval (Fn (v, b)) env => ...
  | eval (App (f, a) env => ...
  | eval (Var v) env => ...

consider writing

fun eval env =
 fn Fn (v, b) => ...
  | App (f, a) => ...
  | Var v => ...


It is a good idea to avoid using lots of irritating superfluous parentheses. An important rule to know is that prefix function application in SML has higher precedence than any infix operator. For example, the outer parentheses in

(square (5 + 1)) + (square (5 * 2))

are superfluous.

People trained in other languages often use superfluous parentheses in a number of places. In particular, the parentheses in the following examples are practically always superfluous and are best avoided:

if (condition) then ... else ...
while (condition) do ...

The same basically applies to case expressions:

case (expression) of ...

It is not uncommon to match a tuple of two or more values:

case (a, b) of
   (A1, B1) => ...
 | (A2, B2) => ...

Such case expressions can be written more concisely with an infix product constructor:

case a & b of
   A1 & B1 => ...
 | A2 & B2 => ...


Repeated sequences of conditionals such as

if x < y then ...
else if x = y then ...
else ...

can often be written more concisely as case expressions such as

case (x, y) of
   LESS => ...
 | EQUAL => ...
 | GREATER => ...

For a custom comparison, you would then define an appropriate datatype and a reification function. An alternative to using datatypes is to use dispatch functions

comparing (x, y)
{lt = fn () => ...,
 eq = fn () => ...,
 gt = fn () => ...}


fun comparing (x, y) {lt, eq, gt} =
    (case (x, y) of
        LESS => lt
      | EQUAL => eq
      | GREATER => gt) ()

An advantage is that no datatype definition is needed. A disadvantage is that you can’t combine multiple dispatch results easily.

Command-Query Fusion

Many are familiar with the Command-Query Separation Principle. Adhering to the principle, a signature for an imperative stack might contain specifications

val isEmpty : 'a t -> bool
val pop : 'a t -> 'a

and use of a stack would look like

if isEmpty stack
then ... pop stack ...
else ...

or, when the element needs to be named,

if isEmpty stack
then let val elem = pop stack in ... end
else ...

For efficiency, correctness, and conciseness, it is often better to combine the query and command and return the result as an option:

val pop : 'a t -> 'a option

A use of a stack would then look like this:

case pop stack of
   NONE => ...
 | SOME elem => ...