------------------------------------------------------------------------
-- Release notes for Agda 2 version 2.2.8
------------------------------------------------------------------------

Important changes since 2.2.6:

Language
--------

* Record pattern matching.

  It is now possible to pattern match on named record constructors.
  Example:

    record Σ (A : Set) (B : A → Set) : Set where
      constructor _,_
      field
        proj₁ : A
        proj₂ : B proj₁

    map : {A B : Set} {P : A → Set} {Q : B → Set}
          (f : A → B) → (∀ {x} → P x → Q (f x)) →
          Σ A P → Σ B Q
    map f g (x , y) = (f x , g y)

  The clause above is internally translated into the following one:

    map f g p = (f (Σ.proj₁ p) , g (Σ.proj₂ p))

  Record patterns containing data type patterns are not translated.
  Example:

    add : ℕ × ℕ → ℕ
    add (zero  , n) = n
    add (suc m , n) = suc (add (m , n))

  Record patterns which do not contain data type patterns, but which
  do contain dot patterns, are currently rejected. Example:

    Foo : {A : Set} (p₁ p₂ : A × A) → proj₁ p₁ ≡ proj₁ p₂ → Set₁
    Foo (x , y) (.x , y′) refl = Set

* Proof irrelevant function types.

  Agda now supports irrelevant non-dependent function types:

    f : .A → B

  This type implies that f does not depend computationally on its
  argument. One intended use case is data structures with embedded
  proofs, like sorted lists:

    postulate
      _≤_ : ℕ → ℕ → Set
      p₁  : 0 ≤ 1
      p₂  : 0 ≤ 1

    data SList (bound : ℕ) : Set where
      []    : SList bound
      scons : (head : ℕ) →
              .(head ≤ bound) →
              (tail : SList head) →
              SList bound

  The effect of the irrelevant type in the signature of scons is that
  scons's second argument is never inspected after Agda has ensured
  that it has the right type. It is even thrown away, leading to
  smaller term sizes and hopefully some gain in efficiency. The
  type-checker ignores irrelevant arguments when checking equality, so
  two lists can be equal even if they contain different proofs:

    l₁ : SList 1
    l₁ = scons 0 p₁ []

    l₂ : SList 1
    l₂ = scons 0 p₂ []

    l₁≡l₂ : l₁ ≡ l₂
    l₁≡l₂ = refl

  Irrelevant arguments can only be used in irrelevant contexts.
  Consider the following subset type:

    data Subset (A : Set) (P : A → Set) : Set where
      _#_ : (elem : A) → .(P elem) → Subset A P

  The following two uses are fine:

    elimSubset : ∀ {A C : Set} {P} →
                 Subset A P → ((a : A) → .(P a) → C) → C
    elimSubset (a # p) k = k a p

    elem : {A : Set} {P : A → Set} → Subset A P → A
    elem (x # p) = x

  However, if we try to project out the proof component, then Agda
  complains that "variable p is declared irrelevant, so it cannot be
  used here":

    prjProof : ∀ {A P} (x : Subset A P) → P (elem x)
    prjProof (a # p) = p

  Matching against irrelevant arguments is also forbidden, except in
  the case of irrefutable matches (record constructor patterns which
  have been translated away). For instance, the match against the
  pattern (p , q) here is accepted:

    elim₂ : ∀ {A C : Set} {P Q : A → Set} →
            Subset A (λ x → Σ (P x) (λ _ → Q x)) →
            ((a : A) → .(P a) → .(Q a) → C) → C
    elim₂ (a # (p , q)) k = k a p q

  Absurd matches () are also allowed.

  Note that record fields can also be irrelevant. Example:

    record Subset (A : Set) (P : A → Set) : Set where
      constructor _#_
      field
        elem   : A
        .proof : P elem

  Irrelevant fields are never in scope, neither inside nor outside the
  record. This means that no record field can depend on an irrelevant
  field, and furthermore projections are not defined for such fields.
  Irrelevant fields can only be accessed using pattern matching, as in
  elimSubset above.

  Irrelevant function types were added very recently, and have not
  been subjected to much experimentation yet, so do not be surprised
  if something is changed before the next release. For instance,
  dependent irrelevant function spaces (.(x : A) → B) might be added
  in the future.

* Mixfix binders.

