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Chapter 8  Language extensions

This chapter describes language extensions and convenience features that are implemented in OCaml, but not described in the OCaml reference manual.

8.1  Integer literals for types int32, int64 and nativeint

(Introduced in Objective Caml 3.07)

constant::= ...  
int32-literal::= integer-literal l  
int64-literal::= integer-literal L  
nativeint-literal::= integer-literal n

An integer literal can be followed by one of the letters l, L or n to indicate that this integer has type int32, int64 or nativeint respectively, instead of the default type int for integer literals. The library modules Int32[Int32], Int64[Int64] and Nativeint[Nativeint] provide operations on these integer types.

8.2  Recursive definitions of values

(Introduced in Objective Caml 1.00)

As mentioned in section 7.7.1, the let rec binding construct, in addition to the definition of recursive functions, also supports a certain class of recursive definitions of non-functional values, such as

let rec name1 = 1 ::  name2 and  name2 = 2 ::  name1 in  expr

which binds name1 to the cyclic list 1::2::1::2::…, and name2 to the cyclic list 2::1::2::1::…Informally, the class of accepted definitions consists of those definitions where the defined names occur only inside function bodies or as argument to a data constructor.

More precisely, consider the expression:

let rec name1 =  expr1 andand  namen =  exprn in  expr

It will be accepted if each one of expr1 …  exprn is statically constructive with respect to name1 …  namen, is not immediately linked to any of name1 …  namen, and is not an array constructor whose arguments have abstract type.

An expression e is said to be statically constructive with respect to the variables name1 …  namen if at least one of the following conditions is true:

An expression e is said to be immediately linked to the variable name in the following cases:

8.3  Lazy patterns

(Introduced in Objective Caml 3.11)

pattern::= ...  
  lazy pattern

The pattern lazy pattern matches a value v of type Lazy.t, provided pattern matches the result of forcing v with Lazy.force. A successful match of a pattern containing lazy sub-patterns forces the corresponding parts of the value being matched, even those that imply no test such as lazy value-name or lazy _. Matching a value with a pattern-matching where some patterns contain lazy sub-patterns may imply forcing parts of the value, even when the pattern selected in the end has no lazy sub-pattern.

For more information, see the description of module Lazy in the standard library ( Module Lazy).

8.4  Recursive modules

(Introduced in Objective Caml 3.07)

definition::= ...  
  module rec module-name :  module-type =  module-expr   { and module-name :  module-type =  module-expr }  
specification::= ...  
  module rec module-name :  module-type  { and module-name:  module-type }

Recursive module definitions, introduced by the module recand … construction, generalize regular module definitions module module-name =  module-expr and module specifications module module-name :  module-type by allowing the defining module-expr and the module-type to refer recursively to the module identifiers being defined. A typical example of a recursive module definition is:

    module rec A : sig
                     type t = Leaf of string | Node of ASet.t
                     val compare: t -> t -> int
                 = struct
                     type t = Leaf of string | Node of ASet.t
                     let compare t1 t2 =
                       match (t1, t2) with
                         (Leaf s1, Leaf s2) -> s1 s2
                       | (Leaf _, Node _) -> 1
                       | (Node _, Leaf _) -> -1
                       | (Node n1, Node n2) -> n1 n2
        and ASet : Set.S with type elt = A.t
                 = Set.Make(A)

It can be given the following specification:

    module rec A : sig
                     type t = Leaf of string | Node of ASet.t
                     val compare: t -> t -> int
        and ASet : Set.S with type elt = A.t

This is an experimental extension of OCaml: the class of recursive definitions accepted, as well as its dynamic semantics are not final and subject to change in future releases.

Currently, the compiler requires that all dependency cycles between the recursively-defined module identifiers go through at least one “safe” module. A module is “safe” if all value definitions that it contains have function types typexpr1 ->  typexpr2. Evaluation of a recursive module definition proceeds by building initial values for the safe modules involved, binding all (functional) values to fun _ -> raise Undefined_recursive_module. The defining module expressions are then evaluated, and the initial values for the safe modules are replaced by the values thus computed. If a function component of a safe module is applied during this computation (which corresponds to an ill-founded recursive definition), the Undefined_recursive_module exception is raised.

Note that, in the specification case, the module-types must be parenthesized if they use the with mod-constraint construct.

8.5  Private types

Private type declarations in module signatures, of the form type t = private ..., enable libraries to reveal some, but not all aspects of the implementation of a type to clients of the library. In this respect, they strike a middle ground between abstract type declarations, where no information is revealed on the type implementation, and data type definitions and type abbreviations, where all aspects of the type implementation are publicized. Private type declarations come in three flavors: for variant and record types (section 8.5.1), for type abbreviations (section 8.5.2), and for row types (section 8.5.3).

8.5.1  Private variant and record types

(Introduced in Objective Caml 3.07)

type-representation::= ...  
  = private [ | ] constr-decl  { | constr-decl }  
  = private record-decl

Values of a variant or record type declared private can be de-structured normally in pattern-matching or via the expr .  field notation for record accesses. However, values of these types cannot be constructed directly by constructor application or record construction. Moreover, assignment on a mutable field of a private record type is not allowed.

The typical use of private types is in the export signature of a module, to ensure that construction of values of the private type always go through the functions provided by the module, while still allowing pattern-matching outside the defining module. For example:

        module M : sig
                     type t = private A | B of int
                     val a : t
                     val b : int -> t
                 = struct
                     type t = A | B of int
                     let a = A
                     let b n = assert (n > 0); B n

Here, the private declaration ensures that in any value of type M.t, the argument to the B constructor is always a positive integer.

With respect to the variance of their parameters, private types are handled like abstract types. That is, if a private type has parameters, their variance is the one explicitly given by prefixing the parameter by a ‘+’ or a ‘-’, it is invariant otherwise.

8.5.2  Private type abbreviations

(Introduced in Objective Caml 3.11)

type-equation::= ...  
  = private typexpr

Unlike a regular type abbreviation, a private type abbreviation declares a type that is distinct from its implementation type typexpr. However, coercions from the type to typexpr are permitted. Moreover, the compiler “knows” the implementation type and can take advantage of this knowledge to perform type-directed optimizations.

The following example uses a private type abbreviation to define a module of nonnegative integers:

        module N : sig
                     type t = private int
                     val of_int: int -> t
                     val to_int: t -> int
                 = struct
                     type t = int
                     let of_int n = assert (n >= 0); n
                     let to_int n = n

The type N.t is incompatible with int, ensuring that nonnegative integers and regular integers are not confused. However, if x has type N.t, the coercion (x :> int) is legal and returns the underlying integer, just like N.to_int x. Deep coercions are also supported: if l has type N.t list, the coercion (l :> int list) returns the list of underlying integers, like N.to_int l but without copying the list l.

