Bluish Coder

Fun Factor Libraries

Factor is a programming language I've written about before and in the early days of Factor development I wrote a number of libraries and contributed to development. It's been a while since I've contributed but I still use Factor. The development environment has a very Smalltalk-like feel to it and it includes full documentation and browseable source code of libraries.

This post isn't about Factor the language, but is about some of the neat fun libraries that people have written that shows off the graphical development system a bit.

Minesweeper

The first example is an implementation of the game Minesweeper in Factor. A blog post by the author explains the implementation. To run it inside Factor, do the following:

"minesweeper" run

A new window will open showing the game. Help can be shown with:

"minesweeper" help

XKCD

Another fun example is displaying XKCD comics inside the Factor REPL. The implementation is explained by the author here.

USE: xkcd
latest-xkcd.
...comic displayed here...
random-xkcd.
...comic displayed here...

Wikipedia

If it seems like all the examples I'm using are from the excellent re-factor blog - well, most of them are. This blog post from re-factor shows pulling historical facts from Wikipedia:

USE: wikipedia
USE: calendar

today historical-events.
...a list of historical events from wikipedia for today...

yesterday historical-births.
...a list of historical births from wikipedia for yesterday...

5 weeks ago historical-deaths.
...a list of historical deaths from wikipedia for five weeks ago...

The items in the list are graphical elements that can be manipulated. Left clicking on the coloured words will open a URL in the default web browser. Right clicking allows you to push the element on the Factor stack and manipulate it.

The calendar vocab has a lot of interesting words that allow doing calculations like "5 weeks ago".

Hacker News

There's a hacker-news vocabulary that provides words to list current articles on the Hacker News website. Like the previous Wikipedia example, the graphical elements are clickable objects:

USE: hacker-news

hacker-news-top.
...list of top articles...

hacker-news-show.
...list articles related to showing projects...

CPU 8080 Emulator

A number of years ago I wrote a CPU 8080 emulator in Factor and used this to implement a Space Invaders Emulator and then emulators for a couple of other 8080 arcade games, Balloon Bomber and Lunar Rescue. These examples require the original arcade ROMs and instructions for using them are in the online help:

"rom.space-invaders" run
...opens in a new window...
"rom.balloon-bomber" run
...opens in a new window...
"rom.lunar-rescue" run
...opens in a new window...

"rom.space-invaders" help
...displays help...

Gopher Implementation

Another magical implementation from the re-factor blog, a Gopher server and a graphical Gopher Client. This is a video I made of the gopher client on YouTube:

I also did a video that shows some Factor development tools on the running Gopher client to show how everything is live in Factor:

And More

There's much more buried inside Factor. The list of articles and list of vocabularies from the online help is a good way to explore. This help system is also available offline in a Factor install. By default many libraries aren't loaded when Factor starts but you can force loading everything using load-all:

load-all
...all vocabs are loaded - prepare to wait for a while...
save
...saves the image so when factor is restarted the vocabs remain loaded...

The benefit of doing this while developing is all the online help, source and words are available via the inbuilt tools like "apropos", "usage", etc.

Defining Types in Shen

The Shen programming language has an extensible type system. Types are defined using sequent calculus and the system is powerful enough to create a variety of exotic types but it can be difficult when first starting with Shen to know how to use that power. In this post I hope to go through some basic examples of defining types in Shen without needing to know too much sequent calculus details.

For an overview of Shen there is Shen in 15 minutes and the Shen OS Kernel Manual. An interactive JavaScript REPL exists to try examples in the browser or pick on one of the existing Shen language ports. For these examples I'm using my Wasp Lisp port of Shen.

Shen is optionally typed. The type checker can be turned off and on. By default it is off and this can be seen in the Shen prompt by the presence of a '-' character:

(0-) ...shen code...

Turning type checking on is done by using (tc +). The '-' in the prompt changes to a '+' to show type checking is active. It can be turned off again with (tc -):

(0-) (tc +)
(1+) (tc -)
(2-) ...

Types in Shen are defined using datatype. The body of the datatype definition contains a series of sequent calculus rules. These rules define how an object in Shen can be proved to belong to a particular type. Rather than go through a detailed description of sequent calculus, I'm going to present common examples of types in Shen to learn by example and dive into details as needed. There's the Shen Language Book for much more detail if needed.

Records

One way of storing collections of data in Shen is to use lists or vectors. For example, given an the concept of a 'person' that has a name and age, this can be stored in a list with functions to get the relevent data:

(tc -)

(define make-person
  Name Age -> [Name Age])

(define get-name
  [Name Age] -> Name)

(define get-age
  [Name Age] -> Age)

(get-age (make-person "Person1" 42))
 => 42

In the typed subset of Shen we can define a type for this person object using datatype:

(datatype person
  N : string; A : number;
  _______________________
  [N A] : person;)

This defines one sequent calculus rule. The way to read it is starting with the code below the underscore line, followed by the code above it. In this case the rule states that if an expression matching the pattern [N A] is encountered, where N is a string and A is a number, then type that expression as person. With that rule defined, we can ask Shen if lists are of the type person:

(0+) ["Person" 42] : person
["Person1" 42] : person

(1+) ["Person1" "Person1"] : person
[error shen "type error"]

(2+) ["Person 42"]
["Person1" 42] : person

Given this person type, we might write a get-age function that is typed such that it only works on person objects as follows (The { ...} syntax in function definitions provides the expected type of the function):

