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 ```agda mutual f : A f = a[f, g] g : B[f] g = b[f, g] ``` you can now write ```agda 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: ```agda -- 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 ```agda 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 ```agda (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: ```agda 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: ```agda 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: ```agda 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 ```agda record old { upd-fields } ``` is checked against a record type `R`, it is expanded to ```agda 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: ```agda 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: ```agda 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](https://github.com/agda/agda/issues/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: ```agda 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, ```agda 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: ```agda 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]: ```agda 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: ```agda 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: ```agda 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: ```agda 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 ```agda record Eq (A : Set) : Set where field equal : A → A → Bool, ``` then we can define the following projection: ```agda equal : {A : Set} {{eq : Eq A}} → A → A → Bool equal {{eq}} = Eq.equal eq ``` Now consider the following expression: ```agda 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: ```agda 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: ```agda 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: ```agda 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: ```agda open Eq {{...}} ``` Instance argument resolution is not recursive. As an example, consider the following "parametrised instance": ```agda 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: ```agda test = equal (1 ∷ 2 ∷ []) (3 ∷ 4 ∷ []) ``` However, we can make the code work by constructing a suitable instance manually: ```agda 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: ```agda 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 ```agda (ih : (a : A) -> P (squash a)). ``` * Records with only irrelevant fields. The following now works: ```agda 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: ```agda 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: ```agda -- 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 ```agda primQNameType (quote zero) ``` is definitionally equal to ```agda 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: ```agda 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: ```agda 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 ```haskell type AgdaIO a b = IO b, ``` we can set up universe-polymorphic `IO` in the following way: ```agda 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 `()`) ```haskell (\_ _ -> return) : forall a. () -> forall b. () -> b -> AgdaIO a b = T [[ ∀ {a} {A : Set a} → A → IO A ]] ``` and ```haskell (\_ _ _ _ -> (>>=)) : 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: ```agda 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: ```agda 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: ```agda 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: ```agda 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: ```agda 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: ```agda 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= .agda ``` Each source `.agda` is compiled into an ECMAScript target `/jAgda..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: ```javascript 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: ```agda 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 (``) 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 `--saf`e 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).