Note that the coercion ( expr :>  typexpr ) is actually an abbreviated form, and will only work in presence of private abbreviations if neither the type of expr nor typexpr contain any type variables. If they do, you must use the full form ( expr :  typexpr1 :>  typexpr2 ) where typexpr1 is the expected type of expr. Concretely, this would be (x : N.t :> int) and (l : N.t list :> int list) for the above examples.

8.5.3  Private row types

(Introduced in Objective Caml 3.09)

type-equation::= ...  
  = private typexpr

Private row types are type abbreviations where part of the structure of the type is left abstract. Concretely typexpr in the above should denote either an object type or a polymorphic variant type, with some possibility of refinement left. If the private declaration is used in an interface, the corresponding implementation may either provide a ground instance, or a refined private type.

   module M : sig type c = private < x : int; .. > val o : c end =
       class c = object method x = 3 method y = 2 end
       let o = new c

This declaration does more than hiding the y method, it also makes the type c incompatible with any other closed object type, meaning that only o will be of type c. In that respect it behaves similarly to private record types. But private row types are more flexible with respect to incremental refinement. This feature can be used in combination with functors.

   module F(X : sig type c = private < x : int; .. > end) =
       let get_x (o : X.c) = o#x
   module G(X : sig type c = private < x : int; y : int; .. > end) =
       include F(X)
       let get_y (o : X.c) = o#y

A polymorphic variant type [t], for example

   type t = [ `A of int | `B of bool ]

can be refined in two ways. A definition [u] may add new field to [t], and the declaration

  type u = private [> t]

will keep those new fields abstract. Construction of values of type [u] is possible using the known variants of [t], but any pattern-matching will require a default case to handle the potential extra fields. Dually, a declaration [u] may restrict the fields of [t] through abstraction: the declaration

  type v = private [< t > `A]

corresponds to private variant types. One cannot create a value of the private type [v], except using the constructors that are explicitly listed as present, (`A n) in this example; yet, when patter-matching on a [v], one should assume that any of the constructors of [t] could be present.

Similarly to abstract types, the variance of type parameters is not inferred, and must be given explicitly.

8.6  Local opens for patterns

(Introduced in OCaml 4.04)

pattern::= ...  
  module-path .(  pattern )  
  module-path .[  pattern ]  
  module-path .[|  pattern |]  
  module-path .{  pattern }

For patterns, local opens are limited to the module-path.( pattern) construction. This construction locally open the module referred to by the module path module-path in the scope of the pattern pattern.

When the body of a local open pattern is delimited by [ ], [| |], or { }, the parentheses can be omitted. For example, module-path.[ pattern] is equivalent to module-path.([ pattern]), and module-path.[|  pattern |] is equivalent to module-path.([|  pattern |]).

8.7  Object copy short notations

(Introduced in OCaml 4.03)

expr::= ...  
  { < expr with  field  [= expr]  { ; field  [= expr] }  [;> }

In an object copy expression, a single identifier id stands for id =  id, and a qualified identifier module-path .  id stands for module-path .  id =  id. For example, all following methods are equivalent:

            val x=0. val y=0. val z=0.
            method f_0 x y = {< x; y >}
            method f_1 x y = {< x = x; y >}
            method f_2 x y = {< x=x ; y = y >}

8.8  Locally abstract types

(Introduced in OCaml 3.12, short syntax added in 4.03)

parameter::= ...  
  ( type {typeconstr-name}+ )

The expression fun ( type typeconstr-name ) ->  expr introduces a type constructor named typeconstr-name which is considered abstract in the scope of the sub-expression, but then replaced by a fresh type variable. Note that contrary to what the syntax could suggest, the expression fun ( type typeconstr-name ) ->  expr itself does not suspend the evaluation of expr as a regular abstraction would. The syntax has been chosen to fit nicely in the context of function declarations, where it is generally used. It is possible to freely mix regular function parameters with pseudo type parameters, as in:

        let f = fun (type t) (foo : t list) -> ...

and even use the alternative syntax for declaring functions:

        let f (type t) (foo : t list) = ...

If several locally abstract types need to be introduced, it is possible to use the syntax fun ( type typeconstr-name1 …  typeconstr-namen ) ->  expr as syntactic sugar for fun ( type typeconstr-name1 ) ->-> fun ( type  typeconstr-namen ) ->  expr. For instance,

        let f = fun (type t u v) -> fun (foo : (t * u * v) list) -> ...
        let f' (type t u v) (foo : (t * u * v) list) = ...

This construction is useful because the type constructors it introduces can be used in places where a type variable is not allowed. For instance, one can use it to define an exception in a local module within a polymorphic function.

        let f (type t) () =
          let module M = struct exception E of t end in
          (fun x -> M.E x), (function M.E x -> Some x | _ -> None)

Here is another example:

        let sort_uniq (type s) (cmp : s -> s -> int) =
          let module S = Set.Make(struct type t = s let compare = cmp end) in
          fun l ->
            S.elements (List.fold_right S.add l S.empty)

It is also extremely useful for first-class modules (see section 8.9) and generalized algebraic datatypes (GADTs: see section 8.14).

Polymorphic syntax

(Introduced in OCaml 4.00)

let-binding::= ...  
  value-name : type  { typeconstr-name }+ .  typexpr =  expr  
class-field::= ...  
  method [privatemethod-name : type  { typeconstr-name }+ .  typexpr =  expr  
  method! [privatemethod-name : type  { typeconstr-name }+ .  typexpr =  expr

The (type typeconstr-name) syntax construction by itself does not make polymorphic the type variable it introduces, but it can be combined with explicit polymorphic annotations where needed. The above rule is provided as syntactic sugar to make this easier:

        let rec f : type t1 t2. t1 * t2 list -> t1 = ...

is automatically expanded into

        let rec f : 't1 't2. 't1 * 't2 list -> 't1 =
          fun (type t1) (type t2) -> (... : t1 * t2 list -> t1)

This syntax can be very useful when defining recursive functions involving GADTs, see the section 8.14 for a more detailed explanation.

The same feature is provided for method definitions. The method! form combines this extension with the “explicit overriding” extension described in section ??.

