As noted in this post, if you want Visual Studio just to have an IDE to work with F#, you can get it for free. Now with Visual Studio 2008, Microsoft has released a bare-bones VS, without any language, that can be used with language extensions and plugins, as is the case of F#. This bare-bones VS is called Visual Studio 2008 Shell (integrated mode).

After downloading and installing VS 2008 Shell (it takes a lot of unpacking and installing), you can install F# 1.9.3.7 and voilĂ , you have a pretty good F# IDE in your box, without having to shell out any cash.

I tested it with F# version 1.9.3.7 in a machine running Windows XP SP2 and no previous version of Visual Studio installed, and it worked. I even compiled and ran some test projects. If it doesn't work at first, take a look at the original post.

## Tuesday, December 11, 2007

## Wednesday, October 17, 2007

### Further news on World Domination

Don Syme blogs about taking F# forward, which means, it seems, that F# will leave the confines of MS Research and be fully integrated into Visual Studio, as a product. If this is right, it's a great step for F# as a language and for functional programming in general, as we'll have a first-class IDE, by a major vendor, shipping with a functional programming language.

F# is already a great language to use, so I look forward to it getting still greater. The next step for Microsoft is to embrace Visual Haskell and fully integrate Haskell in Visual Studio too :)

F# is already a great language to use, so I look forward to it getting still greater. The next step for Microsoft is to embrace Visual Haskell and fully integrate Haskell in Visual Studio too :)

## Monday, September 24, 2007

### Review: OCaml for Scientists

When we think about what makes a programming book good, what separates a classic from a run-of-the-mill for-dummies-learn-in-X-days book, it's not hard to get to the conclusion that the examples are an important piece of what we perceive as quality. I would say that this is even more so for books on programming languages: K&R had great examples; Practical Common Lisp has great examples that are now being copied by many authors; the list could go on.

So it was not that surprising to discover that one of the reasons of all the praise received by Dr. Jon Harrop's book OCaml for Scientists is its set of examples. There are even two entire chapters devoted to examples, the first for simple and the second for more significative ones. They are really good: well-chosen, interesting and well-written. Most of them have a scientific flavor, in keeping with the book's title, but to me this is a plus. Also, I don't recall seeing wavelet transforms as examples in a programming language book before; originality also counts.

The book's title is accurate: it is a book about OCaml primarily targeted for scientific applications. But most of the topics covered are really useful to anyone wanting to learn the OCaml language. Of all the ten chapters, I would say only one -- Chapter 4, Numerical Analysis -- is mostly directed to scientists. Well, probably game programmers too. And programmers of computer graphics applications, and anyone using floating-point arithmetic. Anyway, the other chapters that have somewhat of a scientific bent are: Chapter 6, Visualization, which is really about how to use OpenGL and GLUT in OCaml, which is quite cool in itself; and Chapter 10, Complete Examples, but each example is well explained and can be (mostly) understood without previous knowledge.

To give some idea about the book's contents, here is a quick tour: Chapter 1 is a quick introduction, covering most important concepts of the core language. Chapter 2 is about how to structure bigger programs, including function nesting, modules, objects, and how to manage dependencies and compilation. Chapter 3 is a very interesting chapter on data structures in OCaml, beginning with a section on algorithmic complexity; it covers the more important containers provided in the library, and also how to implement and work with trees. Chapter 4 is the one about numerical analysis, covering the basics about doing calculations with limited-precision numbers, and how to use more precise forms of arithmetic. Chapter 5 tackles input and output in OCaml, going beyond the call of duty to present the lexer generator (ocamllex) and parser generator (ocamlyacc) in the OCaml toolset. Chapter 6 is about visualization with OpenGL and GLUT, Chapter 7 is a very good one about optimization, and Chapter 8 a very useful one about libraries. The final two chapters have examples, and don't be fooled by the title of Chapter 9, Simple Examples. There is good stuff there. There are also two appendices, about more advanced features and troubleshooting advice respectivelly.

To be fair, the book has some small weaknesses that, in the end, are not that important, if you consider its target audience and what's common OCaml style. One is the treatment of objects: it is very cursory, and one of the examples (about real and complex numbers) could easily be considered a bad case of OO design. Considering most OCaml programmers rarely use objects, this is not so troubling. The other weakness I'd like to cite is more of a wish from my part: I wish there were more about advanced topics, especially functors (only very lightly touched in Appendix A).

But it's really a very good book about OCaml, both for beginners and for people with some previous exposure to it. It has advice on good programming style throughout, great examples (shown in color, properly syntax-highlighted), and distilled practical experience on some important topics (optimization, using libraries) that is hard to get elsewhere. It is remarkable not only in the very restricted universe of OCaml books, but as a programming book, in general: it stands between the best I've seen.

So it was not that surprising to discover that one of the reasons of all the praise received by Dr. Jon Harrop's book OCaml for Scientists is its set of examples. There are even two entire chapters devoted to examples, the first for simple and the second for more significative ones. They are really good: well-chosen, interesting and well-written. Most of them have a scientific flavor, in keeping with the book's title, but to me this is a plus. Also, I don't recall seeing wavelet transforms as examples in a programming language book before; originality also counts.

The book's title is accurate: it is a book about OCaml primarily targeted for scientific applications. But most of the topics covered are really useful to anyone wanting to learn the OCaml language. Of all the ten chapters, I would say only one -- Chapter 4, Numerical Analysis -- is mostly directed to scientists. Well, probably game programmers too. And programmers of computer graphics applications, and anyone using floating-point arithmetic. Anyway, the other chapters that have somewhat of a scientific bent are: Chapter 6, Visualization, which is really about how to use OpenGL and GLUT in OCaml, which is quite cool in itself; and Chapter 10, Complete Examples, but each example is well explained and can be (mostly) understood without previous knowledge.

To give some idea about the book's contents, here is a quick tour: Chapter 1 is a quick introduction, covering most important concepts of the core language. Chapter 2 is about how to structure bigger programs, including function nesting, modules, objects, and how to manage dependencies and compilation. Chapter 3 is a very interesting chapter on data structures in OCaml, beginning with a section on algorithmic complexity; it covers the more important containers provided in the library, and also how to implement and work with trees. Chapter 4 is the one about numerical analysis, covering the basics about doing calculations with limited-precision numbers, and how to use more precise forms of arithmetic. Chapter 5 tackles input and output in OCaml, going beyond the call of duty to present the lexer generator (ocamllex) and parser generator (ocamlyacc) in the OCaml toolset. Chapter 6 is about visualization with OpenGL and GLUT, Chapter 7 is a very good one about optimization, and Chapter 8 a very useful one about libraries. The final two chapters have examples, and don't be fooled by the title of Chapter 9, Simple Examples. There is good stuff there. There are also two appendices, about more advanced features and troubleshooting advice respectivelly.

To be fair, the book has some small weaknesses that, in the end, are not that important, if you consider its target audience and what's common OCaml style. One is the treatment of objects: it is very cursory, and one of the examples (about real and complex numbers) could easily be considered a bad case of OO design. Considering most OCaml programmers rarely use objects, this is not so troubling. The other weakness I'd like to cite is more of a wish from my part: I wish there were more about advanced topics, especially functors (only very lightly touched in Appendix A).

But it's really a very good book about OCaml, both for beginners and for people with some previous exposure to it. It has advice on good programming style throughout, great examples (shown in color, properly syntax-highlighted), and distilled practical experience on some important topics (optimization, using libraries) that is hard to get elsewhere. It is remarkable not only in the very restricted universe of OCaml books, but as a programming book, in general: it stands between the best I've seen.

