Part I: Monads

Introduction

This is a tutorial that aims to demonstrate the fundamentals behind using LanguageExt in a practical fashion though step-by-step tutorials which introduce and then build up on concepts.

Furthermore, the tutorial shows how to use ideas such as pipelineing, delcarative style coding and walks through the fundamentals behind Select() SelectMany() and Bind() and Map() while covering implementation via Linq's Fluent and Linq Expression syntax.

Note: The priority is not being 100% accurate in terms of pure functional programming theory but more on actually getting things done using LanguageExt.

The general tutorial is structured like this:

• Monads

• Map/Bind

• Fluent/Expression Linq

• Pipelining

• Declarative Style

• Monad Validation

• Function Composition

• Pure Functions

• Basics of Either<L,R>

• Operations with Lists Eithers<,>

• Basics of Option

• ThrowIfFailed()

• FailureToNone()

Bonus: Functional programming concepts

• Caching - Using pure functions to cache things, ensuring that you need not call expensive calls if they've been done once already.

• Changing object state over time

• Immutability

Note: To run any specific tutorial, right-click on the project in the solution explorer and 'Set as start-up project'

Acknowledgements

Language.Ext library was created by Paul Louthy. See https://github.com/louthy/language-ext

References:

• https://stackoverflow.com/questions/28139259/why-do-we-need-monads Why do we need monads?

• https://github.com/louthy/language-ext/wiki LanguageExt Wiki

• http://www.stuartmathews.com/index.php/component/tags/tag/functional-prograqmming My articles on Functional programming(old)

Scope

Monad Basics

• Tutorial01 - Introduction to the Box type (a Monad)

• Tutorial02 - Shows you how to use Map and Bind (also construction of a Mondad Type)

• Tutorial03 - Shows how Bind is used to create a pipeline of function calls

• Tutorial04 - Performing operations on a Box using Map() and Bind(), Select() and introducing SelectMany()

• Tutorial05 - More examples of performing operations on a Box

• Tutorial06 - This tutorial shows you how pipelining is used to call funtions using Linq Fluent and Expression syntax

• Tutorial07 - Shows you when to use Map() and Bind()

• Tutorial08 - Shows you how to transition from Imperative style coding to Declarative style coding with an example

• Tutorial09 - Shows you that pipelines include automatic validation

• Tutorial10 - Expands on Tutorial09 to show that transformation function always return a Monad

• Tutorial11 - Shows how monad built in validation, affords short-cuircuiting functionality.

• Tutorial12 - Composition of functions

• Tutorial13 - Pure Functions - immutable functions with now side effects ie mathematically correct

Language.Ext

Either<Left,Right> Basics

• Tutorial14 - Shows the basics of Either<L,R> using Bind()

• Tutorial15 - Using BiBind()

• Tutorial16 - Using BiExists()

• Tutorial17 - Using Fold() to change an initial state over time based on the contents of the Either

• Tutorial18 - Using Iter()

• Tutorial19 - Using BiMap()

• Tutorial20 - Using BindLeft()

• Tutorial21 - Using Match()

Operations on Lists of Either<left, Right>

• Tutorial22 - Using BiMapT and MapT

• Tutorial23 - Using BindT

• Tutorial24 - Using IterT

• Tutorial25 - Using Apply

• Tutorial26 - Using Partition

• Tutorial27 - Using Match

Option Basics

• Tutorial28 - Introduction to Option

• Tutorial29 - Basic use-case of Option

• Tutorial30 - Using Option in functions (passing in and returning)

• Tutorial31 - using IfSome() and IfNone()

• Tutorial32 - Creates an entire application of just functions via pipelineing which returning and receive Option

• Tutorial33 - Using ToEither<>

• Tutorial34 - Using BiMap() - see tutorial 19

Custom Specific

• Tutorial35 - Using custom extension method ThrowIfFailed() and introducing Either<IAmFailure, Option> as a standard return type for all functions

• Tutorial36 - Using custom extension method FailureToNone()

• Tutorial37 - Using pure functions to cache things, ensuring that you need not call expensive calls if they've been done once already. (Bonus: FP concepts)

• Tutorial38 - Changing state of an object over time (Fold) including concept of apply events over time to change an object (Bonus: FP concepts)