(define get-age
  { person --> number }
  [N A] -> A)
[error shen "type error in rule 1 of get-age"]

Shen rejects this definition as not being type safe. The reason for this is because our datatype definition only states that [N A] is a person if N is a string and A is a number. It does not state that a person object is constructed only of a string and number. For example, we could have an additional definition as follows:

(datatype person2
  N : string; A : string;
  _______________________
  [N A] : person;)

Now we can create different types of person objects:

(0+) ["Person" 42 ] : person
["Person" 42] : person

(1+) ["Person" "young"] : person
["Person" "young"] : person

get-age is obviously badly typed in the presence of this additional type of person which is why Shen rejected it originally. To resolve this we need to tell Shen that an [N A] is a person if and only if N is a string and A is a person. This is done with what is called a 'left rule'. Such a rule defines how a person object can be deconstructed. It looks like this:

(datatype person3
  N : string, A: number >> P;
  ___________________________
  [N A] : person >> P;)

The way to read this type of rule is that, if [N A] is a person then N is a string and A is a number. With that loaded into Shen, get-age type checks:

(define get-age
   { person --> number }
   [N A] -> A)
get-age : (person --> number)

(0+) (get-age ["Person" 42])
42 : number

The need to create a left rule, dual to the right rule, is common enough that Shen has a short method of defining both in one definition. It looks like this - note the use of '=' instead of '_' in the separator line:

(datatype person
   N : string; A : number;
   =======================
   [N A] : person;)

(define get-age
   { person --> number }
   [N A] -> A)
get-age : (person --> number)

(0+) (get-age ["Person" 42])
42 : number

The above datatype is equivalent to declaring the two rules:

(datatype person
  N : string; A : number;
  _______________________
  [N A] : person;

  N : string, A: number >> P;
  ___________________________
  [N A] : person >> P;)

Controlling type checking

When progamming at the REPL of Shen it's common to create datatype definitions that are no longer needed, or part of a line of thought you don't want to pursue. Shen provides ways of excluding or including rules in the typechecker as needed. When defining a set of rules in a datatype, that datatype is given a name:

(datatype this-is-the-name
   ...
)

The rules within that definition can be removed from selection by the typechecker using preclude, which takes a list of datatype names to ignore during type checking:

(preclude [this-is-the-name])

To re-add a dataype, use include:

(include [this-is-the-name])

There is also include-all-but and preclude-all-but to include or remove all but the listed names. These commands are useful for removing definitions you no longer want to use at the REPL, but also for speeding up type checking in a given file if you know the file only uses a particular set of datatypes.

Enumerations

An example of an enumeration type would be days of the week. In an ML style language this can be done like:

datatype days =   monday | tuesday | wednesday
                | thursday | friday | saturday | sunday

In Shen this would be done using multiple sequent calculus rules.

(datatype days
    ____________
    monday : day;

    ____________
    tuesday : day;

    ____________
    wednesday : day;

    ____________
    thursday : day;

    ____________
    friday : day;

    ____________
    saturday : day;

    ____________
    sunday : day;)

Here there are no rules above the dashed underscore line, meaning that the given symbol is of the type day. A function that uses this type would look like:

(define day-number
  { day --> number }
  monday    -> 0
  tuesday   -> 1
  wednesday -> 2
  thursday  -> 3
  friday    -> 4
  saturday  -> 5
  sunday    -> 6)

It's quite verbose to define a number of enumeration types like this. It's possible to add a test above the dashed underline which allows being more concise. The test is introduced using if:

(datatype days
  if (element? Day [monday tuesday wednesday thursday friday saturday sunday])
  ____________________________________________________________________________
  Day : day;)

(0+) monday : day
monday : day

Any Shen code can be used in these test conditions. Multiple tests can be combined:

(datatype more-tests
  if (number? X)
  if (>= X 5)
  if (<= X 10)
  ___________
  X : between-5-and-10;)

  (2+) 5 : between-5-and-10
  5 : between-5-and-10

  (3+) 4 : between-5-and-10
  [error shen "type error\n"]

Polymorphic types

To create types that are polymorphic (ie. generic), like the built-in list type, include a free variable representing the type. For example, something like the built in list where the list elements are stored as pairs can be approximated with:

(datatype my-list
   _____________________
   my-nil : (my-list A);

   X : A; Y : (my-list A);
   ========================
   (@p X Y) : (my-list A);)


(define my-cons
  { A --> (my-list A) --> (my-list A) }
  X Y -> (@p X Y))

(0+) (my-cons 1 my-nil)
(@p 1 my-nil) : (my-list number)

(1+) (my-cons 1 (my-cons 2 my-nil))
(@p 1 (@p 2 my-nil)) : (my-list number)

(2+) (my-cons "a" (my-cons "b" my-nil))
(@p "a" (@p "b" my-nil)) : (my-list string)

Notice the use of the '=====' rule to combine left and right rules. This is required to enable writing something like my-car which requires proving that the type of the car of the list is of type A:

(define my-car
   { (my-list A) --> A }
   (@p X Y) -> X)

List encoded with size

Using peano numbers we can create a list where the length of the list is part of the type:

(datatype list-n
  ______
  [] : (list-n zero A);

  X : A; Y : (list-n N A);
  ================================
  [ X | Y ] : (list-n (succ N) A);)      

(define my-tail
  { (list-n (succ N) A) --> (list-n N A) }
  [Hd | Tl] -> Tl)