  It is now possible to declare user-defined syntax that binds
  identifiers. Example:

    postulate
      State  : Set → Set → Set
      put    : ∀ {S} → S → State S ⊤
      get    : ∀ {S} → State S S
      return : ∀ {A S} → A → State S A
      bind   : ∀ {A B S} → State S B → (B → State S A) → State S A

    syntax bind e₁ (λ x → e₂) = x ← e₁ , e₂

    increment : State ℕ ⊤
    increment = x ← get ,
                put (1 + x)

  The syntax declaration for bind implies that x is in scope in e₂,
  but not in e₁.

  You can give fixity declarations along with syntax declarations:

    infixr 40 bind
    syntax bind e₁ (λ x → e₂) = x ← e₁ , e₂

  The fixity applies to the syntax, not the name; syntax declarations
  are also restricted to ordinary, non-operator names. The following
  declaration is disallowed:

    syntax _==_ x y = x === y

  Syntax declarations must also be linear; the following declaration
  is disallowed:

    syntax wrong x = x + x

  Syntax declarations were added very recently, and have not been
  subjected to much experimentation yet, so do not be surprised if
  something is changed before the next release.

* Prop has been removed from the language.

  The experimental sort Prop has been disabled. Any program using Prop
  should typecheck if Prop is replaced by Set₀. Note that Prop is still
  a keyword.

* Injective type constructors off by default.

  Automatic injectivity of type constructors has been disabled (by
  default). To enable it, use the flag --injective-type-constructors,
  either on the command line or in an OPTIONS pragma. Note that this
  flag makes Agda anti-classical and possibly inconsistent:

    Agda with excluded middle is inconsistent
    http://thread.gmane.org/gmane.comp.lang.agda/1367

  See test/succeed/InjectiveTypeConstructors.agda for an example.

* Termination checker can count.

  There is a new flag --termination-depth=N accepting values N >= 1
  (with N = 1 being the default) which influences the behavior of the
  termination checker. So far, the termination checker has only
  distinguished three cases when comparing the argument of a recursive
  call with the formal parameter of the callee.

    < : the argument is structurally smaller than the parameter
    = : they are equal
    ? : the argument is bigger or unrelated to the parameter

  This behavior, which is still the default (N = 1), will not
  recognise the following functions as terminating.

    mutual

      f : ℕ → ℕ
      f zero          = zero
      f (suc zero)    = zero
      f (suc (suc n)) = aux n

      aux : ℕ → ℕ
      aux m = f (suc m)

  The call graph

    f --(<)--> aux --(?)--> f

  yields a recursive call from f to f via aux where the relation of
  call argument to callee parameter is computed as "unrelated"
  (composition of < and ?).

  Setting N >= 2 allows a finer analysis: n has two constructors less
  than suc (suc n), and suc m has one more than m, so we get the call
  graph:

    f --(-2)--> aux --(+1)--> f

  The indirect call f --> f is now labeled with (-1), and the
  termination checker can recognise that the call argument is
  decreasing on this path.

  Setting the termination depth to N means that the termination
  checker counts decrease up to N and increase up to N-1. The default,
  N=1, means that no increase is counted, every increase turns to
  "unrelated".

  In practice, examples like the one above sometimes arise when "with"
  is used. As an example, the program

    f : ℕ → ℕ
    f zero          = zero
    f (suc zero)    = zero
    f (suc (suc n)) with zero
    ... | _ = f (suc n)

  is internally represented as

    mutual

      f : ℕ → ℕ
      f zero          = zero
      f (suc zero)    = zero
      f (suc (suc n)) = aux n zero

      aux : ℕ → ℕ → ℕ
      aux m k = f (suc m)

  Thus, by default, the definition of f using "with" is not accepted
  by the termination checker, even though it looks structural (suc n
  is a subterm of suc suc n). Now, the termination checker is
  satisfied if the option "--termination-depth=2" is used.

  Caveats:

  - This is an experimental feature, hopefully being replaced by
    something smarter in the near future.

  - Increasing the termination depth will quickly lead to very long
    termination checking times. So, use with care. Setting termination
    depth to 100 by habit, just to be on the safe side, is not a good
    idea!

  - Increasing termination depth only makes sense for linear data
    types such as ℕ and Size. For other types, increase cannot be
    recognised. For instance, consider a similar example with lists.

      data List : Set where
	nil  : List
	cons : ℕ → List → List

      mutual
	f : List → List
	f nil                  = nil
	f (cons x nil)         = nil
	f (cons x (cons y ys)) = aux y ys

	aux : ℕ → List → List
	aux z zs = f (cons z zs)

    Here the termination checker compares cons z zs to z and also to
    zs. In both cases, the result will be "unrelated", no matter how
    high we set the termination depth. This is because when comparing
    cons z zs to zs, for instance, z is unrelated to zs, thus,
    cons z zs is also unrelated to zs. We cannot say it is just "one
    larger" since z could be a very large term. Note that this points
    to a weakness of untyped termination checking.

