Release notes for Agda 2 version 2.4.0
======================================

Installation and infrastructure
-------------------------------

* A new module called `Agda.Primitive` has been introduced. This
  module is available to all users, even if the standard library is
  not used.  Currently the module contains level primitives and their
  representation in Haskell when compiling with MAlonzo:

  ```agda
  infixl 6 _⊔_

  postulate
    Level : Set
    lzero : Level
    lsuc  : (ℓ : Level) → Level
    _⊔_   : (ℓ₁ ℓ₂ : Level) → Level

  {-# COMPILED_TYPE Level ()      #-}
  {-# COMPILED lzero ()           #-}
  {-# COMPILED lsuc  (\_ -> ())   #-}
  {-# COMPILED _⊔_   (\_ _ -> ()) #-}

  {-# BUILTIN LEVEL     Level  #-}
  {-# BUILTIN LEVELZERO lzero  #-}
  {-# BUILTIN LEVELSUC  lsuc   #-}
  {-# BUILTIN LEVELMAX  _⊔_    #-}
  ```

  To bring these declarations into scope you can use a declaration
  like the following one:

  ```agda
  open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
  ```

  The standard library reexports these primitives (using the names
  `zero` and `suc` instead of `lzero` and `lsuc`) from the `Level`
  module.

  Existing developments using universe polymorphism might now trigger
  the following error message:

  ```
  Duplicate binding for built-in thing LEVEL, previous binding to
    .Agda.Primitive.Level
  ```

  To fix this problem, please remove the duplicate bindings.

  Technical details (perhaps relevant to those who build Agda
  packages):

  The include path now always contains a directory
  `<DATADIR>/lib/prim`, and this directory is supposed to contain a
  subdirectory Agda containing a file `Primitive.agda`.

  The standard location of `<DATADIR>` is system- and
  installation-specific.  E.g., in a Cabal `--user` installation of
  Agda-2.3.4 on a standard single-ghc Linux system it would be
  `$HOME/.cabal/share/Agda-2.3.4` or something similar.

  The location of the `<DATADIR>` directory can be configured at
  compile-time using Cabal flags (`--datadir` and `--datasubdir`).
  The location can also be set at run-time, using the `Agda_datadir`
  environment variable.

Pragmas and options
-------------------

* Pragma `NO_TERMINATION_CHECK` placed within a mutual block is now
  applied to the whole mutual block (rather than being discarded
  silently).  Adding to the uses 1.-4. outlined in the release notes
  for 2.3.2 we allow:

  3a. Skipping an old-style mutual block: Somewhere within `mutual`
      block before a type signature or first function clause.

   ```agda
   mutual
     {-# NO_TERMINATION_CHECK #-}
     c : A
     c = d

     d : A
     d = c
   ```

* New option `--no-pattern-matching`

  Disables all forms of pattern matching (for the current file).
  You can still import files that use pattern matching.

* New option `-v profile:7`

  Prints some stats on which phases Agda spends how much time.
  (Number might not be very reliable, due to garbage collection
  interruptions, and maybe due to laziness of Haskell.)

* New option `--no-sized-types`

  Option `--sized-types` is now default.  `--no-sized-types` will turn
  off an extra (inexpensive) analysis on data types used for subtyping
  of sized types.

Language
--------

* Experimental feature: `quoteContext`

  There is a new keyword `quoteContext` that gives users access to the
  list of names in the current local context. For instance:

  ```agda
  open import Data.Nat
  open import Data.List
  open import Reflection

  foo : ℕ → ℕ → ℕ
  foo 0 m = 0
  foo (suc n) m = quoteContext xs in ?
  ```

  In the remaining goal, the list `xs` will consist of two names, `n`
  and `m`, corresponding to the two local variables. At the moment it
  is not possible to access let bound variables (this feature may be
  added in the future).

* Experimental feature: Varying arity.
  Function clauses may now have different arity, e.g.,

  ```agda
  Sum : ℕ → Set
  Sum 0       = ℕ
  Sum (suc n) = ℕ → Sum n

  sum : (n : ℕ) → ℕ → Sum n
  sum 0       acc   = acc
  sum (suc n) acc m = sum n (m + acc)
  ```

  or,

  ```agda
  T : Bool → Set
  T true  = Bool
  T false = Bool → Bool

  f : (b : Bool) → T b
  f false true  = false
  f false false = true
  f true = true
  ```

  This feature is experimental.  Yet unsupported:
  - Varying arity and `with`.