8.9  First-class modules

(Introduced in OCaml 3.12; pattern syntax and package type inference introduced in 4.00; structural comparison of package types introduced in 4.02.; fewer parens required starting from 4.05)

typexpr::= ...  
  (module package-type)  
module-expr::= ...  
  (val expr  [: package-type])  
expr::= ...  
  (module module-expr  [: package-type])  
pattern::= ...  
  (module module-name  [: package-type])  
package-type::= modtype-path  
  modtype-path with  package-constraint  { and package-constraint }  
package-constraint::= type typeconstr =  typexpr  

Modules are typically thought of as static components. This extension makes it possible to pack a module as a first-class value, which can later be dynamically unpacked into a module.

The expression ( module module-expr :  package-type ) converts the module (structure or functor) denoted by module expression module-expr to a value of the core language that encapsulates this module. The type of this core language value is ( module package-type ). The package-type annotation can be omitted if it can be inferred from the context.

Conversely, the module expression ( val expr :  package-type ) evaluates the core language expression expr to a value, which must have type module package-type, and extracts the module that was encapsulated in this value. Again package-type can be omitted if the type of expr is known. If the module expression is already parenthesized, like the arguments of functors are, no additional parens are needed: Map.Make(val key).

The pattern ( module module-name :  package-type ) matches a package with type package-type and binds it to module-name. It is not allowed in toplevel let bindings. Again package-type can be omitted if it can be inferred from the enclosing pattern.

The package-type syntactic class appearing in the ( module package-type ) type expression and in the annotated forms represents a subset of module types. This subset consists of named module types with optional constraints of a limited form: only non-parametrized types can be specified.

For type-checking purposes (and starting from OCaml 4.02), package types are compared using the structural comparison of module types.

In general, the module expression ( val expr :  package-type ) cannot be used in the body of a functor, because this could cause unsoundness in conjunction with applicative functors. Since OCaml 4.02, this is relaxed in two ways: if package-type does not contain nominal type declarations (i.e. types that are created with a proper identity), then this expression can be used anywhere, and even if it contains such types it can be used inside the body of a generative functor, described in section 8.21. It can also be used anywhere in the context of a local module binding let module module-name = ( val  expr1 :  package-type ) in  expr2.

Basic example

A typical use of first-class modules is to select at run-time among several implementations of a signature. Each implementation is a structure that we can encapsulate as a first-class module, then store in a data structure such as a hash table:

        module type DEVICE = sig ... end
        let devices : (string, (module DEVICE)) Hashtbl.t = Hashtbl.create 17

        module SVG = struct ... end
        let _ = Hashtbl.add devices "SVG" (module SVG : DEVICE)

        module PDF = struct ... end
        let _ = Hashtbl.add devices "PDF" (module PDF: DEVICE)

We can then select one implementation based on command-line arguments, for instance:

        module Device =
          (val (try Hashtbl.find devices (parse_cmdline())
                with Not_found -> eprintf "Unknown device %s\n"; exit 2)
           : DEVICE)

Alternatively, the selection can be performed within a function:

        let draw_using_device device_name picture =
          let module Device =
            (val (Hashtbl.find_devices device_name) : DEVICE)
            Device.draw picture
Advanced examples

With first-class modules, it is possible to parametrize some code over the implementation of a module without using a functor.

        let sort (type s) (module Set : Set.S with type elt = s) l =
          Set.elements (List.fold_right Set.add l Set.empty)
        val sort : (module Set.S with type elt = 'a) -> 'a list -> 'a list

To use this function, one can wrap the Set.Make functor:

        let make_set (type s) cmp =
          let module S = Set.Make(struct
            type t = s
            let compare = cmp
          end) in
          (module S : Set.S with type elt = s)
        val make_set : ('a -> 'a -> int) -> (module Set.S with type elt = 'a)

8.10  Recovering the type of a module

(Introduced in OCaml 3.12)

module-type::= ...  
  module type of module-expr

The construction module type of module-expr expands to the module type (signature or functor type) inferred for the module expression module-expr. To make this module type reusable in many situations, it is intentionally not strengthened: abstract types and datatypes are not explicitly related with the types of the original module. For the same reason, module aliases in the inferred type are expanded.

A typical use, in conjunction with the signature-level include construct, is to extend the signature of an existing structure. In that case, one wants to keep the types equal to types in the original module. This can done using the following idiom.

        module type MYHASH = sig
          include module type of struct include Hashtbl end
          val replace: ('a, 'b) t -> 'a -> 'b -> unit

The signature MYHASH then contains all the fields of the signature of the module Hashtbl (with strengthened type definitions), plus the new field replace. An implementation of this signature can be obtained easily by using the include construct again, but this time at the structure level:

        module MyHash : MYHASH = struct
          include Hashtbl
          let replace t k v = remove t k; add t k v

Another application where the absence of strengthening comes handy, is to provide an alternative implementation for an existing module.

        module MySet : module type of Set = struct

This idiom guarantees that Myset is compatible with Set, but allows it to represent sets internally in a different way.

8.11  Substituting inside a signature

(Introduced in OCaml 3.12, generalized in 4.06)

mod-constraint::= ...  
  type [type-params]  typeconstr-name :=  typexpr  
  module module-path :=  extended-module-path

A “destructive” substitution (with ... := ...) behaves essentially like normal signature constraints (with ... = ...), but it additionally removes the redefined type or module from the signature.

Prior to OCaml 4.06, there were a number of restrictions: one could only remove types and modules at the outermost level (not inside submodules), and in the case of with type the definition had to be another type constructor with the same type parameters.

A natural application of destructive substitution is merging two signatures sharing a type name.

module type Printable = sig type t val print : Format.formatter -> t -> unit end module type Comparable = sig type t val compare : t -> t -> int end module type PrintableComparable = sig include Printable include Comparable with type t := t end

One can also use this to completely remove a field:

module type S = Comparable with type t := int
module type S = sig val compare : int -> int -> int end

or to rename one:

module type S = sig type u include Comparable with type t := u end
module type S = sig type u val compare : u -> u -> int end

Note that you can also remove manifest types, by substituting with the same type.

module type ComparableInt = Comparable with type t = int ;;
module type ComparableInt = sig type t = int val compare : t -> t -> int end
module type CompareInt = ComparableInt with type t := int
module type CompareInt = sig val compare : int -> int -> int end

8.12  Type-level module aliases

(Introduced in OCaml 4.02)

specification::= ...  
  module module-name =  module-path

The above specification, inside a signature, only matches a module definition equal to module-path. Conversely, a type-level module alias can be matched by itself, or by any supertype of the type of the module it references.

