Type Inference with Rank 1 Polymorphism for Type-Directed Compilation of ML

This paper defines an extended polymorphic type system for an ML-style programming language, and develops a sound and complete type inference algorithm. Different from the conventional ML type discipline, the proposed type system allows full rank 1 polymorphism, where polymorphic types can appear in other types such as product types, disjoint union types and range types of function types.

See post below, I guess I should study this.


Sneak Peak: the Hi language

My language is slowly progressing, so a sneak peak at the prelude and some example programs.

After studying some Mondrian code a few years ago, I decided to call my language Hieronymus after my own favorite painter Hieronymus Bosch. However, Hi seems to be so ever more nice.

Good, the interpreter is as good as done. I rewrote it in such a manner that it should be relatively easy to implement a small runtime.

I still got some problems with the type checker and rank-1 polymorphism which I am not sure I want to solve.

namespace system (

interface num = #a where (
def plus: a -> a -> a
def min: a -> a -> a
def mul: a -> a -> a
def div: a -> a -> a

def +: ::num a => a -> a -> a =
\x,y -> x.plus x y

def -: ::num a => a -> a -> a =
\x,y -> x.min x y

def *: ::num a => a -> a -> a =
\x,y -> x.mul x y

def /: ::num a => a -> a -> a =
\x,y -> x.div x y


namespace system (

interface ord = #a where (
def compare: a -> a -> int

def ==: ::ord a => a -> a -> bool =
\x,y -> int_eq (x.compare x y) 0

def <: ::ord a => a -> a -> bool =
\x,y -> int_less (x.compare x y) 0

def <=: ::ord a => a -> a -> bool =
\x,y -> int_less (x.compare x y) 1

def >: ::ord a => a -> a -> bool =
\x,y -> int_less (x.compare y x) 0

def >=: ::ord a => a -> a -> bool =
\x,y -> int_less (x.compare y x) 1


namespace system (

type bool = [ true | false ]

def not: bool -> bool =
[ true -> false
| _ -> true ]

def and: bool -> bool -> bool =
[ true, true -> true
| _ , __ -> false ]

def or: bool -> bool -> bool =
[ false, false -> false
| _ , __ -> true ]

def eq: bool -> bool -> bool =
[ false, false -> true
| true , true -> true
| _ , __ -> false ]

instance ord bool where (
def compare: bool -> bool -> int =
[ false, false -> 0
| true, true -> 0
| false, _ -> 0-1 ]

namespace system (

// type int = [ MININT | ... | -1 | 0 | 1 | 2 | ... | MAXINT ]
type int = {system.int}

def int_monadic_min: int -> int =
\v0 -> {int_monadic_min[v0]}

def int_dyadic_min: int -> int -> int =
\v0,v1 -> {int_dyadic_min[v0,v1]}

def int_plus: int -> int -> int =
\v0,v1 -> {int_plus[v0,v1]}

def int_mul: int -> int -> int =
\v0,v1 -> {int_mul[v0,v1]}

def int_div: int -> int -> int =
\v0,v1 -> {int_div[v0,v1]}

def int_compare: int -> int -> int =
\v0,v1 -> {int_compare[v0,v1]}

def int_eq: int -> int -> bool =
\v0,v1 -> {int_eq[v0,v1]}

def int_less: int -> int -> bool =
\v0,v1 -> {int_less[v0,v1]}

def int_magic_tick: () -> bool =
\v0 -> {int_magic_tick[v0]}

instance num int where (
def plus: int -> int -> int = int_plus
def min: int -> int -> int = int_dyadic_min
def mul: int -> int -> int = int_mul
def div: int -> int -> int = int_div

instance ord int where (
def compare: int -> int -> int = int_compare

namespace system (

type char = {system.char}

def char_compare: char -> char -> char =
\v0,v1 -> {char_compare[v0,v1]}

def char_eq: char -> char -> bool =
\v0,v1 -> {char_eq[v0,v1]}

def char_less: char -> char -> bool =
\v0,v1 -> {char_less[v0,v1]}

def char_ascii_code: char -> int =
\v0 -> {char_ascii_code[v0]}

def char_ascii_char: int -> char =
\v0 -> {char_ascii_char[v0]}

instance ord char where (
def compare: char -> char -> int = char_compare

namespace system (

def file_read: list char -> list char =
\v0 -> {file_read[v0]}

def file_write: list char -> list char -> unit =
\v0,v1 -> {file_write[v0,v1]}


namespace list (

using system

type list = \a => [nil | cons a (list a)]

instance ord (list a) where (
def compare: ::ord a => int =
[ nil , nil -> 0
| nil , _ -> 0-1
| _ , nil -> 1
| cons x xx, cons y yy ->
if x == y then xx.compare xx yy
else x.compare x y ]

def concat: list a -> list a -> list a =
[ nil, yy -> yy
| cons x xx, yy -> cons x (concat xx yy) ]

def map: (a -> b) -> list a -> list b =
[ f, nil -> nil
| f, cons x xx -> cons (f x) (map f xx) ]

def head: list a -> list a = [ cons x xx -> x ]

def tail: list a -> list a = [ cons x xx -> xx ]

namespace system (

type tuple_2_t = \t0 => \t1 => [tuple_2 t0 t1]

instance ::ord t0 => ::ord t1 => ord (tuple_2 t0 t1) where (

def compare: tuple_2_t t0 t1 -> tuple_2_t t0 t1 -> int =
[ tuple_2 x0 x1, tuple_2 y0 y1 ->
let c = x0.compare x0 x1 in
if c == 0 then x1.compare x1 y1 else c ]


type tuple_3_t = \t0 \t1 \t2 => [tuple_3 t0 t1]

/* Some example programs */

using system

using list

def fac: int -> int =
[ 0 -> 1
| 1 -> 1
| n -> n * (fac (n - 1)) ]

def collatz: int -> int =
let even = [n -> (n / 2) * 2 == n] in
[ 1 -> 1
| n -> if even n
then collatz (n / 2)
else collatz (1 + (n * 3)) ]

def fibs: int -> list int =
[ 0 -> cons 1 (cons 1 nil)
| n -> let ff = fibs (n-1) in
cons (head ff + (head (tail ff))) ff]

def main: (int, list int) =
let f = [(x,y) -> y] in
let p = (let n = 3 in (n, fibs n)) in f p



MetaLua is a very interesting metaprogramming Lua dialect.