  - Compilation of functions with varying arity to Haskell, JS, or Epic.

* Experimental feature: copatterns.  (Activated with option `--copatterns`)

  We can now define a record by explaining what happens if you project
  the record.  For instance:

  ```agda
  {-# OPTIONS --copatterns #-}

  record _×_ (A B : Set) : Set where
    constructor _,_
    field
      fst : A
      snd : B
  open _×_

  pair : {A B : Set} → A → B → A × B
  fst (pair a b) = a
  snd (pair a b) = b

  swap : {A B : Set} → A × B → B × A
  fst (swap p) = snd p
  snd (swap p) = fst p

  swap3 : {A B C : Set} → A × (B × C) → C × (B × A)
  fst (swap3 t)       = snd (snd t)
  fst (snd (swap3 t)) = fst (snd t)
  snd (snd (swap3 t)) = fst t
  ```

  Taking a projection on the left hand side (lhs) is called a
  projection pattern, applying to a pattern is called an application
  pattern.  (Alternative terms: projection/application copattern.)

  In the first example, the symbol `pair`, if applied to variable
  patterns `a` and `b` and then projected via `fst`, reduces to
  `a`. `pair` by itself does not reduce.

  A typical application are coinductive records such as streams:

  ```agda
  record Stream (A : Set) : Set where
    coinductive
    field
      head : A
      tail : Stream A
  open Stream

  repeat : {A : Set} (a : A) -> Stream A
  head (repeat a) = a
  tail (repeat a) = repeat a
  ```

  Again, `repeat a` by itself will not reduce, but you can take a
  projection (head or tail) and then it will reduce to the respective
  rhs.  This way, we get the lazy reduction behavior necessary to
  avoid looping corecursive programs.

  Application patterns do not need to be trivial (i.e., variable
  patterns), if we mix with projection patterns.  E.g., we can have

  ```agda
  nats : Nat -> Stream Nat
  head (nats zero) = zero
  tail (nats zero) = nats zero
  head (nats (suc x)) = x
  tail (nats (suc x)) = nats x
  ```

  Here is an example (not involving coinduction) which demostrates
  records with fields of function type:

  ```agda
  -- The State monad

  record State (S A : Set) : Set where
    constructor state
    field
      runState : S → A × S
  open State

  -- The Monad type class

  record Monad (M : Set → Set) : Set1 where
    constructor monad
    field
      return : {A : Set}   → A → M A
      _>>=_  : {A B : Set} → M A → (A → M B) → M B


  -- State is an instance of Monad
  -- Demonstrates the interleaving of projection and application patterns

  stateMonad : {S : Set} → Monad (State S)
  runState (Monad.return stateMonad a  ) s  = a , s
  runState (Monad._>>=_  stateMonad m k) s₀ =
    let a , s₁ = runState m s₀
    in  runState (k a) s₁

  module MonadLawsForState {S : Set} where

    open Monad (stateMonad {S})

    leftId : {A B : Set}(a : A)(k : A → State S B) →
      (return a >>= k) ≡ k a
    leftId a k = refl

    rightId : {A B : Set}(m : State S A) →
      (m >>= return) ≡ m
    rightId m = refl

    assoc : {A B C : Set}(m : State S A)(k : A → State S B)(l : B → State S C) →
      ((m >>= k) >>= l) ≡ (m >>= λ a → (k a >>= l))
    assoc m k l = refl
  ```

  Copatterns are yet experimental and the following does not work:

  - Copatterns and `with` clauses.

  - Compilation of copatterns to Haskell, JS, or Epic.

  - Projections generated by

    ```agda
    open R {{...}}
    ```

    are not handled properly on lhss yet.

  - Conversion checking is slower in the presence of copatterns, since
    stuck definitions of record type do no longer count as neutral,
    since they can become unstuck by applying a projection. Thus,
    comparing two neutrals currently requires comparing all they
    projections, which repeats a lot of work.

* Top-level module no longer required.

  The top-level module can be omitted from an Agda file. The module
  name is then inferred from the file name by dropping the path and
  the `.agda` extension. So, a module defined in `/A/B/C.agda` would get
  the name `C`.

  You can also suppress only the module name of the top-level module
  by writing

  ```agda
  module _ where
  ```

  This works also for parameterised modules.