There are several restrictions on module-path:

  1. it should be of the form M0.M1...Mn (i.e. without functor applications);
  2. inside the body of a functor, M0 should not be one of the functor parameters;
  3. inside a recursive module definition, M0 should not be one of the recursively defined modules.

Such specifications are also inferred. Namely, when P is a path satisfying the above constraints,

module N = P

has type

module N = P

Type-level module aliases are used when checking module path equalities. That is, in a context where module name N is known to be an alias for P, not only these two module paths check as equal, but F (N) and F (P) are also recognized as equal. In the default compilation mode, this is the only difference with the previous approach of module aliases having just the same module type as the module they reference.

When the compiler flag -no-alias-deps is enabled, type-level module aliases are also exploited to avoid introducing dependencies between compilation units. Namely, a module alias referring to a module inside another compilation unit does not introduce a link-time dependency on that compilation unit, as long as it is not dereferenced; it still introduces a compile-time dependency if the interface needs to be read, i.e. if the module is a submodule of the compilation unit, or if some type components are referred to. Additionally, accessing a module alias introduces a link-time dependency on the compilation unit containing the module referenced by the alias, rather than the compilation unit containing the alias. Note that these differences in link-time behavior may be incompatible with the previous behavior, as some compilation units might not be extracted from libraries, and their side-effects ignored.

These weakened dependencies make possible to use module aliases in place of the -pack mechanism. Suppose that you have a library Mylib composed of modules A and B. Using -pack, one would issue the command line

  ocamlc -pack a.cmo b.cmo -o mylib.cmo

and as a result obtain a Mylib compilation unit, containing physically A and B as submodules, and with no dependencies on their respective compilation units. Here is a concrete example of a possible alternative approach:

  1. Rename the files containing A and B to Mylib_A and Mylib_B.
  2. Create a packing interface, containing the following lines.
        module A = Mylib_A
        module B = Mylib_B
  3. Compile using -no-alias-deps, and the other files using -no-alias-deps and -open Mylib (the last one is equivalent to adding the line open! Mylib at the top of each file).
        ocamlc -c -no-alias-deps
        ocamlc -c -no-alias-deps -open Mylib Mylib_*.mli Mylib_*.ml
  4. Finally, create a library containing all the compilation units, and export all the compiled interfaces.
        ocamlc -a Mylib*.cmo -o Mylib.cma

This approach lets you access A and B directly inside the library, and as Mylib.A and Mylib.B from outside. It also has the advantage that Mylib is no longer monolithic: if you use Mylib.A, only Mylib_A will be linked in, not Mylib_B.

8.13  Overriding in open statements

(Introduced in OCaml 4.01)

definition::= ...  
   open! module-path  
specification::= ...  
   open! module-path  
expr::= ...  
  let open! module-path in  expr  
class-body-type::= ...  
   let open! module-path in  class-body-type  
class-expr::= ...  
   let open! module-path in  class-expr  

Since OCaml 4.01, open statements shadowing an existing identifier (which is later used) trigger the warning 44. Adding a ! character after the open keyword indicates that such a shadowing is intentional and should not trigger the warning.

This is also available (since OCaml 4.06) for local opens in class expressions and class type expressions.

8.14  Generalized algebraic datatypes

(Introduced in OCaml 4.00)

constr-decl::= ...  
  constr-name :  [ constr-args -> ]  typexpr  
type-param::= ...  

Generalized algebraic datatypes, or GADTs, extend usual sum types in two ways: constraints on type parameters may change depending on the value constructor, and some type variables may be existentially quantified. Adding constraints is done by giving an explicit return type (the rightmost typexpr in the above syntax), where type parameters are instantiated. This return type must use the same type constructor as the type being defined, and have the same number of parameters. Variables are made existential when they appear inside a constructor’s argument, but not in its return type.

Since the use of a return type often eliminates the need to name type parameters in the left-hand side of a type definition, one can replace them with anonymous types _ in that case.

The constraints associated to each constructor can be recovered through pattern-matching. Namely, if the type of the scrutinee of a pattern-matching contains a locally abstract type, this type can be refined according to the constructor used. These extra constraints are only valid inside the corresponding branch of the pattern-matching. If a constructor has some existential variables, fresh locally abstract types are generated, and they must not escape the scope of this branch.

Recursive functions

Here is a concrete example:

        type _ term =
          | Int : int -> int term
          | Add : (int -> int -> int) term
          | App : ('b -> 'a) term * 'b term -> 'a term

        let rec eval : type a. a term -> a = function
          | Int n    -> n                 (* a = int *)
          | Add      -> (fun x y -> x+y)  (* a = int -> int -> int *)
          | App(f,x) -> (eval f) (eval x)
                  (* eval called at types (b->a) and b for fresh b *)

        let two = eval (App (App (Add, Int 1), Int 1))
        val two : int = 2

It is important to remark that the function eval is using the polymorphic syntax for locally abstract types. When defining a recursive function that manipulates a GADT, explicit polymorphic recursion should generally be used. For instance, the following definition fails with a type error:

        let rec eval (type a) : a term -> a = function
          | Int n    -> n
          | Add      -> (fun x y -> x+y)
          | App(f,x) -> (eval f) (eval x)
(*                            ^
   Error: This expression has type ($App_'b -> a) term but an expression was
   expected of type 'a
   The type constructor $App_'b would escape its scope

In absence of an explicit polymorphic annotation, a monomorphic type is inferred for the recursive function. If a recursive call occurs inside the function definition at a type that involves an existential GADT type variable, this variable flows to the type of the recursive function, and thus escapes its scope. In the above example, this happens in the branch App(f,x) when eval is called with f as an argument. In this branch, the type of f is ($App_ 'b-> a). The prefix $ in $App_ 'b denotes an existential type named by the compiler (see 8.14). Since the type of eval is 'a term -> 'a, the call eval f makes the existential type $App_'b flow to the type variable 'a and escape its scope. This triggers the above error.

Type inference

Type inference for GADTs is notoriously hard. This is due to the fact some types may become ambiguous when escaping from a branch. For instance, in the Int case above, n could have either type int or a, and they are not equivalent outside of that branch. As a first approximation, type inference will always work if a pattern-matching is annotated with types containing no free type variables (both on the scrutinee and the return type). This is the case in the above example, thanks to the type annotation containing only locally abstract types.

