# Grouping Data Into Buckets Using F#

Last week I came across an interesting data grouping problem, which groups the data into different buckets based on the given filters as shown in the image below

In this blog post I am going to share how can we solve this problem very expressively using fsharp.

## Parsing filters and translate to an Abstract Syntax Tree (AST)

The first step to solve this problem is parsing the filters and translate to an AST. The strong type system in fsharp makes this step pretty easy.

``fsharp type Filter = | GreaterThan of int | Between of int * int | LessThan of int

```
The `Filter` type represents the AST of the raw string filter. There are n number of ways to transform this incoming string filter to its strongly typed counterpart.
The most idiomatic way of achieving it in fsharp is through [Partial Active Patterns](http://en.wikibooks.org/wiki/F_Sharp_Programming/Active_Patterns#Partial_Active_Patterns)
```fsharp
let (|Regex|_|) pattern input =
let m = Regex.Match(input, pattern)
if m.Success then Some(List.tail [ for g in m.Groups -> g.Value ])
else None
```

You can easily understand this partial active pattern by thinking it as a function with the following signature

`string -> string -> string list option`

i.e Takes an input, matches it against a pattern. If it matched, then returns the list of matched strings wrapped with the `Some`

type else returns the `None`

type.

Now you may think why we need to write this straight-forward function as a partial active pattern with some weird symbols `(|_|)`

?

We can certainly do that, but we canâ€™t do pattern matching against a function.

The best way to understand this by seeing it in action

`// string -> Filter`

let createFilter filterString =

match filterString with

| Regex "^>(\d+)$" [min] -> GreaterThan(int min)

| Regex "^(\d+)-(\d+)$" [min;max] -> Between(int min,int max)

| Regex "^<(\d+)$" [max] -> LessThan(int max)

| _ -> failwith "Invalid Filter"

The above function transforms the raw string filter into its equivalent fsharp type that we have defined before. The pattern matching makes our job very easier by declaratively saying if it matches this, then do this.

One another important benefit that we are getting here, the return value (list of matched strings) is available as a last parameter in the pattern matching. Itâ€™s just coming for free.

Iâ€™d like to give you an exercise to appreciate this excellent feature in fsharp. Try to implement the above using a function instead of a partial active patterns.

Great! We are done with the first step. Letâ€™s move to the next one.

## Grouping the data using the filter

To do the actual grouping we need to have a function that filters the data based on the given filter. Let me call it as a predicate.

`// Filter -> int -> bool`

let createPredicate = function

| GreaterThan min -> fun n -> n > min

| Between (min, max) -> fun n -> n >= min && n <= max

| LessThan max -> fun n -> n < max

The `createPredicate`

function takes a filter and returns the predicate function `int -> bool`

.

With the functions `createFilter`

and `createPredicate`

in place, we can combine them and create a new function that takes a raw filter string and translate that to a predicate.

`// string -> int -> bool`

let createRule = createFilter >> createPredicate

Let me create a new record type `BucketRule`

which holds this string and the predicate.

`type BucketRule = { Label : string; Rule : int -> bool}`

let createBucketRule filterString =

{ Label = filterString; Rule = createRule filterString }

Now we have all required functions and itâ€™s time to do the data grouping.

`let createBucket numbers bucketRule =`

let bucketContent = numbers |> List.filter bucketRule.Rule

(bucketRule.Label, bucketContent)

let createBuckets numbers filterStrings =

filterStrings

|> List.map createBucketRule

|> List.map (createBucket numbers)

## Summary

Though the problem that we have seen is so trivial, the great features in fsharp make it very pleasant to write expressive code to solve it. The complete code snippet is available in fssnipnet.