Taking the example of writing a parser-unparser pair for a DU.
The unparser function of course uses match expression, where we can count on static exhaustiveness check if new cases are added later.
Now, for the parsing side, the obvious route is (with eg FParsec) use a choice parser with a list of the DU case parsers. This works, but does not have exhaustiveness checking.
My best solution for this, is to create a DU_Case -> parser function that uses match expression, and using runtime reflection get all DU cases, call the function with them, and pass the so generated list to the choice combinator. This works, and does have static exhaustiveness checking, BUT gets pretty clunky fast, especially if the cases have varying fields.
In other words, is there a good pattern other than using reflection for ensuring exhaustiveness when the discriminated union is the output and not the input?
Edit: example on the reflection based solution
By getting clunky, I mean that for every case that has fields, I have to also create the field values dynamically, instead of the simple Array.zeroCreate(0) which is of course always valid. But what in the else branch? There needs to be code to dynamically create the correct number of field values, with their correct (possibly complex) constructors and so on. Not impossible with reflection, but clunky.
FSharpType.GetUnionCases duType
|> Seq.map (fun duCase ->
if duCase.GetFields().Length = 0 then
let case = FSharpValue.MakeUnion(duCase, Array.zeroCreate(0))
else
(*...*)
Related
The language suggestion states that the advantages are detailed in the linked paper. I had a quick skim through and I can't see it spelled out explicitly.
Is the advantage just that each statement gets executed in parallel so I might get a speed boost?
Or is there some kind of logic it caters for, that is not convenient using the usual monadic let!?
I understand that, this being applicative, means that it comes with the limitation that I can't use previous expressions to determine the logic of subsequent expressions. So does that mean the trade off is flexibility for efficiency?
The way I understood Don Syme's description, when I read it a while ago, was every step in the let! ... and! ... chain will be executed, unlike when you use let! ... let! .... Say, for instance, that you use the option CE. Then if you write
option {
let! a = parseInt("a")
let! b = parseInt("b")
return a + b
}
only the first let! will be executed, as the CE short-circuits as soon as it meets a None. Writing instead let! a ... and! b = ... will try to parse both strings; though not necessarily in parallel, as I understand it.
I see a huge benefit in this, when parsing data from external sources. Consider for instance running
parse {
let! name = tryParse<Name>("John Doe")
and! email = tryParse<EMail>("johndoe#")
and! age = tryParse<uint>("abc")
return (name, email, age)
}
and getting an Error(["'johndoe#' isn't a valid e-mail"; "'abc' isn't a valid uint"]) in return, instead of only the first of the errors. That's pretty neat to me.
I am excited for this for two reasons. Potentially better performance and that some things that can't fit into the Monad pattern can fit into the Applicative Functor pattern.
In order to support the already existing let! one need to implement Bind and Return, ie the Monad pattern.
let! and and! requires Apply and Pure (not exactly sure what F# the equivalent are named), ie the Applicative Functor pattern.
Applicative Functors are less powerful than Monads but still very useful. For example, in parsers.
As mentioned by Philip Carter, Applicative Functor can be made more efficient than Monads as it's possible to cache them.
The reason is the signature of Bind: M<'T> -> ('T -> M<'U>) -> M<'U>.
One typical way you implement bind is that you "execute" the first argument to produce a value of 'T and pass it the second argument to get the next step M<'U> which you execute as well.
As the second argument is a function that can return any M<'U> it means caching is not possible.
With Apply the signature is: M<'T -> 'U> -> M<'T> -> M<'U>. As neither of the two inputs are functions you can potentially cache them or do precomputation.
This is useful for parsers, for example in FParsec for performance reasons it's not recommended to use Bind.
In addition; a "drawback" with Bind is that if the first input doesn't produce a value 'T there is no way to get the second computation M<'U>. If you are building some kind of validator monad this means that as soon as a valid value can't be produced because the input is invalid then the validation will stop and you won't get a report of the remaining input.
