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Chapter 4 – Functions

Lambda expressions are written as:

fn var : typ => exp

For example:

fn x : real => Math.sqrt (Math.sqrt x)
(fn x : real => Math.sqrt (Math.sqrt x)) (16.0)
val fourthroot : real -> real =
  fn x : real => Math.sqrt (Math.sqrt x)
fourthroot 16.0

ML provides a special syntax for function bindings that’s more concise:

fun fourthroot (x:real):real = Math.sqrt (Math.sqrt x)

By experimenting (I expect this is covered later), I found the following is sufficient due to type inference:

fun fourthroot x = Math.sqrt (Math.sqrt x)

Local val bindings may shadow parameters and other val bindings. For example, in the following, the last occurrence of x refers to the parameter of h, but the preceding two occurrences of x refer to the local binding with a value of 2.0:

fun h(x:real):real =
  let val x:real = 2.0 in x+x end * x

Chapter 5 – Products and Records

The n-tuple is the simplest form of aggregate data structure. They are of the form:
(val₁, … ,val_n)
An n-tuple is a value of a product type of the form:
typ₁* … *typ_n
For example:

val pair : int * int = (2, 3)
val triple : int * real * string = (2, 2.0, "2")
val pair_of_pairs : (int * int) * (real * real) = ((2,3),(2.0,3.0))

A 0-tuple, also known as a null tuple, is the empty sequence of values, ( ). It is a value of type unit. 1-tuples are absent from the language.

Tuple Patterns

We can use pattern matching to extract portions of an n-tuple. For example, in the code snippet below, r will be equal to 3.14. Underscores indicate “don’t care” positions:

val foo : (int * string) * (real * char) = ((7,"hello"),(3.14,#"z"))
val ((_, _), (r:real, _)) = foo

We can give names to the first and second components of the pair – using the REPL:

- val (is:int*string,rc:real*char) = foo;
val is = (7,"hello") : int * string
val rc = (3.14,#"z") : real * char

A pattern is one of three forms:

1. A variable pattern of the form var : typ
2. A tuple pattern of the form (pat₁, …, pat_n), where each pat_i is a pattern. This includes as a special case the null-tuple pattern, ()
3. A wildcard pattern of the form _

Record Types

Tuples can become more difficult to use as the number of elements increases. Record types allow labeling each component. A record type has the form:
{ lab₁:typ₁, …, lab_n:typ_n}
A record value has the form:
{ lab₁=val₁, …, lab_n=val_n}
A record pattern has the form:
{ lab₁=pat₁, …, lab_n=pat_n}

For example, the record type hyperlink is defined as follows:

type hyperlink =
  { protocol : string,
    address  : string,
    display  : string }

The following record binding defines a variable of type hyperlink:

val mailto : hyperlink =
  { protocol = "mailto",
    address = "foo@bar.com",
    display = "Brian Adkins" }

The following record binding:

val { protocol=prot, display=disp, address=addr } = mailto

decomposes into the three variable bindings:

val prot = "mailto"
val addr = "foo@bar.com"
val disp = "Brian Adkins"

We can use wildcard to extract selected fields:

val {protocol=prot, address=_, display=_ } = mailto

However, this isn’t very helpful with many fields, so we can use ellipsis patterns:

val {protocol=prot, ... } = mailto

ML provides an abbreviated form of record pattern {lab₁,…lab_n} which stands for { lab₁=var₁, …, lab_n=var_n} where the variables have the same name as the corresponding labels. For example, the following:

val { protocol, address, display } = mailto

decomposes into these bindings:

val protocol = "mailto"
val address = "foo@bar.com"
val display = "Brian Adkins"

Multiple Arguments and Multiple Results

fun dist (x:real, y:real):real = sqrt (x*x + y*y)

Keyword parameters are supported through record patterns:

fun dist’ {x=x:real, y=y:real} = sqrt (x*x + y*y)

Invoked as follows:

dist' {x=2.0,y=3.0}

Functions with multiple results may be thought of as functions yield tuples (or records).

fun dist2 (x:real, y:real):real*real
  = (sqrt (x*x+y*y), abs(x-y))

Sharp notation allows us to conveniently access the Nth item in a tuple.