## Tuesday, August 21, 2007

### Monads in OCaml

So, there. Someone who has never programmed in Haskell probably never encountered the idea of monads -- unless it is someone who works in semantics and has read Moggi's works; but I digress. An interesting way to tackle the idea of monads is to look at them outside of Haskell, and see how it works in other languages. Often, other languages don't have what it takes to express the concept of a monad in its full generality, but specific monads can always be implemented. In this regard, there's this page by oleg, and there's this other one about monads in Ruby. I remember seeing somewhere a page that compiled monad implementations in various languages, but I can't seem to find it now.

Anyhow, Brian Hurt has written a very nice tutorial about monads in OCaml. It uses the module system and functors (see comments) to define a reasonably general monad concept in OCaml. It's a good read.

Anyhow, Brian Hurt has written a very nice tutorial about monads in OCaml. It uses the module system and functors (see comments) to define a reasonably general monad concept in OCaml. It's a good read.

## Tuesday, August 7, 2007

### Towards Global Domination

If you haven't yet seen them or heard about them somewhere else, it seems that the videos of Simon Peyton-Jones' talks at OSCON are quite a hit.

And people still look at me funny when I say that functional programming is going to take over the world.

And people still look at me funny when I say that functional programming is going to take over the world.

## Friday, July 13, 2007

### Battle of the OCaml plugins for Eclipse

A new OCaml plugin for Eclipse, called OcaIDE, has just been announced. Apparently, it has been under development for a long time. It seems to be quite complete in features, although I didn't try it yet. The question is that this is the third OCaml plugin being developed currently; there's ODT, about which I talked in a earlier post, and another one being developed as one of the OCaml projects in the Google Summer of Code. The competition is good in some ways, but on the other hand the resulting fragmentation can be a problem to a small community like that of OCaml. It would be best if the teams managed to combine their efforts in some way. Let's see how this plays out.

Speaking of collaboration, there's mention on OcaIDE's site about a free-software license, but the source code doesn't seem to be available.

UPDATE: As someone pointed in the comments, the source is available together with the plugin. See here.

Speaking of collaboration, there's mention on OcaIDE's site about a free-software license, but the source code doesn't seem to be available.

UPDATE: As someone pointed in the comments, the source is available together with the plugin. See here.

## Thursday, July 5, 2007

### Review: Practical OCaml

Executive summary: this is not Practical Common Lisp for OCaml. It's ambitious but disappointing. However, it's not so bad as it seems at first sight.

OCaml is a sexy language that combines the expressiveness and terseness of scripting languages with the static type checking and performance of languages like C++ and Java. A book may be a good investment to learn a new language, and this is one of the few books available on the language. How does it fare?

This book has received very harsh criticism overall, and it mostly deserves it; it is somewhat of a mess. But it is not uniformly bad: some chapters are very bad, others are acceptable or interesting, depending on your background. The problem seems to be that the worst chapters come first; although it shows signs of bad editing throughout, the first few chapters are especially bad. And I mean really bad: bad text, bad editing, bad examples, lots of senseless repetition, conceptual errors, using language features not yet introduced (and that go unexplained), the list goes on. Later chapters are considerably less irritating.

Clearly inspired by Peter Seibel's terrific book Practical Common Lisp, the chapters on this one are divided in two types: the ones that explain the language, and the "Practical" ones, containing extended examples. This is a great idea, and even badly executed as it may be in Practical OCaml, it still results in interesting chapters. Actually, the Practical chapters are overall better than the language ones; from them, a reader can get a real sense of using OCaml in simple but realistic projects, integrating many different libraries and tools, some of them not contained in the standard OCaml distribution. Still, the code in these chapters can be criticized for their style. For one thing, I think the author uses classes and other OO features much more often than they appear on real OCaml programs. Nonetheless, an experienced programmer could get a lot of interesting pointers from these chapters, by knowing what to salvage and what not to replicate from the code.

But the rest of the book, the OCaml chapters, are in really bad shape. They don't explain things very well, and fails miserably at the more difficult aspects of the language. The chapter on modules and functors is so bad as to be almost useless; don't try to learn about functors from this book. Camlp4, the nifty tool for metaprogramming and extension, is other subject with a bad treatment. The chapter on Threads could be improved a lot, but it still gives a general idea of how multithreaded programming in OCaml is. Again, for experienced developers, it should provide pointers for further study.

If experienced developers can get something from this book, novice ones should stay away from it. Not only is the text confusing, but there are a lot of glaring conceptual errors. Maybe some errors are to be expected from a trade book, from an author that is not an academic, but there

are things that are completely confusing. For example, this is the definition of type (page 24): "A type is a thing (or a collection of things) or value." And there is a lot more like this, unfortunately.

Overall, it has interesting parts, but surely not enough to make worth the full cover price. For experienced programmers and people already familiar with other typed functional programming languages (Haskell, F#, SML, etc), the book could serve as an initial guide for OCaml programming, but there are better alternatives around.

OCaml is a sexy language that combines the expressiveness and terseness of scripting languages with the static type checking and performance of languages like C++ and Java. A book may be a good investment to learn a new language, and this is one of the few books available on the language. How does it fare?

This book has received very harsh criticism overall, and it mostly deserves it; it is somewhat of a mess. But it is not uniformly bad: some chapters are very bad, others are acceptable or interesting, depending on your background. The problem seems to be that the worst chapters come first; although it shows signs of bad editing throughout, the first few chapters are especially bad. And I mean really bad: bad text, bad editing, bad examples, lots of senseless repetition, conceptual errors, using language features not yet introduced (and that go unexplained), the list goes on. Later chapters are considerably less irritating.

Clearly inspired by Peter Seibel's terrific book Practical Common Lisp, the chapters on this one are divided in two types: the ones that explain the language, and the "Practical" ones, containing extended examples. This is a great idea, and even badly executed as it may be in Practical OCaml, it still results in interesting chapters. Actually, the Practical chapters are overall better than the language ones; from them, a reader can get a real sense of using OCaml in simple but realistic projects, integrating many different libraries and tools, some of them not contained in the standard OCaml distribution. Still, the code in these chapters can be criticized for their style. For one thing, I think the author uses classes and other OO features much more often than they appear on real OCaml programs. Nonetheless, an experienced programmer could get a lot of interesting pointers from these chapters, by knowing what to salvage and what not to replicate from the code.

But the rest of the book, the OCaml chapters, are in really bad shape. They don't explain things very well, and fails miserably at the more difficult aspects of the language. The chapter on modules and functors is so bad as to be almost useless; don't try to learn about functors from this book. Camlp4, the nifty tool for metaprogramming and extension, is other subject with a bad treatment. The chapter on Threads could be improved a lot, but it still gives a general idea of how multithreaded programming in OCaml is. Again, for experienced developers, it should provide pointers for further study.

If experienced developers can get something from this book, novice ones should stay away from it. Not only is the text confusing, but there are a lot of glaring conceptual errors. Maybe some errors are to be expected from a trade book, from an author that is not an academic, but there

are things that are completely confusing. For example, this is the definition of type (page 24): "A type is a thing (or a collection of things) or value." And there is a lot more like this, unfortunately.

Overall, it has interesting parts, but surely not enough to make worth the full cover price. For experienced programmers and people already familiar with other typed functional programming languages (Haskell, F#, SML, etc), the book could serve as an initial guide for OCaml programming, but there are better alternatives around.

