enso/docs/syntax/functions.md

layout	title	category	tags	order
developer-doc	Defining Functions	syntax	syntax functions	10

Defining Functions

Enso is a purely-functional programming language. As a result it has support for first-class and higher-order functions, meaning that you can pass functions as arguments to other functions, return functions from functions, assign them to variables, store them in data structures and so on.

Functions in Enso are curried by default, meaning that all functions are actually functions in one argument, but may return functions accepting further arguments.

• Lambdas
• Defining Functions
• Methods
• Calling Functions and Methods
• Code Blocks
• Operators
  • Precedence
  • Sections
• Mixfix Functions

Lambdas

The most primitive non-atom construct in Enso is the lambda. This is an anonymous function in one argument. A lambda is defined using the -> operator, where the left hand side is an argument, and the right hand side is the body of the function (containing arbitrary code).

Some functional languages such as Haskell allow for the definition of a lambda with multiple arguments, but in Enso the type signature use of ->and the lambda use of -> are one and the same. We do not want to have to put the components of a type signature in parentheses, so we only allow one argument before each arrow.

• Lambdas can close over variables in their surrounding scope.
• If you want to define a multi-argument lambda, you can do it by having a lambda return another lambda (e.g. a -> b -> a + b).

Additionally, lambdas in Enso have the following properties:

• The lambda introduces a new scope shared by the left and right operands.
• The left operand introduces a pattern context.
• If a lambda occurs in a pattern context, its left-hand-side identifiers are introduced into the scope targeted by the outer pattern context. For example, the following is valid (a -> b) -> a.default + b.
• Lambdas cannot currently occur in a matching context.

Please note that if a later lambda in a chain shadows an earlier lambda (e.g. a -> a -> a), the shadowed arguments by that name are inaccessible. If you want to unify later arguments with previous ones, you must employ the scope reference rule and write (in this case) a -> A -> a.

The actionables for this section are:

• In the future we want to be able to match on function types, so this restriction should be relaxed.
• Do we want any automated unification to take place in the shadowing case?

Defining Functions

A function definition is just syntactic sugar for the definition of a lambda, and hence has all the properties that a lambda does. Syntactically, functions are defined in a similar way to variables. The only difference is that the function name is followed by one or more parameters.

sum x y = x + y

Under the hood, functions are desugared to a lambda assigned to a variable that binds the function name. This means that:

• Like any variable, you can use the : type ascription operator to provide a user-defined type for the function.

  sum : (a: Monoid) -> a -> a
  sum : x -> y -> x + y
  sum x y = x + y
  

• Functions have an arity. Unlike a single lambda which always has an arity of one, function arity refers to the number of arguments in the function definition, which may not always be deduced from the type signature, but may still be inferred.

Methods

Enso makes a distinction between functions and methods. In Enso, a method is a function where the first argument (known as the this argument) is associated with a given atom. Methods are dispatched dynamically based on the type of the this argument, while functions are not.

Methods can be defined in Enso in two ways:

1. In the Body of a Type: A function defined in the body of a type definition is automatically converted to a method on all the atoms defined in the body of that type definition.

type Maybe a
    Nothing
    type Just (value : a)

    isJust = case this of
        Nothing -> False
        Just _ -> True

2. As an Extension Method: A function defined explicitly on an atom counts as an extension method on that atom. It can be defined on a typeset to apply to all the atoms within that typeset.

Number.floor = case this of
    Integer -> ...
    ...

3. As a Function with an Explicit this Argument: A function defined with the type of the this argument specified to be a type.

floor (this : Number) = case this of
    Integer -> ...

If the user does not explicitly specify the this argument by name when defining a method (e.g. they use the Type.name syntax), it is implicitly added to the start of the argument list.

Calling Functions and Methods

Enso makes the distinction between functions and methods. Methods are entities that are dispatched dynamically and looked up at runtime, while functions are defined locally and are looked up at compile time. In order to provide good diagnostics, we distinguish between how functions and methods are called.

• To call a function f on arguments a and b, we write f a b.
• To call a method f defined on a type A (value a, here) on argument b, we write a.f b.

Code Blocks

Top-level blocks in the language are evaluated immediately. This means that the layout of the code has no impact on semantics of the code:

• This means that the following a and b are equivalent.

  a = foo x y
  
  b =
    foo x y
  

• To suspend blocks, we provide a suspend function in the standard library.

• This function takes any expression as an argument (including a block), and suspends the execution of that expression such that it is not evaluated until forced later.

  susp = suspend
    x = foo x y z
    x.do_thing
  

  Alternatively, it is sufficient to type the binding for the block as Suspended a where a is the type of the block.

  susp : Suspended a =
    x = foo x y z
    x.do_thing
  

  It should be noted that this does not yet work.

The following rules apply to code blocks:

• Code blocks are desugared into in-order applications of monadic bind (as in keeping with the fact that all blocks are monadic contexts).
• If an expression that returns a value is not assigned to an identifier, this will issue a warning.
• To suppress this warning you can assign it to a blank (_).

test =
    _ = expr1
    expr2

# Becomes
test =
    expr1 >>= (_ -> expr2)

# Equivalent to
test =
    expr1 >> expr2

• If the trailing line of the block (the return value) is an assignment, it will return Nothing as all assignments do.

foo =
    pat1 = expr1

# Becomes
foo =
    expr1 >>= (pat1 -> Nothing)

Operators

In Enso, an operator is a function with a non-alphanumeric name (e.g. +). We only support binary operators, with left and right arguments.