* Module parameters are now always hidden arguments in projections.
  For instance:

  ```agda
  module M (A : Set) where

    record Prod (B : Set) : Set where
      constructor _,_
      field
        fst : A
        snd : B
    open Prod public

  open M
  ```

  Now, the types of `fst` and `snd` are

  ```agda
  fst : {A : Set}{B : Set} → Prod A B → A
  snd : {A : Set}{B : Set} → Prod A B → B
  ```

  Until 2.3.2, they were

  ```agda
  fst : (A : Set){B : Set} → Prod A B → A
  snd : (A : Set){B : Set} → Prod A B → B
  ```

  This change is a step towards symmetry of constructors and projections.
  (Constructors always took the module parameters as hidden arguments).

* Telescoping lets: Local bindings are now accepted in telescopes
  of modules, function types, and lambda-abstractions.

  The syntax of telescopes as been extended to support `let`:

  ```agda
  id : (let ★ = Set) (A : ★) → A → A
  id A x = x
  ```

  In particular one can now `open` modules inside telescopes:

  ```agda
  module Star where
    ★ : Set₁
    ★ = Set


  module MEndo (let open Star) (A : ★) where
    Endo : ★
    Endo = A → A
  ```

  Finally a shortcut is provided for opening modules:

  ```agda
  module N (open Star) (A : ★) (open MEndo A) (f : Endo) where
    ...
  ```

  The semantics of the latter is

  ```agda
  module _ where
    open Star
    module _ (A : ★) where
      open MEndo A
      module N (f : Endo) where
        ...
  ```

  The semantics of telescoping lets in function types and lambda
  abstractions is just expanding them into ordinary lets.

* More liberal left-hand sides in lets
  [Issue [#1028](https://github.com/agda/agda/issues/1028)]:

  You can now write left-hand sides with arguments also for let
  bindings without a type signature. For instance,

  ```agda
  let f x = suc x in f zero
  ```

  Let bound functions still can't do pattern matching though.

* Ambiguous names in patterns are now optimistically resolved in favor
  of constructors. [Issue [#822](https://github.com/agda/agda/issues/822)]
  In particular, the following succeeds now:

  ```agda
  module M where

    data D : Set₁ where
      [_] : Set → D

  postulate [_] : Set → Set

  open M

  Foo : _ → Set
  Foo [ A ] = A
  ```

* Anonymous `where`-modules are opened
  public. [Issue [#848](https://github.com/agda/agda/issues/848)]

  ```
  <clauses>
  f args = rhs
    module _ telescope where
      body
  <more clauses>
  ```

  means the following (not proper Agda code, since you cannot put a
  module in-between clauses)

  ```
  <clauses>
  module _ {arg-telescope} telescope where
    body

  f args = rhs
  <more clauses>
  ```

  Example:

  ```agda
  A : Set1
  A = B module _ where
    B : Set1
    B = Set

  C : Set1
  C = B
  ```

* Builtin `ZERO` and `SUC` have been merged with `NATURAL`.

  When binding the `NATURAL` builtin, `ZERO` and `SUC` are bound to
  the appropriate constructors automatically. This means that instead
  of writing

  ```agda
  {-# BUILTIN NATURAL Nat #-}
  {-# BUILTIN ZERO zero #-}
  {-# BUILTIN SUC suc #-}
  ```

  you just write

  ```agda
  {-# BUILTIN NATURAL Nat #-}
  ```

* Pattern synonym can now have implicit
  arguments. [Issue [#860](https://github.com/agda/agda/issues/860)]

  For example,

  ```agda
  pattern tail=_ {x} xs = x ∷ xs

  len : ∀ {A} → List A → Nat
  len []         = 0
  len (tail= xs) = 1 + len xs
  ```

* Syntax declarations can now have implicit
  arguments. [Issue [#400](https://github.com/agda/agda/issues/400)]

  For example

  ```agda
  id : ∀ {a}{A : Set a} -> A -> A
  id x = x

  syntax id {A} x = x ∈ A
  ```

* Minor syntax changes

  - `-}` is now parsed as end-comment even if no comment was begun. As
    a consequence, the following definition gives a parse error

    ```agda
    f : {A- : Set} -> Set
    f {A-} = A-
    ```

    because Agda now sees `ID(f) LBRACE ID(A) END-COMMENT`, and no
    longer `ID(f) LBRACE ID(A-) RBRACE`.

    The rational is that the previous lexing was to context-sensitive,
    attempting to comment-out `f` using `{-` and `-}` lead to a parse
    error.