## Sunday, June 17, 2007

### F# Performance

There's a comparison of F# versus IronPython in Robert Pickering's blog. The results show that F# has roughly the same level of conciseness and terseness of Python, while being close in performance to C#. This is a .NET-based comparison, but it would be interesting to compare F# with CPython to see where it stands. If we are to believe this discussion on the python-dev mailing list, it seems that IronPython's performance must be comparable to CPython's, so there we have it: .NET or not, F# strikes an interesting balance in the expressiveness versus performance trade-offs.

This is also my personal experience with OCaml: performance roughly comparable to C/C++, but expressive and concise like scripting languages. It is this interesting position in the expressiveness x performance curve that makes both F# and OCaml very worthwhile languages to learn and use today.

This is also my personal experience with OCaml: performance roughly comparable to C/C++, but expressive and concise like scripting languages. It is this interesting position in the expressiveness x performance curve that makes both F# and OCaml very worthwhile languages to learn and use today.

## Saturday, June 9, 2007

### The EOPL in F# wiki

I've started moving the content for the "EOPL in F#" translation to a wiki. Unfortunately, I have also been insanely busy as of late, so there's only the beginning there. However, as I'll have more free time from now on, I intend to catch up with what's already here and then start posting more sections that I already translated. I also noticed I never posted some parts because I forgot to, so it will be added to the wiki as well. Anyway, here is the link:

EOPL in F# Wiki

EOPL in F# Wiki

## Friday, June 1, 2007

### OCaml with Eclipse

The primary editor on which to write OCaml code has always been Emacs. This tends to be a problem for users on Windows, that mostly aren't familiar with the editor. And of course there are many people that use unix platforms and don't like Emacs.

A good alternative is Eclipse, which has very good plugins for Java programming, and can be extended to handle other languages. ODT, a plugin for OCaml development in Eclipse, is being actively developed by Emmanuel Dieul. Actually there's another plugin in development by someone under the Google Summer of Code, and we hope they can integrate both efforts to get a better plugin in the end.

Anyway, ODT looks interesting right now, and it's been evolving quite fast. Eclipse is quite a memory hog, but if you already use it or are willing to pay the requirements, it can provide a modern IDE for OCaml under Windows or unix, and a good alternative for Emacs. Let's hope ODT keeps improving.

A good alternative is Eclipse, which has very good plugins for Java programming, and can be extended to handle other languages. ODT, a plugin for OCaml development in Eclipse, is being actively developed by Emmanuel Dieul. Actually there's another plugin in development by someone under the Google Summer of Code, and we hope they can integrate both efforts to get a better plugin in the end.

Anyway, ODT looks interesting right now, and it's been evolving quite fast. Eclipse is quite a memory hog, but if you already use it or are willing to pay the requirements, it can provide a modern IDE for OCaml under Windows or unix, and a good alternative for Emacs. Let's hope ODT keeps improving.

## Saturday, May 26, 2007

### Great news in the Haskell Books front

This was recently announced and everyone must already know about it (I was away at a conference), but just in case: O'Reilly will publish a book about Haskell called Real-World Haskell, written by people very active in the Haskell community. Such a book from O'Reilly has the potential to seriously increase Haskell's popularity, and familiarize more people with functional programming.

Considering that a book about F# is already out and another one is on the way, and that APress recently published a book on OCaml (it doesn't seem to be very good, unfortunately), I guess functional programming is really getting more popular.

Maybe there's hope that Haskell will take over the world and everyone will use monads and pure lazy functional programming :)

Considering that a book about F# is already out and another one is on the way, and that APress recently published a book on OCaml (it doesn't seem to be very good, unfortunately), I guess functional programming is really getting more popular.

Maybe there's hope that Haskell will take over the world and everyone will use monads and pure lazy functional programming :)

## Wednesday, May 16, 2007

### The EOPL in F# thing

I have translated more of the EOPL book into F#, but the examples keep growing and proving how unfit the whole enterprise is to the blog format. I knew this from the beginning, and would prefer a wiki, but then I couldn't find a decent wiki server. I may have found one now, and if all goes well I'll link to it here after moving there some of the contents posted here. After this, I don't know if this blog will still be useful, but I'll wait and see.

## Monday, April 30, 2007

### Functional programming in Wall Street

The latest issue of Monad.Reader (a electronic magazine about Haskell) includes an interesting article about Jane Street Capital (a Wall Street trading company) and its use of OCaml. The author points good and bad things about the language; these aren't new, in fact the things pointed are well-known by the community, but it's good to hear them from someone using the language in a production setting.

Anyway, it's a case of large-scale adoption -- in the sense of using it as the main language for all development -- of a functional programming language, which is still rare, unfortunately.

Anyway, it's a case of large-scale adoption -- in the sense of using it as the main language for all development -- of a functional programming language, which is still rare, unfortunately.

Labels:
functional,
ocaml,
real world

## Tuesday, April 3, 2007

### One Language to Rule Them All

A discussion on LtU about the Next Big language, the next Java or something like it. Links to the post by Steve Yegge too. Once again Scala is mentioned as a fine language that anyone needing to develop for the JVM should try.

I don't believe Scala will be the next big language, but it really is fine. At the moment I'm finishing implementation of a simple distributed system written in Scala. It had to run on the JVM to communicate with other Java programs. It was a breeze to do, thanks to the Actors library. Scala's type system is quite interesting too, I plan on giving more attention to it when I have the time.

I don't believe Scala will be the next big language, but it really is fine. At the moment I'm finishing implementation of a simple distributed system written in Scala. It had to run on the JVM to communicate with other Java programs. It was a breeze to do, thanks to the Actors library. Scala's type system is quite interesting too, I plan on giving more attention to it when I have the time.

### EOPL - 3.2 - Exercise 3.5

Exercise 3.5 asks you to add a

In the lexer specification a token for the

And, in the parser, this token must be declared and dealt with:

The remaining parts of these three files are the same as the previous two posts.

`print`

primitive to the language, which prints its argument and returns the value 1. The relevant changes are simple. In module `Eopl_3`

only the definition of type `Primitive`

and function `apply_primitive`

are different:

// in eopl_3.fs (module Eopl_3)

type Primitive = AddPrim | SubtractPrim | MultPrim | IncrPrim

| DecrPrim | PrintPrim

let apply_primitive prim args =

match (prim, args) with

(AddPrim, [a; b]) -> a + b

| (SubtractPrim, [a; b]) -> a - b

| (MultPrim, [a; b]) -> a * b

| (IncrPrim, [a]) -> a + 1

| (DecrPrim, [a]) -> a - 1

| (PrintPrim, [a]) -> (print_endline (string_of_int a); 1)

| _ -> failwith "Incorrect argument list for primitive"

In the lexer specification a token for the

`print`

primitive is added:

rule token = parse

| whitespace { token lexbuf }

| '%' [^ '\n']* { token lexbuf }

| newline { record_newline lexbuf; token lexbuf }

| "+" { PLUS }

| "-" { MINUS }

| "*" { MULT }

| "(" { LPAREN }

| ")" { RPAREN }

| "," { COMMA }

| "add1" { INCR }

| "sub1" { DECR }

| "print" { PRINT }

| id { ID(lexeme lexbuf) }

| ['-']?digit+ { LIT (Int32.Parse(lexeme lexbuf)) }

| eof { EOF }

And, in the parser, this token must be declared and dealt with:

%token PRINT INCR DECR LPAREN RPAREN PLUS MINUS MULT COMMA EOF

Prim: PLUS { AddPrim }

| MINUS { SubtractPrim }

| MULT { MultPrim }

| INCR { IncrPrim }

| DECR { DecrPrim }

| PRINT { PrintPrim }

The remaining parts of these three files are the same as the previous two posts.