• Tutorial39 - Immutability - Designing your objects with immutability in mind: Smart constructors and Immutable data-types (Bonus: FP concepts)

• Tutorial40 - Try - Supressing Exceptions

Todo

• TutorialA - Partial Functions - Allowing multiple arguments to be 'baked' in and still appear as Math like functions (pure functions)

• TutorialB - Threading and parallelism benfits

• TutorialC - Guidelines for writing immutable code, starting with IO on the fringes (bycicle spoke design)

• TutorialD - Custom useful Monad Extensions

Basics

Introduction to the Box type (a Monad)

A Monad is a just type, much like any user-defined type that is created when designing a class. It has its own properties that represent its state, and methods that give the Monad behaviour and, in many cases, manipulates its state through a public interface it provides to the programmers to use.

A simple example of a Monad might be a Box type:

A Box<T>, can hold any type but in this case, it holds and makes provision for an integer type, i.e. Box<int>.

Look at the implementation of the Box<T>, notice it's just a C# Class that's been created:

So far this looks like a normal C# class for the Box type. You can create a Box<T> by specifying the type of contents it can hold, and internally to the class, it is stored as a member called _item. Additionally, you can set the contents of the Box<T> through its Item property. Thus, is it possible to extract and set the contents of the Box<T>:

Monads are types that allow you to transform the contents of the Monad, in this case the contents of the Box<T> which is currently set to 99. A series of defined functions need to exist on a Monad which will define the kinds of transformations that can occur -- they are expected to exist. If a type has a Map, Select and a Bind function, it can generally be considered a Monad.

Transforming the contents of a Monad

The important thing to understand is that whatever the transformation will be, it needs to be provided by the programmer. Calling one of these functions, will then read the contents of the Monad and change the contents somehow -- the programmer will provide a Higher-Ordered Function (HOF), which will define the transformation. The monadic functions, such as Select/Map or Bind acts an execution environment, passing its internal contents into the HOF, where additional checks can be done before or after the transformation is started. The HOF is known as the transformation function and is provided by the programmer using the Monad.

The Select function does exactly this, when called on the Box<T>, it passes the contents of the Box<T> monad into the user-defined transformation function and executes that function, and the results thereof i.e. the transformation become part of the result of the Select function call. Lets see how it does this:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial01\_monad/Box.cs

TA is the type of the content of the Box i.e. Box<TA>, TB is the type that TA will be transformed into, box is the Box<T> type where conceptually T is replaced with TA. The last parameter map is the user-provided function aka the transformation function.

In this example, the transformation function is called map, which will be provided by the programmer defined as Func<TA, TB> which is any function accepting a type of TA (which also happens to be the type which Box holds), and which returns a TB type as its transformation result.

You'll notice how the Box<T>'s Select function wraps the supplied transformation function, map() by first checking if the Box<T> is empty, and if so returns an empty Box<TB>, otherwise executes the map function, producing a transformation of the content. The transformation is represented by the return type of TB, as the original type of the content of the box is TA.

An important distinction is that the transformation result is placed into a new Box<T> but specifically as a transformed representation, Box<TB> and the original Box<T>'s content is not modified during the Select function's operation. This is a preview the concept of immutability, and of how other Monad functions that accept a user-defined transformation function - like Bind, will work.

Using the Select function on a Monad

Box<T>'s Select function is called by the programmer like this:

The x => + 1 syntax is a definition of a lambda function that takes in one argument and the result of the expression after the => is the result, and as such it is a suitable transformation function to pass into the Select function, provided it matches the map parameter's types as defined by Func<TA, TB>.

Incidentally, this notation of explicitly calling the Select function, as defined on the Box<T> type is called the Linq Fluent Syntax. An alternative is to use the Linq Query Expression Syntax:

This form, will fetch or select a value from the box by using the Box<T>'s Select function (this is done implicitly) and passing the expression immediately after the select statement i.e. select number1 +1 as the mapping function for the Select function on the type, in this case a Box<T>.

As noted previously, the 'Linq Expression Syntax' and requires Box<T> to have a Select function for it to work in this way.

