Migrating Higher Order Programming to the Web

My application, HOPE (Higher Order Programming Environment) is, in its simplest definition, a semantic publisher-subscriber application builder.  I’ve been wanting to move it to the web, but this is fraught with security concerns, hence my investigations into Docker technology and using a language like Python for the programming of “receptors” — the autonomous computational units that process semantic data.  Another stumbling block is my lack of experience with HTML5 canvas and graphics rendering.  Regardless though, there was no reason not to put together a proof of concept.

Here’s a quick walkthrough — no, this code is not yet publicly available.

Step 1: create a few receptors.

We’ll do some computations based on inputting a birth date.

Receptor #1: computing the age of a person in terms of years and days:


Notice the class name computeAge.  We’ll talk about this later.

Receptor #2: compute the number of days to the birth day:


Note the class name daysToBirthday.

Receptor #3: Get the interesting people born on the same month and day:


Again, note the class name personsOfInterest.

Step 2: Add the Receptors to the Surface Membrane


Step 3: Inject a semantic JSON object

Run the “membrane” and inject:

{"birthday": {"year": 1962, "month": 8, "day": 19}}


And here’s the result:


The full output being:

 "age": {
 "years": 37,
 "days": 204
 "daysToBirthday": 161
 "personsOfInterest": [
 "1724 Samuel Hood, 1st Viscount Hood, British admiral in the American Revolutionary War and the French Revolutionary Wars, born in Butleigh, England (d. 1816)",
 "1745 John Jay, American statesman, 1st US Chief Justice, born in New York City",
 "1863 Edvard Munch, Norwegian painter and print maker (The Scream), born in Ådalsbruk, Løten, Norway (d. 1944)",
 "1915 Frank Sinatra, American singer (Strangers in the Night, My Way) and actor (From Here to Eternity) known as 'old blue eyes', born in Hoboken, New Jersey (d. 1998)",
 "1932 robert pettit, American NBA star (St Louis Bombers/1959 MVP), born in Baton Rouge, Louisiana"

What’s Going On?

Simply put, a preprocessor creates a mapping between semantic types and receptors (Python classes):

receptorMap = 
  'birthday':[computeAge(), personsOfInterest()],

and the semantic processor engine routes the JSON semantic types to the Python class receptor’s process method.  When you inject “birthday”, it routes that type’s data to the computeAge and personOfInterest receptors.  The output of computeAge, which is of type “age”, is routed to the daysToBirthday receptor.

In this manner, one can create a library of small computational units (receptors) and build interesting “computational stories” by mixing and matching the desired computations.  Creating the receptors in Python makes this approach perfectly suited for running in Docker containers.  My ultimate vision is that people would start publishing interesting receptors in the open source community.

There’s still much more to go, but even as such, it’s a fun prototype to play with!  Some of the interesting problems that come out of this is, how do we let the end user create a visual interface (a UI, in other words) that facilitates both intuitive input of the semantic data as well as displaying real time output of the semantic computations.  Just the kind of challenging stuff I like!


Partial Application and Currying in C# – Clearing the Fog

Partial Application vs. Currying

Most of the examples you’ll see on the regarding partial application and currying (even in F#) often talk about simple functions that take two parameters.  This is sort of pointless because when you partially apply one parameter or curry one parameter, the call to resolve the operation is identical, so you really don’t get an appreciation of the syntactical difference.  I, however, will avoid that by demonstrating the differences between partial application and currying using three (wow!) parameters.

Partial Application

Very simply, partial application lets you assign the first n parameters, returning a function that takes the rest.  Given a function that returns the sum of three values:

Func<int, int, int, int> add = (a, b, c) => a + b + c;

You can partially apply one or two parameters:

Func<int, int, int> needsTwoMoreParams = (b, c) => add(3, b, c);
Func<int, int> needsOneMoreParam = (c) => add(3, 4, c);

Using these functions looks like this:

int twelve = needsTwoMoreParams(4, 5); 
twelve = needsOneMoreParam(5);

Notice we have to explicitly define the return type of the partial application function.  We cannot use var!

var needsOneParam = (b, c) => add(3, b, c);

Cannot assign lambda expression to an implicit-typed variable.