## Friday, March 23, 2007

### Scala web programming

A post on Lambda the Ultimate pointing to this post on David Pollak's blog. In a comment on the Lambda thread, he writes some points about what makes Scala a good language for web programming, comparing with Java and Ruby (with Rails). Having used all three, he gets to the conclusion that Scala has the best of the other two.

## Sunday, March 18, 2007

### EOPL - 3.2 - Front-end for the first interpreter

The previous post showed the code for the interpreter, working on an abstract syntax representation of the interpreted programs. In section 3.2 a front-end is presented to permit working with a concrete syntax. The book uses SLLGEN, a tool developed by the PLT Scheme group, to generate lexers and parsers. I used fslex and fsyacc, the standard tools of F# for such purposes. Here's the lexical specification.

And the grammar to use with fsyacc.

Module

{

// eopl1_lex.fsl

//

// Lexical specification for the first interpreter

// in EOPL (Essentials of Programming Languages)

open System

open Eopl1_par

open Lexing

let record_newline (lexbuf : lexbuf) =

lexbuf.EndPos <- lexbuf.EndPos.AsNewLinePos()

}

// These are some regular expression definitions

let digit = ['0'-'9']

let id = ['a'-'z'] ['a'-'z' '0'-'9']*

let whitespace = [' ' '\t' ]

let newline = ('\n' | '\r' '\n')

rule token = parse

| whitespace { token lexbuf }

| '%' [^ '\n']* { token lexbuf }

| newline { record_newline lexbuf; token lexbuf }

| "+" { PLUS }

| "-" { MINUS }

| "*" { MULT }

| "(" { LPAREN }

| ")" { RPAREN }

| "," { COMMA }

| "add1" { INCR }

| "sub1" { DECR }

| id { ID(lexeme lexbuf) }

| ['-']?digit+ { LIT (Int32.Parse(lexeme lexbuf)) }

| eof { EOF }

And the grammar to use with fsyacc.

// eopl1_par.fsy

// Parser for the first interpreter

// in EOPL (Essentials of Programming Languages)

%{

open Eopl_3

%}

%start start

// terminal symbols

%tokenID

%tokenLIT

%token INCR DECR LPAREN RPAREN PLUS MINUS MULT COMMA EOF

%type < Eopl_3.Program > start

%%

start: Prog { $1 }

Prog: Expr { Exp ($1) }

Expr: ID { VarExp($1) }

| LIT { LitExp($1) }

| Prim LPAREN ArgList RPAREN { PrimAppExp ($1, List.rev $3) }

Prim: PLUS { AddPrim }

| MINUS { SubtractPrim }

| MULT { MultPrim }

| INCR { IncrPrim }

| DECR { DecrPrim }

ArgList: Expr { [$1] }

| ArgList COMMA Expr { $3 :: $1 }

Module

`Eopl_3`

contains all the code from the previous post, including a definition of the abstract syntax. Both specifications above were adapted from an example included in the distribution. Now we only need to run these specifications into fslex and fsyacc, and write a driver for the interpreter, a simple read-eval-print loop. Here it is.

// eopl1_main.fs

//

// Driver for the first interpreter in EOPL

// (Essentials of Programming Languages)

#light

open Eopl_3

open Eopl1_par

open Lexing

let parse str =

let lexbuf = Lexing.from_string str

let prog =

try

Some (Eopl1_par.start Eopl1_lex.token lexbuf)

with e ->

let pos = lexbuf.EndPos

printf "error near line %d, character %d\n%s\n"

pos.pos_cnum

(pos.pos_cnum - pos.pos_bol) (e.ToString());

None

prog

let rec read_eval_print prompt =

let _ = print_string prompt

let line = read_line ()

match line with

"#quit" -> ()

| _ -> match parse line with

None -> read_eval_print prompt

| Some p -> let v = Eopl_3.eval_program p in

(print_endline (string_of_int v);

read_eval_print prompt)

let main() =

read_eval_print "--> "

do main()

## Sunday, March 11, 2007

### EOPL - Section 3.1

This is the first interpreter from Chapter 3, shown in Section 3.1. It needs an implementation of environments, I chose the simplest one and attached it before the code for the interpreter.

// implementation of environments

// (represented as lists of pairs; the first in pair is

// a list of symbols, the second is a list of associated values)

let list_find_position a lst =

let rec loop l =

match l with

[] -> None

| (x :: l') when x = a -> Some (List.length l')

| (x :: l') -> loop l' in

loop (List.rev lst)

let empty_env () =

[]

let extend_env syms vals env =

(syms, vals) :: env

let rec apply_env env sym =

match env with

[] -> failwith (sprintf "No binding for %s" sym)

| (syms, vals) :: env' ->

match list_find_position sym syms with

None -> apply_env env' sym

| Some i -> List.nth vals i

// types for primitives, expressions and programs

type Primitive = AddPrim | SubtractPrim | MultPrim | IncrPrim | DecrPrim

type Expression = LitExp of int | VarExp of string

| PrimAppExp of (Primitive * Expression list)

type Program = Exp of Expression

let apply_primitive prim args =

match (prim, args) with

(AddPrim, [a; b]) -> a + b

| (SubtractPrim, [a; b]) -> a - b

| (MultPrim, [a; b]) -> a * b

| (IncrPrim, [a]) -> a + 1

| (DecrPrim, [a]) -> a - 1

| _ -> failwith "Incorrect argument list for primitive"

let init_env () =

extend_env ["i"; "v"; "x"] [1; 5; 10] (empty_env ())

let rec eval_expression exp env =

match exp with

LitExp datum -> datum

| VarExp id -> apply_env env id

| PrimAppExp (prim, rands) -> let args = eval_rands rands env in

apply_primitive prim args

and eval_rands rands env =

List.map (eval_rand env) rands

and eval_rand env rand =

eval_expression rand env

let eval_program pgm =

match pgm with

Exp body -> eval_expression body (init_env())

## Friday, March 9, 2007

### Scheme programming in ML

As I'm constantly bumping into typing issues when converting EOPL's examples and exercises from Scheme to F# (a ML language), I found this code/article by Oleg Kyseliov relevant. It embeds a Scheme-like language into OCaml, using variant types, and defines functions used in Scheme. The scheme.ml file is quite interesting for going all the way with the Scheme conversion, but the use of variant types to capture the need to work with different types in the same context is known to every ML programmer. I even did it sometimes in the EOPL programs.

Be sure to read Oleg's comments about it.

Be sure to read Oleg's comments about it.

## Wednesday, March 7, 2007

### EOPL - 2.3.4 - Exercise 2.25

Using the data type definitions from the previous exercise, it's easy to define the necessary additional operations and then complete the definition of the unification function.

The occurs check is necessary, of course, to avoid infinity. I won't say more than that, to force people that arrive here looking for solutions to EOPL's exercises to think a little about it, at least.

And this concludes Chapter 2.

let is_var_term t =

match t with Id _ -> true | _ -> false

let unit_subst i t =

extend_subst i t (empty_subst ())

let rec compose_substs s1 s2 =

match s1 with

EmptySub -> s2

| ExtendedSub (i, t, s) -> ExtendedSub (i, t, compose_substs s s2)

let rec unify_term t u =

match t with

Id tid -> if (is_var_term u) ||

(not (List.mem tid (term_all_ids u))) then

Some (unit_subst tid u)

else

None

| _ -> match u with

Id _ -> unify_term u t

| Constant udat ->

(match t with

Constant tdat when tdat = udat -> Some (empty_subst ())

| _ -> None)

| App us -> (match t with

App ts -> unify_terms ts us

| _ -> None)

and unify_terms ts us =

match ts, us with

[], [] -> Some (empty_subst ())

| ([], _) -> None

| (_, []) -> None

| (t :: ts', u :: us') ->

let subst_car = unify_term t u in

match subst_car with

None -> None

| Some s -> let new_ts = subst_in_terms ts' s in

let new_us = subst_in_terms us' s in

let subst_cdr = unify_terms new_ts new_us in

match subst_cdr with

None -> None

| Some s' -> Some (compose_substs s s')

The occurs check is necessary, of course, to avoid infinity. I won't say more than that, to force people that arrive here looking for solutions to EOPL's exercises to think a little about it, at least.

