# Version-2-3-2

------------------------------------------------------------------------ -- Release notes for Agda 2 version 2.3.2 ------------------------------------------------------------------------ Important changes since 2.3.0: Installation ============ * The Agda-executable package has been removed. The executable is now provided as part of the Agda package. * The Emacs mode no longer depends on haskell-mode or GHCi. * Compilation of Emacs mode Lisp files. You can now compile the Emacs mode Lisp files by running "agda-mode compile". This command is run by "make install". Compilation can, in some cases, give a noticeable speedup. WARNING: If you reinstall the Agda mode without recompiling the Emacs Lisp files, then Emacs may continue using the old, compiled files. Pragmas and Options =================== * The --without-K check now reconstructs constructor parameters. New specification of --without-K: If the flag is activated, then Agda only accepts certain case-splits. If the type of the variable to be split is D pars ixs, where D is a data (or record) type, pars stands for the parameters, and ixs the indices, then the following requirements must be satisfied: * The indices ixs must be applications of constructors (or literals) to distinct variables. Constructors are usually not applied to parameters, but for the purposes of this check constructor parameters are treated as other arguments. * These distinct variables must not be free in pars. * Irrelevant arguments are printed as _ by default now. To turn on printing of irrelevant arguments, use option --show-irrelevant * New: Pragma NO_TERMINATION_CHECK to switch off termination checker for individual function definitions and mutual blocks. The pragma must precede a function definition or a mutual block. Examples (see test/succeed/NoTerminationCheck.agda): 1. Skipping a single definition: before type signature. {-# NO_TERMINATION_CHECK #-} a : A a = a 2. Skipping a single definition: before first clause. b : A {-# NO_TERMINATION_CHECK #-} b = b 3. Skipping an old-style mutual block: Before 'mutual' keyword. {-# NO_TERMINATION_CHECK #-} mutual c : A c = d d : A d = c 4. Skipping a new-style mutual block: Anywhere before a type signature or first function clause in the block i : A j : A i = j {-# NO_TERMINATION_CHECK #-} j = i The pragma cannot be used in --safe mode. Language ======== * Let binding record patterns record _×_ (A B : Set) : Set where constructor _,_ field fst : A snd : B open _×_ let (x , (y , z)) = t in u will now be interpreted as let x = fst t y = fst (snd t) z = snd (snd t) in u Note that the type of t needs to be inferable. If you need to provide a type signature, you can write the following: let a : ... a = t (x , (y , z)) = a in u * Pattern synonyms A pattern synonym is a declaration that can be used on the left hand side (when pattern matching) as well as the right hand side (in expressions). For example: pattern z = zero pattern ss x = suc (suc x) f : ℕ -> ℕ f z = z f (suc z) = ss z f (ss n) = n Pattern synonyms are implemented by substitution on the abstract syntax, so definitions are scope-checked but not type-checked. They are particularly useful for universe constructions. * Qualified mixfix operators It is now possible to use a qualified mixfix operator by qualifying the first part of the name. For instance import Data.Nat as Nat import Data.Bool as Bool two = Bool.if true then 1 Nat.+ 1 else 0 * Sections [Issue 735]. Agda now parses anonymous modules as sections: module _ {a} (A : Set a) where data List : Set a where [] : List _∷_ : (x : A) (xs : List) → List module _ {a} {A : Set a} where _++_ : List A → List A → List A [] ++ ys = ys (x ∷ xs) ++ ys = x ∷ (xs ++ ys) test : List Nat test = (5 ∷ []) ++ (3 ∷ []) In general, now the syntax module _ parameters where declarations is accepted and has the same effect as private module M parameters where declarations open M public for a fresh name M. * Instantiating a module in an open import statement [Issue 481]. Now accepted: open import Path.Module args [using/hiding/renaming (...)] This only brings the imported identifiers from Path.Module into scope, not the module itself! Consequently, the following is pointless, and raises an error: import Path.Module args [using/hiding/renaming (...)] You can give a private name M to the instantiated module via import Path.Module args as M [using/hiding/renaming (...)] open import Path.Module args as M [using/hiding/renaming (...)] Try to avoid 'as' as part of the arguments. 