In practice, type inference is a bit more clever than that: type annotations do not need to be immediately on the pattern-matching, and the types do not have to be always closed. As a result, it is usually enough to only annotate functions, as in the example above. Type annotations are propagated in two ways: for the scrutinee, they follow the flow of type inference, in a way similar to polymorphic methods; for the return type, they follow the structure of the program, they are split on functions, propagated to all branches of a pattern matching, and go through tuples, records, and sum types. Moreover, the notion of ambiguity used is stronger: a type is only seen as ambiguous if it was mixed with incompatible types (equated by constraints), without type annotations between them. For instance, the following program types correctly.

        let rec sum : type a. a term -> _ = fun x ->
          let y =
            match x with
            | Int n -> n
            | Add   -> 0
            | App(f,x) -> sum f + sum x
          in y + 1
        val sum : 'a term -> int = <fun>

Here the return type int is never mixed with a, so it is seen as non-ambiguous, and can be inferred. When using such partial type annotations we strongly suggest specifying the -principal mode, to check that inference is principal.

The exhaustiveness check is aware of GADT constraints, and can automatically infer that some cases cannot happen. For instance, the following pattern matching is correctly seen as exhaustive (the Add case cannot happen).

        let get_int : int term -> int = function
          | Int n    -> n
          | App(_,_) -> 0
Refutation cases and redundancy

(Introduced in OCaml 4.03)

Usually, the exhaustiveness check only tries to check whether the cases omitted from the pattern matching are typable or not. However, you can force it to try harder by adding refutation cases:

matching-case::= pattern  [when expr->  expr  
  pattern -> .

In presence of a refutation case, the exhaustiveness check will first compute the intersection of the pattern with the complement of the cases preceding it. It then checks whether the resulting patterns can really match any concrete values by trying to type-check them. Wild cards in the generated patterns are handled in a special way: if their type is a variant type with only GADT constructors, then the pattern is split into the different constructors, in order to check whether any of them is possible (this splitting is not done for arguments of these constructors, to avoid non-termination.) We also split tuples and variant types with only one case, since they may contain GADTs inside. For instance, the following code is deemed exhaustive:

        type _ t =
          | Int : int t
          | Bool : bool t

        let deep : (char t * int) option -> char = function
          | None -> 'c'
          | _ -> .

Namely, the inferred remaining case is Some _, which is split into Some (Int, _) and Some (Bool, _), which are both untypable. Note that the refutation case could be omitted here, because it is automatically added when there is only one case in the pattern matching.

Another addition is that the redundancy check is now aware of GADTs: a case will be detected as redundant if it could be replaced by a refutation case using the same pattern.

Advanced examples

The term type we have defined above is an indexed type, where a type parameter reflects a property of the value contents. Another use of GADTs is singleton types, where a GADT value represents exactly one type. This value can be used as runtime representation for this type, and a function receiving it can have a polytypic behavior.

Here is an example of a polymorphic function that takes the runtime representation of some type t and a value of the same type, then pretty-prints the value as a string:

        type _ typ =
          | Int : int typ
          | String : string typ
          | Pair : 'a typ * 'b typ -> ('a * 'b) typ

        let rec to_string: type t. t typ -> t -> string =
          fun t x ->
          match t with
          | Int -> string_of_int x
          | String -> Printf.sprintf "%S" x
          | Pair(t1,t2) ->
              let (x1, x2) = x in
              Printf.sprintf "(%s,%s)" (to_string t1 x1) (to_string t2 x2)

Another frequent application of GADTs is equality witnesses.

        type (_,_) eq = Eq : ('a,'a) eq

        let cast : type a b. (a,b) eq -> a -> b = fun Eq x -> x

Here type eq has only one constructor, and by matching on it one adds a local constraint allowing the conversion between a and b. By building such equality witnesses, one can make equal types which are syntactically different.

Here is an example using both singleton types and equality witnesses to implement dynamic types.

        let rec eq_type : type a b. a typ -> b typ -> (a,b) eq option =
          fun a b ->
          match a, b with
          | Int, Int -> Some Eq
          | String, String -> Some Eq
          | Pair(a1,a2), Pair(b1,b2) ->
              begin match eq_type a1 b1, eq_type a2 b2 with
              | Some Eq, Some Eq -> Some Eq
              | _ -> None
          | _ -> None

        type dyn = Dyn : 'a typ * 'a -> dyn

        let get_dyn : type a. a typ -> dyn -> a option =
          fun a (Dyn(b,x)) ->
          match eq_type a b with
          | None -> None
          | Some Eq -> Some x
Existential type names in error messages

(Updated in OCaml 4.03.0)

The typing of pattern matching in presence of GADT can generate many existential types. When necessary, error messages refer to these existential types using compiler-generated names. Currently, the compiler generates these names according to the following nomenclature:

As shown by the last item, the current behavior is imperfect and may be improved in future versions.

Equations on non-local abstract types

(Introduced in OCaml 4.04)

GADT pattern-matching may also add type equations to non-local abstract types. The behaviour is the same as with local abstract types. Reusing the above eq type, one can write:

        module M : sig type t val x : t val e : (t,int) eq end = struct
          type t = int
          let x = 33
          let e = Eq

        let x : int = let Eq = M.e in M.x

Of course, not all abstract types can be refined, as this would contradict the exhaustiveness check. Namely, builtin types (those defined by the compiler itself, such as int or array), and abstract types defined by the local module, are non-instantiable, and as such cause a type error rather than introduce an equation.

8.15  Syntax for Bigarray access

(Introduced in Objective Caml 3.00)

expr::= ...  
  expr .{  expr  { , expr } }  
  expr .{  expr  { , expr } } <-  expr

This extension provides syntactic sugar for getting and setting elements in the arrays provided by the Bigarray[Bigarray] library.

The short expressions are translated into calls to functions of the Bigarray module as described in the following table.

expr0.{ expr1}Bigarray.Array1.get expr0  expr1
expr0.{ expr1} <- exprBigarray.Array1.set expr0  expr1  expr
expr0.{ expr1,  expr2}Bigarray.Array2.get expr0  expr1  expr2
expr0.{ expr1,  expr2} <- exprBigarray.Array2.set expr0  expr1  expr2  expr
expr0.{ expr1,  expr2,  expr3}Bigarray.Array3.get expr0  expr1  expr2  expr3
expr0.{ expr1,  expr2,  expr3} <- exprBigarray.Array3.set expr0  expr1  expr2  expr3  expr
expr0.{ expr1,,  exprn}Bigarray.Genarray.get expr0 [|  expr1,,  exprn |]
expr0.{ expr1,,  exprn} <- exprBigarray.Genarray.set expr0 [|  expr1,,  exprn |]  expr

The last two entries are valid for any n > 3.