And this concludes Chapter 2.

### EOPL - 2.3.4 - Exercise 2.24

This exercise asks for an implementation of substitutions on terms, the terms being defined by a previous exercise (2.13). In F#, they are thus defined:

Function

With the substitution data type completed, we can write a substitution function without any difficulties.

I guess

type Value = Integer of int | String of string

type Term = Id of string | Constant of Value | App of Term list

let rec term_all_ids t =

match t with

Id s -> [s]

| Constant _ -> []

| App tl -> List.concat (List.map term_all_ids tl)

Function

`term_all_ids`

gets all identifiers from a term, also part of exercise 2.13. Then for the part specific to exercise 2.24, which are substitutions. I chose to use an abstract syntax tree representation, because it is more convenient in F#. Using the definition, it was easy to write the operations on substitutions.

type Subst = EmptySub | ExtendedSub of string * Term * Subst

let empty_subst () =

EmptySub

let extend_subst i t s =

ExtendedSub (i, t, s)

let rec apply_subst s i =

match s with

EmptySub -> Id i

| ExtendedSub (i', t, s') when i = i' -> t

| ExtendedSub (_, _, s') -> apply_subst s' i

With the substitution data type completed, we can write a substitution function without any difficulties.

let rec subst_in_term s t =

match t with

Id i -> apply_subst s i

| Constant _ -> t

| App tl -> App (List.map (subst_in_term s) tl)

let subst_in_terms lt s =

List.map (subst_in_term s) lt

I guess

`subst_in_terms`

might have been intended as a little more difficult to write. I don't know. In any case, it's just a `map`

.
## Tuesday, March 6, 2007

### EOPL - 2.3.4 - Alternative Representation

A simple representation of environments as a list of pairs

`(syms, vals)`

where `syms`

is a list of symbols and `vals`

is a list of values positionally associated with the symbols.

let list_find_position a lst =

let rec loop l =

match l with

[] -> None

| (x :: l') when x = a -> Some (List.length l')

| (x :: l') -> loop l' in

loop (List.rev lst)

let empty_env () =

[]

let extend_env syms vals env =

(syms, vals) :: env

let rec apply_env env sym =

match env with

[] -> failwith (sprintf "No binding for %s" sym)

| (syms, vals) :: env' ->

match list_find_position sym syms with

None -> apply_env env' sym

| Some i -> List.nth vals i

### EOPL - 2.3.3 - Exercise 2.20

It's simple to add new operations when the data is represented as an abstract syntax tree. Here's the operation

`has_association`

for stacks as defined in the previous exercise:

// Exercise 2.20

let rec has_association env sym =

match env with

EmptyEnv -> false

| ExtendedEnv (syms, vals, env') -> (List.mem sym syms) ||

(has_association env' sym)

### EOPL - 2.3.3 - Exercise 2.19

Another simple exercise.

// Exercise 2.19

type 'a Stack = EmptyStack | ExtendedStack of 'a * 'a Stack

let empty_stack () =

EmptyStack

let push elt stk =

ExtendedStack (elt, stk)

let pop stk =

match stk with

EmptyStack -> failwith "Stack empty"

| ExtendedStack (_, s) -> s

let top stk =

match stk with

EmptyStack -> failwith "Stack empty"

| ExtendedStack (e, _) -> e

let is_stack_empty stk =

stk = EmptyStack

### EOPL - Section 2.3.3

The abstract syntax tree representation for environments is quite straightforward in F#; it is shown below.

type Value = Integer of int | String of string

type Environment = EmptyEnv

| ExtendedEnv of string list *

Value list *

Environment

// helper function

let list_find_position a lst =

let rec loop l =

match l with

[] -> None

| (x :: l') when x = a -> Some (List.length l')

| (x :: l') -> loop l' in

loop (List.rev lst)

let empty_env () =

EmptyEnv

let extend_env syms vals env =

ExtendedEnv (syms, vals, env)

let rec apply_env env sym =

match env with

EmptyEnv -> failwith (sprintf "No binding for %s" sym)

| ExtendedEnv (syms, vals, env') ->

match list_find_position sym syms with

None -> apply_env env' sym

| Some i -> List.nth vals i

## Monday, March 5, 2007

### EOPL - 2.3.2 - Exercise 2.16

Easy one, in two versions.

Version 1

Version 2

Version 2 was obtained by observing similarities in Version 1. The idea appeared in previous examples: pattern guards do not always lead to shorter code.

Version 1

let rec list_find_last_position sym los =

match los with

[] -> None

| (s :: los') when s = sym ->

(match list_find_last_position sym los' with

None -> Some 0

| Some i -> Some (i + 1))

| (s :: los') ->

(match list_find_last_position sym los' with

None -> None

| Some i -> Some (i + 1))

Version 2

let rec list_find_last_position sym los =

match los with

[] -> None

| (s :: los') ->

match list_find_last_position sym los' with

None -> if s = sym then Some 0 else None

| Some i -> Some (i + 1)

Version 2 was obtained by observing similarities in Version 1. The idea appeared in previous examples: pattern guards do not always lead to shorter code.

### EOPL - 2.3.2 - Exercise 2.15

I solved this exercise in quite a "lispy" way, so it's a bit alien in F#. It works, but in a quite awkward way. The idea was to maintain the stack as a pair containing the current top element and the old stack, and this means that, in F#, each operation that adds or removes elements produces a stack with a different type than the original. An interesting consequence of this is that the stack size is reflected in its type, so that we could define functions that work on "stacks of size 3" or so on. Who needs dependent types? :)

So here's the code. It first defines a type synonym to ease working with stacks, and then the functions that implement basic operations.

And it is used like this: you must assign a type for the

Then you can push elements into

If you pop elements, the types get back to what they were, obviously. A funny side-effect of this strange definition is that

There must be a more type-friendly implementation of stacks using a procedural representation, but I decided to leave it for now and publish this solution because it is quite interesting by itself (although almost unusable in real code).

So here's the code. It first defines a type synonym to ease working with stacks, and then the functions that implement basic operations.

type 'a stack = (unit -> 'a) * (unit -> bool)

let empty_stack () =

let top () = failwith "The stack is empty, no top element" in

let is_empty_stack () = true in

(top, is_empty_stack)

let push elt stk =

let top () = (elt, stk) in

let is_empty_stack () = false in

(top, is_empty_stack)

let pop stk =

let oldstk : 'a stack = snd ((fst stk) ()) in

let top = fst oldstk in

let is_empty_stack = snd oldstk in

(top, is_empty_stack)

let is_empty_stack stk =

let empty = snd stk in empty ()

let top stk =

let t = fst stk in fst (t ())

And it is used like this: you must assign a type for the

`empty_stack`

call, otherwise you are nagged by the value restriction again. That's where the type synonym comes in handy:

> let (x : int stack) = (empty_stack());;

val x : int stack

Then you can push elements into

`x`

. Note how the type of the result is different from `int stack`

, even considering type synonyms.