Any type you define that has a Select function defined on it as an extension method can be used in both Linq Fluent and Expression syntax forms.

The resulting program illustrates the concepts discussed thus far:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial01_monad/Program.cs

Many Monads in Language-Ext are utilized by taking advantage of C#'s Query Expression Syntax notation for accessing the Select function in this way. This is also largely due to being able to define an extension method for any type this way.

When working with Language-Ext in general, the already defined monad types such as Option<T>, Either<L,R> and Try<T> already have suitable Select, Map and Bind functions defined and as such its not needed to define them, and only need to pass in the transformation function, that is unless you want to create our own Monad like our Box<T> monad, and in which case, you now know how.

Why do we need to perform transformations? Traditional programming revolves around having functions. Almost every programming language allows you to define functions which take input and process it and then produce and output. This is what transformation is. So instead of defining explicit hard-coded functions in your source code, you can now pass around functions -- transformation functions. Monads are datatypes that allow you to work on their contents but providing the transformation function, where the input of the transformation function will be the contents of the Monad. Monads to a little bit more, they can run checks to validate if that function should run or not, and how it will behave. In this was Monads provide monadic functions like Select, Map and Bind to house the incoming transformation function that the user will provide, and acts as an execution vehicle for running that function and passing to it, its own contents.

Next, we'll put the Select function aside, and discuss its relatives Map and Bind.

Understanding Map and Bind

Now we're going to look into the other monadic functions, map and bind. Like select, the both allow the programmer to provide a customer transformation function. The difference between the two is how that transformation is returned to the programmer.

As suggested previously, like Select, both Map and Bind serve as an execution environment for the transformation function provided by the user, and they follow a certain interesting pattern before performing the transformation function. This can be described using the acronym VETL or Validate, Extract, Transform and Lift/Leave. These phases all apply to the how the Select, map and bind functions work and dictate how they ultimately call the user-defined transformation function.

Let's have a look at Map and Bind for the Box<T> Monad. As show previously with Select, these are just two extension methods on the Box<T> type. Also shown is the previously talked about, Select method which shows how it too features the same VETL convention.

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial02\_transformations\_1/Box.cs

First, there is no difference between Map and Select. They are identical functions, and function as previously described i.e. it validates if the Box<T> is empty, it Extracts the content of the Monad, our Box<T>'s _Item member in this case, runs the user-provided transformation function on that content and Lifts the result of the transformation into a new Box object. In this way, it follows the above pattern of VETL.

Map and Bind do much the same, however they differ only in how they return the transformed result i.e. the Lift/leave phase. In all cases the transformation function is run, however the requirements of the transformation's functions arguments and return type have changed:

Bind requires the programmer to define and provide a transformation function that will take as input the item provided to it by the Bind function, but crucially it needs to transform it in such a way that the result is a new Box<TB> while Map, only requires the transformation function to return the transformation from TA to TB without needing to place it into a new Box<TB>.

Fundamentally, what this means is that both Map and Bind do the same transformation, but package up the result in different ways.

Let have a look at this in an example

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial02\_transformations\_1/Program.cs

Now the Boxes contains another kind of thing, a list of integers. So effectively the Boxes are boxes containing numbers. Two Box<int[]> variables are defined that contain a list of numbers. As the Box*<T>* type has Map and Bind defined for it, we can call them by providing a transformation functions i.e. MyFunction() and MyFunction2().

Notice how MyFunction takes in a list of numbers, i.e int[] which is the T in the Box<T> definition when Box<T> is defined as Box<int[]>. This is the same for MyFunction2. The difference is what they return, and as a consequence, limits each one to being used in either Map i.e MyFunction2 or Bind i.e MyFunction. They can't switched around because Map and Bind have different type requirements for the transformation functions.

Here the contents of the Boxes are fed into the transformation functions as lambda expressions:

Ultimately the return type of the enclosing Map and Bind functions, i.e. the vehicles for the user-defined function need to return a Monad or a Box<int[]> in this case. So, depending on if we're calling Map or Bind, internally these two functions need to know if the transformation function will lift the transformation result into the Monad type or not, hence why Map and Bind function lift or leave the result of transformed content respectively.

