# Version-2–4−0

------------------------------------------------------------------------ — Release notes for Agda 2 version 2.4.0 ------------------------------------------------------------------------ Important changes since 2.3.2: 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: 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: 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. 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 ======== TODO: Document quoteContext. * Experimental feature: Varying arity. Function clauses may now have different arity, e.g., 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, 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: {-# 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: 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 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: — 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 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 module _ where This works also for parameterised modules. * Module parameters are now always hidden arguments in projections. For instance: 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 fst : {A : Set}{B : Set} → Prod A B → A snd : {A : Set}{B : Set} → Prod A B → B Until 2.3.2, they were 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’: id : (let ★ = Set) (A : ★) → A → A id A x = x In particular one can now ‘open’ modules inside telescopes: module Star where ★ : Set₁ ★ = Set module MEndo (let open Star) (A : ★) where Endo : ★ Endo = A → A Finally a shortcut is provided for opening modules: module N (open Star) (A : ★) (open MEndo A) (f : Endo) where … The semantics of the latter is 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]: You can now write left-hand sides with arguments also for let bindings without a type signature. For instance, 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] In particular, the following succeeds now: 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] <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: 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 {-# BUILTIN NATURAL Nat #-} {-# BUILTIN ZERO zero #-} {-# BUILTIN SUC suc #-} you just write {-# BUILTIN NATURAL Nat #-} * Pattern synonym can now have implicit arguments. [Issue 860] For example, pattern tail=_ {x} xs = x ∷ xs len : ∀ Ā → List A → Nat len [] = 0 len (tail= xs) = 1 + len xs * Syntax declarations can now have implicit arguments. [Issue 400] For example id : ∀ ā{A : Set a} → A → A id x = x syntax id Ā 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 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] infix −1 _myop_ * Postulates are now allowed in mutual blocks. [Issue 977] * Empty where blocks are now allowed. [Issue 947] * Pattern synonyms are now allowed in parameterised modules. [Issue 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] 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] * 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] Type checking ============= * [ issue 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.: 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: 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.: 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] For a simple example, consider test : ∀ Ā → Σ Nat λ n → Vec A n proj₁ test = zero proj₂ test = [] For the second clause, the lhs and rhs are typed as 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]. The amended description of primTrustMe is (cf. release notes for 2.2.6): 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, 635] 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: 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: 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 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] In particular, the following code type-checks now: 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, Issue 865, Issue 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. 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 This definition is accepted since unification of x with y doesn’t require deletion or injectivity. * The K rule is rejected. 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. 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. 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 ≤. 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 ] 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] * 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 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: 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: 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: 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: 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 snoc : ∀ Ā {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. [Issue207] 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 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: [TODO: Simplification should be explained somewhere.] 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. [TODO: As part of the release of Agda 2.3.4 the key binding page on the wiki should be updated.] 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/latex-backend/succeed/UnicodeInput.lagda): \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: \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/latex-backend/succeed/Links.lagda): \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: \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.