> push 3 x;;

val it : (unit -> int * int stack) * (unit -> bool)

= (<fun:push@173>, <fun:push@174>)

> push 4 (push 3 x);;

val it : (unit -> int *

((unit -> int * int stack) * (unit -> bool))) *

(unit -> bool)

= (<fun:push@173>, <fun:push@174>)

>

If you pop elements, the types get back to what they were, obviously. A funny side-effect of this strange definition is that

`top`

and `pop`

don't work on empty stacks because of type-checking, not any run-time checking -- so that the `failwith`

in the definition of `empty_stack`

will never be executed. Empty stacks have actually a different type. There must be a more type-friendly implementation of stacks using a procedural representation, but I decided to leave it for now and publish this solution because it is quite interesting by itself (although almost unusable in real code).

### EOPL - 2.3.2 - Procedural Representation

Section 2.3 is about strategies for representing data types. In section 2.3.1 an abstract interface for environments is presented, and then in section 2.3.2, Figure 2.3 shows a procedural implementation for the environment interface. Translated into F#, Figure 2.3 would be like the following:

In this case, function

let find_index a lst =

let rec loop l =

match l with

[] -> raise Not_found

| (x :: l') when x = a -> List.length l'

| (x :: l') -> loop l' in

loop (List.rev lst)

let list_find_position sym los =

if List.mem sym los then

Some (find_index sym los)

else

None

let empty_env () =

fun sym -> failwith (sprintf "No binding for %s" sym)

let apply_env env sym =

env sym

let extend_env syms vals env =

fun sym -> match list_find_position sym syms with

None -> apply_env env sym

| Some i -> List.nth vals i

In this case, function

`find_list_position`

is redundant, because `find_index`

does not take a predicate, so it's less generic than the version in the book. It shouldn't be a problem at this point, though. Function `find_index`

reverses the list, we can write a version that does without that:

let rec find_index2 a lst =

match lst with

[] -> raise Not_found

| (x :: lst') when x = a -> 0

| (x :: lst') -> 1 + find_index2 a lst'

## Wednesday, February 21, 2007

### EOPL - 2.2.2 - Exercise 2.12

This one asks you to implement alpha, beta and eta conversion on lambda-calculus expressions based on the substitution function of the previous exercise. For this we need a function to see if an identifier occurs free in an expression, similar to the one presented on section 1.3 and easy enough. The conversion functions can then be implemented quite simply:

These conversion functions simply return the same expression if they aren't of the right form. They could signal an error, depending on the application.

let rec occurs_free v exp =

match exp with

Identifier i when v = i -> true

| Lambda (x, e) when v <> x -> occurs_free v e

| App (e1, e2) -> (occurs_free v e1) || (occurs_free v e2)

| Prim (p, e1, e2) -> (occurs_free v e1) || (occurs_free v e2)

| _ -> false

let alpha_conversion exp new_id =

match exp with

Lambda (id, body) when not (occurs_free new_id body) ->

Lambda (new_id, lambda_calculus_subst body (Identifier new_id) id)

| _ -> exp

let beta_conversion exp =

match exp with

App (Lambda (id, body), e) -> lambda_calculus_subst body e id

| _ -> exp

let eta_conversion exp =

match exp with

Lambda (id, App (e, Identifier id'))

when (id=id') && (not (occurs_free id e)) -> e

| _ -> exp

These conversion functions simply return the same expression if they aren't of the right form. They could signal an error, depending on the application.

### EOPL - 2.2.2 - Exercise 2.11

Exercise 2.11 asks you to correct the definition of a substitution function on the lambda-calculus, to avoid variable capture. To do that, we need function

To define the new lambda-calculus expression type, we first define a type to specify primitives:

And here is the code for auxiliary functions and the substitution function:

The substitution function always does an alpha conversion (substitution of the identifier bound by the lambda) unless the bound identifier is the same as the one being substituted for. This surely works, as alpha conversion doesn't change the meaning of a lambda expression. An alternative would be to alpha convert only when a capture would occur, but this would require a further check like

It would make the code bigger, but not better. Both versions require linear scans of the body, so the efficiency shouldn't differ much between them.

`fresh-id`

from the previous exercise, but alas, we can't use it as is, because it is also asked to extend the definition of a lambda-calculus expression to includes literals and primitives. Nevertheless, it's an easy exercise.To define the new lambda-calculus expression type, we first define a type to specify primitives:

type Primitive = Sum | Mult

type LPExp = Identifier of string | Lambda of string * LPExp

| App of LPExp * LPExp | Literal of int

| Prim of Primitive * LPExp * LPExp

And here is the code for auxiliary functions and the substitution function:

let rec all_ids exp =

match exp with

Identifier i -> [i]

| Lambda (x, e) -> x :: (all_ids e)

| App (e1, e2) -> (all_ids e1) @ (all_ids e2)

| _ -> []

let fresh_id exp s =

let syms = all_ids' exp in

let rec loop n =

let sym = s + (string_of_int n) in

if List.mem sym syms then loop (n + 1) else sym in

loop 0

let rec lambda_calculus_subst exp subst_exp subst_id =

let rec subst exp =

match exp with

Identifier id when id = subst_id -> subst_exp

| Identifier id -> exp

| Lambda (id, body) when id = subst_id -> exp

| Lambda (id, body) ->

let id'=fresh_id body id in

let body'=lambda_calculus_subst body (Identifier id') id in

Lambda (id', subst body')

| App (e1, e2) -> App (subst e1, subst e2)

| Literal l -> exp

| Prim (p, e1, e2) -> Prim (p, subst e1, subst e2) in

subst exp

The substitution function always does an alpha conversion (substitution of the identifier bound by the lambda) unless the bound identifier is the same as the one being substituted for. This surely works, as alpha conversion doesn't change the meaning of a lambda expression. An alternative would be to alpha convert only when a capture would occur, but this would require a further check like

if List.mem id (all_ids body) then

// do alpha conversion

else

// just simple substitution

It would make the code bigger, but not better. Both versions require linear scans of the body, so the efficiency shouldn't differ much between them.

## Tuesday, February 20, 2007

### EOPL - 2.2.2 - Exercise 2.10

Chapter 2 includes examples and exercises for parsing and unparsing textual representations (e.g.

So here is Exercise 2.10 about generating fresh identifiers for renaming of variables that might be captured. I first defined a type for lambda-calculus expressions.

Then there's

`parse-expression`

on page 51). The parsing functions assume a Scheme reader, and just convert from a list representation to an abstract syntax-tree representation based on `define-datatype`

. The unparsing functions do the converse, from the syntax-tree representation to a list representation. As we don't have a list reader in F#, I skipped the examples and exercises related to parsing and unparsing. I also skipped other exercises that I felt wouldn't add much.So here is Exercise 2.10 about generating fresh identifiers for renaming of variables that might be captured. I first defined a type for lambda-calculus expressions.

type Exp = Identifier of string | Lambda of string * Exp

| App of Exp * Exp

Then there's

`all-ids`

and a converted version of `fresh-id`

:

let rec all_ids exp =

match exp with

Identifier i -> [i]

| Lambda (x, e) -> x :: (all_ids e)

| App (e1, e2) -> (all_ids e1) @ (all_ids e2)

let fresh_id exp s =

let syms = all_ids exp in

let rec loop n =

let sym = s + (string_of_int n) in

if List.mem sym syms then loop (n + 1)

else Identifier sym in

loop 0

## Monday, February 19, 2007

### EOPL - Chapter 2, Exercise 2.5

Chapter 2 is about data abstraction. Section 2.1 describes the concepts of interface, representation and implementation, and how a single interface may be implemented by different representations. Not much code there. Section 2.2 presents the constructions

Exercise 2.5 is a simple pattern-matching exercise to work with the definition of a binary tree data type, expressed in F# as

Then we can define

But this is a case where it's actually shorter to just use a single pattern match and a conditional, instead of pattern guards:

Even so, the function is somewhat big, and could be broken in two, but we'll let it as it is.