How Map or Bind does this is by expecting a certain return-type of the user-provided transformation function and either automatically lifting the result into a Box<T> where the transformation function does not do that, as is the case with the Map function, or leaving the user-provided transformation function to do so, as is the case with the Bind function. This is why they require different forms of the user-provided transformation function, but ultimately the transformation is the same for both map and bind. In many cases you can use them interchangeably with the exception that the supplied lambda function or transformation function meets the requirements of either returning a Monad or not.

The take away is that Map() and Bind() do the same thing but Bind() requires you to put your transformation result back in the Box, while Map doesn't.

Both methods 'manage' your user defined transform function by running it only if it deems it should (if validation passes) and then depending on the specific function, it will either lift the result of the transformation(Map) or require that your transformation function's signature explicitly says it will do it itself (Bind)

This means, with a you don't have to return a Box (like you do when you with Bind), when transforming with the Map() function...it automatically does this for you

But here is something sneaky but very useful to know: The user-provided transformation function by definition can change the return type of the content it is transforming:

Look, we've been able to change the type of the Box from a int[] to a string!

This is by virtue of the fact that it's what your transformation function returned, and it thus transformed the return type also, and put it back into a box(because that's what map does). It's still in a Box<T> but is a box of a string now instead of a box of numbers....

Map() and Bind() can do this, and this is what makes these function really useful for chaining transformations together. His behaviour allows use to instead of designing hard coded functions like other programming languages like C or Pascal does, we can instead pass our functions into our Monads when designing logic that works with them, instead of passing out Monads into function, which is the old way of thinking.

We'll explore this next but before working further on out Monad Box, why do we need Monads? Why do we have to have Map() and Bind()..

Here is why: https://stackoverflow.com/questions/28139259/why-do-we-need-monads

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial02\_transformations\_1/Box.cs

Pipelining transformation workloads (3)

We will continue to define and explain our Monad type, Box<T> and showing how transformations are use in real time as well as previewing an implicit behaviour of Monads: short-circuiting.

Short-circuiting works when chaining or cascading multiple Bind() or Map() transformations together as part of a pipeline. Lets look at an example, which we'll go through shortly:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial03\_pipelines/Program.cs

As can be seen in the example, we're creating a pipeline of Bind operations, each one doing its defined transformation as provided by the user, and each time the Bind returns a Monad, which is a valid type for the next Bind extension method to work on. These cascade into a series of transformations, but this has hidden and useful feature: short-circuiting.

Put differently, this code transform the contents of the box by passing it down a series of Bind() operations,

so there are multiple associated VETL->VETL->VETL steps that represents the Binds()

effectively representing a pipeline of data going in and out of Bind(VETL) functions

Remember that the 'validate' step is implicit and is actually hard-coded directly into the Bind() or Map() functions that we previously looked at.

The validity of a box in this case, is if it is empty or not (remember that at the Bind functions' code that explicitly checks this),

If it is empty(invalid) it will not run the user provided transformation function, otherwise it will.

This is an example of 'short-circuiting' out of the pipeline of stacked transformations early on. So, if the first Bind short-circuits, i.e. the box is empty (the validation phase fails), the next Bind or Map will do the same and so they will not run the user-provided transformation function, as the validation phase failed.

When the validation phase fails, it returns a 'bad' result which is what other bind function will detect during their validation phase, in this case whenever an empty Box is encountered, skipping the transformation execute phase and returning the 'bad' or empty box to the next bind in the pipeline -- which too will return early. In this way, the pipeline has short-circuited and none of the other remining transformation functions are run.

Many Language.Ext monads such as Option<T>, Either<L,R> and Try<T> work like this.

Again, you will notice, that during each transformation, it is possible to change the content's type in the monad being passed into the next bind, as previously discussed.

Next we'll discuss the SelectMany() function which like Map/Select and Bind is used to transform the contents of monads, and like the those, it has a new requirement on the user-provided transformation function.

Monadic functions: Complete example (4)

Now let's look at a complete example showing all the operations on a Box<T> using Map() and Bind() and introducing a new SelectMany() extension method on Box<T>:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial04_methods_1/Program.cs

This example starts by showing the passing of Monads into functions. Each function DoubleBox n..4 will demonstrate a different variant to help you get familiar with their usages and occurances.