    To regain the benefit of increased termination depth, we need to
    index our lists by a linear type such as ℕ or Size. With
    termination depth 2, the above example is accepted for vectors
    instead of lists.

* The codata keyword has been removed. To use coinduction, use the
  following new builtins: INFINITY, SHARP and FLAT. Example:

    {-# OPTIONS --universe-polymorphism #-}

    module Coinduction where

    open import Level

    infix 1000 ♯_

    postulate
      ∞  : ∀ {a} (A : Set a) → Set a
      ♯_ : ∀ {a} {A : Set a} → A → ∞ A
      ♭  : ∀ {a} {A : Set a} → ∞ A → A

    {-# BUILTIN INFINITY ∞  #-}
    {-# BUILTIN SHARP    ♯_ #-}
    {-# BUILTIN FLAT     ♭  #-}

  Note that (non-dependent) pattern matching on SHARP is no longer
  allowed.

  Note also that strange things might happen if you try to combine the
  pragmas above with COMPILED_TYPE, COMPILED_DATA or COMPILED pragmas,
  or if the pragmas do not occur right after the postulates.

  The compiler compiles the INFINITY builtin to nothing (more or
  less), so that the use of coinduction does not get in the way of FFI
  declarations:

    data Colist (A : Set) : Set where
      []  : Colist A
      _∷_ : (x : A) (xs : ∞ (Colist A)) → Colist A

    {-# COMPILED_DATA Colist [] [] (:) #-}

* Infinite types.

  If the new flag --guardedness-preserving-type-constructors is used,
  then type constructors are treated as inductive constructors when we
  check productivity (but only in parameters, and only if they are
  used strictly positively or not at all). This makes examples such as
  the following possible:

    data Rec (A : ∞ Set) : Set where
      fold : ♭ A → Rec A

    -- Σ cannot be a record type below.

    data Σ (A : Set) (B : A → Set) : Set where
      _,_ : (x : A) → B x → Σ A B

    syntax Σ A (λ x → B) = Σ[ x ∶ A ] B

    -- Corecursive definition of the W-type.

    W : (A : Set) → (A → Set) → Set
    W A B = Rec (♯ (Σ[ x ∶ A ] (B x → W A B)))

    syntax W A (λ x → B) = W[ x ∶ A ] B

    sup : {A : Set} {B : A → Set} (x : A) (f : B x → W A B) → W A B
    sup x f = fold (x , f)

    W-rec : {A : Set} {B : A → Set}
            (P : W A B → Set) →
            (∀ {x} {f : B x → W A B} → (∀ y → P (f y)) → P (sup x f)) →
            ∀ x → P x
    W-rec P h (fold (x , f)) = h (λ y → W-rec P h (f y))

    -- Induction-recursion encoded as corecursion-recursion.

    data Label : Set where
      ′0 ′1 ′2 ′σ ′π ′w : Label

    mutual

      U : Set
      U = Σ Label U′

      U′ : Label → Set
      U′ ′0 = ⊤
      U′ ′1 = ⊤
      U′ ′2 = ⊤
      U′ ′σ = Rec (♯ (Σ[ a ∶ U ] (El a → U)))
      U′ ′π = Rec (♯ (Σ[ a ∶ U ] (El a → U)))
      U′ ′w = Rec (♯ (Σ[ a ∶ U ] (El a → U)))

      El : U → Set
      El (′0 , _)            = ⊥
      El (′1 , _)            = ⊤
      El (′2 , _)            = Bool
      El (′σ , fold (a , b)) = Σ[ x ∶ El a ]  El (b x)
      El (′π , fold (a , b)) =   (x : El a) → El (b x)
      El (′w , fold (a , b)) = W[ x ∶ El a ]  El (b x)

