agda/doc/release-notes/2.3.0.md

Release notes for Agda 2 version 2.3.0

Language

• New more liberal syntax for mutually recursive definitions.

It is no longer necessary to use the mutual keyword to define mutually recursive functions or datatypes. Instead, it is enough to declare things before they are used. Instead of

  mutual
    f : A
    f = a[f, g]

    g : B[f]
    g = b[f, g]

you can now write

  f : A
  g : B[f]
  f = a[f, g]
  g = b[f, g].

With the new style you have more freedom in choosing the order in which things are type checked (previously type signatures were always checked before definitions). Furthermore you can mix arbitrary declarations, such as modules and postulates, with mutually recursive definitions.

For data types and records the following new syntax is used to separate the declaration from the definition:

  -- Declaration.
  data Vec (A : Set) : Nat → Set  -- Note the absence of 'where'.

  -- Definition.
  data Vec A where
    []   : Vec A zero
    _::_ : {n : Nat} → A → Vec A n → Vec A (suc n)

  -- Declaration.
  record Sigma (A : Set) (B : A → Set) : Set

  -- Definition.
  record Sigma A B where
    constructor _,_
    field fst : A
          snd : B fst

When making separated declarations/definitions private or abstract you should attach the private keyword to the declaration and the abstract keyword to the definition. For instance, a private, abstract function can be defined as

  private
    f : A
  abstract
    f = e

Finally it may be worth noting that the old style of mutually recursive definitions is still supported (it basically desugars into the new style).

• Pattern matching lambdas.

Anonymous pattern matching functions can be defined using the syntax

  \ { p11 .. p1n -> e1 ; ... ; pm1 .. pmn -> em }

(where, as usual, \ and -> can be replaced by λ and →). Internally this is translated into a function definition of the following form:

  .extlam p11 .. p1n = e1
  ...
  .extlam pm1 .. pmn = em

This means that anonymous pattern matching functions are generative. For instance, refl will not be accepted as an inhabitant of the type

  (λ { true → true ; false → false }) ≡
  (λ { true → true ; false → false }),

because this is equivalent to extlam1 ≡ extlam2 for some distinct fresh names extlam1 and extlam2.

Currently the where and with constructions are not allowed in (the top-level clauses of) anonymous pattern matching functions.

Examples:

  and : Bool → Bool → Bool
  and = λ { true x → x ; false _ → false }

  xor : Bool → Bool → Bool
  xor = λ { true  true  → false
          ; false false → false
          ; _     _     → true
          }

  fst : {A : Set} {B : A → Set} → Σ A B → A
  fst = λ { (a , b) → a }

  snd : {A : Set} {B : A → Set} (p : Σ A B) → B (fst p)
  snd = λ { (a , b) → b }

• Record update syntax.

Assume that we have a record type and a corresponding value:

  record MyRecord : Set where
    field
      a b c : ℕ

  old : MyRecord
  old = record { a = 1; b = 2; c = 3 }

Then we can update (some of) the record value's fields in the following way:

  new : MyRecord
  new = record old { a = 0; c = 5 }

Here new normalises to record { a = 0; b = 2; c = 5 }. Any expression yielding a value of type MyRecord can be used instead of old.

Record updating is not allowed to change types: the resulting value must have the same type as the original one, including the record parameters. Thus, the type of a record update can be inferred if the type of the original record can be inferred.

The record update syntax is expanded before type checking. When the expression

  record old { upd-fields }

is checked against a record type R, it is expanded to

  let r = old in record { new-fields },

where old is required to have type R and new-fields is defined as follows: for each field x in R,

- if `x = e` is contained in `upd-fields` then `x = e` is included in
  `new-fields`, and otherwise

- if `x` is an explicit field then `x = R.x r` is included in
  `new-fields`, and

- if `x` is an implicit or instance field, then it is omitted from
  `new-fields`.

(Instance arguments are explained below.) The reason for treating implicit and instance fields specially is to allow code like the following:

  record R : Set where
    field
      {length} : ℕ
      vec      : Vec ℕ length
      -- More fields…

  xs : R
  xs = record { vec = 0 ∷ 1 ∷ 2 ∷ [] }

  ys = record xs { vec = 0 ∷ [] }

Without the special treatment the last expression would need to include a new binding for length (for instance length = _).