`define-datatype`

and `cases`

, to define and pattern-match over variant data types (or disjoint unions, or sum types, choose your preferred terminology). That is roughly equivalent to facilities already present in F#, so there's not much new here. Exercise 2.5 is a simple pattern-matching exercise to work with the definition of a binary tree data type, expressed in F# as

type BinTree = Leaf of int | Interior of string * BinTree * BinTree

Then we can define

`max-interior`

using pattern guards, which aren't available in the Scheme `cases`

construct:

let max_interior bt =

let rec maxint t =

match t with

Leaf _ -> failwith "Shouldn't get here"

| Interior (tag, Leaf l1, Leaf l2) -> (tag, l1 + l2)

| Interior (tag, Leaf l1, t2) ->

let tg, s = maxint t2 in

if s > s + l1 then (tg, s) else (tag, s+l1)

| Interior (tag, t1, Leaf l2) ->

let tg, s = maxint t1 in

if s > s + l2 then (tg, s) else (tag, s+l2)

| Interior (tag, t1, t2) ->

let tg1, s1 = maxint t1 in

let tg2, s2 = maxint t2 in

if s1 > s2 then

if s1 > s1 + s2 then (tg1, s1) else (tag, s1+s2)

else

if s2 > s1 + s2 then (tg2, s2) else (tag, s1+s2) in

fst (maxint bt)

But this is a case where it's actually shorter to just use a single pattern match and a conditional, instead of pattern guards:

let max_interior bt =

let rec maxint t =

match t with

Leaf i -> (None, i)

| Interior (tag, t1, t2) ->

let tg1, s1 = maxint t1 in

let tg2, s2 = maxint t2 in

if tg1 = None && tg2 = None then

(Some tag, s1 + s2)

elif s1 > s2 || tg2 = None then

if s1 > s1+s2 then (tg1, s1)

else (Some tag, s1+s2)

else

if s2 > s1+s2 then (tg2, s2)

else (Some tag, s1+s2) in

match bt with

Leaf _ -> failwith "Shouldn't happen"

| t -> maxint t |> fst |> Option.get

Even so, the function is somewhat big, and could be broken in two, but we'll let it as it is.

## Monday, February 12, 2007

### Scala

My choice for a functional programming language that integrates with .NET is F#. By the same token, when I think about writing software for the Java platform and wish to use a language better suited to my tastes, my choice is Scala. It's a pretty cool language that mixes OO and functional programming quite neatly, and with interesting theoretical studies to support it. The syntax was chosen to be similar to Java, which I don't like, but it's a minor problem. It's actively supported and developed, and is gaining momentum right now, which can be a good thing.

I need to write a simple program to talk to a Java program in the next few days, so I'll probably be using Scala for it. This means I may write posts about it in the near future.

I need to write a simple program to talk to a Java program in the next few days, so I'll probably be using Scala for it. This means I may write posts about it in the near future.

## Thursday, January 25, 2007

### EOPL - 1.2.4 - Exercise 1.18

Exercise 1.18 takes advantage of Scheme's uniform treatment of code and data, so the functions proposed should return lists that can be

Next, I defined a data type to represent list operations:

So it's easy to define

Thus we get

So we have a description of the necessary list operations, but it's not directly executable as in Scheme. So we need a function to execute the list operations returned on a list, and this is

The case that leads to an exception is to find a single

It's quite easy to define a function to execute these

`eval`

uated to get some effect. Furthermore, there are typing issues, so adaptations are needed. The first function, `compose`

, is easy enough:

let compose p1 p2 = fun x -> p1 (p2 x)

Next, I defined a data type to represent list operations:

type ListOp = Car | Cdr | Compose of ListOp * ListOp | Error

So it's easy to define

`car_cdr`

, but it doesn't return a list to evaluate, rather a `ListOp`

object. Also, because of typing it was easier to include a variant `Error`

of type `ListOp`

and eliminate parameter `errval`

.

let rec car_cdr s slist =

match slist with

[] -> Error

| s1 :: rslist when s1 = s -> Car

| _ :: rslist -> Compose (car_cdr s rslist, Cdr)

Thus we get

> car_cdr "c" ["a"; "b"; "c"];;

val it : ListOp = Compose (Compose (Car,Cdr),Cdr)

So we have a description of the necessary list operations, but it's not directly executable as in Scheme. So we need a function to execute the list operations returned on a list, and this is

`run_listop`

let rec run_listop op lst =

match op with

Car -> List.hd lst

| Compose (c1, Cdr) -> run_listop c1 (List.tl lst)

| _ -> failwith "can't do"

The case that leads to an exception is to find a single

`Cdr`

without a previous `Car`

. This is a good indication that the type was not designed properly, but we will not bother with this here. Function `car_cdr2`

doesn't need explicit `Compose`

operations, and returns a list of list operations that must be applied in succession.

let car_cdr2 s slist errval =

let rec loop lst =

match lst with

[] -> []

| l :: rlst when s = l -> [Car]

| _ :: rlst -> Cdr :: (loop rlst) in

List.rev (loop slist)

It's quite easy to define a function to execute these

`ListOp`

lists, but not that interesting at this point.
## Monday, January 15, 2007

### EOPL - 1.2.4 - Exercise 1.17, sorting

Another exercise. This one involves binary trees and sorting. For the bintrees and finding a path through them to an element, we define two types:

Then we can define function

For sorting, I chose to implement a rudimentary quicksort (with the first element as pivot). As with previous functions, beware of the value restriction.

I wrote the internal function

To sort with a different predicate is a straightforward change in either version. Here is the longer version working with a predicate:

Finally, just for fun, I wrote a merge sort function too.

It's quite long, but I didn't bother trying to get a shorter version.

type BinTree = Empty | Node of int * BinTree * BinTree

type direction = Left | Right

Then we can define function

`path`

, returning a list of directions:

let rec path n bst =

match bst with

Empty -> failwith ("number " + (string_of_int n) + " not found in tree")

| (Node (x, left, right)) when n = x -> []

| (Node (x, left, right)) when n < x -> Left :: path n left

| (Node (_, left, right)) -> Right :: path n right

For sorting, I chose to implement a rudimentary quicksort (with the first element as pivot). As with previous functions, beware of the value restriction.

let rec sort lst =

let left_part x (lp, rp) = (x :: lp, rp) in

let right_part x (lp, rp) = (lp, x :: rp) in

let rec partition p lst =

match lst with

[] -> ([], [])

| (x :: rlst) when x < p -> left_part x (partition p rlst)

| (x :: rlst) when x > p -> right_part x (partition p rlst)

| (x :: rlst) -> partition p rlst in

match lst with

[] -> []

| (x :: rlst) -> let lp, rp = partition x lst in

(sort lp) @ [x] @ (sort rp)

I wrote the internal function

`partition`

because it was part of the exercise, but it is already there in the standard library. Using this fact, we can get a much shorter version of quicksort:

let rec sort lst =

match lst with

[] -> []

| (x :: rlst) -> let lp, rp = List.partition (fun n -> n < x) rlst in

(sort lp) @ [x] @ (sort rp)