(define my-head
  { (list-n (succ N) A) --> A }
  [Hd | Tl] -> Hd)

This gives a typesafe head and tail operation whereby they can't be called on an empty list:

(0+) [] : (list-n zero number)
[] : (list-n zero number)

(1+) [1] : (list-n (succ zero) number)
[1] : (list-n (succ zero) number)

(2+) (my-head [])
[error shen "type error\n"]

(3+) (my-head [1])
1 : number

(4+) (my-tail [1 2 3])
[2 3] : (list-n (succ (succ zero)) number)

(5+) (my-tail [])
[error shen "type error\n"]      

Power and Responsibility

Shen gives a lot of power in creating types, but trusts you to make those types consistent. For example, the following creates an inconsistent type:

(datatype person
  N : string; A : number;
  _______________________
  [N A] : person;

  N : string; A : string;
  _______________________
  [N A] : person;

  N : string, A: number >> P;
  ___________________________
  [N A] : person >> P;)

Here we are telling Shen that a string and number in a list is a person, and so too is a string and another string. But the third rule states that given a person, that is is composed of a string and a number only. This leads to:

(0+) (get-age ["Person" "Person"])
...

This will hang for a long time as Shen attempts to resolve the error we've created.

Conclusion

Shen provides a programmable type system, but the responsibility lies on the programmer for making sure the types are consisitent. The examples given here provide a brief overview. For much more see The Book of Shen. The Shen OS Kernel Manual also gives some examples. There are posts on the Shen Mailing List that have more advanced examples of Shen types. Mark Tarver has a case study showing converting a lisp interpreter in Shen to use types.

Getting Started with Mercury

Mercury is a logic programming language, similar to Prolog, but with static types. It feels like a combination of SML and Prolog at times. It was designed to help with programming large systems - that is large programs, large teams and better reliability, etc. The commercial product Prince XML is written in Mercury.

I've played around with Mercury in the past but haven't done anything substantial with it. Recently I picked it up again. This post is a short introduction to building Mercury, and some example "Hello World" style programs to test the install.

Build

Mercury is written in the Mercury language itself. This means it needs a Mercury compiler to bootstrap from. The way I got a build going from source was to download the source for a release of the day version, build that, then use that build to build the Mercury source from github. The steps are outlined in the README.bootstrap file, but the following commands are the basic steps:

$ wget http://dl.mercurylang.org/rotd/mercury-srcdist-rotd-2019-06-22.tar.gz
$ tar xvf mercury-srcdist-rotd-2019-06-22.tar.gz
$ cd mercury-srcdist-rotd-2019-06-22
$ ./configure --enable-minimal-install --prefix=/tmp/mercury
$ make
$ make install
$ cd ..
$ export PATH=/tmp/mercury/bin:$PATH

With this minimal compiler the main source can be built. Mercury has a number of backends, called 'grades' in the documentation. Each of these grades makes a number of tradeoffs in terms of generated code. They define the platform (C, assembler, Java, etc), whether GC is used, what type of threading model is available (if any), etc. The Adventures in Mercury blog has an article on some of the different grades. Building all of them can take a long time - multiple hours - so it pays to limit it if you don't need some of the backends.

For my purposes I didn't need the CSharp backend, but wanted to explore the others. I was ok with the time tradeoff of building the system. To build from the master branch of the github repository I did the following steps:

$ git clone https://github.com/Mercury-Language/mercury
$ cd mercury
$ ./prepare.sh
$ ./configure --enable-nogc-grades --disable-csharp-grade \
              --prefix=/home/myuser/mercury
$ make PARALLEL=-j4
$ make install PARALLEL=-j4
$ export PATH=/home/myuser/mercury/bin:$PATH

Change the prefix to where you want Mercury installed. Add the relevant directories to the PATH as specified by the end of the build process.

Hello World

A basic "Hello World" program in Mercury looks like the following:

:- module hello.

:- interface.
:- import_module io.
:- pred main(io, io).
:- mode main(di, uo) is det.

:- implementation.
main(IO0, IO1) :-
    io.write_string("Hello World!\n", IO0, IO1).

With this code in a hello.m file, it can be built and run with:

$ mmc --make hello
Making Mercury/int3s/hello.int3
Making Mercury/ints/hello.int
Making Mercury/cs/hello.c
Making Mercury/os/hello.o
Making hello    
$ ./hello
Hello World!

The first line defines the name of the module:

:- module hello.

Following that is the definitions of the public interface of the module:

:- interface.
:- import_module io.
:- pred main(io, io).
:- mode main(di, uo) is det.

We publically import the io module, as we use io definitions in the main predicate. This is followed by a declaration of the interface of main - like C this is the user function called by the runtime to execute the program. The definition here declares that main is a predicate, it takes two arguments, of type io. This is a special type that represents the "state of the world" and is how I/O is handled in Mercury. The first argument is the "input world state" and the second argument is the "output world state". All I/O functions take these two arguments - the state of the world before the function and the state of the world after.

The mode line declares aspects of a predicate related to the logic programming side of things. In this case we declare that the two arguments passed to main have the "destructive input" mode and the "unique output" mode respectively. These modes operate similar to how linear types work in other languages, and the reference manual has a section describing them. For now the details can be ignored. The is det portion identifies the function as being deterministic. It always succeeds, doesn't backtrack and only has one result.