• Record patterns which do not contain data type patterns, but which do contain dot patterns, are no longer rejected.

• When the --without-K flag is used literals are now treated as constructors.

• Under-applied functions can now reduce.

Consider the following definition:

  id : {A : Set} → A → A
  id x = x

Previously the expression id would not reduce. This has been changed so that it now reduces to λ x → x. Usually this makes little difference, but it can be important in conjunction with with. See Issue #365 for an example.

• Unused AgdaLight legacy syntax (x y : A; z v : B) for telescopes has been removed.

Universe polymorphism

• Universe polymorphism is now enabled by default. Use --no-universe-polymorphism to disable it.

• Universe levels are no longer defined as a data type.

The basic level combinators can be introduced in the following way:

  postulate
    Level : Set
    zero  : Level
    suc   : Level → Level
    max   : Level → Level → Level

  {-# BUILTIN LEVEL     Level #-}
  {-# BUILTIN LEVELZERO zero  #-}
  {-# BUILTIN LEVELSUC  suc   #-}
  {-# BUILTIN LEVELMAX  max   #-}

• The BUILTIN equality is now required to be universe-polymorphic.

• trustMe is now universe-polymorphic.

Meta-variables and unification

• Unsolved meta-variables are now frozen after every mutual block. This means that they cannot be instantiated by subsequent code. For instance,

  one : Nat
  one = _

  bla : one ≡ suc zero
  bla = refl

leads to an error now, whereas previously it lead to the instantiation of _ with suc zero. If you want to make use of the old behaviour, put the two definitions in a mutual block.

All meta-variables are unfrozen during interactive editing, so that the user can fill holes interactively. Note that type-checking of interactively given terms is not perfect: Agda sometimes refuses to load a file, even though no complaints were raised during the interactive construction of the file. This is because certain checks (for instance, positivity) are only invoked when a file is loaded.

• Record types can now be inferred.

If there is a unique known record type with fields matching the fields in a record expression, then the type of the expression will be inferred to be the record type applied to unknown parameters.

If there is no known record type with the given fields the type checker will give an error instead of producing lots of unsolved meta-variables.

Note that "known record type" refers to any record type in any imported module, not just types which are in scope.

• The occurrence checker distinguishes rigid and strongly rigid occurrences [Reed, LFMTP 2009; Abel & Pientka, TLCA 2011].

The completeness checker now accepts the following code:

  h : (n : Nat) → n ≡ suc n → Nat
  h n ()

Internally this generates a constraint _n = suc _n where the meta-variable _n occurs strongly rigidly, i.e. on a constructor path from the root, in its own defining term tree. This is never solvable.

Weakly rigid recursive occurrences may have a solution [Jason Reed's PhD thesis, page 106]:

  test : (k : Nat) →
         let X : (Nat → Nat) → Nat
             X = _
         in
         (f : Nat → Nat) → X f ≡ suc (f (X (λ x → k)))
  test k f = refl

The constraint _X k f = suc (f (_X k (λ x → k))) has the solution _X k f = suc (f (suc k)), despite the recursive occurrence of _X. Here _X is not strongly rigid, because it occurs under the bound variable f. Previously Agda rejected this code; now it instead complains about an unsolved meta-variable.

• Equation constraints involving the same meta-variable in the head now trigger pruning [Pientka, PhD, Sec. 3.1.2; Abel & Pientka, TLCA 2011]. Example:

  same : let X : A → A → A → A × A
             X = _
         in {x y z : A} → X x y y ≡ (x , y)
                        × X x x y ≡ X x y y
  same = refl , refl

The second equation implies that X cannot depend on its second argument. After pruning the first equation is linear and can be solved.

• Instance arguments.

A new type of hidden function arguments has been added: instance arguments. This new feature is based on influences from Scala's implicits and Agda's existing implicit arguments.

Plain implicit arguments are marked by single braces: {…}. Instance arguments are instead marked by double braces: {{…}}. Example:

  postulate
    A : Set
    B : A → Set
    a : A
    f : {{a : A}} → B a

Instead of the double braces you can use the symbols ⦃ and ⦄, but these symbols must in many cases be surrounded by whitespace. (If you are using Emacs and the Agda input method, then you can conjure up the symbols by typing \{{ and \}}, respectively.)

