Composing quoted functions using computation expressions

Question

I've looked around and struggled to get an answer to this; I'm sure there's an obvious answer but I just can't seem to find it; or I've hit a limitation of quotations that I can't pass when used with computation expressions.

Basically I want to work with an quoted lambda defined as below using a computation F# workflow. The problem comes when trying to compose these workflows together. Ideally I want to compose the Workflow<'Env, 'Result> instances together using the let! syntax. My somewhat naive attempt is below:

type Workflow<'Env, 'Result> = Expr<'Env -> 'Result>
type WorkflowSource<'Env, 'Result> = 'Env -> 'Result

type WorkflowBuilder() = 
    member x.Bind
        (workflow: WorkflowSource<'Env, 'OldResult>,
         selector: 'OldResult -> WorkflowSource<'Env, 'NewResult>) : WorkflowSource<'Env, 'NewResult> =
         (fun env -> (selector (workflow env) env))
    member x.Bind
        (workflow: Workflow<'Env, 'OldResult>,
         selector: 'OldResult -> WorkflowSource<'Env, 'NewResult>) 
         : Workflow<'Env, 'NewResult> =
         <@ (fun env -> (selector ((%workflow) env) env)) @>
    // This bind is where the trouble is
    member x.Bind
        (workflow: WorkflowSource<'Env, 'OldResult>,
         selector: 'OldResult -> Workflow<'Env, 'NewResult>) 
         : Workflow<'Env, 'NewResult> =
         <@ fun env -> 
                let newResultWorkflow = %(selector (workflow env))
                newResultWorkflow env @>
    member __.Return(x) = fun env -> x
    member __.ReturnFrom(x : WorkflowSource<_, _>) = x
    member __.Quote(x : Expr<WorkflowSource<_, _>>) : Workflow<_, _> = x

let workflow = new WorkflowBuilder()

The third bind member gives me the compiler error: "The variable "env" is bound in a quotation but used in a sliced expression" which kinda makes sense. The question is how do I get around it. I've defined the above as an attempt to try to get the simple below cases to work.

let getNumber (env: EnvironmentContext) = (new Random()).Next()

let workflow1 = workflow {
    let! randomNumber = getNumber
    let customValue = randomNumber * 10
    return (globalId * customValue)
}

// From expression to non expression bind case
let workflow2a = workflow {
    let! workflow1 = workflow1
    let! randomNumber = getNumber
    return (randomNumber + workflow1)
}

// From non-expression to expression bind case
let workflow2 = workflow {
    let! randomNumber = getNumber
    let! workflow1 = workflow1
    return (randomNumber + workflow1)
}

Just wondering whether what I'm trying to achieve is possible or am I doing something wrong? Is it possible to get the above simple cases working while capturing the user functions inside the final quoted expression?

EDIT: I've also tried without the WorkflowSource type taking into account Tomas' answer. No luck still with error: System.InvalidOperationException: first class uses of '%' or '%%' are not permitted at Microsoft.FSharp.Core.ExtraTopLevelOperators.SpliceExpression[T](FSharpExpr`1 expression)

type WorkflowBuilder() = 
    member x.Bind
        (workflow: Workflow<'Env, 'OldResult>,
         selector: 'OldResult -> Workflow<'Env, 'NewResult>) 
         : Workflow<'Env, 'NewResult> =
         fun env -> <@ %(selector (%(workflow env)) env) @>
    member __.Return(x) = fun Env -> <@ x @>
    member __.ReturnFrom(x: Workflow<_, _>) = x
    member __.Quote(expr: Expr<Workflow<'Env, 'Result>>) = expr
    // This run method fails
    member __.Run(x : Expr<Workflow<'Env, 'Result>>) : Workflow<'Env, 'Result> = fun (env: Expr<'Env>) -> <@ %((%x) env) @>

let workflow = new WorkflowBuilder()

// Env of type int for testing
let getRandomNumber (kernel: Expr<int>) = <@ (new Random()).Next() @> 

let workflow1 = workflow {
    let! randomNumber = getRandomNumber
    let otherValue = 2
    let! randomNumber2 = getRandomNumber
    return randomNumber + otherValue + randomNumber2
}
// This fails due to quotation slicing issue
workflow1 <@ 0 @>

Answer 1

This is just a rough sketch of an idea, but I think you can get further if you represent workflow not as a quoted function, but as a function that takes a quoted environment and returns a quoted result:

type Workflow<'Env, 'Result> = Expr<'Env> -> Expr<'Result>

Then you can certainly implement all of the binds:

member x.Bind
    (workflow: WorkflowSource<'Env, 'OldResult>,
     selector: 'OldResult -> WorkflowSource<'Env, 'NewResult>) : WorkflowSource<'Env, 'NewResult> =
     (fun env -> (selector (workflow env) env))
member x.Bind
    (workflow: Workflow<'Env, 'OldResult>,
     selector: 'OldResult -> WorkflowSource<'Env, 'NewResult>) 
     : Workflow<'Env, 'NewResult> =
     fun env -> <@ selector %(workflow env) %env @>

// This bind is where the trouble is
member x.Bind
    (workflow: WorkflowSource<'Env, 'OldResult>,
     selector: 'OldResult -> Workflow<'Env, 'NewResult>) 
     : Workflow<'Env, 'NewResult> =
     fun env -> <@ %(selector (workflow %env) env) @>

That said, I think this is not quite all you need - it seems that the compiler is ignoring code in Quote, so even if we add quote that turns WorkflowSource into Workflow, you still get errors because there are Expr<WorkflowSource<_>> values - but I think another overload of bind might solve that.

member __.Quote(x : Expr<WorkflowSource<_, _>>) : Workflow<_, _> = 
  fun env -> <@ (%x) %env @>