DoubleBox1 calls DoubleNumbers which accepts a Box<int[]> Monad and transforms it using Bind, thus DoubleNumbers needs to return a Box<T> type.

DoubleBox2 instead using Map which uses a necessary function DoubleNumbersNoLift to show that that function does not return a Box<T> and as such the Map function can be used with it, which will lift it into a Monad automatically.

These are familiar based on what we've learnt so far and it puts this into practise, in a practical fashion.

DoubleBox3 however uses Box<T>'s SelectMany function implicitly through its use in the Linq Query Expression Syntax.

This is new, we will discuss this now. Lets look at how SelectMany() is defined, as we've already seen how Select/Map and Bind look.

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial04\_methods\_1/Box.cs

You'll notice that this again, looks remarkably like the other monadic function, Select/Map and Bind in as much as they follow the Validate, Extract, Transform, and Lift/Load process. However, with SelectMany there is an additional step: Once the transformation function is run, bind in this case, a 2^nd^ new function can be provided by the user, namely project.

Project will take the newly transformed and lifted Monad, along with the original content and allow that to be transformed into a 3^rd^ Type, TC.

Its not clear yet why this additional bootstrapping is required until you look at how the Linq Query Expression Syntax is used and how powerful it is: it allows this function's internals (as read above) to be exposed and manipulated dynamically in LINQ. Here is an example:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial04\_methods\_1/Program.cs

DoubleBox3 and DoubleBox11 are equivalent with DoubleBox3 being the function used in the previous example. DoubleBox11 is used here to highlight how it actually works:

The first from statement calls Select on boxOfIntegers and exposes the Extract phase of the call, effectively extracting the contents of boxOfIntegers into start. The transformation function has not been run yet - the transformation function is only run in the 2^nd^ from, see the invocation of the user-provided transform function, DoTransformToAnyBox which now using the item extracted from the first from, start as its input(as one would expect for a transformation function compatible with the bind function). This is effectively the user-provided transform function used for passing into Bind. This results in the transformed result, startTransformed.

So far, this has shown how the Linq Query Syntax can open up both the Select() and Bind() functions and expose it as a Linq Query Expression. The next part is is the select statement which is effectively the project function called implicitly. The project function has access to the start variable as well as the startTransformed variable (its in scope) and as such it can use it to perform a transformation expression using the two, as per the project function definition:

Note too, that the result of the project transformation function is put into a Box<T> and so just like Bind and Map, need to return a Monad.

This has shown how defining a SelectMany() function on the Box<T> monad, allows LINQ access to specifying the bind transformation function inline as well as the projection transformation function in one LINQ query expression. The benefit of doing transformation this way is clearly that you can define transformation functions inline and have access to previous expression results, as they remain in scope!

This becomes more useful when you see it in an example with multiple from statements, simulating chaining of the transformations:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial07\_transformations\_2/Program.cs

We will investigate examples like this later, but for now its useful to see how the LINQ query expression syntax can reach deep into Select(), Bind() and SelectMany() and provides an alternative to specifying transformation and chaining the results.

Next, we'll bring what we've learnt thus far into a cohesive example:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial05\_methods\_2/Program.cs

Notice how transformation functions passed to Bind return Monads explicitly, while those passed to Map do not. Also Notice we can use either Map or Bind for transformation within a pipeline, but it becomes necessary to choose/use a specific one depending on if or not the provided transformation function returns a box or not (lifts or doesn't), i.e. is transformed in a call to Bind() or Map().

Next, we'll spend more time concentrating on using the LINQ fluent vs Expression syntax styles when working with monads.

Using LINQ Fluent and Expression syntax (6)

The following shows the two approaches, which yield the same result but look syntactically different. Remember, the LINQ expression syntax allow access to previous transformation results, while the fluent notation, only provides you access to the last transformation:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial06\_Linq/Program.cs

Shown: Using the select many way, i.e. the LINQ expression syntax as shown below allows an extracted item from the box, then to be passed down a series of transforms by way of those transform functions being compatible with the bind() phase of the SelectMany() function.

Each can see the prior transformation and can act on it subsequently.

