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// the function definitions you were given
let comp(f, g)(x) = g(f(x))
let h(f)(x) = f(x), comp(f,f)(x)
// the function definitions you are passing in on the last line
let add1(x) = x + 1
let times3(x) = x * 3

// So the function that is built on the last line is this
let a(x) = h(comp(add1, times3))(x)
// We can define a little helper function to clear up the code

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(*
A computational expression embedding Arithmetic Logic Unit (ALU) programming (see https://adventofcode.com/2021/day/24) in F#

This doesn't actually help with solving the Advent of Code challenge, but I thought it would be fun to
play with writing DSLs in computational expressions

Note: the `mod` instruction had to be renamed to `mod'` to avoid conflicting with the reserved keyword `mod`
*)

/// Type representing allowed variable names

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module Platform

#if FABLE_COMPILER_RUST

open Fable.Core

module Performance =
    [<Erase; Emit("std::time::Duration")>]
    type Duration =
        abstract as_millis: unit -> uint64 // actually u128

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<Project Sdk="Microsoft.NET.Sdk">

  <PropertyGroup>
    <OutputType>Exe</OutputType>
    <TargetFramework>net7.0</TargetFramework>
    <ImplicitUsings>enable</ImplicitUsings>
    <Nullable>enable</Nullable>
  </PropertyGroup>

  <ItemGroup>

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From conversation on F# discord: https://discord.com/channels/196693847965696000/1109160345316098058

So first off, I converted the input type to list<'a * Set<'b>> instead of list<'a * list<'b>> for now to make some of the implementation clearer, but we can change the types back later if you want.

Okay, so with any complex problem we don't know how to solve, we should break it down into smaller pieces that we can solve. So at the root of this, we need to be able to compare two elements of the input list and if their sets share any elements, return the first part of each element. So if we write a function to do this, it is going to need to return an option<'a * 'a>, since for some inputs we want to return a 'a * 'a, but for other inputs we won't.

let compareElements
    (this: 'a, these: Set<'b>)
    (that: 'a, those: Set<'b>)
    : option<'a * 'a> =

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Benchmark Results:

Method	N	Mean	Error	StdDev	Median
QueryCE	1000	45.73 us	0.351 us	0.311 us	45.74 us
QueryEquivalent	1000	45.87 us	0.450 us	0.421 us	45.87 us
Seq	1000	12.17 us	0.090 us	0.080 us	12.18 us
Linq	1000	12.72 us	0.170 us	0.350 us	12.63 us
QueryCE	10000	454.09 us	4.722 us	4.417 us	452.38 us
QueryEquivalent	10000	448.92 us	3.715 us	3.293 us	449.28 us
Seq	10000	115.37 us	0.618 us	0.578 us	115.45 us

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open System

type MeasurementObservable<'data> () =
  let observers = ResizeArray<IObserver<'data>>()

  member _.report (value: 'data) =
    observers
    |> Seq.iter (fun obs -> obs.OnNext value)

  interface IObservable<'data> with