Instance arguments behave as ordinary implicit arguments, except for one important aspect: resolution of arguments which are not provided explicitly. For instance, consider the following code:

    test = f

Here Agda will notice that f's instance argument was not provided explicitly, and try to infer it. All definitions in scope at f's call site, as well as all variables in the context, are considered. If exactly one of these names has the required type A, then the instance argument will be instantiated to this name.

This feature can be used as an alternative to Haskell type classes. If we define

  record Eq (A : Set) : Set where
    field equal : A → A → Bool,

then we can define the following projection:

  equal : {A : Set} {{eq : Eq A}} → A → A → Bool
  equal {{eq}} = Eq.equal eq

Now consider the following expression:

  equal false false ∨ equal 3 4

If the following Eq "instances" for Bool and ℕ are in scope, and no others, then the expression is accepted:

  eq-Bool : Eq Bool
  eq-Bool = record { equal = … }

  eq-ℕ : Eq ℕ
  eq-ℕ = record { equal = … }

A shorthand notation is provided to avoid the need to define projection functions manually:

  module Eq-with-implicits = Eq {{...}}

This notation creates a variant of Eq's record module, where the main Eq argument is an instance argument instead of an explicit one. It is equivalent to the following definition:

  module Eq-with-implicits {A : Set} {{eq : Eq A}} = Eq eq

Note that the short-hand notation allows you to avoid naming the "-with-implicits" module:

  open Eq {{...}}

Instance argument resolution is not recursive. As an example, consider the following "parametrised instance":

  eq-List : {A : Set} → Eq A → Eq (List A)
  eq-List {A} eq = record { equal = eq-List-A }
    where
    eq-List-A : List A → List A → Bool
    eq-List-A []       []       = true
    eq-List-A (a ∷ as) (b ∷ bs) = equal a b ∧ eq-List-A as bs
    eq-List-A _        _        = false

Assume that the only Eq instances in scope are eq-List and eq-ℕ. Then the following code does not type-check:

  test = equal (1 ∷ 2 ∷ []) (3 ∷ 4 ∷ [])

However, we can make the code work by constructing a suitable instance manually:

  test′ = equal (1 ∷ 2 ∷ []) (3 ∷ 4 ∷ [])
    where eq-List-ℕ = eq-List eq-ℕ

By restricting the "instance search" to be non-recursive we avoid introducing a new, compile-time-only evaluation model to Agda.

For more information about instance arguments, see Devriese & Piessens [ICFP 2011]. Some examples are also available in the examples/instance-arguments subdirectory of the Agda distribution.

Irrelevance

• Dependent irrelevant function types.

Some examples illustrating the syntax of dependent irrelevant function types:

  .(x y : A) → B    .{x y z : A} → B
  ∀ x .y → B        ∀ x .{y} {z} .v → B

The declaration

  f : .(x : A) → B[x]
  f x = t[x]

requires that x is irrelevant both in t[x] and in B[x]. This is possible if, for instance, B[x] = B′ x, with B′ : .A → Set.

Dependent irrelevance allows us to define the eliminator for the Squash type:

  record Squash (A : Set) : Set where
    constructor squash
    field
      .proof : A

  elim-Squash : {A : Set} (P : Squash A → Set)
                (ih : .(a : A) → P (squash a)) →
                (a⁻ : Squash A) → P a⁻
  elim-Squash P ih (squash a) = ih a

Note that this would not type-check with

  (ih : (a : A) -> P (squash a)).

• Records with only irrelevant fields.

The following now works:

  record IsEquivalence {A : Set} (_≈_ : A → A → Set) : Set where
    field
      .refl  : Reflexive _≈_
      .sym   : Symmetric _≈_
      .trans : Transitive _≈_

  record Setoid : Set₁ where
    infix 4 _≈_
    field
      Carrier        : Set
      _≈_            : Carrier → Carrier → Set
      .isEquivalence : IsEquivalence _≈_

    open IsEquivalence isEquivalence public

Previously Agda complained about the application IsEquivalence isEquivalence, because isEquivalence is irrelevant and the IsEquivalence module expected a relevant argument. Now, when record modules are generated for records consisting solely of irrelevant arguments, the record parameter is made irrelevant:

  module IsEquivalence {A : Set} {_≈_ : A → A → Set}
                       .(r : IsEquivalence {A = A} _≈_) where
    …

• Irrelevant things are no longer erased internally. This means that they are printed as ordinary terms, not as _ as before.