With Applicative Functor you can execute all validators to produce a validation report for the entire document.
So I think it's pretty cool!
I am trying to port a small compiler from C# to F# to take advantage of features like pattern matching and discriminated unions. Currently, I am modeling the AST using a pattern based on System.Linq.Expressions: A an abstract base "Expression" class, derived classes for each expression type, and a NodeType enum allowing for switching on expressions without lots of casting. I had hoped to greatly reduce this using an F# discriminated union, but I've run into several seeming limitations:
Forced public default constructor (I'd like to do type-checking and argument validation on expression construction, as System.Linq.Expressions does with it's static factory methods)
Lack of named properties (seems like this is fixed in F# 3.1)
Inability to refer to a case type directly. For example, it seems like I can't declare a function that takes in only one type from the union (e. g. let f (x : TYPE) = x compiles for Expression (the union type) but not for Add or Expression.Add. This seems to sacrifice some type-safety over my C# approach.
Are there good workarounds for these or design patterns which make them less frustrating?
I think, you are stuck a little too much with the idea that a DU is a class hierarchy. It is more helpful to think of it as data, really. As such:
Forced public default constructor (I'd like to do type-checking and argument validation on expression construction, as
System.Linq.Expressions does with it's static factory methods)
A DU is just data, pretty much like say a string or a number, not functionality. Why don't you make a function that returns you an Expression option to express, that your data might be invalid.
Lack of named properties (seems like this is fixed in F# 3.1)
If you feel like you need named properties, you probably have an inappropriate type like say string * string * string * int * float as the data for your Expression. Better make a record instead, something like AddInfo and make your case of the DU use that instead, like say | Add of AddInfo. This way you have properties in pattern matches, intellisense, etc.
Inability to refer to a case type directly. For example, it seems like I can't declare a function that takes in only one type from the
union (e. g. let f (x : TYPE) = x compiles for Expression (the union
type) but not for Add or Expression.Add. This seems to sacrifice some
type-safety over my C# approach.
You cannot request something to be the Add case, but you definitely do can write a function, that takes an AddInfo. Plus you can always do it in a monadic way and have functions that take any Expression and only return an option. In that case, you can pattern match, that your input is of the appropriate type and return None if it is not. At the call site, you then can "use" the value in the good case, using functions like Option.bind.
Basically try not to think of a DU as a set of classes, but really just cases of data. Kind of like an enum.
You can make the implementation private. This allows you the full power of DUs in your implementation but presents a limited view to consumers of your API. See this answer to a related question about records (although it also applies to DUs).
EDIT
I can't find the syntax on MSDN, but here it is:
type T =
private
| A
| B
private here means "private to the module."
Reading about F# today and I'm not clear on one thing:
From: http://msdn.microsoft.com/en-us/library/dd233200.aspx
you need only one element of the tuple, the wildcard character (the underscore) can be used to avoid creating a new name for a variable that you do not need
let (a, _) = (1, 2)
I can't think of a time that I've been in this situation. Why would you avoid creating a variable name?
Because you don't need the value. I use this often. It documents the fact that a value is unused and saves naming variables unused, dummy, etc. Great feature if you ask me.
Interesting question. There are many trade-offs involved here.
Your comparisons have been with the Ruby programming language so perhaps the first trade-off you should consider is static typing. If you use the pattern x, _, _ then F# knows you are referring to the first element of a triple of exactly three elements and will enforce this constraint at compile time. Ruby cannot. F# also checks patterns for exhaustiveness and redundancy. Again, Ruby cannot.
Your comparisons have also used only flat patterns. Consider the patterns _, (x, _) or x, None | _, Some x or [] | [_] and so on. These are not so easily translated.
Finally, I'd mention that Standard ML is a programming language related to F# and it does provide operators called #1 etc. to extract the first element of a tuple with an arbitrary number of elements (see here) so this idea was implemented and discarded decades ago. I believe this is because SML's #n notation culminates in incomprehensible error messages within the constraints of the type system. For example, a function that uses #n is not making it clear what the arity of the tuple is but functions cannot be generic over tuple arity so this must result in an error message saying that you must give more type information but many users found that confusing. With the CAML/OCaml/F# approach there is no such confusion.