  - Fixities (binding strengths) can now be negative numbers as
    well. [Issue [#1109](https://github.com/agda/agda/issues/1109)]

    ```agda
    infix -1 _myop_
    ```

  - Postulates are now allowed in mutual
    blocks. [Issue [#977](https://github.com/agda/agda/issues/977)]

  - Empty where blocks are now
    allowed. [Issue [#947](https://github.com/agda/agda/issues/947)]

  - Pattern synonyms are now allowed in parameterised
    modules. [Issue [#941](https://github.com/agda/agda/issues/941)]

  - Empty hiding and renaming lists in module directives are now allowed.

  - Module directives `using`, `hiding`, `renaming` and `public` can
    now appear in arbitrary order. Multiple
    `using`/`hiding`/`renaming` directives are allowed, but you still
    cannot have both using and `hiding` (because that doesn't make
    sense). [Issue [#493](https://github.com/agda/agda/issues/493)]

Goal and error display
----------------------

* The error message `Refuse to construct infinite term` has been
  removed, instead one gets unsolved meta variables.  Reason: the
  error was thrown over-eagerly.
  [Issue [#795](https://github.com/agda/agda/issues/795)]

* If an interactive case split fails with message

  ```
    Since goal is solved, further case distinction is not supported;
    try `Solve constraints' instead
  ```

  then the associated interaction meta is assigned to a solution.
  Press `C-c C-=` (Show constraints) to view the solution and `C-c
  C-s` (Solve constraints) to apply it.
  [Issue [#289](https://github.com/agda/agda/issues/289)]

Type checking
-------------

* [ Issue [#376](https://github.com/agda/agda/issues/376) ]
  Implemented expansion of bound record variables during meta
  assignment.  Now Agda can solve for metas X that are applied to
  projected variables, e.g.:

  ```agda
  X (fst z) (snd z) = z

  X (fst z)         = fst z
  ```

  Technically, this is realized by substituting `(x , y)` for `z` with fresh
  bound variables `x` and `y`.  Here the full code for the examples:

  ```agda
  record Sigma (A : Set)(B : A -> Set) : Set where
    constructor _,_
    field
      fst : A
      snd : B fst
  open Sigma

  test : (A : Set) (B : A -> Set) ->
    let X : (x : A) (y : B x) -> Sigma A B
        X = _
    in  (z : Sigma A B) -> X (fst z) (snd z) ≡ z
  test A B z = refl

  test' : (A : Set) (B : A -> Set) ->
    let X : A -> A
        X = _
    in  (z : Sigma A B) -> X (fst z) ≡ fst z
  test' A B z = refl
  ```

  The fresh bound variables are named `fst(z)` and `snd(z)` and can appear
  in error messages, e.g.:

  ```agda
  fail : (A : Set) (B : A -> Set) ->
    let X : A -> Sigma A B
        X = _
    in  (z : Sigma A B) -> X (fst z) ≡ z
  fail A B z = refl
  ```

  results in error:

  ```
  Cannot instantiate the metavariable _7 to solution fst(z) , snd(z)
  since it contains the variable snd(z) which is not in scope of the
  metavariable or irrelevant in the metavariable but relevant in the
  solution
  when checking that the expression refl has type _7 A B (fst z) ≡ z
  ```

* Dependent record types and definitions by copatterns require
  reduction with previous function clauses while checking the current
  clause. [Issue [#907](https://github.com/agda/agda/issues/907)]

  For a simple example, consider

  ```agda
  test : ∀ {A} → Σ Nat λ n → Vec A n
  proj₁ test = zero
  proj₂ test = []
  ```

  For the second clause, the lhs and rhs are typed as

  ```agda
  proj₂ test : Vec A (proj₁ test)
  []         : Vec A zero
  ```

  In order for these types to match, we have to reduce the lhs type
  with the first function clause.

  Note that termination checking comes after type checking, so be
  careful to avoid non-termination!  Otherwise, the type checker
  might get into an infinite loop.

* The implementation of the primitive `primTrustMe` has changed.  It
  now only reduces to `REFL` if the two arguments `x` and `y` have the
  same computational normal form.  Before, it reduced when `x` and `y`
  were definitionally equal, which included type-directed equality
  laws such as eta-equality.  Yet because reduction is untyped,
  calling conversion from reduction lead to Agda crashes
  [Issue [#882](https://github.com/agda/agda/issues/882)].

