Programming in Juvix: Syntax Guide

This document is heavily inspired by the Idris syntax guide.

File Organization

A file contains zero or more Top Level Declarations

For example

-- this is a function with a signature!
sig foo : Natural
let foo = 3

-- this is a data type declaration
type list a = Cons a (List a)
            | Nil

-- this is a module declaration!
mod Boo =
  let fi = 10


Comments are denoted by two dashes, --. The two dashes and all characters up until the end of the line are discarded.


-- This is a comment!


Symbols are used for any name declared in the Juvix programming language. Symbols are broken into two categories, infix and prefix.

Prefix symbols start with either an letter or an underscore, which can be followed up by any alphanumeric character, underscores, punctuation(?, !), or dashes.

-- a valid symbol

-- another valid symbol

-- another valid symbol. Typically '?' denotes that the symbol is a predicate

-- An important action

-- not a valid prefix symbol

An infix symbol starts with any character other than a letter or an underscore.

-- This is a valid infix symbol


-- this is also another valid infix symbol


-- this is not a valid infix symbol, but instead a comment of a -


-- here is an arrow infix symbol


Top Level Declarations


Functions are started by writing let which is followed by any valid prefix symbol or an infix symbol surrounded by parentheses which shall be referred to as the function name. Then, there are zero or more arguments, with implicit arguments surrounded by curly braces ({}). The argument list ends when an equal sign (=) is placed, which denotes the start of the body.


-- this is a valid function
let f x = x + 3

-- this is another valid variable/function
let y = 5

-- this is a valid infix symbol
let (+) = plus

-- a function with an implicit argument
let foo {prf} x = x

Another important part of a function is the signature.

A signature is denoted first by sig, then the function name. From here colon (:) denotes the start of the type of the function name. Subsequently, any valid type can be written.


-- a valid signature and function
sig foo : int -> int
let foo x = x + 3

-- an example of a dependent signature
sig add-nat-int
    :  x : nat
    -> y : int
    -> if | x > y -> nat
          | else  -> int
let add-nat-int = (+)


Types are very similar to Haskell and Idris ADT and GADT declarations.

Types are declared by writing type following by the name of the type and arguments much like function syntax. Optionally a type signature can be given at this point, by writing colon (:) followed by the type.

An equals sign (=) denotes the start of the body of the type declaration.

From here a declaration can take a few forms.

  1. Zero or more sums, each of which starts with pipe (|) and contains a tagged product.
  2. A tagged product which starts with the new constructor name and either the arguments separated by spaces, a colon (:) followed by the arguments separated by arrows, or a base record.
  3. A base record which is denoted by curly braces ({}). inside the curly braces, a name is given to every argument, which type is started via colon and terminated by a comma (,).
-- This is a valid type
-- the a is a type argument
type list a
  -- Cons is the constructor
  -- Cons takes an item of type a and a List of a
  = Cons a (list a)
  -- Nil is another constructor taking no arguments
  | Nil

-- this is the same type, but GADT style arrow syntax
-- is given to the constructor
type list a : a -> list a
-- Curly braces can be used here to name the arguments
  = Cons { car : a,
           cdr : list a }
  | Nil

-- Same type again but using GADT syntax in the constructors
-- The first product can have a pipe!
type list a =
  | Cons : a -> list a -> list a
  | Nil  : list a

-- an example of a base record!
type coords a = {
  x : a,
  y : a

-- Same example but we have a trailing comma
type cords a = {
  x : a,
  y : a,

-- An example of a dependent type
type vect : (len : nat) -> (elem : set) -> set =
  | Nil  : vect 0 elem
  | Cons : elem -> vect len elem -> vect (succ len) elem


modules are denoted similarly to functions except that instead of using let, mod is used instead.

Instead of an expression, the body consists of zero or more top-level declarations followed by end.

-- example defining a module

mod Foo =
  sig bar : nat
  let bar = 3

  -- The type is inferred here
  let baz = 5

-- end ends the module definition

-- example using a module
let test = + Foo.baz


A module can be imported in two ways.

Importing a module unqualified via =open=ing them means that every symbol in the module becomes unqualified.