The remaining code is the implementation. In this case it's just the implementation of the main function:

main(IO0, IO1) :-
    io.write_string("Hello World!\n", IO0, IO1).

The two arguments to main, are the io types representing the before and after representation of the world. We call write_string to display a string, passing it the input world state, IO0 and receiving the new world state in IO1. If we wanted to call an additional output function we'd need to thread these variables, passing the obtained output state as the input to the new function, and receiving a new output state. For example:

main(IO0, IO1) :-
    io.write_string("Hello World!\n", IO0, IO1),
    io.write_string("Hello Again!\n", IO1, IO2).

This state threading can be tedious, especially when refactoring - the need to renumber or rename variables is a pain point. Mercury has syntactic sugar for this called state variables, enabling this function to be written like this:

main(!IO) :-
    io.write_string("Hello World!\n", !IO),
    io.write_string("Hello Again!\n", !IO).

When the compiler sees !Variable_name in an argument list it creates two arguments with automatically generated names as needed.

Another syntactic short cut can be done in the pred and mode lines. They can be combined into one line that looks like:

:- pred main(io::di, io::uo) is det.

Here the modes di and uo are appended to the type prefixed with a ::. The resulting program looks like:

- module hello.

:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.

:- implementation.
main(!IO) :-
    io.write_string("Hello World!\n", !IO),
    io.write_string("Hello Again!\n", !IO).

Factorial

The following is an implementation of factorial:

:- module fact.

:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.

:- implementation.
:- import_module int.
:- pred fact(int::in, int::out) is det.

fact(N, X) :-
  ( N = 1 -> X = 1 ; fact(N - 1, X0), X = N * X0 ).

main(!IO) :-
  fact(5, X),
  io.print("fact(5, ", !IO),
  io.print(X, !IO),
  io.print(")\n", !IO).

In the implementation section here we import the int module to access functions across machine integers. The fact predicate is declared to take two arguments, both of type int, the first an input argument and the second an output argument.

The definition of fact uses Prolog syntax for an if/then statement. It states that if N is 1 then (the -> token) the output variable, X is 1. Otherwise (the ; token), calculate the factorial recursively using an intermediate variable X0 to hold the temporary result.

There's a few other ways this could be written. Instead of the Prolog style if/then, we can use an if/then syntax that Mercury has:

fact(N, X) :-
  ( if N = 1 then X = 1 else fact(N - 1, X0), X = N * X0 ).

Instead of using predicates we can declare fact to be a function. A function has no output variables, instead it returns a result just like functions in standard functional programming languages. The changes for this are to declare it as a function:

:- func fact(int) = int.
fact(N) = X :-
  ( if N = 1 then X = 1 else X = N * fact(N - 1) ).

main(!IO) :-
  io.print("fact(5, ", !IO),
  io.print(fact(5), !IO),
  io.print(")\n", !IO)

Notice now that the call to fact looks like a standard function call and is inlined into the print call in main. A final syntactic shortening of function implementations enables removing the X return variable name and returning directly:

fact(N) = (if N = 1 then 1 else N * fact(N - 1)).

Because this implementation uses machine integers it won't work for values that can overflow. Mercury comes with an arbitrary precision integer module, integer, that allows larger factorials. Replacing the use of the int module with integer and converting the static integer numbers is all that is needed:

:- module fact.

:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.

:- implementation.
:- import_module integer.
:- func fact(integer) = integer.

fact(N) = (if N = one then one else N * fact(N - one)).

main(!IO) :-
  io.print("fact(1000, ", !IO),
  io.print(fact(integer(1000)), !IO),
  io.print(")\n", !IO).

Conclusion

There's a lot more to Mercury. These are just first steps to test the system works. I'll write more about it in later posts. Some further reading:

• Adventures in Mercury
• Library reference manual
• Users guide
• Language Reference Manual
• Ralph Becket Mercury Tutorial (PDF)
• Mercury Wiki

Generalized Algebraic Data Types in ATS

The ATS programming language supports defining Generalized Algebraic Data Types (GADTS). They allow defining datatypes where the constructors for the datatype are explicitly defined by the programmer. This has a number of uses and I'll go through some examples in this post. GADTs are sometimes referred to as Guarded Recursive Datatypes.

Some useful resources for reading up on GADTs that I used to write this post are:

• Wikipedia page on GADT
• Haskell/GADT Wikibook
• GADTs for Dummies
• Guarded Recursive Datatype Constructors

The examples here were tested with ATS2-0.3.11.

Arithmetic Expressions

This is probably the most common demonstration of GADT usage and it's useful to see how to do it in ATS. The example is taken from the Haskell/GADT Wikibook.