  The amended description of `primTrustMe` is (cf. release notes
  for 2.2.6):

  ```agda
  primTrustMe : {A : Set} {x y : A} → x ≡ y
  ```

  Here `_≡_` is the builtin equality (see BUILTIN hooks for equality,
  above).

  If `x` and `y` have the same computational normal form, then
  `primTrustMe {x = x} {y = y}` reduces to `refl`.

  A note on `primTrustMe`'s runtime behavior: The MAlonzo compiler
  replaces all uses of `primTrustMe` with the `REFL` builtin, without
  any check for definitional equality. Incorrect uses of `primTrustMe`
  can potentially lead to segfaults or similar problems of the
  compiled code.

* Implicit patterns of record type are now only eta-expanded if there
  is a record constructor.
  [Issues [#473](https://github.com/agda/agda/issues/473),
  [#635](https://github.com/agda/agda/issues/635)]

  ```agda
  data D : Set where
    d : D

  data P : D → Set where
    p : P d

  record Rc : Set where
    constructor c
    field f : D

  works : {r : Rc} → P (Rc.f r) → Set
  works p = D
  ```

  This works since the implicit pattern `r` is eta-expanded to `c x`
  which allows the type of `p` to reduce to `P x` and `x` to be
  unified with `d`. The corresponding explicit version is:

  ```agda
  works' : (r : Rc) → P (Rc.f r) → Set
  works' (c .d) p = D
  ```

  However, if the record constructor is removed, the same example will
  fail:

  ```agda
  record R : Set where
    field f : D

  fails : {r : R} → P (R.f r) → Set
  fails p = D

  -- d != R.f r of type D
  -- when checking that the pattern p has type P (R.f r)
  ```

  The error is justified since there is no pattern we could write down
  for `r`.  It would have to look like

  ```agda
  record { f = .d }
  ```

  but anonymous record patterns are not part of the language.

* Absurd lambdas at different source locations are no longer
  different. [Issue [#857](https://github.com/agda/agda/issues/857)]
  In particular, the following code type-checks now:

  ```agda
  absurd-equality : _≡_ {A = ⊥ → ⊥} (λ()) λ()
  absurd-equality = refl
  ```

  Which is a good thing!

* Printing of named implicit function types.

  When printing terms in a context with bound variables Agda renames
  new bindings to avoid clashes with the previously bound names. For
  instance, if `A` is in scope, the type `(A : Set) → A` is printed as
  `(A₁ : Set) → A₁`. However, for implicit function types the name of
  the binding matters, since it can be used when giving implicit
  arguments.

  For this situation, the following new syntax has been introduced:
  `{x = y : A} → B` is an implicit function type whose bound variable
  (in scope in `B`) is `y`, but where the name of the argument is `x`
  for the purposes of giving it explicitly. For instance, with `A` in
  scope, the type `{A : Set} → A` is now printed as `{A = A₁ : Set} →
  A₁`.

  This syntax is only used when printing and is currently not being parsed.

* Changed the semantics of `--without-K`.
  [Issue [#712](https://github.com/agda/agda/issues/712),
  Issue [#865](https://github.com/agda/agda/issues/865),
  Issue [#1025](https://github.com/agda/agda/issues/1025)]

  New specification of `--without-K`:

  When `--without-K` is enabled, the unification of indices for
  pattern matching is restricted in two ways:

  1. Reflexive equations of the form `x == x` are no longer solved,
     instead Agda gives an error when such an equation is encountered.

  2. When unifying two same-headed constructor forms `c us` and `c vs`
     of type `D pars ixs`, the datatype indices `ixs` (but not the
     parameters) have to be *self-unifiable*, i.e. unification of
     `ixs` with itself should succeed positively. This is a nontrivial
     requirement because of point 1.

  Examples:

  - The J rule is accepted.

    ```agda
    J : {A : Set} (P : {x y : A} → x ≡ y → Set) →
        (∀ x → P (refl x)) →
        ∀ {x y} (x≡y : x ≡ y) → P x≡y
    J P p (refl x) = p x
    ```agda

    This definition is accepted since unification of `x` with `y`
    doesn't require deletion or injectivity.

  - The K rule is rejected.

    ```agda
    K : {A : Set} (P : {x : A} → x ≡ x → Set) →
        (∀ x → P (refl {x = x})) →
       ∀ {x} (x≡x : x ≡ x) → P x≡x
    K P p refl = p _
    ```

    Definition is rejected with the following error:

    ```
    Cannot eliminate reflexive equation x = x of type A because K has
    been disabled.
    when checking that the pattern refl has type x ≡ x
    ```

  - Symmetry of the new criterion.