-- the "-{...}" means that we're going to do compile-time
-- stuff (here, syntax extension)
-{ block:
-- Register the additional keywords in mlp.lexer
mlp.lexer:add{ "let", "in" }

-- Extend the expression parser; code generation is
-- delegated to the function let_in_builder() below.
"let", mlp.id, "=", mlp.expr, "in", mlp.expr,
builder = let_in_builder }

-- This creates the code returned by the macro.
-- Notice the holes-in-quote-in-splice.
local function let_in_builder (x)
local variable, value, expr = unpack (x)
return +{

function (-{variable})
return -{expr}
end (-{value}) }

} -- back to "normal" code

a, b, c = 1, 1, -2
roots = let sqrt_delta = (b^2-4*a*c)^0.5 in
{ (sqrt_delta-b)/(2*a), (-sqrt_delta-b)/(2*a) }


SML# Project

SML# is a new SML dialect developed by Atsushi Ohori (among others). It extends SML with a number of constructs and uses the MLton runtime system.

From their site:

SML# supports the following practically important new features:

  • Seamless Interoperablility with C

  • Record polymorphism

  • Rank1 polymorphism

SML# is carefully designed so that

  • it is a conservative extension of Standard ML: SML# compiler compiles any program that conforms to the Definition of Standard ML.

  • it supports the Basis Library.

Currently, SML# (0.20 release version) is available in the following forms.

  • source package (that can be build on linux, solaris, cygwin)

  • Mac OS Intel/PowerPC universal binary package

  • Windows binary installer


Erlang and Concurrency by Pang

“After a long and careful analysis the results are clear: 11 out of 10 people can't handle threads.”

Todd Hoff

From this talk, from which there is this movie.

Ah well, who doesn't know Erlang these cheap-information days?


OCaml and Emily In a Walnut

I program a lot of ocaml code. Not to say that there are no nicer languages, for all it is worth, ocaml is just the closest to my personal programming style: plain typed functional programming with an occasional impure construct.

Ocaml is old by now, it is older than Java. Some tools are pretty mature, one of the tools I really want to look at is Emily, of which I didn't know so far. Actually, I am not sure I quite grok it yet. Compiled-in security policies? Ouch.


Just a Song

My mistake, just two songs:

And some gossip: Amy Winehouse Arrested For Interfering With Husband's Assault Case: Report


S has a Left Inverse

Text below is by Shin-Cheng Mu 穆信成. Can you spot a bug ;-)

S is injective

Recall the definition of S:

S : (A -> B -> C) -> (A -> B) -> A -> C
S = λ x y a -> x a (y a)

I am assuming a simple semantics of sets and functions, and by S being injective I mean that S x = S x' ⇒ x = x', which can be trivially shown below:

S x = S x'
≡ { η expansion, for all y : A -> B, a : A }
(∀ a, y : S x y a = S x' y a)
≡ { definition of S }
(∀ a, y : x a (y a) = x' a (y a))
⇒ { choose y = K b for some b }
(∀ a, b : x a (K b a) = x' a (K b a))
≡ { definition of K: K b a = b }
(∀ a, b : x a b = x' a b)
≡ { pointwise equality }
x = x'

Now that we know S is injective, there ought to exist some function S⁻¹ such that S⁻¹ ○ S = id. Nakano san claimed that a definition would be:

S⁻¹ : ((A -> B) -> A -> C) -> A -> B -> C
S⁻¹ = λ x a b -> x (K b) a

That S⁻¹ ○ S = id is easy to see:

S⁻¹ (S x) a b
= (S x) (K b) a
= x a (K b a)
= x a b

From another direction, we have only S ○ S⁻¹ ⊆ id since S is not a surjective function. How the range of S look like? Inspecting the definition of S. Since y is applied only once to a, the value of y on other input does not matter. That is, the range of S consists of only functions e such that:

e y a = e y' a for all y, y' such that y a = y' a ......(1)

We will show that S (S⁻¹ e) = e for all e satisfying (1):

S (S⁻¹ e) y a
= { definition of S }
S⁻¹ e a (y a)
= { definition of S⁻¹ }
e (K (y a)) a
= { by (1), since K (y a) a = y a }
e y a

Inverting higher-order functions?

Some endnotes. Once Nakano and I thought we discovered how to invert higher-order functions (and even derive the necessary side conditions, like the one on e above) by drawing λ expressions as trees and manipulating them. It turned out that I overlooked something obvious in the very beginning and the result was a disaster.

Wiimote Interactive Whiteboard


Humanitarian Scientific Achievement Award

Burnham Institute for Medical Research
Professor Yu Yamaguchi, M.D., Ph.D., was recently awarded The Humanitarian Scientific Achievement Award by the MHE Research Foundation. The focus of the foundation is to find a cure for Multiple Hereditary Exostoses, a rare genetic bone disorder. The disorder causes people to grow exostoses (bone tumors) on their bones. MHE patients can also suffer from non-skeletal medical issues including mental and neurological issues.