• The new flag --experimental-irrelevance enables irrelevant universe levels and matching on irrelevant data when only one constructor is available. These features are very experimental and likely to change or disappear.

Reflection

• The reflection API has been extended to mirror features like irrelevance, instance arguments and universe polymorphism, and to give (limited) access to definitions. For completeness all the builtins and primitives are listed below:

  -- Names.

  postulate Name : Set

  {-# BUILTIN QNAME Name #-}

  primitive
    -- Equality of names.
    primQNameEquality : Name → Name → Bool

  -- Is the argument visible (explicit), hidden (implicit), or an
  -- instance argument?

  data Visibility : Set where
    visible hidden instance : Visibility

  {-# BUILTIN HIDING   Visibility #-}
  {-# BUILTIN VISIBLE  visible    #-}
  {-# BUILTIN HIDDEN   hidden     #-}
  {-# BUILTIN INSTANCE instance   #-}

  -- Arguments can be relevant or irrelevant.

  data Relevance : Set where
    relevant irrelevant : Relevance

  {-# BUILTIN RELEVANCE  Relevance  #-}
  {-# BUILTIN RELEVANT   relevant   #-}
  {-# BUILTIN IRRELEVANT irrelevant #-}

  -- Arguments.

  data Arg A : Set where
    arg : (v : Visibility) (r : Relevance) (x : A) → Arg A

  {-# BUILTIN ARG    Arg #-}
  {-# BUILTIN ARGARG arg #-}

  -- Terms.

  mutual
    data Term : Set where
      -- Variable applied to arguments.
      var     : (x : ℕ) (args : List (Arg Term)) → Term
      -- Constructor applied to arguments.
      con     : (c : Name) (args : List (Arg Term)) → Term
      -- Identifier applied to arguments.
      def     : (f : Name) (args : List (Arg Term)) → Term
      -- Different kinds of λ-abstraction.
      lam     : (v : Visibility) (t : Term) → Term
      -- Pi-type.
      pi      : (t₁ : Arg Type) (t₂ : Type) → Term
      -- A sort.
      sort    : Sort → Term
      -- Anything else.
      unknown : Term

    data Type : Set where
      el : (s : Sort) (t : Term) → Type

    data Sort : Set where
      -- A Set of a given (possibly neutral) level.
      set     : (t : Term) → Sort
      -- A Set of a given concrete level.
      lit     : (n : ℕ) → Sort
      -- Anything else.
      unknown : Sort

  {-# BUILTIN AGDASORT            Sort    #-}
  {-# BUILTIN AGDATYPE            Type    #-}
  {-# BUILTIN AGDATERM            Term    #-}
  {-# BUILTIN AGDATERMVAR         var     #-}
  {-# BUILTIN AGDATERMCON         con     #-}
  {-# BUILTIN AGDATERMDEF         def     #-}
  {-# BUILTIN AGDATERMLAM         lam     #-}
  {-# BUILTIN AGDATERMPI          pi      #-}
  {-# BUILTIN AGDATERMSORT        sort    #-}
  {-# BUILTIN AGDATERMUNSUPPORTED unknown #-}
  {-# BUILTIN AGDATYPEEL          el      #-}
  {-# BUILTIN AGDASORTSET         set     #-}
  {-# BUILTIN AGDASORTLIT         lit     #-}
  {-# BUILTIN AGDASORTUNSUPPORTED unknown #-}

  postulate
    -- Function definition.
    Function  : Set
    -- Data type definition.
    Data-type : Set
    -- Record type definition.
    Record    : Set

  {-# BUILTIN AGDAFUNDEF    Function  #-}
  {-# BUILTIN AGDADATADEF   Data-type #-}
  {-# BUILTIN AGDARECORDDEF Record    #-}

  -- Definitions.

  data Definition : Set where
    function     : Function  → Definition
    data-type    : Data-type → Definition
    record′      : Record    → Definition
    constructor′ : Definition
    axiom        : Definition
    primitive′   : Definition