And as each transformation function is run as part of the SelectMany()'s implementation in Box, it will also be subject to the VETL phases, which means if the input is not valid, it will return an invalid value and subsequent transforms upon receiving that invalid input will also return an invalid input and in all those cases, the underlying transform is not run (short-circuiting). This is also an illustration of Lazy-evaluation, where a function does not need to be run unless is necessary (i.e. valid in this case).

I need to use Map in the transformation pipeline of doubled2 because DoSomethingWith() does not return a Box and the result of a Map(will always do that).

The doSomethingWith function, represents a valid Map function to use with a Map, as map will automatically lift this and so this function does not have to lift its result. Note we don't have to return a Box<T> because as we''ll be running within a SelectMany() expression - it automatically lifts the result, in this case an object type. Note that this function will be acting as the bind() transformation function within the SelectMany() function defined for the Box class (see SelectMany())

The DoubleNumbers function is a valid bind function to be used in a Bind() because it lifts the result.

This function does something with the numbers we extracted from the box and then put them back in the box again because this function will be run in the bind() phase of the SelectMany() function (see the selectMany function implementation) and that function requires a signature of : int[] => Box<int[]>

When to use Map() or Bind() (7)

As an extension of the previous example, this shows you how to structure and deal with situations when choosing what function will be used in the bind(), map() functions and how choices you make impact the subsequent invocations of those functions when pipe-lining or chaining these functions together

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial07\_transformations\_2/Program.cs

This shows that you can use either Map or Bind (they do the same thing i.e. both transform their input) but map will lift automatically and Bind() needs its transform function to explicitly do that.

This choice of using Map or Bind will only impact on how the associated transformation functions require to produce either a lifted (Box<T>) or a non-lifted result.

Next, we'll look into defining the imperative and declarative style. Imperative refers the procedural view of having functions, and passing data into them, while declarative refers to having data and passing functions into them, a-la Monads!

Transitioning from Imperative to Declarative style (8)

Moving from traditional programming approaches which centre around defining imperative construction of logic within programs, we well look at what is required to convert from a Procedural way of thinking to declarative and as a consequence a Pipeline way of thinking.

As previously discussed, pipelining allows the movement of data from one Monad to the next, through a series of transformations that occurs through the pipelines. This simulates what procedural code does by calling function upon function to establish a set of logic for a program. We can do this using declarative style also:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial08\_declarative\_style/Program.cs

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial08\_declarative\_style/Program.cs

As can be seen from the above example, using either LINQ fluent or query syntax as the base of defining a declarative transformations using Monads to express logic.

Monad validation (9)

When using a Monad like Box<T> in a SelectMany statement like LINQ expression style used above, remember the implementation of the Monads SelectMany(), i.e for each bind() phase of the SelectMany(), that phase requires a function such PopulatePortfolioHoldings1() and any following ones to transform the extracted item and then put it back into a Box, so thats why each function must return a Box<> in the pipeline.

Also note how the logical way of planning the steps can be replicated in both the procedural and pipeline ways (you don't have to think that differently)

But wait, I can make a pipeline too without chaining Bind() or Map() statements too? Why can't I just do this:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial09\_automatic\_validation/Program.cs

The problem with this is you don't get automatic validation i.e. (V)ET it's not short-circuit-able.

You could do it but it would mean every function would need to have internal validation and check for invalid data whereas in a Monad like Box, that validation is built into the Select and SelectMany() implementation as thus us automatic each usage of those function on the monad!

This is another key aspect of using monads.

Returning Monads: transformations always return a Monad (10)

Let's have a bit of a recap:

Map and Bind both extract and validate the item within the box (that it's not empty) i.e. do VETL and then proceeds to run the transform function on it if it's not empty, otherwise returns empty box.

Both are equivalent in as much as they perform VETL but differ in what form they require their transform function to either lift or not lift the transformation (the function prototype must match what a Map or Bind() function requires)

In the LINQ Query Expression Syntax method, Box's SelectMany() is used to transform successive transformations, and you have access to each of the transformed results, as well as much earlier transformations. The final select statement is run via the Box<T>'s Select() function (technically this is the projection() function) and therefor it will automatically be lifted and you don't need to do it.