The let-binding you've given is an example of a language facility called pattern matching, which can be used to destructure many types, not just tuples. In pattern matches, underscores are the idiomatic way to express that you won't refer to a value.
Directly accessing the elements of a tuple can be more concise, but it's less general. Pattern matching allows you to look at the structure of some data and dispatch to an approprate handling case.
match x with
| (x, _, 20) -> x
| (_, y, _) -> y
This pattern match will return the first item in x only if the third element is 20. Otherwise it returns the second element. Once you get beyond trivial cases, the underscores are an important readability aid. Compare the above with:
match x with
| (x, y, 20) -> x
| (x, y, z) -> y
In the first code sample, it's much easier to tell which bindings you care about in the pattern.
Sometimes a method will return multiple values but the code you're writing is only interested in a select few (or one) of them. You can use multiple underscores to essentially ignore the values you don't need, rather than having a bunch of variables hanging around in local scope.
Why is it that functions in F# and OCaml (and possibly other languages) are not by default recursive?
In other words, why did the language designers decide it was a good idea to explicitly make you type rec in a declaration like:
let rec foo ... = ...
and not give the function recursive capability by default? Why the need for an explicit rec construct?
The French and British descendants of the original ML made different choices and their choices have been inherited through the decades to the modern variants. So this is just legacy but it does affect idioms in these languages.
Functions are not recursive by default in the French CAML family of languages (including OCaml). This choice makes it easy to supercede function (and variable) definitions using let in those languages because you can refer to the previous definition inside the body of a new definition. F# inherited this syntax from OCaml.
For example, superceding the function p when computing the Shannon entropy of a sequence in OCaml:
let shannon fold p =
let p x = p x *. log(p x) /. log 2.0 in
let p t x = t +. p x in
-. fold p 0.0
Note how the argument p to the higher-order shannon function is superceded by another p in the first line of the body and then another p in the second line of the body.
Conversely, the British SML branch of the ML family of languages took the other choice and SML's fun-bound functions are recursive by default. When most function definitions do not need access to previous bindings of their function name, this results in simpler code. However, superceded functions are made to use different names (f1, f2 etc.) which pollutes the scope and makes it possible to accidentally invoke the wrong "version" of a function. And there is now a discrepancy between implicitly-recursive fun-bound functions and non-recursive val-bound functions.
Haskell makes it possible to infer the dependencies between definitions by restricting them to be pure. This makes toy samples look simpler but comes at a grave cost elsewhere.
Note that the answers given by Ganesh and Eddie are red herrings. They explained why groups of functions cannot be placed inside a giant let rec ... and ... because it affects when type variables get generalized. This has nothing to do with rec being default in SML but not OCaml.
One crucial reason for the explicit use of rec is to do with Hindley-Milner type inference, which underlies all staticly typed functional programming languages (albeit changed and extended in various ways).
If you have a definition let f x = x, you'd expect it to have type 'a -> 'a and to be applicable on different 'a types at different points. But equally, if you write let g x = (x + 1) + ..., you'd expect x to be treated as an int in the rest of the body of g.
The way that Hindley-Milner inference deals with this distinction is through an explicit generalisation step. At certain points when processing your program, the type system stops and says "ok, the types of these definitions will be generalised at this point, so that when someone uses them, any free type variables in their type will be freshly instantiated, and thus won't interfere with any other uses of this definition."
It turns out that the sensible place to do this generalisation is after checking a mutually recursive set of functions. Any earlier, and you'll generalise too much, leading to situations where types could actually collide. Any later, and you'll generalise too little, making definitions that can't be used with multiple type instantiations.