8.16  Attributes

(Introduced in OCaml 4.02, infix notations for constructs other than expressions added in 4.03)

Attributes are “decorations” of the syntax tree which are mostly ignored by the type-checker but can be used by external tools. An attribute is made of an identifier and a payload, which can be a structure, a type expression (prefixed with :), a signature (prefixed with :) or a pattern (prefixed with ?) optionally followed by a when clause:

attr-id::= lowercase-ident  
   attr-id .  attr-id  
attr-payload::=module-items ]  
   : typexpr  
   : [ specification ]  
   ? pattern  [when expr]  

The first form of attributes is attached with a postfix notation on “algebraic” categories:

attribute::= [@ attr-id  attr-payload ]  
expr::= ...  
  expr  attribute  
typexpr::= ...  
  typexpr  attribute  
pattern::= ...  
  pattern  attribute  
module-expr::= ...  
  module-expr  attribute  
module-type::= ...  
  module-type  attribute  
class-expr::= ...  
  class-expr  attribute  
class-type::= ...  
  class-type  attribute  

This form of attributes can also be inserted after the `tag-name in polymorphic variant type expressions (tag-spec-first, tag-spec, tag-spec-full) or after the method-name in method-type.

The same syntactic form is also used to attach attributes to labels and constructors in type declarations:

field-decl::= [mutablefield-name :  poly-typexpr  {attribute}  
constr-decl::= (constr-name ∣  ()) [ of constr-args ]  {attribute}  

Note: when a label declaration is followed by a semi-colon, attributes can also be put after the semi-colon (in which case they are merged to those specified before).

The second form of attributes are attached to “blocks” such as type declarations, class fields, etc:

item-attribute::= [@@ attr-id  attr-payload ]  
typedef::= ...  
  typedef  item-attribute  
exception-definition::= exception constr-decl  
  exception constr-name =  constr  
module-items::= [;;] ( definition ∣  expr  { item-attribute } )  { [;;definition ∣  ;; expr  { item-attribute } }  [;;]  
class-binding::= ...  
  class-binding  item-attribute  
class-spec::= ...  
  class-spec  item-attribute  
classtype-def::= ...  
  classtype-def  item-attribute  
definition::= let [reclet-binding  { and let-binding }  
  external value-name :  typexpr =  external-declaration  { item-attribute }  
  exception-definition  { item-attribute }  
  module module-name  { ( module-name :  module-type ) }  [ : module-type ]  =  module-expr  { item-attribute }  
  module type modtype-name =  module-type  { item-attribute }  
  open module-path  { item-attribute }  
  include module-expr  { item-attribute }  
  module rec module-name :  module-type =   module-expr  { item-attribute }   { and module-name :  module-type =  module-expr   { item-attribute } }  
specification::= val value-name :  typexpr  { item-attribute }  
  external value-name :  typexpr =  external-declaration  { item-attribute }  
  exception constr-decl  { item-attribute }  
  module module-name :  module-type  { item-attribute }  
  module module-name  { ( module-name :  module-type ) } :  module-type  { item-attribute }  
  module type modtype-name  { item-attribute }  
  module type modtype-name =  module-type  { item-attribute }  
  open module-path  { item-attribute }  
  include module-type  { item-attribute }  
class-field-spec::= ...  
  class-field-spec  item-attribute  
class-field::= ...  
  class-field  item-attribute  

A third form of attributes appears as stand-alone structure or signature items in the module or class sub-languages. They are not attached to any specific node in the syntax tree:

floating-attribute::= [@@@ attr-id  attr-payload ]  
definition::= ...  
specification::= ...  
class-field-spec::= ...  
class-field::= ...  

(Note: contrary to what the grammar above describes, item-attributes cannot be attached to these floating attributes in class-field-spec and class-field.)

It is also possible to specify attributes using an infix syntax. For instance:

let[@foo] x = 2 in x + 1          === (let x = 2 [@@foo] in x + 1)
begin[@foo][@bar x] ... end       === (begin ... end)[@foo][@@bar x]
module[@foo] M = ...              === module M = ... [@@foo]
type[@foo] t = T                  === type t = T [@@foo]
method[@foo] m = ...              === method m = ... [@@foo]

For let, the attributes are applied to each bindings:

let[@foo] x = 2 and y = 3 in x + y === (let x = 2 [@@foo] and y = 3 in x + y)
let[@foo] x = 2
and[@bar] y = 3 in x + y           === (let x = 2 [@@foo] and y = 3 [@bar] in x + y)

8.16.1  Built-in attributes

Some attributes are understood by the type-checker:

module X = struct
  [@@@warning "+9"]  (* locally enable warning 9 in this structure *)
  [@@deprecated "Please use module 'Y' instead."]

let x = begin[@warning "+9"] ... end in ....

type t = A | B
  [@@deprecated "Please use type 's' instead."]

let f x =
  assert (x >= 0) [@ppwarning "TODO: remove this later"];

let rec no_op = function
  | [] -> ()
  | _ :: q -> (no_op[@tailcall]) q;;

let f x = x [@@inline]

let () = (f[@inlined]) ()

type fragile =
  | Int of int [@warn_on_literal_pattern]
  | String of string [@warn_on_literal_pattern]

let f = function
| Int 0 | String "constant" -> () (* trigger warning 52 *)
| _ -> ()

module Immediate: sig
  type t [@@immediate]
  val x: t ref
end = struct
  type t = A | B
  let x = ref 0

8.17  Extension nodes

(Introduced in OCaml 4.02, infix notations for constructs other than expressions added in 4.03, infix notation (e1 ;%ext e2) added in 4.04. )

Extension nodes are generic placeholders in the syntax tree. They are rejected by the type-checker and are intended to be “expanded” by external tools such as -ppx rewriters.

Extension nodes share the same notion of identifier and payload as attributes 8.16.

The first form of extension node is used for “algebraic” categories:

extension::= [% attr-id  attr-payload ]  
expr::= ...  
typexpr::= ...  
pattern::= ...  
module-expr::= ...  
module-type::= ...  
class-expr::= ...  
class-type::= ...  

A second form of extension node can be used in structures and signatures, both in the module and object languages:

item-extension::= [%% attr-id  attr-payload ]  
definition::= ...  
specification::= ...  
class-field-spec::= ...  
class-field::= ...  