    ```agda
    test₁ : {k l m : ℕ} → k + l ≡ m → ℕ
    test₁ refl = zero

    test₂ : {k l m : ℕ} → k ≡ l + m → ℕ
    test₂ refl = zero
    ```

    Both versions are now accepted (previously only the first one was).

  - Handling of parameters.

    ```agda
    cons-injective : {A : Set} (x y : A) → (x ∷ []) ≡ (y ∷ []) → x ≡ y
    cons-injective x .x refl = refl
    ```

    Parameters are not unified, so they are ignored by the new criterion.

  - A larger example: antisymmetry of ≤.

    ```agda
    data _≤_ : ℕ → ℕ → Set where
      lz : (n : ℕ) → zero ≤ n
      ls : (m n : ℕ) → m ≤ n → suc m ≤ suc n

    ≤-antisym : (m n : ℕ) → m ≤ n → n ≤ m → m ≡ n
    ≤-antisym .zero    .zero    (lz .zero) (lz .zero)   = refl
    ≤-antisym .(suc m) .(suc n) (ls m n p) (ls .n .m q) =
                 cong suc (≤-antisym m n p q)
    ```

  - [ Issue [#1025](https://github.com/agda/agda/issues/1025) ]

    ```agda
    postulate mySpace : Set
    postulate myPoint : mySpace

    data Foo : myPoint ≡ myPoint → Set where
      foo : Foo refl

    test : (i : foo ≡ foo) → i ≡ refl
    test refl = {!!}
    ```

    When applying injectivity to the equation `foo ≡ foo` of type `Foo
    refl`, it is checked that the index `refl` of type `myPoint ≡
    myPoint` is self-unifiable. The equation `refl ≡ refl` again
    requires injectivity, so now the index `myPoint` is checked for
    self-unifiability, hence the error:

    ```
    Cannot eliminate reflexive equation myPoint = myPoint of type
    mySpace because K has been disabled.
    when checking that the pattern refl has type foo ≡ foo
    ```

Termination checking
--------------------

* A buggy facility coined "matrix-shaped orders" that supported
  uncurried functions (which take tuples of arguments instead of one
  argument after another) has been removed from the termination
  checker. [Issue [#787](https://github.com/agda/agda/issues/787)]

* Definitions which fail the termination checker are not unfolded any
  longer to avoid loops or stack overflows in Agda.  However, the
  termination checker for a mutual block is only invoked after
  type-checking, so there can still be loops if you define a
  non-terminating function.  But termination checking now happens
  before the other supplementary checks: positivity, polarity,
  injectivity and projection-likeness.  Note that with the pragma `{-#
  NO_TERMINATION_CHECK #-}` you can make Agda treat any function as
  terminating.

* Termination checking of functions defined by `with` has been improved.

  Cases which previously required `--termination-depth` to pass the
  termination checker (due to use of `with`) no longer need the
  flag. For example

  ```agda
  merge : List A → List A → List A
  merge [] ys = ys
  merge xs [] = xs
  merge (x ∷ xs) (y ∷ ys) with x ≤ y
  merge (x ∷ xs) (y ∷ ys)    | false = y ∷ merge (x ∷ xs) ys
  merge (x ∷ xs) (y ∷ ys)    | true  = x ∷ merge xs (y ∷ ys)
  ```

  This failed to termination check previously, since the `with`
  expands to an auxiliary function `merge-aux`:

  ```agda
  merge-aux x y xs ys false = y ∷ merge (x ∷ xs) ys
  merge-aux x y xs ys true  = x ∷ merge xs (y ∷ ys)
  ```

  This function makes a call to `merge` in which the size of one of
  the arguments is increasing. To make this pass the termination
  checker now inlines the definition of `merge-aux` before checking,
  thus effectively termination checking the original source program.

  As a result of this transformation doing `with` on a variable no longer
  preserves termination. For instance, this does not termination check:

  ```agda
  bad : Nat → Nat
  bad n with n
  ... | zero  = zero
  ... | suc m = bad m
  ```

* The performance of the termination checker has been improved.  For
  higher `--termination-depth` the improvement is significant.  While
  the default `--termination-depth` is still 1, checking with higher
  `--termination-depth` should now be feasible.