So, given that the type checker needs to know about which sets of definitions are mutually recursive, what can it do? One possibility is to simply do a dependency analysis on all the definitions in a scope, and reorder them into the smallest possible groups. Haskell actually does this, but in languages like F# (and OCaml and SML) which have unrestricted side-effects, this is a bad idea because it might reorder the side-effects too. So instead it asks the user to explicitly mark which definitions are mutually recursive, and thus by extension where generalisation should occur.
There are two key reasons this is a good idea:
First, if you enable recursive definitions then you can't refer to a previous binding of a value of the same name. This is often a useful idiom when you are doing something like extending an existing module.
Second, recursive values, and especially sets of mutually recursive values, are much harder to reason about then are definitions that proceed in order, each new definition building on top of what has been already defined. It is nice when reading such code to have the guarantee that, except for definitions explicitly marked as recursive, new definitions can only refer to previous definitions.
Some guesses:
let is not only used to bind functions, but also other regular values. Most forms of values are not allowed to be recursive. Certain forms of recursive values are allowed (e.g. functions, lazy expressions, etc.), so it needs an explicit syntax to indicate this.
It might be easier to optimize non-recursive functions
The closure created when you create a recursive function needs to include an entry that points to the function itself (so the function can recursively call itself), which makes recursive closures more complicated than non-recursive closures. So it might be nice to be able to create simpler non-recursive closures when you don't need recursion
It allows you to define a function in terms of a previously-defined function or value of the same name; although I think this is bad practice
Extra safety? Makes sure that you are doing what you intended. e.g. If you don't intend it to be recursive but you accidentally used a name inside the function with the same name as the function itself, it will most likely complain (unless the name has been defined before)
The let construct is similar to the let construct in Lisp and Scheme; which are non-recursive. There is a separate letrec construct in Scheme for recursive let's
Given this:
let f x = ... and g y = ...;;
Compare:
let f a = f (g a)
With this:
let rec f a = f (g a)
The former redefines f to apply the previously defined f to the result of applying g to a. The latter redefines f to loop forever applying g to a, which is usually not what you want in ML variants.
That said, it's a language designer style thing. Just go with it.
A big part of it is that it gives the programmer more control over the complexity of their local scopes. The spectrum of let, let* and let rec offer an increasing level of both power and cost. let* and let rec are in essence nested versions of the simple let, so using either one is more expensive. This grading allows you to micromanage the optimization of your program as you can choose which level of let you need for the task at hand. If you don't need recursion or the ability to refer to previous bindings, then you can fall back on a simple let to save a bit of performance.
It's similar to the graded equality predicates in Scheme. (i.e. eq?, eqv? and equal?)
I have been trying to explain the difference between switch statements and pattern matching(F#) to a couple of people but I haven't really been able to explain it well..most of the time they just look at me and say "so why don't you just use if..then..else".
How would you explain it to them?
EDIT! Thanks everyone for the great answers, I really wish I could mark multiple right answers.
Having formerly been one of "those people", I don't know that there's a succinct way to sum up why pattern-matching is such tasty goodness. It's experiential.
Back when I had just glanced at pattern-matching and thought it was a glorified switch statement, I think that I didn't have experience programming with algebraic data types (tuples and discriminated unions) and didn't quite see that pattern matching was both a control construct and a binding construct. Now that I've been programming with F#, I finally "get it". Pattern-matching's coolness is due to a confluence of features found in functional programming languages, and so it's non-trivial for the outsider-looking-in to appreciate.
I tried to sum up one aspect of why pattern-matching is useful in the second of a short two-part blog series on language and API design; check out part one and part two.
Patterns give you a small language to describe the structure of the values you want to match. The structure can be arbitrarily deep and you can bind variables to parts of the structured value.
This allows you to write things extremely succinctly. You can illustrate this with a small example, such as a derivative function for a simple type of mathematical expressions:
type expr =
| Int of int
| Var of string
| Add of expr * expr
| Mul of expr * expr;;
let rec d(f, x) =
match f with
| Var y when x=y -> Int 1
| Int _ | Var _ -> Int 0
| Add(f, g) -> Add(d(f, x), d(g, x))
| Mul(f, g) -> Add(Mul(f, d(g, x)), Mul(g, d(f, x)));;
Additionally, because pattern matching is a static construct for static types, the compiler can (i) verify that you covered all cases (ii) detect redundant branches that can never match any value (iii) provide a very efficient implementation (with jumps etc.).
