[Examples] Add F# example

[martincostello]

Changes

Add an example for an ASP.NET Core application using F#.

This was inspired by a conversation @alanwest and myself had at OTel Unplugged with an end-user who wondered why there wasn't an F# SDK for OpenTelemetry.

The example here is based on the AspNetCore example, and then converted with the help of GitHub Copilot. I'm no F# developer, so it might not be as idiomatic as it could be.

While working on this I found some issues with the Docker Compose setup copied from the ASP.NET Core example so I'm going to park this for now while I fix that #6877.

Feedback welcome.

Merge requirement checklist

• CONTRIBUTING guidelines followed (license requirements, nullable enabled, static analysis, etc.)
• Unit tests added/updated
• Appropriate CHANGELOG.md files updated for non-trivial changes
• Changes in public API reviewed (if applicable)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.08%. Comparing base (1dd61d2) to head (5f82e17).
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6875      +/-   ##
==========================================
- Coverage   87.33%   87.08%   -0.26%     
==========================================
  Files         263      263              
  Lines       12387    12387              
==========================================
- Hits        10818    10787      -31     
- Misses       1569     1600      +31     

Flag	Coverage Δ
unittests-Project-Experimental	87.04% <ø> (-0.15%)	⬇️
unittests-Project-Stable	87.05% <ø> (-0.20%)	⬇️
unittests-Solution	86.83% <ø> (-0.33%)	⬇️
unittests-UnstableCoreLibraries-Experimental	89.32% <ø> (-0.10%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.
see 7 files with indirect coverage changes

[martincostello]

Paging some F# fans I know in case they have any opinions 😃

/cc @slang25 @MrBliz @baronfel

[baronfel]

Looks mostly good, but I have a couple tiny notes to clean it up a bit.

[Copilot]

Pull request overview

Adds a new F# ASP.NET Core Web API example demonstrating OpenTelemetry logging, metrics, and tracing, aligning with the existing C# AspNetCore example and wiring it into the repo solution/build.

Changes:

• Introduces a new F# example app (project, program, controller, instrumentation helper, model) with OTLP/Console/Prometheus switching via configuration.
• Adds supporting example assets (README, appsettings, docker-compose for grafana/otel-lgtm).
• Wires the new example into the solution and central package versions.

Reviewed changes

Copilot reviewed 10 out of 10 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
examples/FSharp/docker-compose.yaml	Adds docker-compose to run grafana/otel-lgtm dependencies for the example.
examples/FSharp/appsettings.json	Adds configuration for exporters, OTLP endpoint, and instrumentation options.
examples/FSharp/WeatherForecast.fs	Adds the sample model used by the controller.
examples/FSharp/README.md	Documents running the F# example and optional OTLP export + Docker deps.
examples/FSharp/Program.fs	Configures OpenTelemetry logging/metrics/tracing and ASP.NET Core pipeline.
examples/FSharp/InstrumentationSource.fs	Adds ActivitySource/Meter/counter holder for manual instrumentation.
examples/FSharp/Examples.FSharp.fsproj	Adds the new F# example project and dependencies.
examples/FSharp/Controllers/WeatherForecastController.fs	Adds the sample controller emitting telemetry and logs.
OpenTelemetry.slnx	Adds the new F# example project to the solution.
Directory.Packages.props	Adds central package version entry for FSharp.Core.

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