  1. Mild social interaction deficits (excessive shyness, adherence to routines)

  2. Heightened sensitivities to sensory stimulation (sounds, touch, taste)

  3. Difficulties to concentrate

  4. Muscle weakness (easy to get tired)

  5. Reduced levels of fear/anxiety (well, just in mice, that is)

He believes these symptoms can be explained by the deficiency of heparan sulfate in nerve and muscle cells.

Also of interest, HSV immune sog9 cells?


Birdflu Breaking News

Nice application of interactive media for a news aggregator which interactively shows where the latest news/epedemic originates.

See http://www.birdflubreakingnews.com/.



Obligatory advertisement:

The reactable is a collaborative electronic music instrument with a tabletop tangible multi-touch interface. Several simultaneous performers share complete control over the instrument by moving and rotating physical objects on a luminous round table surface. By moving and relating these objects, representing components of a classic modular synthesizer, users can create complex and dynamic sonic topologies, with generators, filters and modulators, in a kind of tangible modular synthesizer or graspable flow-controlled programming language.


The Life and Death of Colonel Blimp

Michael Powell and Emeric Pressburger's first Technicolor masterpiece, The Life and Death of Colonel Blimp (1943), transcends its narrow wartime propaganda to portray in warm-hearted detail the life and loves of one extraordinary man. The film's clever narrative structure first presents us with the imposingly rotund General Clive Wynne-Candy (Roger Livesey in his greatest screen performance), a blustering old duffer who seems the epitome of stuffy, outmoded values. But traveling backwards 40 years we see a different man altogether: the young and dashing officer "Sugar" Candy. Through a series of affecting relationships with three women (all played to perfection by Deborah Kerr) and his touching lifelong friendship with a German officer (Anton Wallbrook), we see Candy's life unfold and come to understand how difficult it is for him to adapt his sense of military honor to modern notions of "total war." Notoriously, this is the film that Winston Churchill tried to have banned, and indeed its sympathetic portrayal of a German officer was contentious in 1943, though one suspects that Churchill's own blimpishness was a factor too.
[Through IMDB]


Marieke J.H. Devillers-van Agtmaal (1943-2007)

My mother unexpectedly passed away this morning after a life of struggling with her mental illness. Above a piece of art from her.


On One-Pass CPS Transformations

I don't like my stack based interpreter anymore. Possibly, I should go for CPS too?


Convergent Anycast

Convergent Anycast
is a protocol which avoids the need for all nodes in a network to synchronize duty cycles in order to communicate [Kai-Wei Fan, Sha Liu, and Prasun Sinha from the Computer Science & Engineering department of Ohio State University].


Software Radio Implementation for Sensor Networking

Software Radio Implementation of Short-range Wireless Standards for Sensor Networking by Thomas Schmid (demo abstract).

Lectures on Types and Programming Languages

Somehow it helps when you are from Glasgow, or go to lectures there.

Lecture Times

  • Monday 11.00 Boyd Orr LT B (until 30th October), then F121,
    17 Lilybank Gardens

  • Wednesday 9.00 2 University Gardens (209)

  • Friday 10.00 Maths 214

Simon Gay's lectures on Types and Programming Languages are a great resource.


Eriks SunSPOT Adventures

We are using the TinyNodes from ShockFish in our curriculum, which are excellent. This new platform from Sun really is beautiful though.

Short informal battle list, some figures are guessed.

Power Consumptionvery low, 20mA, 6microA100 mA, 32 microA
LanguageNesCJava (not realtime)
Ledsred (red, yellow, green)8 tri-color LEDs
Poweradapter or two AAs3.7V rechargeable, 750 mAh, USB
Light Sensoryesyes
Accelero Meterno3-axis
Temperature Sensoryesyes
SimulatorMatureUnder Development
PricingEuro 600,-to be announced

A cool and fun device, maybe not particularly well-suited for embedded extremely low-power applications, but damned ... cool and fun.

Why do they need all that memory?


Medics Allegedly Sneak Peek at George Clooney's Private Records

Another slow day, some people -yeah, even me, it seems- just have to read up on celebs.

Twenty-seven employees at Palisades Medical Center have reportedly been suspended for a month without pay for allegedly accessing George Clooney's medical records after the actor/director was hospitalized with injuries from a motorcycle crash in September. The investigation reportedly is continuing, with more than 40 employees under the crosshairs.

Through eWeek


Thin Clients

I want to buy an inexpensive thin client and am looking at a number of options now, listed below for further reference:

  1. Koolu

  2. Fit-PC

  3. Linutop


Hughes on Testing

Quickcheck is a marvelous spin-off of Haskell. John Hughes has started a company Quviq which now markets the technology behind it.


Comic 202 of xkcd.

Stuff I've seen my students looking at the last weeks in class: YouTube, games, poker, MSN, community sites, blogs, and Pr0n.


Counting in Tossim

Just a silly application I wrote. A very naive approach to counting in a small sensor network. Programmed in NesC under TinyOS 1.0 and tested under tinyviz.

Since my students might read my blog, and this is an assignment for them, no source code but a simple description.

The network builds a small spanning tree in which a node continuously broadcasts the total of the branch of which it is the root.

All nodes run the same application, node 0 starts as the root of the tree. All nodes remain silent until they receive a broadcast message, node 0 initiates the algorithm.