'as' is not a keyword; the following can be legal, although slightly obfuscated Agda code: open import as as as as as as * Implicit module parameters can be given by name. E.g. open M {namedArg = bla} This feature has been introduced in Agda 2.3.0 already. * Multiple type signatures sharing a same type can now be written as a single type signature. one two : ℕ one = suc zero two = suc one Goal and error display ====================== * Meta-variables that were introduced by hidden argument `arg' are now printed as _arg_number instead of just _number. [Issue 526] * Agda expands identifiers in anonymous modules when printing. Should make some goals nicer to read. [Issue 721] * When a module identifier is ambiguous, Agda tells you if one of them is a data type module. [Issues 318, 705] Type checking ============= * Improved coverage checker. The coverage checker splits on arguments that have constructor or literal pattern, committing to the left-most split that makes progress. Consider the lookup function for vectors: data Fin : Nat → Set where zero : {n : Nat} → Fin (suc n) suc : {n : Nat} → Fin n → Fin (suc n) data Vec (A : Set) : Nat → Set where [] : Vec A zero _∷_ : {n : Nat} → A → Vec A n → Vec A (suc n) _!!_ : {A : Set}{n : Nat} → Vec A n → Fin n → A (x ∷ xs) !! zero = x (x ∷ xs) !! suc i = xs !! i In Agda up to 2.3.0, this definition is rejected unless we add an absurd clause [] !! () This is because the coverage checker committed on splitting on the vector argument, even though this inevitably lead to failed coverage, because a case for the empty vector [] is missing. The improvement to the coverage checker consists on committing only on splits that have a chance of covering, since all possible constructor patterns are present. Thus, Agda will now split first on the Fin argument, since cases for both zero and suc are present. Then, it can split on the Vec argument, since the empty vector is already ruled out by instantiating n to a suc _. * Instance arguments resolution will now consider candidates which still expect hidden arguments. For example: record Eq (A : Set) : Set where field eq : A → A → Bool open Eq {{...}} eqFin : {n : ℕ} → Eq (Fin n) eqFin = record { eq = primEqFin } testFin : Bool testFin = eq fin1 fin2 The type-checker will now resolve the instance argument of the eq function to eqFin {_}. This is only done for hidden arguments, not instance arguments, so that the instance search stays non-recursive. * Constraint solving: Upgraded Miller patterns to record patterns. [Issue 456] Agda now solves meta-variables that are applied to record patterns. A typical (but here, artificial) case is: record Sigma (A : Set)(B : A -> Set) : Set where constructor _,_ field fst : A snd : B fst test : (A : Set)(B : A -> Set) -> let X : Sigma A B -> Sigma A B X = _ in (x : A)(y : B x) -> X (x , y) ≡ (x , y) test A B x y = refl This yields a constraint of the form _X A B (x , y) := t[x,y] (with t[x,y] = (x, y)) which is not a Miller pattern. However, Agda now solves this as _X A B z := t[fst z,snd z]. * Changed: solving recursive constraints. [Issue 585] Until 2.3.0, Agda sometimes inferred values that did not pass the termination checker later, or would even make Agda loop. To prevent this, the occurs check now also looks into the definitions of the current mutual block, to avoid constructing recursive solutions. As a consequence, also terminating recursive solutions are no longer found automatically. This effects a programming pattern where the recursively computed type of a recursive function is left to Agda to solve. mutual T : D -> Set T pattern1 = _ T pattern2 = _ f : (d : D) -> T d f pattern1 = rhs1 f pattern2 = rhs2 This might no longer work from now on. See examples test/fail/Issue585*.agda * Less eager introduction of implicit parameters. [Issue 679] Until Agda 2.3.0, trailing hidden parameters were introduced eagerly on the left hand side of a definition. For instance, one could not write test : {A : Set} -> Set test = \ {A} -> A because internally, the hidden argument {A : Set} was added to the left-hand side, yielding test {_} = \ {A} -> A which raised a type error. Now, Agda only introduces the trailing implicit parameters it has to, in order to maintain uniform function arity. For instance, in test : Bool -> {A B C : Set} -> Set test true {A} = A test false {B = B} = B Agda will introduce parameters A and B in all clauses, but not C, resulting in test : Bool -> {A B C : Set} -> Set test true {A} {_} = A test false {_} {B = B} = B Note that for checking where-clauses, still all hidden trailing parameters are in scope. For instance: id : {i : Level}{A : Set i} -> A -> A id = myId where myId : forall {A} -> A -> A myId x = x To be able to fill in the meta variable _1 in myId : {A : Set _1} -> A -> A the hidden parameter {i : Level} needs to be in scope. As a result of this more lazy introduction of implicit parameters, the following code now passes. data Unit : Set where unit : Unit T : Unit → Set T unit = {u : Unit} → Unit test : (u : Unit) → T u test unit with unit ... | _ = λ {v} → v Before, Agda would eagerly introduce the hidden parameter {v} as unnamed left-hand side parameter, leaving no way to refer to it. The related issue 655 has also been addressed. It is now possible to make `synonym' definitions name = expression even when the type of expression begins with a hidden quantifier. Simple example: id2 = id That resulted in unsolved metas until 2.3.0. * Agda detects unused arguments and ignores them during equality checking. [Issue 691, solves also issue 44.] Agda's polarity checker now assigns 'Nonvariant' to arguments that are not actually used (except for absurd matches). If f's first argument is Nonvariant, then f x is definitionally equal to f y regardless of x and y. It is similar to irrelevance, but does not require user annotation. For instance, unused module parameters do no longer get in the way: module M (x : Bool) where not : Bool → Bool not true = false not false = true open M true open M false renaming (not to not′) test : (y : Bool) → not y ≡ not′ y test y = refl Matching against record or absurd patterns does not count as `use', so we get some form of proof irrelevance: data ⊥ : Set where record ⊤ : Set where constructor trivial data Bool : Set where true false : Bool True : Bool → Set True true = ⊤ True false = ⊥ fun : (b : Bool) → True b → Bool fun true trivial = true fun false () test : (b : Bool) → (x y : True b) → fun b x ≡ fun b y test b x y = refl More examples in test/succeed/NonvariantPolarity.agda. Phantom arguments: Parameters of record and data types are considered `used' even if they are not actually used. Consider: False : Nat → Set False zero = ⊥ False (suc n) = False n module Invariant where record Bla (n : Nat)(p : False n) : Set where module Nonvariant where Bla : (n : Nat) → False n → Set Bla n p = ⊤ Even though record `Bla' does not use its parameters n and p, they are considered as used, allowing "phantom type" techniques. In contrast, the arguments of function `Bla' are recognized as unused. The following code type-checks if we open Invariant but leaves unsolved metas if we open Nonvariant. drop-suc : {n : Nat}{p : False n} → Bla (suc n) p → Bla n p drop-suc _ = _ bla : (n : Nat) → {p : False n} → Bla n p → ⊥ bla zero {()} b bla (suc n) b = bla n (drop-suc b) If `Bla' is considered invariant, the hidden argument in the recursive call can be inferred to be `p'. If it is considered non-variant, then `Bla n X = Bla n p' does not entail `X = p' and the hidden argument remains unsolved. Since `bla' does not actually use its hidden argument, its value is not important and it could be searched for. Unfortunately, polarity analysis of `bla' happens only after type checking, thus, the information that `bla' is non-variant in `p' is not available yet when meta-variables are solved. (See test/fail/BrokenInferenceDueToNonvariantPolarity.agda) * Agda now expands simple definitions (one clause, terminating) to check whether a function is constructor headed. [Issue 747] For instance, the following now also works: MyPair : Set -> Set -> Set MyPair A B = Pair A B Vec : Set -> Nat -> Set Vec A zero = Unit Vec A (suc n) = MyPair A (Vec A n) Here, Unit and Pair are data or record types. Compiler backends ================= * -Werror is now overridable. To enable compilation of Haskell modules containing warnings, the -Werror flag for the MAlonzo backend has been made overridable. If, for example, --ghc-flag=-Wwarn is passed when compiling, one can get away with things like: data PartialBool : Set where true : PartialBool {-# COMPILED_DATA PartialBool Bool True #-} The default behavior remains as it used to be and rejects the above program. Tools ===== Emacs mode ---------- * Asynchronous Emacs mode. One can now use Emacs while a buffer is type-checked. If the buffer is edited while the type-checker runs, then syntax highlighting will not be updated when type-checking is complete. * Interactive syntax highlighting. The syntax highlighting is updated while a buffer is type-checked: • At first the buffer is highlighted in a somewhat crude way (without go-to-definition information for overloaded constructors). • If the highlighting level is "interactive", then the piece of code that is currently being type-checked is highlighted as such. (The default is "non-interactive".) • When a mutual block has been type-checked it is highlighted properly (this highlighting includes warnings for potential non-termination). The highlighting level can be controlled via the new configuration variable agda2-highlight-level. * Multiple case-splits can now be performed in one go. Consider the following example: _==_ : Bool → Bool → Bool b₁ == b₂ = {!!