  {-# BUILTIN AGDADEFINITION                Definition   #-}
  {-# BUILTIN AGDADEFINITIONFUNDEF          function     #-}
  {-# BUILTIN AGDADEFINITIONDATADEF         data-type    #-}
  {-# BUILTIN AGDADEFINITIONRECORDDEF       record′      #-}
  {-# BUILTIN AGDADEFINITIONDATACONSTRUCTOR constructor′ #-}
  {-# BUILTIN AGDADEFINITIONPOSTULATE       axiom        #-}
  {-# BUILTIN AGDADEFINITIONPRIMITIVE       primitive′   #-}

  primitive
    -- The type of the thing with the given name.
    primQNameType        : Name → Type
    -- The definition of the thing with the given name.
    primQNameDefinition  : Name → Definition
    -- The constructors of the given data type.
    primDataConstructors : Data-type → List Name

As an example the expression

  primQNameType (quote zero)

is definitionally equal to

  el (lit 0) (def (quote ℕ) [])

(if zero is a constructor of the data type ℕ).

• New keyword: unquote.

The construction unquote t converts a representation of an Agda term to actual Agda code in the following way:

1. The argument t must have type Term (see the reflection API above).

2. The argument is normalised.

3. The entire construction is replaced by the normal form, which is treated as syntax written by the user and type-checked in the usual way.

Examples:

  test : unquote (def (quote ℕ) []) ≡ ℕ
  test = refl

  id : (A : Set) → A → A
  id = unquote (lam visible (lam visible (var 0 [])))

  id-ok : id ≡ (λ A (x : A) → x)
  id-ok = refl

• New keyword: quoteTerm.

The construction quoteTerm t is similar to quote n, but whereas quote is restricted to names n, quoteTerm accepts terms t. The construction is handled in the following way:

1. The type of t is inferred. The term t must be type-correct.

2. The term t is normalised.

3. The construction is replaced by the Term representation (see the reflection API above) of the normal form. Any unsolved metavariables in the term are represented by the unknown term constructor.

Examples:

  test₁ : quoteTerm (λ {A : Set} (x : A) → x) ≡
          lam hidden (lam visible (var 0 []))
  test₁ = refl

  -- Local variables are represented as de Bruijn indices.
  test₂ : (λ {A : Set} (x : A) → quoteTerm x) ≡ (λ x → var 0 [])
  test₂ = refl

  -- Terms are normalised before being quoted.
  test₃ : quoteTerm (0 + 0) ≡ con (quote zero) []
  test₃ = refl

Compiler backends

MAlonzo

• The MAlonzo backend's FFI now handles universe polymorphism in a better way.

The translation of Agda types and kinds into Haskell now supports universe-polymorphic postulates. The core changes are that the translation of function types has been changed from

  T[[ Pi (x : A) B ]] =
    if A has a Haskell kind then
      forall x. () -> T[[ B ]]
    else if x in fv B then
      undef
    else
      T[[ A ]] -> T[[ B ]]

into

  T[[ Pi (x : A) B ]] =
    if x in fv B then
      forall x. T[[ A ]] -> T[[ B ]]  -- Note: T[[A]] not Unit.
    else
      T[[ A ]] -> T[[ B ]],

and that the translation of constants (postulates, constructors and literals) has been changed from

  T[[ k As ]] =
    if COMPILED_TYPE k T then
      T T[[ As ]]
    else
      undef

into

  T[[ k As ]] =
    if COMPILED_TYPE k T then
      T T[[ As ]]
    else if COMPILED k E then
      ()
    else
      undef.