A node alternatingly broadcasts an AskTotal() to everybody or an AnswerTotal(id,total) message to it's parent. The parent of a node is the first node from which it received an AskTotal().
Nodes store (id,total) pairs in a set. The total send by a node is the sum of the totals in this set plus one. (I guess I should restrict the protocol to just one message.)

The result is a pretty robust algorithm for static networks of a fixed maximal size and fixed maximal degree on the nodes. The algorithm gives the correct total in twice the depth of the tree time. For the shown network of 30 nodes, it calculates a correct answer in about 20 seconds.

Of course, you should never do it this way...


Area-Time Complexity of Binary Multiplication

Seems I am getting interested in an old hobby again. Anyway, the following is an interesting result.

"The area-time complexity of binary multiplication," written by R. P. Brent and H. T. Kung.

Three posts on one day. Oops, should get back to work.

Computing Solutions Uniquely Collapses the Polynomial Hierarchy

From siteseer, I am reading this, references the well-known "NP is as easy as detecting unique solutions" by Valiant and Vazirani (I lost my digital copy of that article).

The zoo comes in handy when reading an article like this.

Two for One: Scheme Interpreter in Python

Through this blog, a simple continuation-based scheme interpreter in Python.

#This is a implementations of an interpreter
#for a small subset of scheme.
#What it has:
# Look at the function 'eval'
# look at the dictionary 'predefineds'
#1)Fibonacci numbers
#python scheme.py
#>>>(define fibonacci
#... (lambda (n)
#... (define fib
#... (lambda (n1 n2 cnt)
#... (if (= cnt n)
#... n1
#... (fib n2 (+ n1 n2) (+ cnt 1)))))
#... (fib 0 1 0)))
#>>>(display (fibonacci 10))
#python scheme.py
#>>>(define list (lambda l l))
#>>>(define message
#... (lambda (cont msg)
#... (call/cc
#... (lambda (newCont)
#... (cont (cons newCont msg))))))
#>>>(define f
#... (lambda (fname cont msg)
#... (display (cons fname msg))
#... (define msgList (message cont (+ 1 msg)))
#... (f fname (car msgList) (cdr msgList))))
#>>>(define msg
#... (call/cc (lambda (cont)
#... (f "f1:" cont 1))))
#>>>(f "f2" (car msg) (cdr msg))
#24-Feb-2005 Added quote and the quote symbol '
#25-Feb-2005 Fixed a bug with begin
#25-Feb-2005 Added eval
#25-Feb-2005 Added py-eval and py-exec

#Uncomment the following line if you are using python 2.2
#from __future__ import generators
import re

py_context = {}
py_eval_func = eval

class context:
def setVars(self, names, values):
if names == None:
elif isinstance(names, symbol):
self.vars[str(names)] = values
(name, restNames) = names
(value, restValues) = values
self.setVars(restNames, restValues)

def __init__(self, parent, var_names = None, values = None):
self.parent = parent
self.vars = {}
self.setVars(var_names, values)

def get(self, var_name):
if self.vars.has_key(var_name):
return self.vars[var_name]
elif self.parent != None:
return self.parent.get(var_name)
raise KeyError("Unknown variable "+var_name)

def set(self, var_name, value):
if self.vars.has_key(var_name):
self.vars[var_name] = value
elif self.parent != None:
return self.parent.set(var_name, value)
raise Key("Unknown variable " + var_name)

def define(self, var_name, value):
self.vars[var_name] = value

class symbol:
def __init__(self, value):
self.value = value

def __str__(self):
return self.value

def __repr__(self):
return "symbol('"+self.value+"')"

def __eq__(self, value):
if isinstance(value, symbol):
return self.value == value.value
return False

# Predefined Symbols (can't be redefined)
LAMBDA = symbol("lambda")
IF = symbol("if")
BEGIN = symbol("begin")
SET = symbol("set!")
DEFINE = symbol("define")
LOAD = symbol("load")
QUOTE = symbol("quote")

#The tokenizer

#Token Types
ATOM = 3
DOT = 5

tokens_re = re.compile(r'\(|\)|(?:[\w+\-*/<>=!?.]+)|'+
def tokenize(code):
"""This is a very simple tokenizer,
it accepts a string that represents
the code an returns a list of
token type, token paris"""

tokens = tokens_re.findall(code)
for token in tokens:
if token == "(":
yield (OPENBRACKET, token)
elif token == ")":
yield (CLOSEBRACKET, token)
elif token == ".":
yield (DOT, token)
elif token == "'":
yield (SINGLE_QUOTE, token)
elif token.isdigit():
yield (ATOM, int(token))
elif token[0]=='"':
yield (ATOM, token[1:-1].replace(r'\\', "\\").replace(r'\"', r'"'))
elif token[0]=="#":
if token[1]=="\\":
char = token[2:]
if char == "space":
char = " "
if char == "newline":
char = "\n"
yield (ATOM, char)
elif token[1]=="t":
yield (ATOM, True)
elif token[1]=="f":
yield (ATOM, False)
raise Exception("Invalid token "+ token)
yield (SYMBOL, symbol(token))

def process_sexpr(tokens):
token_type, value = tokens.next()
if token_type == SINGLE_QUOTE:
return [QUOTE, [process_sexpr(tokens), None]]
elif token_type == OPENBRACKET:
cons = [None, None]
lst = cons
token = None
while True :
token = process_sexpr(tokens)
if token not in [")", "."]:
cons[1] = [token, None]
cons = cons[1]
if token == ".":
cons[1] = process_sexpr(tokens)
token_type, token = tokens.next()
if token == ")":
return lst[1]
raise Exception("expected close bracket for expression "+
return value

def sexpr(text):
return process_sexpr(tokenize(text))

def sexprs(text):
"""Build an s-expression from a string"""
lst = [None, None]
cur = lst
tokens = tokenize(text)
while True:
cur[1] = [process_sexpr(tokens), None]
cur = cur[1]
except StopIteration:
return lst[1]