In a functional programming language like F#, the type is inferred:

> let add a b c = a + b + c;;
val add : a:int -> b:int -> c:int -> int

> let add3 = add 3;;
val add3 : (int -> int -> int)

> let add3and4 = add 3 4;;
val add3and4 : (int -> int)

The key thing to note with partial application in C# is the construct (b, c) for the remaining parameters in the needsTwoMoreParams function.  This is what tells you it’s a partial application rather than currying!

You can do the same thing with functions that are not C# Func types but Action types:

Action<int, int, int> xadd = (a, b, c) => Console.WriteLine(a + b + c);
Action<int, int> xoneParam = (b, c) => add(3, b, c);
Action<int> xtwoParams = (c) => add(3, 4, c);


As Jon Skeet so eloquently wrote: “currying effectively decomposes the function into functions taking a single parameter.”  Study this example carefully:

Func<int, Func<int, Func<int, int>>> curried = a => b => c => a + b + c;
int twelve = curried(3)(4)(5);
Func<int, Func<int, int>> oneParam = curried(3);
Func<int, int> twoParams = curried(3)(4);
twelve = twoParams(5);

Note how the parameters of the curried function are called as separate parameters: (3)(4)(5).  Also note that the function is defined with a => b
=> c=>
, which tells you this is a curried function!

Interestingly, we can use var in this case:

var oneParam = curried(3);
var twoParams = curried(3)(4);

Again however, the syntax in C# for defining the curried function must be explicit – “a function that takes an int that returns a function that takes an int and returns a function that takes an int and returns an int.”  This gets ugly real quick, and again, in F#, the inference engine knows you’re doing currying:

> add(3);;
val it : (int -> int -> int) = <fun:it@9>

> let add3 = add(3);;
val add3 : (int -> int -> int)

> let add3and4 = add(3)(4);;
val add3and4 : (int -> int)

> add3and4(5);;
val it : int = 12

Also notice this in F#:

add3(4, 5);;
add3(4, 5);;

stdin(13,6): error FS0001: This expression was expected to have type
but here has type
''a * 'b'

The correct syntax, in F# looks just like C# – one parameter per “function”:

> add3(4)(5);;
val it : int = 12

Again, once you create a curried function, you have to treat it like a curried function, same as in C#.

What about curried functions of an Action?  It would look like this:

Func<int, Func<int, Action<int>>> curried = a => b => c => Console.WriteLine(a + b + c);
var oneParam = curried(3);
var twoParams = curried(3)(4);
twoParams(5);  // prints 12

Note how the final result of last Func is an Action that takes the last value.

So now hopefully you have a clear understanding of the difference between partial application and currying.

FlowSharpCode, continued…


A simple example, but the “problem” is that the three Drakon shapes (begin loop, output, and end loop) each still have individual C# code-behind in each shape.  For example, the begin loop has the code-behind:

 var n in Enumerable.Range(1, 10)

My original idea was that the Drakon shape description should not define the language-specific syntax, instead that should be implemented by the developer in the code-behind.

In practice (and I’ve written a complex application in FlowSharpCode, so I know) it becomes unwieldy to deal with one-liner code behind, the result of which is that I tend not to use Drakon shapes, but that results in nothing better than a meaningless box with some code in it.

I’m also reluctant to put the code in the shape label (though this is supported) as again we’re now dealing with language specific syntax.

I’m also reluctant to create a meta-language for Drakon shapes, for example, something that could interpret:

n = 1..10

into C#, Python, whatever.  What if the developer wants to write:

Count from 1 to 10

So, what I’m considering is letting the developer create the Domain Specific Language (DSL) so that they can expressively communicate the semantics of a Drakon shape and also provide the rules for how the semantics is parsed, ideally in an intermediate language (IL), for example, something that expresses a for loop, a method call, whatever.

The advantage to this is that the developer can create whatever DSL they like to work in, the IL glues it together into the concrete language.

Two things happen then:

  1. The DSL is interchangeable.  Any IL can be super-composed into your DSL choice.
  2. The IL is language independent, so it can be de-composed into language specific syntax.

Item #2 of course imposes some significant limitations — what if a language doesn’t support classes, or interfaces, or yield operator, or whatever?  I’m not particularly too concerned about that as a language-independent DSL/IL is more of a curiosity piece, as it becomes rapidly untenable when your code starts calling language-framework-platform dependencies.

However, I’d love to hear my readers thoughts on this DSL/IL concept I’m considering.