To sort with a different predicate is a straightforward change in either version. Here is the longer version working with a predicate:

let rec sort pred lst =

let left_part x (lp, rp) = (x :: lp, rp) in

let right_part x (lp, rp) = (lp, x :: rp) in

let rec partition p lst =

match lst with

[] -> ([], [])

| (x :: rlst) when x = p -> partition p rlst

| (x :: rlst) when (pred x p) -> left_part x (partition p rlst)

| (x :: rlst) -> right_part x (partition p rlst) in

match lst with

[] -> []

| (x :: rlst) -> let lp, rp = partition x lst in

(sort pred lp) @ [x] @ (sort pred rp)

Finally, just for fun, I wrote a merge sort function too.

let rec merge_sort (lst:'a list) =

let merge_pairs (ll1, rl1) (ll2, rl2) =

(ll1 @ ll2, rl1 @ rl2) in

let split_pairs i x =

if i < (lst.Length / 2) then ([x], []) else ([], [x]) in

let split l =

List.fold_right merge_pairs (List.mapi split_pairs l) ([], []) in

let rec merge lon1 lon2 =

match (lon1, lon2) with

([], _) -> lon2

| (_, []) -> lon1

| (x :: rlon1, y :: rlon2) when x <= y -> x :: (merge rlon1 lon2)

| (x :: rlon1, y :: rlon2) -> y :: (merge lon1 rlon2) in

match lst with

[] -> []

| [x] -> [x]

| _ -> let l, r = split lst in merge (merge_sort l) (merge_sort r)

It's quite long, but I didn't bother trying to get a shorter version.

## Sunday, January 14, 2007

### EOPL - 1.2.4 - Exercise 1.16

And now back to business, nothing really exciting yet: the next batch of exercises. The first is function

This is the Scheme version of

The next functions work on lists of symbols, so we repeat here the necessary type definition for symbol expressions.

And the functions can thus be written:

`up`

that in F# ends up being the same as concat, unless we define some new type.

// if not defining a new type that may be a list or a single element,

// up will work like concat, on lists of lists

let rec up lst =

match lst with

[] -> []

| (l :: rlst) -> l @ (up rlst)

This is the Scheme version of

`up`

, for comparison:

(define up

(lambda (lst)

(if (null? lst)

'()

(if (list? (car lst)

(append (car lst) (up (cdr lst)))

(cons (car lst) (up (cdr lst)))))))

The next functions work on lists of symbols, so we repeat here the necessary type definition for symbol expressions.

type SymbolExp = Symbol of string | SList of SymbolExp list

And the functions can thus be written:

let rec swapper s1 s2 slist =

match slist with

[] -> []

| (s :: rslist) -> swapper_in_symbol_exp s1 s2 s ::

(swapper s1 s2 rslist)

and swapper_in_symbol_exp s1 s2 sexp =

match sexp with

(Symbol s) when s = s1 -> Symbol s2

| (Symbol s) when s = s2 -> Symbol s1

| (SList sl) -> SList (swapper s1 s2 sl)

| _ -> sexp

let rec count_occurrences sym slist =

match slist with

[] -> 0

| (s :: rsl) -> (count_occurrences_sexp sym s) +

(count_occurrences sym rsl)

and count_occurrences_sexp sym sexp =

match sexp with

(Symbol s) when s = sym -> 1

| (SList sl) -> count_occurrences sym sl

| _ -> 0

let rec flatten slist =

match slist with

[] -> []

| ((Symbol s) :: rsl) -> (Symbol s) :: (flatten rsl)

| ((SList sl) :: rsl) -> (flatten sl) @ (flatten rsl)

// lon1 and lon2 are sorted lists of numbers

let rec merge lon1 lon2 =

match (lon1, lon2) with

([], _) -> lon2

| (_, []) -> lon1

| (x :: rlon1, y :: rlon2) when x <= y -> x :: (merge rlon1 lon2)

| (x :: rlon1, y :: rlon2) -> y :: (merge lon1 rlon2)

## Tuesday, January 2, 2007

### EOPL - 1.2.3 - Other Patterns of Recursion

Forgot to post the code for this section. Simple stuff, and only three functions.

let rec list_sum l =

match l with

[] -> 0

| (x :: rl) -> x + list_sum rl

let rec partial_vector_sum von n =

if n = 0 then 0

else von.(n - 1) + partial_vector_sum von (n - 1)

let vector_sum von =

partial_vector_sum von von.Length

### EOPL - 1.2.4 - Some Exercises - 1.15

These are F# solutions to Exercise 1.15. In some places the functions proposed in the exercise are not completely suited to a ML language, so I made notes in the comments, but otherwise there is little that is exciting about these functions. I did alternative versions in some cases, even though the whole point of this exercise (and the rest from Section 1.2) is to write recursive functions to get a feel for them.

The function

The function

`product`

once again runs into troubles with the value restriction. If one of the parameters is an empty list, the F# system won't recognize the result as a simple data value, so it will complain. The only way around it is to use type annotations, as noted in the comments after both versions of the function.

let rec duple n x =

if n = 0 then [] else x :: (duple (n - 1) x)

// invert would probably accept a list of real pairs in F#

let invert lp =

let invpair p =

match p with

[] -> []

| (a :: b :: []) -> [b; a]

| _ -> failwith "invalid list" in

List.map invpair lp

let rec filter_in p lst =

match lst with

[] -> []

| (x :: rl) when p x -> x :: (filter_in p rl)

| (_ :: rl) -> filter_in p rl

let rec every p lst =

match lst with

[] -> true

| (x :: rl) when p x -> every p rl

| _ -> false

let every2 p lst =

List.fold_left (fun b x -> b && p x) true lst

let rec exists p lst =

match lst with

[] -> false

| (x :: rl) when p x -> true

| (_ :: rl) -> exists p rl

// It's not possible to return numbers and booleans, so we could

// use an algebraic data type, or int option, which seems better

let vector_index p (v:'a array) =

let rec search i =

if i = v.Length then None

elif p v.(i) then Some i

else search (i + 1) in

search 0

// the test given can't be easily expressed in F#

// also: fragile for negative n

let rec list_set lst n x =

match (lst, n) with

([], _) -> []

| (elt :: rl, 0) -> x :: rl

| (elt :: rl, i) -> elt :: (list_set rl (n - 1) x)

// value restriction troubles: any empty list gives an error

let rec product l1 l2 =

match (l1, l2) with

(_, []) -> []

| ([], _) -> []

| (x :: rl1, _) -> (List.map (fun e -> (x, e)) l2) @ (product rl1 l2)

// value restriction troubles: any empty list gives an error

let product2 l1 l2 =

List.concat (List.map (fun x -> List.map (fun e -> (x, e)) l2) l1)

(*

To call product with an empty list as argument, you must annotate its type:

> product [1; 2; 3] ([] : int list);;

val it : (int * int) list = []

*)

// once again, this function makes less sense in F# than in Scheme

let down lst =

List.map (fun x -> [x]) lst

// explicitly recursive version:

let rec down2 lst =

match lst with [] -> [] | (x::rl) -> [x] :: (down2 rl)

// scheme version

(*

(define down

(lambda (lst)

(if (null? lst)

'()

(cons (list (car lst))

(down (cdr lst))))))

*)

// more type inference nuances: these types must be written down

let vector_append_list (v:'a array) (lst:'a list) =

let rec copy src dst i =

if i = 0 then ()

else (dst.(i-1) <- src.(i-1); copy src dst (i-1)) in

let rec copy_list_to_vector ls vc i =

match ls with

[] -> ()

| (x :: rls) -> (vc.(i) <- x;

copy_list_to_vector rls vc (i + 1)) in

let newv = Array.create (v.Length + lst.Length) 0 in

(copy v newv v.Length;

copy_list_to_vector lst newv v.Length;

newv)

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