#Pedefined Functions

#Convert a python function into a form
#suitable for the interpreter
def predefined_function(function):
def func(continuation, args):
argList = []
while args!=None:
arg, args = args
return continuation, function(*argList)
return func

#Some basic predefined functions

def display(obj):
print obj

def callcc(continuation, args):
(func, nil) = args
def cont_func(cont, (arg, nil)):
return (continuation, arg)
return func(continuation, (cont_func, None))

def gen_eval(context):
def eval_func(continuation, arg):
expr, nil = arg
return (eval_continuation(continuation, context, expr), None)
return eval_func

def py_exec(continuation, arg):
code, nil = arg
exec code in py_context
return (continuation, None)

def py_eval(continuation, arg):
code, nil = arg
return (continuation, py_eval_func(code, py_context))

global_context = context(None)

predefineds = {"+":predefined_function(lambda *args:sum(args)),
"*":predefined_function(lambda *args:reduce(int.__mul__, args)),
"-":predefined_function(lambda a, b:a - b),
"<":predefined_function(lambda a, b:a < b),
">":predefined_function(lambda a, b:a > b),
"=":predefined_function(lambda a, b:a == b),
"cons":predefined_function(lambda a, b:[a, b]),
"car":predefined_function(lambda(a, b):a),
"cdr":predefined_function(lambda(a, b):b),

global_context.vars = predefineds


#A continuation for the evaluation of an expression
class eval_continuation:

def __init__(self, continuation, context, expr):
self.next = continuation
self.context = context
self.expr = expr

def run(self, val):
return eval(self.next, self.context, self.expr)

def eval_str(continuation, context, code):
if isinstance(code, str):
code = sexpr(code)
return eval(continuation, context, code)

#The eval method
def eval(continuation, context, code):
if isinstance(code, list):
if code[0] == LAMBDA:
return eval_lambda(continuation, context, code)
elif code[0] == IF:
return eval_if(continuation, context, code)
elif code[0]== BEGIN:
return eval_begin(continuation, context, code)
elif code[0] == DEFINE:
return eval_define(continuation, context, code)
elif code[0] == SET:
return eval_set(continuation, context, code)
elif code[0] == QUOTE:
return eval_quote(continuation, context, code)
elif code[0] == LOAD:
return eval_load(continuation, context, code)
return eval_apply(continuation, context, code)
elif isinstance(code, symbol):
return (continuation, context.get(str(code)))
return (continuation, code)

#Helper to evaluate a list of expressions
class expr_list_continuation:
def __init__(self, continuation, context, exprs):
expr, rest = exprs
self.expr = expr
if rest == None:
self.continuation = continuation
self.continuation = expr_list_continuation(continuation,
context, rest)
self.context = context

def run(self, value):
return eval(self.continuation, self.context, self.expr)

def eval_expr_list(continuation, context, exprs):
return (expr_list_continuation(continuation, context, exprs), None)

def eval_quote(continuation, context, code):
(quote, (item, nil)) = code
return (continuation, item)

def eval_load(continuation, context, code):
(load, (filepath, nil)) = code
fi = file(filepath)
exprs = sexprs(fi.read())
return eval_expr_list(continuation, context, exprs)

def eval_begin(continuation, context, code):
begin, exprs = code
return eval_expr_list(continuation, context, exprs)

def eval_lambda(continuation, parent_context, code):
(lmbda, (params, exprs)) = code
def func(continuation, args):
new_context = context(parent_context, params, args)
return eval_expr_list(continuation, new_context, exprs)
return (continuation, func)

class define_continuation:
def __init__(self, continuation, context, var_name):
self.continuation = continuation
self.context = context
self.var_name = var_name

def run(self, value):
self.context.define(self.var_name, value)
return self.continuation, None

def eval_define(continuation, context, code):
(define, (var_name, (expr, nil))) = code
continuation = define_continuation(continuation,
context, str(var_name))
return eval(continuation, context, expr)

class set_continuation:
def __init__(self, continuation, context, var_name):
self.continuation = continuation
self.context = context
self.var_name = var_name

def run(self, value):
self.context.set(self.var_name, value)
return self.continuation, None

def eval_set(continuation, context, code):
(set, (var_name, (expr, nil))) = code
continuation = set_continuation(continuation, context,
return eval(continuation, context, expr)

class if_continuation:
def __init__(self, continuation, context, ifTrue, ifFalse):
self.continuation = continuation
self.context = context
self.ifTrue = ifTrue
self.ifFalse = ifFalse

def run(self, value):
if value:
return eval(self.continuation,
self.context, self.ifTrue)
return eval(self.continuation,
self.context, self.ifFalse)

def eval_if(continuation, context, code):
(If, (predicate, (ifTrue, rest))) = code
if rest==None:
ifFalse = None
ifFalse = rest[0]
return eval(if_continuation(continuation, context, ifTrue, ifFalse),
context, predicate)


class apply_continuation:
def __init__(self, continuation):
self.continuation = continuation

def run(self, func):
return func(self.continuation, self.params)

class param_continuation:
def __init__(self, continuation, prev):
self.continuation = continuation
self.prev = prev
self.params = None

def run(self, value):
self.prev.params = (value, self.params)
return (self.continuation, None)