} If you split on "b₁ b₂", then you get the following code: _==_ : Bool → Bool → Bool true == true = {!!} true == false = {!!} false == true = {!!} false == false = {!!} The order of the variables matters. Consider the following code: lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A lookup xs i = {!!} If you split on "xs i", then you get the following code: lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A lookup [] () lookup (x ∷ xs) zero = {!!} lookup (x ∷ xs) (suc i) = {!!} However, if you split on "i xs", then you get the following code instead: lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A lookup (x ∷ xs) zero = ? lookup (x ∷ xs) (suc i) = ? This code is rejected by Agda 2.3.0, but accepted by 2.3.2 thanks to improved coverage checking (see above). * The Emacs mode now presents information about which module is currently being type-checked. * New global menu entry: Information about the character at point. If this entry is selected, then information about the character at point is displayed, including (in many cases) information about how to type the character. * Commenting/uncommenting the rest of the buffer. One can now comment or uncomment the rest of the buffer by typing C-c C-x M-; or by selecting the menu entry "Comment/uncomment the rest of the buffer". * The Emacs mode now uses the Agda executable instead of GHCi. The *ghci* buffer has been renamed to *agda2*. A new configuration variable has been introduced: agda2-program-name, the name of the Agda executable (by default agda). The variable agda2-ghci-options has been replaced by agda2-program-args: extra arguments given to the Agda executable (by default none). If you want to limit Agda's memory consumption you can add some arguments to agda2-program-args, for instance +RTS -M1.5G -RTS. * The Emacs mode no longer depends on haskell-mode. Users who have customised certain haskell-mode variables (such as haskell-ghci-program-args) may want to update their configuration. LaTeX-backend ------------- An experimental LaTeX-backend which does precise highlighting a la the HTML-backend and code alignment a la lhs2TeX has been added. Here is a sample input literate Agda file: \documentclass{article} \usepackage{agda} \begin{document} The following module declaration will be hidden in the output. \AgdaHide{ \begin{code} module M where \end{code} } Two or more spaces can be used to make the backend align stuff. \begin{code} data ℕ : Set where zero : ℕ suc : ℕ → ℕ _+_ : ℕ → ℕ → ℕ zero + n = n suc m + n = suc (m + n) \end{code} \end{document} To produce an output PDF issue the following commands: agda --latex -i . <file>.lagda pdflatex latex/<file>.tex Only the top-most module is processed, like with lhs2tex and unlike with the HTML-backend. If you want to process imported modules you have to call agda --latex manually on each of those modules. There are still issues related to formatting, see the bug tracker for more information: https://code.google.com/p/agda/issues/detail?id=697 The default agda.sty might therefore change in backwards-incompatible ways, as work proceeds in trying to resolve those problems. Implemented features: * Two or more spaces can be used to force alignment of things, like with lhs2tex. See example above. * The highlighting information produced by the type checker is used to generate the output. For example, the data declaration in the example above, produces: \AgdaKeyword{data} \AgdaDatatype{ℕ} \AgdaSymbol{:} \AgdaPrimitiveType{Set} \AgdaKeyword{where} These latex commands are defined in agda.sty (which is imported by \usepackage{agda}) and cause the highlighting. * The latex-backend checks if agda.sty is found by the latex environment, if it isn't a default agda.sty is copied from Agda's data-dir into the working directory (and thus made available to the latex environment). If the default agda.sty isn't satisfactory (colors, fonts, spacing, etc) then the user can modify it and make put it somewhere where the latex environment can find it. Hopefully most aspects should be modifiable via agda.sty rather than having to tweak the implementation. * --latex-dir can be used to change the default output directory.