First we'll create datatype to represent a simple expression language, and write an evaluation function for it, without using GADTs:

#include "share/atspre_define.hats"
#include "share/atspre_staload.hats"

datatype Expr  =
  | I of int
  | Add of (Expr, Expr)
  | Mul of (Expr, Expr)

fun eval (x:Expr): int =
  case+ x of
  | I i => i
  | Add (t1, t2) => eval(t1) + eval(t2)
  | Mul (t1, t2) => eval(t1) * eval(t2)


implement main0() = let
  val term = Mul(I(2), I(4))
  val res = eval(term)
in
  println!("res=", res)
end

Expr is a datatype with three constructors. I represents an integer, Add adds two expressions together and Mul multiples two expressions. The eval function pattern matches on these and evaluates them. The example can be compiled with the following if placed in a file arith1.dats:

$ patscc -DATS_MEMALLOC_LIBC -o arith1 arith1.dats
$ ./arith1
res=8

Now we extend the expression language with another type, booleans, and add an Expr constructor to compare for equality:

datatype Expr  =
  | I of int
  | B of bool
  | Add of (Expr, Expr)
  | Mul of (Expr, Expr)
  | Eq of (Expr, Expr)

(* Does not typecheck *)
fun eval (x:Expr): int =
  case+ x of
  | I i => i
  | B b => b
  | Add (t1, t2) => eval(t1) + eval(t2)
  | Mul (t1, t2) => eval(t1) * eval(t2)
  | Eq (t1, t2) => eval(t1) = eval(t2)

This code fails to typecheck - the eval function is defined to return an int but the B b pattern match returns a boolean. We can work around this by making the result value of eval return a datatype that can represent either an int or a bool but then we have to add code throughout eval to detect the invalid addition or multiplication of a boolean and raise a runtime error. Ideally we'd like to have make it impossible to construct invalid expressions such that they error out at compile time.

We can imagine the type constructors for Expr as if they were functions with a type signature. The type signature of the constructors would be:

fun I(n:int): Expr
fun B(b:bool): Expr
fun Add(t1:Expr, t2:Expr): Expr
fun Mul(t1:Expr, t1:Expr): Expr
fun Eq(t1:Expr, t2:Expr): Expr

The problem here is that Add and Mul both take Expr as arguments but we want to restrict them to integer expressions only - we need to differentiate between integer and boolean expressions. We'd like to add a type index to the Expr datatype that indicates if it is a boolean or an integer expression and change the constructors so they have types like:

fun I(n:int): Expr int
fun B(b:bool): Expr bool
fun Add(t1:Expr int, t2:Expr int): Expr int
fun Mul(t1:Expr int, t1:Expr int): Expr int
fun Eq(t1:Expr int, t2:Expr int): Expr bool

Using these constructors would make it impossible to create an expression that would give a runtime error in an eval function. Creating an Expr with a type index looks like:

datatype Expr(a:t@ype)  =
  | I(a) of int
  | B(a) of bool
  | Add(a) of (Expr int, Expr int)
  | Mul(a) of (Expr int, Expr int)
  | Eq(a) of (Expr int, Expr int)

This adds a type index of sort t@ype. A 'sort' in ATS is the type of type indexes. The t@ype is for types that have a flat memory structure of an unknown size. The '@' sigil looks odd inside the name, but '@' is used elsewhere in ATS when defining flat records and tuples which is a useful mnemonic for remembering what the '@' within the sort name means.

This doesn't help our case though as the type signatures for the constructors would be:

fun I(n:int): Expr a
fun B(b:bool): Expr a
fun Add(t1:Expr int, t2:Expr int): Expr a
fun Mul(t1:Expr int, t1:Expr int): Expr a
fun Eq(t1:Expr int, t2:Expr int): Expr a

There is still the problem that an Expr a is not an Expr int for Add, Mul and Eq, and requiring runtime errors when pattern matching. This is where GADTs come in. GADTs enable defining a datatype that provides constructors where the generic a of the type index can be constrained to a specific type, different for each constructor. The Expr datatype becomes:

datatype Expr(t@ype)  =
  | I(int) of int
  | B(bool) of bool
  | Add(int) of (Expr int, Expr int)
  | Mul(int) of (Expr int, Expr int)
  | Eq(bool) of (Expr int, Expr int)

The constructor type signature now match those that we wanted earlier and it becomes possible to check at compile time for invalid expressions. The eval functions looks similar, but is parameterized over the type index:

fun{a:t@ype} eval(x:Expr a): a =
  case+ x of
  | I i => i
  | B b => b
  | Add (t1, t2) => eval(t1) + eval(t2)
  | Mul (t1, t2) => eval(t1) * eval(t2)
  | Eq (t1, t2) => eval(t1) = eval(t2)

The "{a:t@ype}" syntax following fun is ATS' way of defining a function template where a is the template argument. ATS will generate a new function specific for each a type used in the program.

An example main function to demonstrate the new GADT enabled Expr and eval:

implement main0() = let
  val term1 = Eq(I(5), Add(I(1), I(4)))
  val term2 = Mul(I(2), I(4))
  val res1 = eval(term1)
  val res2 = eval(term2)
in
  println!("res1=", res1, " and res2=", res2)
end

$ patscc -DATS_MEMALLOC_LIBC -o arith2 arith2.dats
$ ./arith2
res1=true and res2=8

You may have noticed that our Expr type can't represent equality between booleans, or between booleans and integers. It's defined to only allow equality between integers. It's possible to make equality polymorphic but I'll go through this later as it brings up some more complicated edge cases in types with ATS beyond just using GADTs.

Typesafe sprintf

This example of GADT usage in ATS tries to implement a sprintf function that allows providing a format specification to sprintf which then processes it and accepts arguments of types as defined by the format specification.