    U-rec : (P : ∀ u → El u → Set) →
            P (′1 , _) tt →
            P (′2 , _) true →
            P (′2 , _) false →
            (∀ {a b x y} →
             P a x → P (b x) y → P (′σ , fold (a , b)) (x , y)) →
            (∀ {a b f} →
             (∀ x → P (b x) (f x)) → P (′π , fold (a , b)) f) →
            (∀ {a b x f} →
             (∀ y → P (′w , fold (a , b)) (f y)) →
             P (′w , fold (a , b)) (sup x f)) →
            ∀ u (x : El u) → P u x
    U-rec P P1 P2t P2f Pσ Pπ Pw = rec
      where
      rec : ∀ u (x : El u) → P u x
      rec (′0 , _)            ()
      rec (′1 , _)            _              = P1
      rec (′2 , _)            true           = P2t
      rec (′2 , _)            false          = P2f
      rec (′σ , fold (a , b)) (x , y)        = Pσ (rec _ x) (rec _ y)
      rec (′π , fold (a , b)) f              = Pπ (λ x → rec _ (f x))
      rec (′w , fold (a , b)) (fold (x , f)) = Pw (λ y → rec _ (f y))

  The --guardedness-preserving-type-constructors extension is based on
  a rather operational understanding of ∞/♯_; it's not yet clear if
  this extension is consistent.

* Qualified constructors.

  Constructors can now be referred to qualified by their data type.
  For instance, given

    data Nat : Set where
      zero : Nat
      suc  : Nat → Nat

    data Fin : Nat → Set where
      zero : ∀ {n} → Fin (suc n)
      suc  : ∀ {n} → Fin n → Fin (suc n)

  you can refer to the constructors unambiguously as Nat.zero,
  Nat.suc, Fin.zero, and Fin.suc (Nat and Fin are modules containing
  the respective constructors). Example:

    inj : (n m : Nat) → Nat.suc n ≡ suc m → n ≡ m
    inj .m m refl = refl

  Previously you had to write something like

    inj : (n m : Nat) → _≡_ {Nat} (suc n) (suc m) → n ≡ m

  to make the type checker able to figure out that you wanted the
  natural number suc in this case.

* Reflection.

  There are two new constructs for reflection:

    - quoteGoal x in e

      In e the value of x will be a representation of the goal type
      (the type expected of the whole expression) as an element in a
      datatype of Agda terms (see below). For instance,

      example : ℕ
      example = quoteGoal x in {! at this point x = def (quote ℕ) [] !}

    - quote x : Name

      If x is the name of a definition (function, datatype, record, or
      a constructor), quote x gives you the representation of x as a
      value in the primitive type Name (see below).

  Quoted terms use the following BUILTINs and primitives (available
  from the standard library module Reflection):

    -- The type of Agda names.

    postulate Name : Set

    {-# BUILTIN QNAME Name #-}

    primitive primQNameEquality : Name → Name → Bool

    -- Arguments.

    Explicit? = Bool

    data Arg A : Set where
      arg : Explicit? → A → Arg A

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

    -- The type of Agda terms.

    data Term : Set where
      var     : ℕ → List (Arg Term) → Term
      con     : Name → List (Arg Term) → Term
      def     : Name → List (Arg Term) → Term
      lam     : Explicit? → Term → Term
      pi      : Arg Term → Term → Term
      sort    : Term
      unknown : Term

    {-# BUILTIN AGDATERM            Term    #-}
    {-# BUILTIN AGDATERMVAR         var     #-}
    {-# BUILTIN AGDATERMCON         con     #-}
    {-# BUILTIN AGDATERMDEF         def     #-}
    {-# BUILTIN AGDATERMLAM         lam     #-}
    {-# BUILTIN AGDATERMPI          pi      #-}
    {-# BUILTIN AGDATERMSORT        sort    #-}
    {-# BUILTIN AGDATERMUNSUPPORTED unknown #-}

  Reflection may be useful when working with internal decision
  procedures, such as the standard library's ring solver.

* Minor record definition improvement.

  The definition of a record type is now available when type checking
  record module definitions. This means that you can define things
  like the following:

    record Cat : Set₁ where
      field
        Obj  : Set
        _=>_ : Obj → Obj → Set
        -- ...

      -- not possible before:
      op : Cat
      op = record { Obj = Obj; _=>_ = λ A B → B => A }

Tools
-----

* The "Goal type and context" command now shows the goal type before
  the context, and the context is shown in reverse order. The "Goal
  type, context and inferred type" command has been modified in a
  similar way.

* Show module contents command.

  Given a module name M the Emacs mode can now display all the
  top-level modules and names inside M, along with types for the
  names. The command is activated using C-c C-o or the menus.

* Auto command.

  A command which searches for type inhabitants has been added. The
  command is invoked by pressing C-C C-a (or using the goal menu).
  There are several flags and parameters, e.g. '-c' which enables
  case-splitting in the search. For further information, see the Agda
  wiki:

    http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.Auto

* HTML generation is now possible for a module with unsolved
  meta-variables, provided that the --allow-unsolved-metas flag is
  used.