Compiler backends
-----------------

* The MAlonzo compiler backend now has support for compiling modules
  that are not full programs (i.e. don't have a main function). The
  goal is that you can write part of a program in Agda and the rest in
  Haskell, and invoke the Agda functions from the Haskell code. The
  following features were added for this reason:

  - A new command-line option `--compile-no-main`: the command

    ```
    agda --compile-no-main Test.agda
    ```

    will compile `Test.agda` and all its dependencies to Haskell and
    compile the resulting Haskell files with `--make`, but (unlike
    `--compile`) not tell GHC to treat `Test.hs` as the main
    module. This type of compilation can be invoked from Emacs by
    customizing the `agda2-backend` variable to value `MAlonzoNoMain` and
    then calling `C-c C-x C-c` as before.

  - A new pragma `COMPILED_EXPORT` was added as part of the MAlonzo
    FFI. If we have an Agda file containing the following:

    ```agda
     module A.B where

     test : SomeType
     test = someImplementation

     {-# COMPILED_EXPORT test someHaskellId #-}
    ```

    then test will be compiled to a Haskell function called
    `someHaskellId` in module `MAlonzo.Code.A.B` that can be invoked
    from other Haskell code. Its type will be translated according to
    the normal MAlonzo rules.

Tools
-----

### Emacs mode

* A new goal command `Helper Function Type` (`C-c C-h`) has been added.

  If you write an application of an undefined function in a goal, the
  `Helper Function Type` command will print the type that the function
  needs to have in order for it to fit the goal. The type is also
  added to the Emacs kill-ring and can be pasted into the buffer using
  `C-y`.

  The application must be of the form `f args` where `f` is the name of the
  helper function you want to create. The arguments can use all the normal
  features like named implicits or instance arguments.

  Example:

  Here's a start on a naive reverse on vectors:

  ```agda
  reverse : ∀ {A n} → Vec A n → Vec A n
  reverse [] = []
  reverse (x ∷ xs) = {!snoc (reverse xs) x!}
  ```

  Calling `C-c C-h` in the goal prints

  ```agda
  snoc : ∀ {A} {n} → Vec A n → A → Vec A (suc n)
  ```

* A new command `Explain why a particular name is in scope` (`C-c
  C-w`) has been added.
  [Issue [#207](https://github.com/agda/agda/issues/207)]

  This command can be called from a goal or from the top-level and will as the
  name suggests explain why a particular name is in scope.

  For each definition or module that the given name can refer to a trace is
  printed of all open statements and module applications leading back to the
  original definition of the name.

  For example, given

  ```agda
  module A (X : Set₁) where
    data Foo : Set where
      mkFoo : Foo
  module B (Y : Set₁) where
    open A Y public
  module C = B Set
  open C
  ```

  Calling `C-c C-w` on `mkFoo` at the top-level prints

  ```
  mkFoo is in scope as
  * a constructor Issue207.C._.Foo.mkFoo brought into scope by
    - the opening of C at Issue207.agda:13,6-7
    - the application of B at Issue207.agda:11,12-13
    - the application of A at Issue207.agda:9,8-9
    - its definition at Issue207.agda:6,5-10
  ```

  This command is useful if Agda complains about an ambiguous name and
  you need to figure out how to hide the undesired interpretations.

* Improvements to the `make case` command (`C-c C-c`)

  - One can now also split on hidden variables, using the name
    (starting with `.`) with which they are printed.  Use `C-c C-`, to
    see all variables in context.

  - Concerning the printing of generated clauses:

    * Uses named implicit arguments to improve readability.

    * Picks explicit occurrences over implicit ones when there is a
      choice of binding site for a variable.

    * Avoids binding variables in implicit positions by replacing dot
      patterns that uses them by wildcards (`._`).

* Key bindings for lots of "mathematical" characters (examples: 𝐴𝑨𝒜𝓐𝔄)
  have been added to the Agda input method.  Example: type
  `\MiA\MIA\McA\MCA\MfA` to get 𝐴𝑨𝒜𝓐𝔄.

  Note: `\McB` does not exist in Unicode (as well as others in that style),
  but the `\MC` (bold) alphabet is complete.

* Key bindings for "blackboard bold" B (𝔹) and 0-9 (𝟘-𝟡) have been
  added to the Agda input method (`\bb` and `\b[0-9]`).

* Key bindings for controlling simplification/normalisation:

  Commands like `Goal type and context` (`C-c C-,`) could previously
  be invoked in two ways. By default the output was normalised, but if
  a prefix argument was used (for instance via `C-u C-c C-,`), then no
  explicit normalisation was performed. Now there are three options:

  - By default (`C-c C-,`) the output is simplified.