The format specification is defined as a GADT:

datatype Format (a:type) =
  | I(int -<cloref1> a) of (Format a)
  | S_(a) of (string, Format a)
  | S0(string) of string

Each constructor represents part of a format string. The type index is the type that sprintf will return given a format string for that type. sprintf is declared as:

fun sprintf {a:type} (fmt: Format a): a

Here are some example invocations and the types that should result:

// Returns a string
sprintf (S0 "hello")

// Returns a string
sprintf (S_ ("hello", S0 "world"))

// Returns a function that takes an int and returns a string
sprintf (I (S0 "<- is a number"))

The last example shows how sprintf emulates variable arguments using closures. By returning a function any immediately following tokens are treated as arguments to that function. For example:

sprintf (I (S0 "<- is a number")) 42
(int -> string) 42

With some syntactic sugar using currying we can make this look nicer. Curried functions is a feature that isn't often used in ATS as it requires the garbage collector (to clean up partially curried functions) and performance is diminished due to the allocation of closures but it's useful for this example.

With the Format datatype defined, here's the implementation of sprintf:

fun sprintf {a:type} (fmt: Format a): a = let
  fun aux {a:type}(pre: string, fmt': Format a): a =
    case fmt' of
    | I fmt => (lam (i) => aux(append(pre, int2string(i)), fmt))
    | S_ (s, fmt) => aux(append(pre, s), fmt)
    | S0 s => append(pre, s)
in
  aux("", fmt)
end

It uses an inner function, aux, that does the work of deconstructing the format argument and returning a closure when needed, and appending strings as the result string is computed. For this example I'm cheating with memory management to keep the focus on GADT, and off dealing with the intricacies of linear strings. The example should be run with the garbage collector to free the allocated strings.

Here's an example of executing what we have so far:

implement main0() = let
  val fmt = S_ ("X: ", (I (S_ (" Y: ", (I (S0 ""))))))
  val s = sprintf fmt 5 10
in
  println!(s)
end

$ ./format
X: 5 Y: 10

The format string is pretty ugly though. Some helper functions make it a bit more friendly:

fun Str {a:type} (s: string) (fmt: Format a) = S_ (s, fmt)
fun Int {a:type} (fmt: Format a) = I (fmt)
fun End (s:string) = S0 (s)

infixr 0 >:
macdef >: (f, x) = ,(f) ,(x)

Now the format definition is:

val fmt = Str "X: " >: Int >: Str " Y: " >: Int >: End ""

The string handling functions that I threw together to append strings and convert an integer to a string without dealing with linear strings follow.

fun append(s0: string, s1: string): string = let
  extern castfn from(s:string):<> Strptr1
  extern castfn to(s:Strptr0):<> string
  extern prfun drop(s:Strptr1):<> void
  val s0' = from(s0)
  val s1' = from(s1)
  val r = strptr_append(s0', s1')
  prval () = drop(s0')
  prval () = drop(s1')
in
  to(r)
end

fun int2string(x: int): string =
  tostring(g0int2string x) where {
    extern castfn tostring(Strptr0):<> string
  }

Issues

These example of GADT usage were pulled from the papers and articles mentioned at the beginning of the post. They were written for Haskell or Dependent ML (a predecessor to ATS). There may be better ways of approaching the problem in ATS and some constraints on the way ATS generates C code limits how GADTs can be used. One example of the limitation was mentioned in the first example of the expression evaluator.

If the Expr datatype is changed so that Eq can work on any type, not just int, then a compile error results:

datatype Expr(a:t@ype)  =
  | I(a) of int
  | B(a) of bool
  | Add(a) of (Expr int, Expr int)
  | Mul(a) of (Expr int, Expr int)
  | Eq(a) of (Expr a, Expr a)

The error occurs due to the Eq branch in the case statement in eval:

fun{a:t@ype} eval(x:Expr a): a =
  case+ x of
  | I i => i
  | B b => b
  | Add (t1, t2) => eval(t1) + eval(t2)
  | Mul (t1, t2) => eval(t1) * eval(t2)
  | Eq (t1, t2) => eval(t1) = eval(t2)

The compiler is unable to find a match for the overloaded = call for the general case of any a (vs the specific case of int as it was before). This is something I've written about before and the workaround in that post gets us past that error:

extern fun{a:t@ype} equals(t1:a, t2:a): bool
implement equals<int>(t1,t2) = g0int_eq(t1,t2)
implement equals<bool>(t1,t2) = eq_bool0_bool0(t1,t2)

fun{a:t@ype} eval(x:Expr a): a =
  case+ x of
  | I i => i
  | B b => b
  | Add (t1, t2) => eval(t1) + eval(t2)
  | Mul (t1, t2) => eval(t1) * eval(t2)
  | Eq (t1, t2) => equals(eval(t1), eval (t2))

Now the program typechecks but fails to compile the generated C code. This can usually be resolved by explicitly stating the template parameters in template function calls:

fun{a:t@ype} eval(x:Expr a): a =
  case+ x of
  | I i => i
  | B b => b
  | Add (t1, t2) => eval<int>(t1) + eval<int>(t2)
  | Mul (t1, t2) => eval<int>(t1) * eval<int>(t2)
  | Eq (t1, t2) => equals<?>(eval<?>(t1), eval<?>(t2))

The problem here is what types to put in the '?' in this snippet? The Expr type defines this as being any a but we want to constrain it to the index used by t1 and t2 but I don't think ATS allows us to declare that. This mailing list thread discusses the issue with some workarounds.

Concurrent and Distributed Programming in Web Prolog

SWI Prolog is an open source Prolog implementation with good documentation and many interesting libraries. One library that was published recently is Web Prolog. While branded as a 'Web Logic Programming Language' the implementation in the github repository runs under SWI Prolog and adds Erlang style distributed concurrency. There is a PDF Book in the repository that goes into detail about the system. In this post I explore some of features.