For instance, assuming a Haskell definition

    type AgdaIO a b = IO b,

we can set up universe-polymorphic IO in the following way:

  postulate
    IO     : ∀ {ℓ} → Set ℓ → Set ℓ
    return : ∀ {a} {A : Set a} → A → IO A
    _>>=_  : ∀ {a b} {A : Set a} {B : Set b} →
             IO A → (A → IO B) → IO B

  {-# COMPILED_TYPE IO AgdaIO              #-}
  {-# COMPILED return  (\_ _ -> return)    #-}
  {-# COMPILED _>>=_   (\_ _ _ _ -> (>>=)) #-}

This is accepted because (assuming that the universe level type is translated to the Haskell unit type ())

  (\_ _ -> return)
    : forall a. () -> forall b. () -> b -> AgdaIO a b
    = T [[ ∀ {a} {A : Set a} → A → IO A ]]

and

  (\_ _ _ _ -> (>>=))
    : forall a. () -> forall b. () ->
        forall c. () -> forall d. () ->
          AgdaIO a c -> (c -> AgdaIO b d) -> AgdaIO b d
    = T [[ ∀ {a b} {A : Set a} {B : Set b} →
             IO A → (A → IO B) → IO B ]].

Epic

• New Epic backend pragma: STATIC.

In the Epic backend, functions marked with the STATIC pragma will be normalised before compilation. Example usage:

  {-# STATIC power #-}

  power : ℕ → ℕ → ℕ
  power 0       x = 1
  power 1       x = x
  power (suc n) x = power n x * x

Occurrences of power 4 x will be replaced by ((x * x) * x) * x.

• Some new optimisations have been implemented in the Epic backend:

  • Removal of unused arguments.

A worker/wrapper transformation is performed so that unused arguments can be removed by Epic's inliner. For instance, the map function is transformed in the following way:

  map_wrap : (A B : Set) → (A → B) → List A → List B
  map_wrap A B f xs = map_work f xs

  map_work f []       = []
  map_work f (x ∷ xs) = f x ∷ map_work f xs

If map_wrap is inlined (which it will be in any saturated call), then A and B disappear in the generated code.

Unused arguments are found using abstract interpretation. The bodies of all functions in a module are inspected to decide which variables are used. The behaviour of postulates is approximated based on their types. Consider return, for instance:

  postulate return : {A : Set} → A → IO A

The first argument of return can be removed, because it is of type Set and thus cannot affect the outcome of a program at runtime.

• Injection detection.

At runtime many functions may turn out to be inefficient variants of the identity function. This is especially true after forcing. Injection detection replaces some of these functions with more efficient versions. Example:

  inject : {n : ℕ} → Fin n → Fin (1 + n)
  inject {suc n} zero    = zero
  inject {suc n} (suc i) = suc (inject {n} i)

Forcing removes the Fin constructors' ℕ arguments, so this function is an inefficient identity function that can be replaced by the following one:

  inject {_} x = x

To actually find this function, we make the induction hypothesis that inject is an identity function in its second argument and look at the branches of the function to decide if this holds.

Injection detection also works over data type barriers. Example:

  forget : {A : Set} {n : ℕ} → Vec A n → List A
  forget []       = []
  forget (x ∷ xs) = x ∷ forget xs

Given that the constructor tags (in the compiled Epic code) for Vec.[] and List.[] are the same, and that the tags for Vec._∷_ and List._∷_ are also the same, this is also an identity function. We can hence replace the definition with the following one:

  forget {_} xs = xs

To get this to apply as often as possible, constructor tags are chosen after injection detection has been run, in a way to make as many functions as possible injections.

Constructor tags are chosen once per source file, so it may be advantageous to define conversion functions like forget in the same module as one of the data types. For instance, if Vec.agda imports List.agda, then the forget function should be put in Vec.agda to ensure that vectors and lists get the same tags (unless some other injection function, which puts different constraints on the tags, is prioritised).

• Smashing.

This optimisation finds types whose values are inferable at runtime:

* A data type with only one constructor where all fields are
  inferable is itself inferable.

* `Set ℓ` is inferable (as it has no runtime representation).

A function returning an inferable data type can be smashed, which means that it is replaced by a function which simply returns the inferred value.

An important example of an inferable type is the usual propositional equality type (_≡_). Any function returning a propositional equality can simply return the reflexivity constructor directly without computing anything.

This optimisation makes more arguments unused. It also makes the Epic code size smaller, which in turn speeds up compilation.

JavaScript

• ECMAScript compiler backend.

A new compiler backend is being implemented, targetting ECMAScript (also known as JavaScript), with the goal of allowing Agda programs to be run in browsers or other ECMAScript environments.

The backend is still at an experimental stage: the core language is implemented, but many features are still missing.