class list_param_continuation:
def __init__(self, continuation, prev):
self.continuation = continuation
self.prev = prev
def run(self, value):
self.prev.params = value
return (self.continuation, None)

def construct_param_continuations(continuation,
prev, context, code):
if isinstance(code, list):
expr, rest = code
paramContinuation = param_continuation(continuation, prev)
continuation = eval_continuation(paramContinuation, context, expr)
if rest == None:
return continuation
return construct_param_continuations(continuation, paramContinuation,
context, rest)
continuation = list_param_continuation(continuation, prev)
return eval_continuation(continuation, context, code)

def eval_apply(continuation, context, code):
(operator, exprs) = code
apply_cont = apply_continuation(continuation)
continuation = eval_continuation(apply_cont, context, operator)
continuation = construct_param_continuations(continuation, apply_cont,
context, exprs)
return (continuation, None)

#The read eval loop

class read_eval_continuation:
def __init__(self, context, reader):
self.context = context
self.reader = reader
self.code = None
self.continuation = None

def run(self, value):
if self.code == None:
self.code = self.reader.next()
self.continuation = read_eval_continuation(self.context,
except StopIteration:
return None, value
return eval_str(self.continuation, self.context, self.code)

def expression_reader(fi):
code = ""
brackets = 0
while True:
if code == "":
prompt = ">>>"
prompt = "..."
ln = raw_input(prompt)
code+=ln+" "
brackets+=ln.count("(") - ln.count(")")
if brackets == 0 and len(ln.strip())!=0:
yield code
code = ""

def read_eval_loop(fi):
reader = expression_reader(fi)
continuation = read_eval_continuation(global_context, reader)
value = "Simple scheme!!!"
(continuation, value) = continuation.run(value)

if __name__=="__main__":
import sys


A Thousand Miles Behind

The new album "A Thousand Miles Behind" from David Gray is coming out next monday, October 8, 2007.

"Please forgive me," a song from his best known album "White Ladder."


Parallel Haskell in EETimes

As the title says: pHaskell in Embedded (EET). (Foto through Lennart Augustsson's page.)


Wisents on the Move

To read: "Embedded WiSeNts Research Roadmap".

According to a market study performed by ON World Inc. on Wireless Sensor Networks called “Wireless Sensor Networks – Growing Markets, Accelerating Demands” from July 2005, 127 million wireless sensor network nodes are expected to be deployed in 2010 and the growth of this market later on is expected to increase in certain application domains.

Wireless Sensor Networks are a canonical example of a wider field dealing with Cooperating Objects that attempts to create the necessary technologies to make Weiser’s vision of the disappearing computer a reality. Cooperating Objects are, in the most general case, small computing devices equipped with wireless communication capabilities that are able to cooperate and organise themselves autonomously into networks to achieve a common task.


Programs cannot be Understood

Sunday afternoon: a small arm-chair mind game.

Ontology is the study of being or existence. One of the more dubious questions one might ask about programs is if they exist and, if so, where they exist.

Of course, when we look at the physical dimensions of a program, we can only conclude that a program is a series of bits residing somewhere in memory. The purpose of a program is to be executed by a processor, which will result in some effect, usually the manipulation of other bits and the change of state of devices. For most people, the users of programs, a program is a thing observable by the effect it sorts.

For a programmer, the program usually is the code, or script, he writes which will have some effect when executed. He deals with mental abstractions of state and computation and, in general, is hardly aware of the underlying machinery which will cause the intended effect.

By necessity, for people, the observable behavior of a program, or the observable abstract representation of a program through source code, gives an incomplete view on its existence.

A program is a poorly understood series of bits.

Then again, who cares about ontology?


Principles of Embedded Networked Systems Design

Another book which may be interesting for the course I am teaching.

Tutorial: Forth Interpreter in i368 Assembly

A "How-to write a Forth Interpreter" by Richard W.M. Jones.

/* A sometimes minimal FORTH compiler and tutorial for Linux / i386 systems. -*- asm -*-
By Richard W.M. Jones <rich@annexia.org> http://annexia.org/forth
This is PUBLIC DOMAIN (see public domain release statement below).
$Id: jonesforth.S,v 1.35 2007/09/26 22:55:50 rich Exp $

gcc -m32 -nostdlib -static -Wl,-Ttext,0 -o jonesforth jonesforth.S
INTRODUCTION ----------------------------------------------------------------------

FORTH is one of those alien languages which most working programmers regard in the same
way as Haskell, LISP, and so on. Something so strange that they'd rather any thoughts
of it just go away so they can get on with writing this paying code. But that's wrong
and if you care at all about programming then you should at least understand all these
languages, even if you will never use them.

LISP is the ultimate high-level language, and features from LISP are being added every
decade to the more common languages. But FORTH is in some ways the ultimate in low level
programming. Out of the box it lacks features like dynamic memory management and even
strings. In fact, at its primitive level it lacks even basic concepts like IF-statements
and loops.

Why then would you want to learn FORTH? There are several very good reasons. First
and foremost, FORTH is minimal. You really can write a complete FORTH in, say, 2000
lines of code. I don't just mean a FORTH program, I mean a complete FORTH operating
system, environment and language. You could boot such a FORTH on a bare PC and it would
come up with a prompt where you could start doing useful work. The FORTH you have here
isn't minimal and uses a Linux process as its 'base PC' (both for the purposes of making
it a good tutorial). It's possible to completely understand the system. Who can say they
completely understand how Linux works, or gcc?