An infix form is available for extension nodes when the payload is of the same kind (expression with expression, pattern with pattern ...).


let%foo x = 2 in x + 1     === [%foo let x = 2 in x + 1]
begin%foo ... end          === [%foo begin ... end]
x ;%foo 2                  === [%foo x; 2]
module%foo M = ..          === [%%foo module M = ... ]
val%foo x : t              === [%%foo: val x : t]

When this form is used together with the infix syntax for attributes, the attributes are considered to apply to the payload:

fun%foo[@bar] x -> x + 1 === [%foo (fun x -> x + 1)[@foo ] ];

8.17.1  Built-in extension nodes

(Introduced in OCaml 4.03)

Some extension nodes are understood by the compiler itself:

type t = .. type t += X of int | Y of string let x = [%extension_constructor X] let y = [%extension_constructor Y]
x <> y;;
- : bool = true

8.18  Quoted strings

(Introduced in OCaml 4.02)

Quoted strings {foo|...|foo} provide a different lexical syntax to write string literals in OCaml code. They are useful to represent strings of arbitrary content without escaping – as long as the delimiter you chose (here |foo}) does not occur in the string itself.

string-literal::= ...  
   { quoted-string-id |  ........ |  quoted-string-id }  
quoted-string-id::=a...z ∣  _ }  

The opening delimiter has the form {id| where id is a (possibly empty) sequence of lowercase letters and underscores. The corresponding closing delimiter is |id} (with the same identifier). Unlike regular OCaml string literals, quoted strings do not interpret any character in a special way.


String.length {|\"|}         (* returns 2 *)
String.length {foo|\"|foo}   (* returns 2 *)

Quoted strings are interesting in particular in conjunction to extension nodes [%foo ...] (see 8.17) to embed foreign syntax fragments to be interpreted by a preprocessor and turned into OCaml code: you can use [%sql {|...|}] for example to represent arbitrary SQL statements – assuming you have a ppx-rewriter that recognizes the %sql extension – without requiring escaping quotes.

Note that the non-extension form, for example {sql|...|sql}, should not be used for this purpose, as the user cannot see in the code that this string literal has a different semantics than they expect, and giving a semantics to a specific delimiter limits the freedom to change the delimiter to avoid escaping issues.

8.19  Exception cases in pattern matching

(Introduced in OCaml 4.02)

A new form of exception patterns is allowed, only as a toplevel pattern under a match...with pattern-matching (other occurrences are rejected by the type-checker).

pattern::= ...  
  exception pattern  

Cases with such a toplevel pattern are called “exception cases”, as opposed to regular “value cases”. Exception cases are applied when the evaluation of the matched expression raises an exception. The exception value is then matched against all the exception cases and re-raised if none of them accept the exception (as for a try...with block). Since the bodies of all exception and value cases is outside the scope of the exception handler, they are all considered to be in tail-position: if the match...with block itself is in tail position in the current function, any function call in tail position in one of the case bodies results in an actual tail call.

It is an error if all cases are exception cases in a given pattern matching.

8.20  Extensible variant types

(Introduced in OCaml 4.02)

type-representation::= ...  
  = ..  
specification::= ...  
  type [type-params]  typeconstr  type-extension-spec  
definition::= ...  
  type [type-params]  typeconstr  type-extension-def  
type-extension-spec::= += [private] [|constr-decl  { | constr-decl }  
type-extension-def::= += [private] [|constr-def  { | constr-def }  
constr-def::= constr-decl  
  constr-name =  constr  

Extensible variant types are variant types which can be extended with new variant constructors. Extensible variant types are defined using ... New variant constructors are added using +=.

        type attr = ..

        type attr += Str of string

        type attr +=
          | Int of int
          | Float of float

Pattern matching on an extensible variant type requires a default case to handle unknown variant constructors:

        let to_string = function
          | Str s -> s
          | Int i -> string_of_int i
          | Float f -> string_of_float f
          | _ -> "?"

A preexisting example of an extensible variant type is the built-in exn type used for exceptions. Indeed, exception constructors can be declared using the type extension syntax:

        type exn += Exc of int

Extensible variant constructors can be rebound to a different name. This allows exporting variants from another module.

        type Expr.attr += Str = Expr.Str

Extensible variant constructors can be declared private. As with regular variants, this prevents them from being constructed directly by constructor application while still allowing them to be de-structured in pattern-matching.

        module Bool : sig
          type attr += private Bool of int
          val bool : bool -> attr
        end = struct
          type attr += Bool of int
          let bool p = if p then Bool 1 else Bool 0

8.20.1  Private extensible variant types

(Introduced in OCaml 4.06)

type-representation::= ...  
  = private ..  

Extensible variant types can be declared private. This prevents new constructors from being declared directly, but allows extension constructors to be referred to in interfaces.

        module Msg : sig
          type t = private ..
          module MkConstr (X : sig type t end) : sig
            type t += C of X.t
        end = struct
          type t = ..
          module MkConstr (X : sig type t end) = struct
            type t += C of X.t

8.21  Generative functors

(Introduced in OCaml 4.02)

module-expr::= ...  
  functor () -> module-expr  
  module-expr ()  
definition::= ...  
  module module-name  { ( module-name :  module-type ) ∣  () } [ : module-type ]  =  module-expr  
module-type::= ...  
  functor () -> module-type  
specification::= ...  
  module module-name  { ( module-name :  module-type ) ∣  () } : module-type  

A generative functor takes a unit () argument. In order to use it, one must necessarily apply it to this unit argument, ensuring that all type components in the result of the functor behave in a generative way, i.e. they are different from types obtained by other applications of the same functor. This is equivalent to taking an argument of signature sig end, and always applying to struct end, but not to some defined module (in the latter case, applying twice to the same module would return identical types).

As a side-effect of this generativity, one is allowed to unpack first-class modules in the body of generative functors.

8.22  Extension-only syntax

(Introduced in OCaml 4.02.2, extended in 4.03)

Some syntactic constructions are accepted during parsing and rejected during type checking. These syntactic constructions can therefore not be used directly in vanilla OCaml. However, -ppx rewriters and other external tools can exploit this parser leniency to extend the language with these new syntactic constructions by rewriting them to vanilla constructions.

8.22.1  Extension operators

(Introduced in OCaml 4.02.2)

infix-symbol::= ...  
  # {operator-chars#   {operator-char | #}  

Operator names starting with a # character and containing more than one # character are reserved for extensions.