Excerpt from this blog article:
Pattern matching has several advantages over switch statements and method dispatch:
Pattern matches can act upon ints,
floats, strings and other types as
well as objects.
Pattern matches can act upon several
different values simultaneously:
parallel pattern matching. Method
dispatch and switch are limited to a single
value, e.g. "this".
Patterns can be nested, allowing
dispatch over trees of arbitrary
depth. Method dispatch and switch are limited
to the non-nested case.
Or-patterns allow subpatterns to be
shared. Method dispatch only allows
sharing when methods are from
classes that happen to share a base
class. Otherwise you must manually
factor out the commonality into a
separate function (giving it a
name) and then manually insert calls
from all appropriate places to your
unnecessary function.
Pattern matching provides redundancy
checking which catches errors.
Nested and/or parallel pattern
matches are optimized for you by the
F# compiler. The OO equivalent must
be written by hand and constantly
reoptimized by hand during
development, which is prohibitively
tedious and error prone so
production-quality OO code tends to
be extremely slow in comparison.
Active patterns allow you to inject
custom dispatch semantics.
Off the top of my head:
The compiler can tell if you haven't covered all possibilities in your matches
You can use a match as an assignment
If you have a discriminated union, each match can have a different 'type'
Tuples have "," and Variants have Ctor args .. these are constructors, they create things.
Patterns are destructors, they rip them apart.
They're dual concepts.
To put this more forcefully: the notion of a tuple or variant cannot be described merely by its constructor: the destructor is required or the value you made is useless. It is these dual descriptions which define a value.
Generally we think of constructors as data, and destructors as control flow. Variant destructors are alternate branches (one of many), tuple destructors are parallel threads (all of many).
The parallelism is evident in operations like
(f * g) . (h * k) = (f . h * g . k)
if you think of control flowing through a function, tuples provide a way to split up a calculation into parallel threads of control.
Looked at this way, expressions are ways to compose tuples and variants to make complicated data structures (think of an AST).
And pattern matches are ways to compose the destructors (again, think of an AST).
Switch is the two front wheels.
Pattern-matching is the entire car.
Pattern matches in OCaml, in addition to being more expressive as mentioned in several ways that have been described above, also give some very important static guarantees. The compiler will prove for you that the case-analysis embodied by your pattern-match statement is:
exhaustive (no cases are missed)
non-redundant (no cases that can never be hit because they are pre-empted by a previous case)
sound (no patterns that are impossible given the datatype in question)
This is a really big deal. It's helpful when you're writing the program for the first time, and enormously useful when your program is evolving. Used properly, match-statements make it easier to change the types in your code reliably, because the type system points you at the broken match statements, which are a decent indicator of where you have code that needs to be fixed.
If-Else (or switch) statements are about choosing different ways to process a value (input) depending on properties of the value at hand.
Pattern matching is about defining how to process a value given its structure, (also note that single case pattern matches make sense).
Thus pattern matching is more about deconstructing values than making choices, this makes them a very convenient mechanism for defining (recursive) functions on inductive structures (recursive union types), which explains why they are so abundantly used in languages like Ocaml etc.
PS: You might know the pattern-match and If-Else "patterns" from their ad-hoc use in math;
"if x has property A then y else z" (If-Else)
"some term in p1..pn where .... is the prime decomposition of x.." ((single case) pattern match)
Perhaps you could draw an analogy with strings and regular expressions? You describe what you are looking for, and let the compiler figure out how for itself. It makes your code much simpler and clearer.
As an aside: I find that the most useful thing about pattern matching is that it encourages good habits. I deal with the corner cases first, and it's easy to check that I've covered every case.