Install SWI Prolog

The first step is to install and run the SWI Prolog development version. There is documentation on this but the following are the basic steps to download and build from the SWI Prolog github repository:

$ git clone https://github.com/SWI-Prolog/swipl-devel
$ cd swipl-devel
$ ./prepare
... answer yes to the various prompts ...
$ cp build.tmpl build
$ vim build
...change PREFIX to where you want to install...
$ make install
$ export PATH=<install location>/bin:$PATH

There may be errors about building optional libraries. They can be ignored or view dependancies to see how to install.

The newly installed SWI Prolog build can be run with:

$ swipl
Welcome to SWI-Prolog (threaded, 64 bits, version 7.7.19-47-g4c3d70a09)
SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software.
Please run ?- license. for legal details.

For online help and background, visit http://www.swi-prolog.org
For built-in help, use ?- help(Topic). or ?- apropos(Word).

?- 

I recommend reading Basic Concepts in The Power of Prolog to get a grasp of Prolog syntax if you're not familiar with it.

Starting a Web Prolog node

Installing the Web Prolog libraries involves cloning the github repository and loading the prolog libraries held within. The system includes a web based tutorial and IDE where each connected web page is a web prolog node that can send and receive messages to other web prolog nodes. I'll beiefly mention this later but won't cover it in detail in this post - for now some simple examples will just use the SWI Prolog REPL. We'll need two nodes running, which can be done by running on different machines. On each machine run:

$ git clone https://github.com/Web-Prolog/swi-web-prolog/
$ cd swi-web-prolog
$ swipl
...
?- [web_prolog].
...

The [web_prolog]. command at the prolog prompt loads the web prolog libraries. Once loaded we need to instantiate a node, which starts the socket server and machinery that handles messaging:

?- node.
% Started server at http://localhost:3060/
true.

This starts a node on the default port 3060. If you're running multiple nodes on the same machine you can change the port by passing an argument to node:

?- node(localhost:3061).
% Started server at http://localhost:3061/
true.

In the rest of this post I refer to node A and node B for the two nodes started above.

Basic example

Each process has an id that can be used to reference it. It is obtained via self:

?- self(Self).
Self = thread(1)@'http://localhost:3061'.

We can send a message using '!'. Like Erlang, it takes a process to send to and the data to send:

?- self(Self),
   Self ! 'Hello World'.

This posts 'Hello World' to the current process mailbox. Messages can be received using receive. This takes a series of patterns to match against and code to run if an item in the process mailbox matches that pattern. Like Erlang it is a selective receive - it will look through messages in the mailbox that match the pattern, not just the topmost message:

?- receive({ M -> writeln(M) }).
Hello World
M = 'Hello World'.

Notice the receive rules are enclosed in '{ ... }' and are comprised of a pattern to match against and the code to run separated by ->. Variables in the pattern are assigned the value of what they match. In this case M is set to Hello World as that's the message we sent earlier. More complex patterns are possible:

?- $Self ! foo(1, 2, bar('hi', [ 'a', 'b', 'c' ])).
Self = thread(1)@'http://localhost:3061'.

?- receive({ foo(A, B, bar(C, [D | E])) -> true }).
A = 1,
B = 2,
C = hi,
D = a,
E = [b, c].

Here I make use of a feature of the SWI Prolog REPL - prefixing a variable with $ will use the value that was assigned to that variable in a previous REPL command. This also shows matching on the head and tail of a list with the [Head | Tail] syntax.

To send to another process we just need to use the process identifier. In this case I can send a message from node A to node B:

# In Node A
?- self(Self).
Self = thread(1)@'http://localhost:3060'.

# This call blocks
?- receive({ M -> format('I got: ~s~n', [M])}).

# In Node B
?- thread(1)@'http://localhost:3060' ! 'Hi World'.
true.

# Node A unblocks
I got: Hi World
M = 'Hi World'.

Spawning processes

Use spawn to spawn a new process the runs concurrencly on a node. It will have its own process Id:

?- spawn((self(Self),
          format('My process id is ~w~n', [Self]))).
true.
My process id is 21421552@http://localhost:3060

The code to run in the process is passed as the first argument to spawn and must be between brackets. An optional second argument will provide the process id to the caller:

?- spawn((self(Self),
          format('My process id is ~w~n', [Self])),
         Pid).
My process id is 33869438@http://localhost:3060
Pid = '33869438'.

A third argument can be provided to pass options to control spawning. These include the ability to link processes, monitor them or register a name to identify it in a registry.

Using the REPL we can define new rules and run them in processes, either by consulting a file, or entering them via [user]. The following code will define the code for a 'ping' server process:

server :-
   receive({
     ping(Pid) -> Pid ! pong, server
   }).

This can be added to a file and loaded in the REPL with consult, or it can be entered directly using [user] (note the use of Ctrl+D to exit the user input):

# on Node A 
?- [user].
|: server :-
|:   receive({
|:     ping(Pid) -> Pid ! pong, server
|:   }).
|: ^D
% user://1 compiled 0.01 sec, 1 clauses
true.

server blocks receiving messages looking for a ping(Pid) message. It sends a pong message back to the process id it extracted from the message and calls itself recursively using a tail call. Run on the node with:

# on node A
?- spawn((server), Pid).
Pid = '18268992'.

Send a message from another node by referencing the Pid along with the nodes address:

# on node B
?- self(Self), 18268992@'http://localhost:3060' ! ping(Self).
Self = thread(1)@'http://localhost:30601.

?- flush.
% Got pong
true.