The ECMAScript compiler can be invoked from the command line using the flag --js:

  agda --js --compile-dir=<DIR> <FILE>.agda

Each source <FILE>.agda is compiled into an ECMAScript target <DIR>/jAgda.<TOP-LEVEL MODULE NAME>.js. The compiler can also be invoked using the Emacs mode (the variable agda2-backend controls which backend is used).

Note that ECMAScript is a strict rather than lazy language. Since Agda programs are total, this should not impact program semantics, but it may impact their space or time usage.

ECMAScript does not support algebraic datatypes or pattern-matching. These features are translated to a use of the visitor pattern. For instance, the standard library's List data type and null function are translated into the following code:

  exports["List"] = {};
  exports["List"]["[]"] = function (x0) {
      return x0["[]"]();
    };
  exports["List"]["_∷_"] = function (x0) {
      return function (x1) {
        return function (x2) {
          return x2["_∷_"](x0, x1);
        };
      };
    };

  exports["null"] = function (x0) {
      return function (x1) {
        return function (x2) {
          return x2({
            "[]": function () {
              return jAgda_Data_Bool["Bool"]["true"];
            },
            "_∷_": function (x3, x4) {
              return jAgda_Data_Bool["Bool"]["false"];
            }
          });
        };
      };
    };

Agda records are translated to ECMAScript objects, preserving field names.

Top-level Agda modules are translated to ECMAScript modules, following the common.js module specification. A top-level Agda module Foo.Bar is translated to an ECMAScript module jAgda.Foo.Bar.

The ECMAScript compiler does not compile to Haskell, so the pragmas related to the Haskell FFI (IMPORT, COMPILED_DATA and COMPILED) are not used by the ECMAScript backend. Instead, there is a COMPILED_JS pragma which may be applied to any declaration. For postulates, primitives, functions and values, it gives the ECMAScript code to be emitted by the compiler. For data types, it gives a function which is applied to a value of that type, and a visitor object. For instance, a binding of natural numbers to ECMAScript integers (ignoring overflow errors) is:

  data ℕ : Set where
    zero : ℕ
    suc  : ℕ → ℕ

  {-# COMPILED_JS ℕ function (x,v) {
      if (x < 1) { return v.zero(); } else { return v.suc(x-1); }
    } #-}
  {-# COMPILED_JS zero 0 #-}
  {-# COMPILED_JS suc function (x) { return x+1; } #-}

  _+_ : ℕ → ℕ → ℕ
  zero  + n = n
  suc m + n = suc (m + n)

  {-# COMPILED_JS _+_ function (x) { return function (y) {
                        return x+y; };
    } #-}

To allow FFI code to be optimised, the ECMAScript in a COMPILED_JS declaration is parsed, using a simple parser that recognises a pure functional subset of ECMAScript, consisting of functions, function applications, return, if-statements, if-expressions, side-effect-free binary operators (no precedence, left associative), side-effect-free prefix operators, objects (where all member names are quoted), field accesses, and string and integer literals. Modules may be imported using the require (<module-id>) syntax: any impure code, or code outside the supported fragment, can be placed in a module and imported.

Tools

• New flag --safe, which can be used to type-check untrusted code.

This flag disables postulates, primTrustMe, and "unsafe" OPTIONS pragmas, some of which are known to make Agda inconsistent.

Rejected pragmas:

  --allow-unsolved-metas
  --experimental-irrelevance
  --guardedness-preserving-type-construtors
  --injective-type-constructors
  --no-coverage-check
  --no-positivity-check
  --no-termination-check
  --sized-types
  --type-in-type

Note that, at the moment, it is not possible to define the universe level or coinduction primitives when --safe is used (because they must be introduced as postulates). This can be worked around by type-checking trusted files in a first pass, without using --safe, and then using --safe in a second pass. Modules which have already been type-checked are not re-type-checked just because --safe is used.

• Dependency graphs.

The new flag --dependency-graph=FILE can be used to generate a DOT file containing a module dependency graph. The generated file (FILE) can be rendered using a tool like dot.

• The --no-unreachable-check flag has been removed.

• Projection functions are highlighted as functions instead of as fields. Field names (in record definitions and record values) are still highlighted as fields.

• Support for jumping to positions mentioned in the information buffer has been added.

• The make install command no longer installs Agda globally (by default).