- val foo = (3,7,5,2);
val foo = (3,7,5,2) : int * int * int * int
- #3 foo;
val it = 5 : int

A similar notation is used for record field selection:

 - val foo = { name = "Brian", phone = "555-1212" };
val foo = {name="Brian",phone="555-1212"} : {name:string, phone:string}
- #name foo;
val it = "Brian" : string

However, Harper states, “Use of the sharp notation is strongly discouraged!“

Table of Contents

• Part Two
• Part Three

The posts in this series will be notes & highlights from working through “Programming in Standard ML” by Robert Harper. See Getting Started with Standard ML for a link to the PDF. I may not always use quotes in this series, but it should be assumed that any factual information about Standard ML that I write in this series has been obtained from the PDF above – this series is, in effect, a summarization of Robert Harper’s PDF.

Overview

Attributes of Standard ML:

• Type-safe programming language
• Statically typed
• Extensible type system
• Polymorphic type inference
• Automatic storage management
• Encourages functional (effect-free) programming
• Allows imperative (effect-ful) programming where appropriate
• Pattern matching
• Extensible exception mechanism for handling error conditions
• Expressive and flexible module system
• Portable due to its precise definition
• Portable standard basis library

Chapter 1 – Programming in Standard ML

This chapter provides a brief overview of the language by considering an implementation of a regular expression package. It was slightly more familiar to me because of my brief studies of Haskell; otherwise, I think it would’ve appeared very foreign. I prefer more of a bottom up approach as much as possible instead of looking at language features that haven’t been described.

Currying

I do think that currying & partial application are cool features. Consider the following function declaration:

val match : RegExp.regexp -> string -> bool

Coming from a non-currying background, I would describe match as a function that accepts a regular expression and a string, and returns a boolean value indicating whether the string matches the regular expression, but Robert describes it this way:

It contains a function match that, when given a regular expression, returns a function that determines whether or not a given string matches that expression.

This was one of the features that made a strong impression on me when I first started looking at functional programming languages.

Chapter 2 – Types, Values, and Effects

Computation in ML is of a somewhat different nature. The emphasis in ML is on computation by evaluation of expressions, rather than execution of commands.

An expressions has three characteristics:

• It may or may not have a type
• It may or may not have a value
• It may or may not create an effect

Effects will be ignored until chapter 13, so until then, it’s assumed that all expressions are effect-free, or pure. A type is defined by specifying three things:

• a name for the type,
• the values of the type, and
• the operations that may be performed on values of the type

Notes:

• Negative numbers, as literals, are indicated with a tilde instead of a hypen e.g. ~7
• div is used for integers, / for reals

A typing assertion has the form: exp : typ For example: 3 : int 4 div 3 : int ML does not perform any implicit conversions between types. Use real(3) + 4.3, or 3 + round(4.3) Conditional expression (exp1 and exp2 must have the same type): if exp then exp1 else exp2 if not exp then exp1 else exp2

Chapter 3 – Declarations

Once a variable is bound to a value, it is bound to it for life; there is no possibility of changing the binding of a variable once it has been bound. Examples of type bindings:

type float = real
type count = int and average = real

Examples of value bindings:

val m : int = 3+2
val pi : real = 3.14 and e : real = 2.17

One thing to keep in mind is that binding is not assignment. The binding of a variable never changes; once bound to a value, it is always bound to that value (within the scope of the binding). However, we may shadow a binding by introducing a second binding for a variable within the scope of the first binding.

Limiting scope with let expressions:

let
  val m : int = 3
  val n : int = m*m
in
  m*n
end

The following expression evaluates to 54 because the binding of m is temporarily overridden during the evaluation of the let expression, then restored upon completion of this evaluation:

val m : int = 2
val r : int =
    let
        val m : int = 3
        val n : int = m*m
    in
        m*n
    end * m