Channels and Isomorphisms

isomorphism n. Some crazy Greek mathematical thing. See the Wikipedia page for the gory details.

TL;DR it's a function, 'a -> 'b, and its inverse, 'b -> 'a

Isos

In SharpBoomerang, isomorphisms are represented by this type:

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type Iso<'a,'b> = ('a -> 'b) * ('b -> 'a)

Let's take numerical addition, whose inverse is simply subtraction. Here's an isomorphism representing adding one to a number (and subtracting it):

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let add1 = (fun n -> n + 1), (fun n -> n - 1)

See, that's really simple, right? Well sometimes SharpBoomerang can make it even simpler by inferring the inverse function. Thus, we can simplify the definition further and only define the 'a -> 'b function:

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let add1_2 = Iso.ofFn (fun n -> n + 1)

This feature can be very useful when maintaining both the function and its inverse is especially tedious or error-prone. A good example of this is a mapping function:

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let numbers = Iso.ofFn (function
                        | 0 -> "zero"
                        | 1 -> "one"
                        | 2 -> "two"
                        | 3 -> "three"
                        | 4 -> "four"
                        | 5 -> "five"
                        | _ -> failwith "Too big")

(snd numbers) "three" // -> 3

Channels

By themselves, isos aren't that useful, but they become very powerful when you combine them with channels. Here's a more complex example to whet our appetite:

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let raw = Channel.pipeWith "abc" // create a channel that initially contains "abc"
let map = raw |> Channel.map(Iso.ofFn (fun str -> str.ToUpperInvariant()))

raw.Read(printfn "%A") // prints "abc"
map.Read(printfn "%A") // prints "ABC"

map.Write("DEF")

raw.Read(printfn "%A") // prints "def"
map.Read(printfn "%A") // prints "DEF"

Channels and isos are a couple of the powerful tools SharpBoomerang uses to achieve its bidirectionality.

• Docs
• Introduction
• Channels and Isos
• Examples
• Parsing JSON