  - If `C-u` is used exactly once (`C-u C-c C-,`), then the result is
    neither (explicitly) normalised nor simplified.

  - If `C-u` is used twice (`C-u C-u C-c C-,`), then the result is
    normalised.

### LaTeX-backend

* Two new color scheme options were added to `agda.sty`:

  `\usepackage[bw]{agda}`, which highlights in black and white;
  `\usepackage[conor]{agda}`, which highlights using Conor's colors.

  The default (no options passed) is to use the standard colors.

* If `agda.sty` cannot be found by the LateX environment, it is now
  copied into the LateX output directory (`latex` by default) instead
  of the working directory. This means that the commands needed to
  produce a PDF now is

  ```
  agda --latex -i . <file>.lagda
  cd latex
  pdflatex <file>.tex
  ```

* The LaTeX-backend has been made more tool agnostic, in particular
  XeLaTeX and LuaLaTeX should now work. Here is a small example
  (`test/LaTeXAndHTML/succeed/UnicodeInput.lagda`):

  ```latex
  \documentclass{article}
  \usepackage{agda}
  \begin{document}

  \begin{code}
  data αβγδεζθικλμνξρστυφχψω : Set₁ where

  postulate
    →⇒⇛⇉⇄↦⇨↠⇀⇁ : Set
  \end{code}

  \[
  ∀X [ ∅ ∉ X ⇒ ∃f:X ⟶  ⋃ X\ ∀A ∈ X (f(A) ∈ A) ]
  \]
  \end{document}
  ```

  Compiled as follows, it should produce a nice looking PDF (tested with
  TeX Live 2012):

  ```
  agda --latex <file>.lagda
  cd latex
  xelatex <file>.tex (or lualatex <file>.tex)
  ```

  If symbols are missing or XeLaTeX/LuaLaTeX complains about the font
  missing, try setting a different font using:

  ```latex
  \setmathfont{<math-font>}
  ```

  Use the `fc-list` tool to list available fonts.

* Add experimental support for hyperlinks to identifiers

  If the `hyperref` LateX package is loaded before the Agda package
  and the links option is passed to the Agda package, then the Agda
  package provides a function called `\AgdaTarget`. Identifiers which
  have been declared targets, by the user, will become clickable
  hyperlinks in the rest of the document. Here is a small example
  (`test/LaTeXAndHTML/succeed/Links.lagda`):

  ```latex
  \documentclass{article}
  \usepackage{hyperref}
  \usepackage[links]{agda}
  \begin{document}

  \AgdaTarget{ℕ}
  \AgdaTarget{zero}
  \begin{code}
  data ℕ : Set where
    zero  : ℕ
    suc   : ℕ → ℕ
  \end{code}

  See next page for how to define \AgdaFunction{two} (doesn't turn into a
  link because the target hasn't been defined yet). We could do it
  manually though; \hyperlink{two}{\AgdaDatatype{two}}.

  \newpage

  \AgdaTarget{two}
  \hypertarget{two}{}
  \begin{code}
  two : ℕ
  two = suc (suc zero)
  \end{code}

  \AgdaInductiveConstructor{zero} is of type
  \AgdaDatatype{ℕ}. \AgdaInductiveConstructor{suc} has not been defined to
  be a target so it doesn't turn into a link.

  \newpage

  Now that the target for \AgdaFunction{two} has been defined the link
  works automatically.

  \begin{code}
  data Bool : Set where
    true false : Bool
  \end{code}

  The AgdaTarget command takes a list as input, enabling several
  targets to be specified as follows:

  \AgdaTarget{if, then, else, if\_then\_else\_}
  \begin{code}
  if_then_else_ : {A : Set} → Bool → A → A → A
  if true  then t else f = t
  if false then t else f = f
  \end{code}

  \newpage

  Mixfix identifier need their underscores escaped:
  \AgdaFunction{if\_then\_else\_}.

  \end{document}
  ```

  The boarders around the links can be suppressed using hyperref's
  hidelinks option:

  ```latex
    \usepackage[hidelinks]{hyperref}
  ```

  Note that the current approach to links does not keep track of scoping
  or types, and hence overloaded names might create links which point to
  the wrong place. Therefore it is recommended to not overload names
  when using the links option at the moment, this might get fixed in the
  future.