Enso provides a significant amount of flexibility for developers who want to define custom operators. Formally, any sequence of the following characters forms an operators .!$%&*+-/<>?^~\. Operator definitions have three main parts:

• Definition: This defines a function that is called on the arguments provided to the operator.
• Precedence: This is an optional block that defines the precedence relation for the operator. Precedence in Enso is specified in relation to existing operators. If you do not provide this information, no precedence relations will be defined.
• Associativity: This is an optional block that defines the operator associativity to be either left, right, or none. If you do not provide this, the operator's associativity will default to left.

@prec  [> *, < $]
@assoc left
^ a n = a * a ^ (n-1)

Type Ascriptions and Operator Resolution

Just like with any other function definition in Enso operator arguments may be associated with type ascriptions. Having a type Num we can add + operator to it as:

Num.+ self that:Num -> Num = # add somehow

This inlined ascribed arguments increase type safety of the program by checking the types of values passed as arguments at runtime and yielding a Type_Error automatically when the types don't match. Moreover they support flexibility by automatically using conversions when the actual argument values don't match, but there is a way to make them match. Should there be a conversion from an Integer:

Num.from (that:Integer) = # convert somehow

then one can invoke the + on Num with Integer argument:

add_five n:Num = n+5

the above statement first converts the Integer literal 5 used as second argument of the operator to Num using the above defined Num.from conversion method and then it invokes the Num.+ operator with n and Num value representing 5 obtained from the conversion method. This is a regular behavior of every Enso function.

However, in order to support extensibility of types, the operators also offer additional resolution based on that argument. Because (while it is possible to write add_five method as shown above) the following wouldn't be properly typed according to standard Enso function dispatch rules:

five_add n:Num = 5+n

this would fail as the Integer.+ expects both arguments to be Integer and here we are trying to pass Num as the second argument. Should + be a regular function (and not an operator) we would get Type_Error. However the special binary operator resolution based on that argument kicks in and finds out the that argument type is Num and the type Num also defines + operator. Moreover there is a conversion from Integer (type of the self argument) to Num. Hence the Enso runtime system decides to convert 5 to Num and perform the addition by invoking Num.+. This behavior allows one to write libraries that extend existing number types with Complex_Number, Rational_Number and make them behave as first class citizen numbers.

Custom Equality

The == operator is special. A consistency with hash code is necessary to make any Enso object behave correctly and work effectively in Set and Map implementations. To guarantee such level of consistency there is a Any.== definition providing universal equality that shall not be overriden.

The == behavior is predefined for builtin types, atoms and other Enso objects. In addition to that it remains possible to define own comparators, including a comparator capable to work with already existing types. To create such comparator define:

• conversion between existing type and the new type (as described in previous section)
• comparator (see documentation of Ordering type)
• define two conversion method that return the same comparator

To extend the previous definition of Num also for equality one might do for example:

type Num_Comparator
    compare a:Num b:Num = # compare somehow
    hash a:Num = # hash somehow

Num.from (that:Integer) = # convert somehow
Comparable.from (_:Num) = Num_Comparator
Comparable.from (_:Integer) = Num_Comparator

with such a structure the internal implementation of Any.== performs necessary conversions of Integer argument in case the other argument is Num and invokes the Num_Comparator.compare to handle the comparision.

A care must be taken to keep consistency between hash values of original and converted types - e.g. hash of n:Integer and hash of Num.from n must be the same (otherwise consistency required for Set and Map would be compromised).

Precedence

Operator precedence in Enso is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given expression that contains operators. However, operator precedence in Enso differs from many other programming languages.

• Precedence is not set at fixed levels, but is instead defined in relation to the precedence of other operators.
• Precedence of an operator in Enso depends on whether a particular operator is surrounded by spaces or not. This means that the precedence of any operator not surrounded by spaces is always higher than the precedence of any operator surrounded by spaces. The only exception to this rule is the , operator, which retains the same precedence level regardless of whether it is surrounded by spaces or not.

This space-based precedence may seem strange coming from other languages, but it allows for writing far cleaner code than other functional languages. This is best demonstrated by example. Consider the following code:

list       = 1 .. 100
randomList = list . each random
headOfList = randomList . take 10
result     = headOfList . sort

This could easily be refactored to the following one-liner:

result = (((1 .. 100).each random).take 10).sort

This is still quite noisy, however, so using the whitespace-sensitive operator precedence rules, combined with the fact that the operator . is a regular operator, we get the following.

result = 1..100 . each random . take 10 . sort

Sections

An operator section is a nice shorthand for partially applying an operator. It works as follows.

• Where an argument is not applied to an operator, the missing argument is replaced by an implicit _.
• The application is then translated based upon the rules for underscore arguments described later.
• The whitespace-based precedence rules discussed above also apply to operator sections.

Mixfix Functions

A mixfix function is a function that is made up of multiple sections. They are defined using a special syntax, and operate as follows:

• They are defined using a 'split snake case'. The first section is written as normal, but subsequent sections are prefixed by an underscore (if c _then a, for example).
• The layout rules applied to mixfix functions operate as if each section was a separate operator, allowing you to write an indented block of code after each section.

Probably the best-known example of a mixfix function is if-then-else, which is indeed defined in the Enso standard library.

if foo == bar then frob else
    thing1
    thing2