A module can be open-ed:


-- A valid open
open Foo

-- opening the module Baz in the moudle Bar in the moudle Bar
open Foo.Bar.Baz

-- This is the same statement as above.
open Foo
open Bar.Baz

-- let us define a module
mod IntMod =
  let t = int

  sig of-nat : int -> t
  let of-nat x = x

  sig add : t -> t -> t
  let add = (+)

-- now we shall open it into our scope
open IntMod

-- we can now use it unqualified
sig use-int-mod : nat -> nat -> t
let use-int-mod x y = add (of-nat x) (of-nat y)

A module can also be aliased with a let:


-- a valid module alias
let F = Foo



  1. If

    If expressions have a non-zero number of clauses. Each clause consists of a boolean test, followed by a body term.


    -- this is a valid if expression!
    if | x == 3 -> 5
       | else   -> 6
    -- ^ test      ^ consequence
    -- this is also a valid a valid if expression
    if | x == 10     -> 25
       | positive? x -> x
       | negative? x -> abs x
       | else        -> 0

    The else name is just an alias for True.

  2. Case

    Case expressions have a non-zero number of clauses. Each clause consists of a pattern, followed by a consequence.

    A pattern works much like Haskell or Idris, in that one can deconstruct on a record or a constructor. We also allow record punning on matches.


    type tree a = Branch (tree a) a (tree a)
                | Leaf a
                | Empty
    -- an example with match!
    sig func : Tree nat -> nat
    let func foo =
      case foo of
      | Branch left ele right ->
        func left + ele + func right
      | Leaf ele ->
      | Empty ->
    -- This is the same function!
    let func2 (Branch left ele right) =
      func2 left + ele + func2 right
    let func2 (Leaf ele) =
    let func2 Empty =
    type coords = {
      x : int,
      y : int
    -- match on record
    sig origin? : coords -> boolean
    let origin? {x, y}
      | x == y && x == 0 = True
      | else             = False
    -- same function as origin
    sig origin2? : coords -> boolean
    let origin2? {x = origX, y = origY}
      | origX == origY && origX == 0 =
      | else = False
    1. Dependent matching


Definitions within an expression are like their top level counterparts, except that in followed by an expression must be written after the definition.

  1. Let

    let foo =
      let bar = 3 in
      bar + 10
  2. Modules

    let foo =
      mod Bar =
        let foo = 3
        let bat = 10
      end in + Bar.bat
  3. Signatures

  4. Types

    let foo =
      type bar = Foo int
               | Bar nat
      in [Foo 3, Bar 10]


List literals are started by the open bracket character ([). Within, elements are separated by commas (,) before ending with a closing bracket (]).

List literal syntax is just sugar for the Cons and Nil constructors.


-- this is a valid list

-- another valid list

-- the same list without sugar
Cons 1 (Cons 2 (Cons 3 Nil))


Tuples are formatted like lists, however instead of using brackets, parenthesis are used instead ( ( ) ).


-- this is a tuple
(1, 2)

-- this is not a tuple

-- this is a 5 tuple!


Record literals are started by an open curly brace ({). Within, elements are bound to the corresponding name of the record via the equals sign (=), or punned by the name directly. Elements, like lists, are separated by commas (,) before ending with a closing brace (}).


type coords = {
  x : int,
  y : int

-- a new construct called foo for coords
sig create-cords : int -> int -> coords
let create-cords x-dir y-dir = {
  x = x-dir,
  y = y-dir

-- same function with punning
sig create-cords : int -> int -> coords
let create-cords x y = {x, y}
  1. Record updating syntax


  1. String Literals

    Strings are enclosed by double quotes (")


    let foo =
      "this is a string!"
  2. Integers/Naturals

    numbers are denoted by the characters 123456789.


    -- a valid number literal
    let foo = 123
    -- another valid number
    let number-one = 1

Do Notation

Do notation works similarly as it does in Haskell with changes to make it indent insensitive. Namely, this means that after every binding a semicolon (;) is needed to start the next expression. Further, no do is needed, the semicolon is enough to determine if an expression is in do syntax or not.

Thus like Haskell to bind terms, one states the name, then a left arrow (<-), then the monadic expression terminated by a semicolon.

For non bindings, just the monadic expression with a semicolon is needed.

The last expression in do notation does not need a semicolon.


let foo my =
  x <- Just 5;
  y <- my;
  pure (x + y)

let bar =
  Out.print "hello";
  name <- In.prompt "What is your name";
  Out.print ("hello" <> name)

Local opens

Local opens work just like global opens, however one has to write in then a body like other inner definitions.


let foo xs ys zs =
  open List in
  append xs (append ys zs)

There is also a more brief syntax where the module is then following by .( ... code here ... )


let foo xs ys zs =
  List.(append xs (append ys zs))