The Fluent mechanism also uses Box<T>'s Map and Bind functions.

Each fluent style Map and Bind has access to the last transformation before it, and unlike the LINQ expression syntax cannot see before the last transformation (as that is the only input it gets).

Transformations from a call to Bind and Map must result in a Box<T> either explicitly via Bind() or automatically via Map()

Your logical planning or thinking of logical programming tasks in your design can equally be represented procedurally and using pipelining.

Another key aspect when using monads, particularly when they are involved in successive chained calls such as within a pipeline, is that each returns a monad that the other uses as input.

Extending the last example by removing the transformation function and exposing them as inline lambda expressions, you can see how each must conform the function prototypes for transformation functions within the Map() or Bind() functions that exist on Box<T>:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial10\_returning\_monads/Program.cs

Built-in validation and short-circuiting in Monads (11)

We now turn to a specific example of short-circuiting behaviour of monads with special emphasis in seeing it in action when using LINQ query expression syntax:

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial11\_short\_circuiting/Program.cs

An empty box, i.e aBoxOfNumbers2 will cause the entire pipeline to return an Empty Box<T> instead of the ultimate result of transforming all the boxes contents. This is by design and later when this is not desired, you can use LanguageExt's match() function to determine how to deal with invalid data and how the pipeline should proceed. For now we'll leave this ideas until later, when we cover match.

A diversion: composition of functions (12)

Now we turn our attention to function composition, see: https://github.com/louthy/language-ext/wiki/Thinking-Functionally:-Function-composition for more details.

Scenario:

You have a program that has existing functions. You change one of those functions to now return a Monad. You need to ensure that you program still works i.e. existing functions can use your Monad returning function, even though it does not expect a Monad!

So, we'll compose a new function that will take the monad, and adapt it to the interface of the original function.

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial12\_function\_compositionial12/Program.cs

A diversion: Pure Functions (13)

A pure function's return value is a product of its arguments i.e. only its arguments are used to determine the return value.

The expectation is that if it does this, then the same input to the function will yield the same output too.

To ensure this, you need to further restrict the function to not use/depend on anything that might jeopardise this, i.e. fetch/use a source that today might be one thing and tomorrow might be something else.

For instance, if you get a value from the DB today, tomorrow it might be removed and then the guarantee you made that the function will return the same value breaks.

So, you can't use Input/output or anything that is a source of changeable circumstances.

Side note: Pure functions are immediately parallelizable and can be used for Memoization (storing the result and input of the function requires that the function never needs to run again)

https://github.com/stumathews/UnderstandingLanguageExt/blob/master/Tutorial13_pure_functions/Program.cs

The last three sections don't fit well with the narrative of the proceeding sections. Should better integrate them with relatable use cases.There might be some better examples in Mazer.

Part II: Language-Ext

The proceeding section will have suitably prepared you for your fist encounter with LanguageExt monads, how they work and what you can come to expect from them. Essentially, they are not very different to the Box<T> monad.

We'll cover Either, Option and Try Monads and everything you've learnt thus far about Box<T> applies to them also, including calling there Map, Bind and using them in LINQ expressions in a declarative way.

The Either<L,R> Monad

Introducing the Either monad (14)

This tutorial shows you what a what an Either<> type is and how to use it generally

Operations on Either<L,R>

Using BiBind (15)

This tutorial shows you what a what an Either<>'s BiBind() functionality

Using BiExists

This tutorial shows you what a what an Either<>'s BiExists()

Using Fold() to change an initial state over time based on the contents of the Either

This tutorial shows you what fold() does

Using Iter

Iter: run an arbitary function on the Either<> if its value is right type or chose BiIter() to specify a function to run on both types

Using BiMap (19)

Using BiMap() to make provision for a transform function for both the left and right types of the either. The transform is automatically lifted.

Using BindLeft (20)

Shows the basics of Either<L,R>, using BindLeft() to make provision for a transform function for the left types of the either (which is unusual for the default Bind() function).

The transform is NOT automatically lifted(this is a bind() after all).