The flush call will remove all messages from the process' queue and display them. In this case, the pong reply from the other nodes server.

Spawning on remote nodes

Web Prolog provides the ability to spawn processes to run on remote nodes. This is done by passing a node option to spawn. To demonstrate, enter the following to create an add rule in node A:

# on node A
?- [user].
|: add(X,Y,Z) :- Z is X + Y.
|: ^D
% user://1 compiled 0.01 sec, 1 clauses
true.

This creates an 'add' predicate that works as follows:

# on node A
?- add(1,2,Z).
Z = 3.

We can call this predicate from node B by spawning a remote process that executes code in node A. In node B, it looks like this:

# on node B
?- self(Self),
   spawn((
     call(add(10, 20, Z)),
     Self ! Z
   ), Pid, [
     node('http://localhost:3060'),
     monitor(true)
   ]),
   receive({ M -> format('Result is ~w~n', [M])})
Result is 30
Self = thread(1)@'http://localhost:3061',
Pid = '24931627'@'http://localhost:3060',
M = 30.

Passing node as an option to spawn/3 results in a process being spawned on that referenced node and the code runs there. In the code we call the add predicate that only exists on node A and return it by sending it to node B's identifier. The monitor option provides status information about the remote process - including getting a message when the process exits. Calling flush on node B shows that the process on node A exits:

# on Node B
?- flush.
% Got down('24931627'@'http://localhost:3060',exit)
true.

Note the indirection in the spawn call where add isn't called directly, instead call is used to call it. For some reason Web Prolog requires add to exist on node B even though it is not called. The following gives an error on node B for example:

# on node B
?- self(Self),
   spawn((
     add(10, 20, Z),
     Self ! Z
   ), Pid, [
     node('http://localhost:3060'),
     monitor(true)
   ]),
   receive({ M -> format('Result is ~w~n', [M])})
ERROR: Undefined procedure: add/3 (DWIM could not correct goal)

I'm unsure if this is an error in web prolog or something I'm doing.

RPC calls

The previous example can be simplified using RPC functions provided by web prolog. A synchronous RPC call from node B can be done that is aproximately equivalent to the above:

?- rpc('http://localhost:3060', add(1,2,Z)).
Z = 3.

Or ansynchronously using promises:

?- promise('http://localhost:3060', add(1,2,Z), Ref).
Ref = '119435902516515459454946972679206500389'.

?- yield($Ref, Answer).
Answer = success(anonymous, [add(1, 2, 3)], false),
Ref = '119435902516515459454946972679206500389'.

Upgrading a process

The following example, based on one I did for Wasp Lisp, is a process that maintains a count that can be incremented, decremented or retrieved:

server(Count) :-
  receive({
    inc -> Count2 is Count + 1, server(Count2);
    dec -> Count2 is Count - 1, server(Count2);
    get(Pid) -> Pid ! value(Count), server(Count)
  }).

Once defined, it can be spawned in node A with:

?- spawn((server(0)), Pid).
Pid = '33403644'.

And called from Node B with code like:

?- self(Self), 33403644@'http://localhost:3060' ! get(Self).
Self = thread(1)@'http://localhost:3061'.

?- flush.
% Got value(0)
true.

?- 33403644@'http://localhost:3060' ! inc.
true.

?- self(Self), 33403644@'http://localhost:3060' ! get(Self).
Self = thread(1)@'http://localhost:3061'.

?- flush.
% Got value(1)
true.

We can modify the server so it accepts an upgrade message that contains the new code that the server will execute:

server(Count) :-
  writeln("server receive"),
  receive({
    inc -> Count2 is Count + 1, server(Count2);
    dec -> Count2 is Count - 1, server(Count2);
    get(Pid) -> Pid ! value(Count), server(Count);
    upgrade(Pred) -> writeln('upgrading...'), call(Pred, Count)
  }).

Run the server and send it some messages. Then define a new_server on node A's REPL:

new_server(Count) :-
  writeln("new_server receive"),
  receive({
    inc -> Count2 is Count + 1, new_server(Count2);
    dec -> Count2 is Count - 1, new_server(Count2);
    mul(X) -> Count2 is Count * X, new_server(Count2);
    get(Pid) -> Pid ! value(Count), new_server(Count);
    upgrade(Pred) -> writeln(Pred), writeln(Count), call(Pred, Count)
  }).

And send an upgrade message to the existing server:

# on node A
?- $Pid ! upgrade(new_server).
upgrading...
new_server receive

Now the server understands the mul message without having to be shut down and restarted.

Web IDE and tutorial

There's a web based IDE and tutorial based on SWISH, the online SWI-Prolog system. To start this on a local node, run the following script from the web prolog source:

$ cd web-client
$ swipl run.pl

Now visit http://localhost:3060/apps/swish/index.html in a web browser. This displays a tutorial on the left and a REPL on the right. Each loaded web page has its own namespace and local environment. You can send messages to and from individual web pages and the processes running in the local node. It uses websockets to send data to and from instances.

Conclusion

There's a lot to the Web Prolog system and the implementation for SWI Prolog has some rough edges but it's usable to experiment with and get a feel for the system. I hope to write a more about some of the features of it, and SWI Prolog, as I get more familiar with it.