## ﻿10.19 Extended indexing operators

- 10.19.1 Multi-index notation

(Introduced in 4.06)

dot-ext | ::= |
| ∣ | dot-operator-char{operator-char}
dot-operator-char | ::= | !∣?∣core-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
# dict.Dict.%{"one"};;
- : int = 1
# let open Dict in dict.%{"two"};;
- : int = 2

### ﻿10.19.1 Multi-index notation

expr | ::= | ...
| ∣ | expr .[module-path .]dot-ext ( expr{; expr}+ )[<- expr]
| ∣ | expr .[module-path .]dot-ext [ expr{; expr}+ ][<- expr]
| ∣ | expr .[module-path .]dot-ext { expr{; expr}+ }[<- expr]
operator-name | ::= | ...
| ∣ | . dot-ext((;..)∣[;..]∣{;..}) [<-]

Multi-index are also supported through a second variant of indexing operators

let (.%[;..]) = Bigarray.Genarray.get let (.%{;..}) = Bigarray.Genarray.get let (.%(;..)) = Bigarray.Genarray.get

which is called when an index literals contain a semicolon separated list of expressions with two and more elements:

let sum x y = x.%[1;2;3] + y.%[1;2] (* is equivalent to *) let sum x y = (.%[;..]) x [|1;2;3|] + (.%[;..]) y [|1;2|]

In particular this multi-index notation makes it possible to uniformly handle indexing Genarray and other implementations of multidimensional arrays.

module A = Bigarray.Genarray let (.%{;..}) = A.get let (.%{;..}<- ) = A.set let (.%{ }) a k = A.get a [|k|] let (.%{ }<-) a k x = A.set a [|k|] x let syntax_compare vec mat t3 t4 = vec.%{0} = A.get vec [|0|] && mat.%{0;0} = A.get mat [|0;0|] && t3.%{0;0;0} = A.get t3 [|0;0;0|] && t4.%{0;0;0;0} = t4.{0,0,0,0}

Beware that the differentiation between the multi-index and single index operators is purely syntactic: multi-index operators are restricted to index expressions that contain one or more semicolons ;. For instance,

let pair vec mat = vec.%{0}, mat.%{0;0}

is equivalent to

let pair vec mat = (.%{ }) vec 0, (.%{;..}) mat [|0;0|]

Notice that in the vec case, we are calling the single index operator, (.%{}), and not the multi-index variant, (.{;..}). For this reason, it is expected that most users of multi-index operators will need to define conjointly a single index variant

let (.%{;..}) = A.get let (.%{ }) a k = A.get a [|k|]

to handle both cases uniformly.