agda/doc/release-notes/2.2.6.md

Release notes for Agda 2 version 2.2.6

Language

• Universe polymorphism (experimental extension).

To enable universe polymorphism give the flag --universe-polymorphism on the command line or (recommended) as an OPTIONS pragma.

When universe polymorphism is enabled Set takes an argument which is the universe level. For instance, the type of universe polymorphic identity is

  id : {a : Level} {A : Set a} → A → A.

The type Level is isomorphic to the unary natural numbers and should be specified using the BUILTINs LEVEL, LEVELZERO, and LEVELSUC:

  data Level : Set where
    zero : Level
    suc  : Level → Level

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

There is an additional BUILTIN LEVELMAX for taking the maximum of two levels:

  max : Level → Level → Level
  max  zero    m      = m
  max (suc n)  zero   = suc n
  max (suc n) (suc m) = suc (max n m)

  {-# BUILTIN LEVELMAX max #-}

The non-polymorphic universe levels Set, Set₁ and so on are sugar for Set zero, Set (suc zero), etc.

At present there is no automatic lifting of types from one level to another. It can still be done (rather clumsily) by defining types like the following one:

  data Lifted {a} (A : Set a) : Set (suc a) where
    lift : A → Lifted A

However, it is likely that automatic lifting is introduced at some point in the future.

• Multiple constructors, record fields, postulates or primitives can be declared using a single type signature:

  data Bool : Set where
    false true : Bool

  postulate
    A B : Set

• Record fields can be implicit:

  record R : Set₁ where
    field
      {A}         : Set
      f           : A → A
      {B C} D {E} : Set
      g           : B → C → E

By default implicit fields are not printed.

• Record constructors can be defined:

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

In this example _,_ gets the type

   (proj₁ : A) → B proj₁ → Σ A B.

For implicit fields the corresponding constructor arguments become implicit.

Note that the constructor is defined in the outer scope, so any fixity declaration has to be given outside the record definition. The constructor is not in scope inside the record module.

Note also that pattern matching for records has not been implemented yet.

• BUILTIN hooks for equality.

The data type

  data _≡_ {A : Set} (x : A) : A → Set where
    refl : x ≡ x

can be specified as the builtin equality type using the following pragmas:

  {-# BUILTIN EQUALITY _≡_  #-}
  {-# BUILTIN REFL     refl #-}

The builtin equality is used for the new rewrite construct and the primTrustMe primitive described below.

• New rewrite construct.

If eqn : a ≡ b, where _≡_ is the builtin equality (see above) you can now write

  f ps rewrite eqn = rhs

instead of

    f ps with a | eqn
    ... | ._ | refl = rhs

The rewrite construct has the effect of rewriting the goal and the context by the given equation (left to right).

You can rewrite using several equations (in sequence) by separating them with vertical bars (|):

  f ps rewrite eqn₁ | eqn₂ | … = rhs

It is also possible to add with-clauses after rewriting:

  f ps rewrite eqns with e
  ... | p = rhs

Note that pattern matching happens before rewriting—if you want to rewrite and then do pattern matching you can use a with after the rewrite.

See test/Succeed/Rewrite.agda for some examples.

• A new primitive, primTrustMe, has been added:

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

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

If x and y are definitionally equal, then primTrustMe {x = x} {y = y} reduces to refl.

Note that the 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.

For an example of the use of primTrustMe, see Data.String in version 0.3 of the standard library, where it is used to implement decidable equality on strings using the primitive boolean equality.

• Changes to the syntax and semantics of IMPORT pragmas, which are used by the Haskell FFI. Such pragmas must now have the following form:

  {-# IMPORT <module name> #-}

These pragmas are interpreted as qualified imports, so Haskell names need to be given qualified (unless they come from the Haskell prelude).

• The horizontal tab character (U+0009) is no longer treated as white space.

• Line pragmas are no longer supported.

• The --include-path flag can no longer be used as a pragma.

• The experimental and incomplete support for proof irrelevance has been disabled.

Tools

• New intro command in the Emacs mode. When there is a canonical way of building something of the goal type (for instance, if the goal type is a pair), the goal can be refined in this way. The command works for the following goal types:

  • A data type where only one of its constructors can be used to construct an element of the goal type. (For instance, if the goal is a non-empty vector, a cons will be introduced.)

  • A record type. A record value will be introduced. Implicit fields will not be included unless showing of implicit arguments is switched on.

  • A function type. A lambda binding as many variables as possible will be introduced. The variable names will be chosen from the goal type if its normal form is a dependent function type, otherwise they will be variations on x. Implicit lambdas will only be inserted if showing of implicit arguments is switched on.

This command can be invoked by using the refine command (C-c C-r) when the goal is empty. (The old behaviour of the refine command in this situation was to ask for an expression using the minibuffer.)

• The Emacs mode displays Checked in the mode line if the current file type checked successfully without any warnings.

• If a file F is loaded, and this file defines the module M, it is an error if F is not the file which defines M according to the include path.

Note that the command-line tool and the Emacs mode define the meaning of relative include paths differently: the command-line tool interprets them relative to the current working directory, whereas the Emacs mode interprets them relative to the root directory of the current project. (As an example, if the module A.B.C is loaded from the file <some-path>/A/B/C.agda, then the root directory is <some-path>.)

• It is an error if there are several files on the include path which match a given module name.

• Interface files are relocatable. You can move around source trees as long as the include path is updated in a corresponding way. Note that a module M may be re-typechecked if its time stamp is strictly newer than that of the corresponding interface file (M.agdai).

• Type-checking is no longer done when an up-to-date interface exists. (Previously the initial module was always type-checked.)

• Syntax highlighting files for Emacs (.agda.el) are no longer used. The --emacs flag has been removed. (Syntax highlighting information is cached in the interface files.)

• The Agate and Alonzo compilers have been retired. The options --agate, --alonzo and --malonzo have been removed.

• The default directory for MAlonzo output is the project's root directory. The --malonzo-dir flag has been renamed to --compile-dir.

• Emacs mode: C-c C-x C-d no longer resets the type checking state. C-c C-x C-r can be used for a more complete reset. C-c C-x C-s (which used to reload the syntax highlighting information) has been removed. C-c C-l can be used instead.

• The Emacs mode used to define some "abbrevs", unless the user explicitly turned this feature off. The new default is not to add any abbrevs. The old default can be obtained by customising agda2-mode-abbrevs-use-defaults (a customisation buffer can be obtained by typing M-x customize-group agda2 RET after an Agda file has been loaded).