---
name: "Set"
section: "3o"
platform: "linux"
package: "ocaml"
version: "5.5.0-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/Set/3o"
---

# Set(3o)

Sets over ordered types.

## NAME

Set - Sets over ordered types.

## Module

Module   Set

## Documentation

Module **Set**\
  :  **sig end**

Sets over ordered types.

This module implements the set data structure, given a total ordering function over the set elements. All operations over sets are purely applicative (no side-effects). The implementation uses balanced binary trees, and is therefore reasonably efficient: insertion and membership take time logarithmic in the size of the set, for instance.

The  **Set.Make** functor constructs implementations for any type, given a **compare** function. For instance:

```
     module IntPairs =
       struct
         type t = int * int
         let compare (x0,y0) (x1,y1) =
           match Stdlib.compare x0 x1 with
               0 -> Stdlib.compare y0 y1
             | c -> c
       end
     module PairsSet = Set.Make(IntPairs)
     let m = PairsSet.(empty |> add (2,3) |> add (5,7) |> add (11,13))

```

This creates a new module  **PairsSet** , with a new type  **PairsSet.t** of sets of  **int \* int** .

*module type OrderedType =* **sig end**

Input signature of the functor  **Set.Make** .

*module type S =* **sig end**

Output signature of the functor  **Set.Make** .

*module Make :* **(Ord : OrderedType) -\> sig end**

Functor building an implementation of the set structure given a totally ordered type.