Secondly FORTH has a peculiar bootstrapping property. By that I mean that after writing
a little bit of assembly to talk to the hardware and implement a few primitives, all the
rest of the language and compiler is written in FORTH itself. Remember I said before
that FORTH lacked IF-statements and loops? Well of course it doesn't really because
such a lanuage would be useless, but my point was rather that IF-statements and loops are
written in FORTH itself.

Now of course this is common in other languages as well, and in those languages we call
them 'libraries'. For example in C, 'printf' is a library function written in C. But
in FORTH this goes way beyond mere libraries. Can you imagine writing C's 'if' in C?
And that brings me to my third reason: If you can write 'if' in FORTH, then why restrict
yourself to the usual if/while/for/switch constructs? You want a construct that iterates
over every other element in a list of numbers? You can add it to the language. What
about an operator which pulls in variables directly from a configuration file and makes
them available as FORTH variables? Or how about adding Makefile-like dependencies to
the language? No problem in FORTH. How about modifying the FORTH compiler to allow
complex inlining strategies -- simple. This concept isn't common in programming languages,
but it has a name (in fact two names): "macros" (by which I mean LISP-style macros, not
the lame C preprocessor) and "domain specific languages" (DSLs).

This tutorial isn't about learning FORTH as the language. I'll point you to some references
you should read if you're not familiar with using FORTH. This tutorial is about how to
write FORTH. In fact, until you understand how FORTH is written, you'll have only a very
superficial understanding of how to use it.

So if you're not familiar with FORTH or want to refresh your memory here are some online
references to read:





Here is another "Why FORTH?" essay: http://www.jwdt.com/~paysan/why-forth.html

Discussion and criticism of this FORTH here: http://lambda-the-ultimate.org/node/2452

ACKNOWLEDGEMENTS ----------------------------------------------------------------------

This code draws heavily on the design of LINA FORTH (http://home.hccnet.nl/a.w.m.van.der.horst/lina.html)
by Albert van der Horst. Any similarities in the code are probably not accidental.

Some parts of this FORTH are also based on this IOCCC entry from 1992:
I was very proud when Sean Barrett, the original author of the IOCCC entry, commented in the LtU thread
http://lambda-the-ultimate.org/node/2452#comment-36818 about this FORTH.

And finally I'd like to acknowledge the (possibly forgotten?) authors of ARTIC FORTH because their
original program which I still have on original cassette tape kept nagging away at me all these years.

PUBLIC DOMAIN ----------------------------------------------------------------------

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible, I grant any entity the right to use this work for any purpose,
without any conditions, unless such conditions are required by law.

SETTING UP ----------------------------------------------------------------------

Let's get a few housekeeping things out of the way. Firstly because I need to draw lots of
ASCII-art diagrams to explain concepts, the best way to look at this is using a window which
uses a fixed width font and is at least this wide:


Secondly make sure TABS are set to 8 characters. The following should be a vertical
line. If not, sort out your tabs.


Thirdly I assume that your screen is at least 50 characters high.

ASSEMBLING ----------------------------------------------------------------------

If you want to actually run this FORTH, rather than just read it, you will need Linux on an
i386. Linux because instead of programming directly to the hardware on a bare PC which I
could have done, I went for a simpler tutorial by assuming that the 'hardware' is a Linux
process with a few basic system calls (read, write and exit and that's about all). i386
is needed because I had to write the assembly for a processor, and i386 is by far the most
common. (Of course when I say 'i386', any 32- or 64-bit x86 processor will do. I'm compiling
this on a 64 bit AMD Opteron).

Again, to assemble this you will need gcc and gas (the GNU assembler). The commands to
assemble and run the code (save this file as 'jonesforth.S') are:

gcc -m32 -nostdlib -static -Wl,-Ttext,0 -o jonesforth jonesforth.S
cat jonesforth.f - | ./jonesforth

If you want to run your own FORTH programs you can do:

cat jonesforth.f myprog.f | ./jonesforth

If you want to load your own FORTH code and then continue reading user commands, you can do:

cat jonesforth.f myfunctions.f - | ./jonesforth

ASSEMBLER ----------------------------------------------------------------------

(You can just skip to the next section -- you don't need to be able to read assembler to
follow this tutorial).

However if you do want to read the assembly code here are a few notes about gas (the GNU assembler):

(1) Register names are prefixed with '%', so %eax is the 32 bit i386 accumulator. The registers
available on i386 are: %eax, %ebx, %ecx, %edx, %esi, %edi, %ebp and %esp, and most of them
have special purposes.

(2) Add, mov, etc. take arguments in the form SRC,DEST. So mov %eax,%ecx moves %eax -> %ecx

(3) Constants are prefixed with '$', and you mustn't forget it! If you forget it then it
causes a read from memory instead, so:
mov $2,%eax moves number 2 into %eax
mov 2,%eax reads the 32 bit word from address 2 into %eax (ie. most likely a mistake)

(4) gas has a funky syntax for local labels, where '1f' (etc.) means label '1:' "forwards"
and '1b' (etc.) means label '1:' "backwards".

(5) 'ja' is "jump if above", 'jb' for "jump if below", 'je' "jump if equal" etc.

(6) gas has a reasonably nice .macro syntax, and I use them a lot to make the code shorter and
less repetitive.

For more help reading the assembler, do "info gas" at the Linux prompt.

Now the tutorial starts in earnest.

THE DICTIONARY ----------------------------------------------------------------------

In FORTH as you will know, functions are called "words", and just as in other languages they
have a name and a definition. Here are two FORTH words:

: DOUBLE DUP + ; \ name is "DOUBLE", definition is "DUP +"

Words, both built-in ones and ones which the programmer defines later, are stored in a dictionary
which is just a linked list of dictionary entries.