8.22.2  Extension literals

(Introduced in OCaml 4.03)

float-literal::= ...  
  [-] (09) { 09∣ _ } [. { 09∣ _ }] [(e∣ E) [+∣ -] (09) { 09∣ _ }] [gz∣ GZ]  
  [-] (0x∣ 0X) (09∣ AF∣ af) { 09∣ AF∣ af∣ _ } [. { 09∣ AF∣ af∣ _ }] [(p∣ P) [+∣ -] (09) { 09∣ _ }] [gz∣ GZ]  
int-literal::= ...  
  [-] (09) { 09 ∣  _ }[gz∣ GZ]  
  [-] (0x∣ 0X) (09∣ AF∣ af) { 09∣ AF∣ af∣ _ } [gz∣ GZ]  
  [-] (0o∣ 0O) (07) { 07∣ _ } [gz∣ GZ]  
  [-] (0b∣ 0B) (01) { 01∣ _ } [gz∣ GZ]  

Int and float literals followed by an one-letter identifier in the range [g..zG..Z] are extension-only literals.

8.23  Inline records

(Introduced in OCaml 4.03)

constr-args::= ...  

The arguments of a sum-type constructors can now be defined using the same syntax as records. Mutable and polymorphic fields are allowed. GADT syntax is supported. Attributes can be specified on individual fields.

Syntactically, building or matching constructors with such an inline record argument is similar to working with a unary constructor whose unique argument is a declared record type. A pattern can bind the inline record as a pseudo-value, but the record cannot escape the scope of the binding and can only be used with the dot-notation to extract or modify fields or to build new constructor values.

type t =
  | Point of {width: int; mutable x: float; mutable y: float}
  | ...

let v = Point {width = 10; x = 0.; y = 0.}

let scale l = function
  | Point p -> Point {p with x = l *. p.x; y = l *. p.y}
  | ....

let print = function
  | Point {x; y; _} -> Printf.printf "%f/%f" x y
  | ....

let reset = function
  | Point p -> p.x <- 0.; p.y <- 0.
  | ...

let invalid = function
  | Point p -> p  (* INVALID *)
  | ...

8.24  Local exceptions

(Introduced in OCaml 4.04)

It is possible to define local exceptions in expressions:

expr::= ...  
  let exception constr-decl in  expr

The syntactic scope of the exception constructor is the inner expression, but nothing prevents exception values created with this constructor from escaping this scope. Two executions of the definition above result in two incompatible exception constructors (as for any exception definition).

8.25  Documentation comments

(Introduced in OCaml 4.03)

Comments which start with ** are treated specially by the compiler. They are automatically converted during parsing into attributes (see 8.16) to allow tools to process them as documentation.

Such comments can take three forms: floating comments, item comments and label comments. Any comment starting with ** which does not match one of these forms will cause the compiler to emit warning 50.

Comments which start with ** are also used by the ocamldoc documentation generator (see 16). The three comment forms recognised by the compiler are a subset of the forms accepted by ocamldoc (see 16.2).

8.25.1  Floating comments

Comments surrounded by blank lines that appear within structures, signatures, classes or class types are converted into floating-attributes. For example:

type t = T

(** Now some definitions for [t] *)

let mkT = T

will be converted to:

type t = T

[@@@ocaml.text " Now some definitions for [t] "]

let mkT = T

8.25.2  Item comments

Comments which appear immediately before or immediately after a structure item, signature item, class item or class type item are converted into item-attributes. Immediately before or immediately after means that there must be no blank lines, ;;, or other documentation comments between them. For example:

type t = T
(** A description of [t] *)


(** A description of [t] *)
type t = T

will be converted to:

type t = T
[@@ocaml.doc " A description of [t] "]

Note that, if a comment appears immediately next to multiple items, as in:

type t = T
(** An ambiguous comment *)
type s = S

then it will be attached to both items:

type t = T
[@@ocaml.doc " An ambiguous comment "]
type s = S
[@@ocaml.doc " An ambiguous comment "]

and the compiler will emit warning 50.

8.25.3  Label comments

Comments which appear immediately after a labelled argument, record field, variant constructor, object method or polymorphic variant constructor are are converted into attributes. Immediately after means that there must be no blank lines or other documentation comments between them. For example:

type t1 = lbl:int (** Labelled argument *) -> unit

type t2 = {
  fld: int; (** Record field *)
  fld2: float;

type t3 =
  | Cstr of string (** Variant constructor *)
  | Cstr2 of string

type t4 = < meth: int * int; (** Object method *) >

type t5 = [
  `PCstr (** Polymorphic variant constructor *)

will be converted to:

type t1 = lbl:(int [@ocaml.doc " Labelled argument "]) -> unit

type t2 = {
  fld: int [@ocaml.doc " Record field "];
  fld2: float;

type t3 =
  | Cstr of string [@ocaml.doc " Variant constructor "]
  | Cstr2 of string

type t4 = < meth : int * int [@ocaml.doc " Object method "] >

type t5 = [
  `PCstr [@ocaml.doc " Polymorphic variant constructor "]

Note that label comments take precedence over item comments, so:

type t = T of string
(** Attaches to T not t *)

will be converted to:

type t =  T of string [@ocaml.doc " Attaches to T not t "]


type t = T of string
(** Attaches to T not t *)
(** Attaches to t *)

will be converted to:

type t =  T of string [@ocaml.doc " Attaches to T not t "]
[@@ocaml.doc " Attaches to t "]

In the absence of meaningful comment on the last constructor of a type, an empty comment (**) can be used instead:

type t = T of string
(** Attaches to t *)

will be converted directly to

type t =  T of string
[@@ocaml.doc " Attaches to t "]

8.26  Extended indexing operators

(Introduced in 4.06)

  (!∣ $∣ %∣ &∣ *∣ +∣ -∣ /∣ :∣ =∣ >∣ ?∣ @∣ ^∣ |∣ ~) { operator-char }  
expr::= ...  
  expr .  [module-path .]  dot-ext  ( ( expr ) ∣  [ expr ] ∣  { expr } )  [ <- expr ]  
operator-name::= ...  
  . dot-ext  (() ∣  [] ∣  {}) [<-]  

This extension provides syntactic sugar for getting and setting elements for user-defined indexed types. For instance, we can define python-like dictionaries with

module Dict = struct include Hashtbl let ( .%{} ) tabl index = find tabl index let ( .%{}<- ) tabl index value = add tabl index value end let dict = let dict = Dict.create 10 in let () = dict.Dict.%{"one"} <- 1; let open Dict in dict.%{"two"} <- 2 in dict
- : int = 1
let open Dict in dict.%{"two"};;
- : int = 2

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