Fiddling with ASP.NET Core and F# with Suave
Suave is a possible replacement for the ASP.NET stack, but with some help, the two can be used together to build composable F# web applications.
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ASP.NET Core WebAPI in Azure App Service
In my opinion, Azure App Services are an easy and direct way to launch your ASP.NET Core application for the outside world to access.
Exploring F# with .NET Core and Kestrel
While not the primary focus of Microsoft's efforts, F# makes for an excellent language choice for applications targeting .NET Core.