Using Match (21)

Using Match to extract the contents of an Either<> but not put it back into and either types (as map() and Bind() would do)

Operating on Lists of Either<left, Right>

Using BiMapT and MapT

This tutorial shows you how you can transform a List of Eithers, effectively doing a Map on each either in the list, and this Bi variety allows you to specify how make provision to map/transform both types

When a Bind/Map function is called on a list of monads, it is BindT or BiMapT, otherwise operating on a single monad, use Bind() or Map() alone

Using BindT

This tutorial shows you how you can transform a List of Eithers, effectively doing a Bind on each either in the list and a Bi variety allows you to specify how make provision to map/transform both types

Using IterT

This tutorial shows you how you can call a function on each right value for the list of monads in the list, using IterT() (Either is a monad)

Using Apply

Using Apply both on a simple Either<> and a List of Eithers to demonstrates its simplicity

Using Partition

Using Partition to easily get both the lefts() and the Rights() in one call - as a tuple of (lefts,rights)

Using Match

Shows the basics of transforming a list of Eithers using match to understand whats in them (both left and right values) and

then transform them based on their values into a single type that represents either in one way (a string)

Along with Map() and Bind() this extracts the value from the Either and provides transformation functions for both Left and Right sides of the Either

The Option<T> Monad

Introduction to Option<T> (28)

Option<T> type effectively removes the need to use NULL in your code. Nulls can produce unexpected behavior and as such have no place in pure functions where unexpected behavior would

render them otherwise impure

Basic use-case of Option<T> (29)

Using Option<T> in functions (passing in and returning)

Contrived example of passing around Option<T> arguments

using IfSome() and IfNone()

Demonstrates the usage of IfNone and IfSome which runs a user defined function provided the option is None or Some respectively

Pipelining with Options<T> (32)

Rosetta code! Procedural -> Fluent -> Query Syntax

Using ToEither<>

ToEither extension method to convert a value to a right sided Either<L,R>

Using BiMap() (34)

Bimap

The Try<T> Monad

Supressing Exceptions

This tutorial demonstrates the use of the Try<> Monad.

Part III: Everything else

Bonus

ThrowIfFailed() and introducing Either<IAmFailure, Option<T>>

ThrowIfFailed and a way to make functions return a standard return type of an Either of Right(T) or a failure(Left).

T can be any type your function deals with, as you'd use in any normal function you create, only you make it an Option.

You also bundle with your return type a failure if there is one, by returning an all encompassing return value of Either<IAmFailure, Option<T>>

Program.cs

CustomExtensions:

IamFailure:

Using custom extension method FailureToNone()

We can convert a 'failed' standard wrapped function to a None. This is helpful if you want to turn a failure into a 'valid' standard function either but with None Right value

Memoization

This tutorial exposes how functional programming, particularly caching results from pure functions, aids memoization, as they always return the same output for same input.

Now because we've cached decrypted results for phrases, when we see that encrypted phrase we can use the cached decrypted result for that encrypted phrase to get without having to run the SimpleDecrypt() function again.

This is the same with all caching mechanism, which make the obvious seem transparent, however with a pure function, you know for certain that there is no chance that our cached decrypted result could be different from running a SimpleDecrypt() on the encrypted string we have - so we have double certainty that we dont have to run the SimpleDecrypt() function.

If SimpleEncrypt() or SimpleDecrypt() could sometimes return different outputs for the same input, then we'd have to cal SimpleDecrypt() to return what the decrypted result is that/this time.

Note using Monads, Select, Bind() within your functions you're making it unlikely that you functions will

never throw exceptions becasue you're catering for both the expected and unexpected data by virtue of using Monads (which ensure that you need to ie. they contain both failure and success logic such as Some/None or Either left or right emedded into themselves so you can and indeed have to cater for them)

In catering for them by extracting their values using Match() or transforming via Select()/Bind()/Map().

Now use cache to decrypt known inputs against outputs produced by pure function SimpleEncrypt():

Apply events over time to change an object

This tutorial shows how you can use the Fold() function in languageExt to change the state of an object over time

Smart constructors and Immutable data-types

This tutorial demonstrates creating immutable objects using Smart Constructors, and using them as you would use any other OOP objects.

However, this object is immutable in as much as its specifically designed not to have its state changed by operations

The operations that it does have, create a new object with the modification and leaves the original object untouched.