<--- DICTIONARY ENTRY (HEADER) ----------------------->
+------------------------+--------+---------- - - - - +----------- - - - -
| | FLAGS | |
+--- (4 bytes) ----------+- byte -+- n bytes - - - - +----------- - - - -

I'll come to the definition of the word later. For now just look at the header. The first
4 bytes are the link pointer. This points back to the previous word in the dictionary, or, for
the first word in the dictionary it is just a NULL pointer. Then comes a length/flags byte.
The length of the word can be up to 31 characters (5 bits used) and the top three bits are used
for various flags which I'll come to later. This is followed by the name itself, and in this
implementation the name is rounded up to a multiple of 4 bytes by padding it with zero bytes.
That's just to ensure that the definition starts on a 32 bit boundary.

A FORTH variable called LATEST contains a pointer to the most recently defined word, in
other words, the head of this linked list.

DOUBLE and QUADRUPLE might look like this:

pointer to previous word
+--|------+---+---+---+---+---+---+---+---+------------- - - - -
| LINK | 6 | D | O | U | B | L | E | 0 | (definition ...)
+---------+---+---+---+---+---+---+---+---+------------- - - - -
^ len padding
+--|------+---+---+---+---+---+---+---+---+---+---+---+---+------------- - - - -
| LINK | 9 | Q | U | A | D | R | U | P | L | E | 0 | 0 | (definition ...)
+---------+---+---+---+---+---+---+---+---+---+---+---+---+------------- - - - -
^ len padding

You should be able to see from this how you might implement functions to find a word in
the dictionary (just walk along the dictionary entries starting at LATEST and matching
the names until you either find a match or hit the NULL pointer at the end of the dictionary);
and add a word to the dictionary (create a new definition, set its LINK to LATEST, and set
LATEST to point to the new word). We'll see precisely these functions implemented in
assembly code later on.

One interesting consequence of using a linked list is that you can redefine words, and
a newer definition of a word overrides an older one. This is an important concept in
FORTH because it means that any word (even "built-in" or "standard" words) can be
overridden with a new definition, either to enhance it, to make it faster or even to
disable it. However because of the way that FORTH words get compiled, which you'll
understand below, words defined using the old definition of a word continue to use
the old definition. Only words defined after the new definition use the new definition.

DIRECT THREADED CODE ----------------------------------------------------------------------

Now we'll get to the really crucial bit in understanding FORTH, so go and get a cup of tea
or coffee and settle down. It's fair to say that if you don't understand this section, then you
won't "get" how FORTH works, and that would be a failure on my part for not explaining it well.
So if after reading this section a few times you don't understand it, please email me

Let's talk first about what "threaded code" means. Imagine a peculiar version of C where
you are only allowed to call functions without arguments. (Don't worry for now that such a
language would be completely useless!) So in our peculiar C, code would look like this:

f ()
a ();
b ();
c ();

and so on. How would a function, say 'f' above, be compiled by a standard C compiler?
Probably into assembly code like this. On the right hand side I've written the actual
i386 machine code.

CALL a E8 08 00 00 00
CALL b E8 1C 00 00 00
CALL c E8 2C 00 00 00
; ignore the return from the function for now

"E8" is the x86 machine code to "CALL" a function. In the first 20 years of computing
memory was hideously expensive and we might have worried about the wasted space being used
by the repeated "E8" bytes. We can save 20% in code size (and therefore, in expensive memory)
by compressing this into just:

08 00 00 00 Just the function addresses, without
1C 00 00 00 the CALL prefix.
2C 00 00 00

On a 16-bit machine like the ones which originally ran FORTH the savings are even greater - 33%.

[Historical note: If the execution model that FORTH uses looks strange from the following
paragraphs, then it was motivated entirely by the need to save memory on early computers.
This code compression isn't so important now when our machines have more memory in their L1
caches than those early computers had in total, but the execution model still has some
useful properties].

Of course this code won't run directly any more. Instead we need to write an interpreter
which takes each pair of bytes and calls it.

On an i386 machine it turns out that we can write this interpreter rather easily, in just
two assembly instructions which turn into just 3 bytes of machine code. Let's store the
pointer to the next word to execute in the %esi register:

08 00 00 00 <- We're executing this one now. %esi is the _next_ one to execute.
%esi -> 1C 00 00 00
2C 00 00 00

The all-important i386 instruction is called LODSL (or in Intel manuals, LODSW). It does
two things. Firstly it reads the memory at %esi into the accumulator (%eax). Secondly it
increments %esi by 4 bytes. So after LODSL, the situation now looks like this:

08 00 00 00 <- We're still executing this one
1C 00 00 00 <- %eax now contains this address (0x0000001C)
%esi -> 2C 00 00 00

Now we just need to jump to the address in %eax. This is again just a single x86 instruction
written JMP *(%eax). And after doing the jump, the situation looks like:

08 00 00 00
1C 00 00 00 <- Now we're executing this subroutine.
%esi -> 2C 00 00 00

To make this work, each subroutine is followed by the two instructions 'LODSL; JMP *(%eax)'
which literally make the jump to the next subroutine.

And that brings us to our first piece of actual code! Well, it's a macro.

/* NEXT macro. */
.macro NEXT
jmp *(%eax)

/* The macro is called NEXT. That's a FORTH-ism. It expands to those two instructions.

Every FORTH primitive that we write has to be ended by NEXT. Think of it kind of like
a return.

The above describes what is known as direct threaded code.

To sum up: We compress our function calls down to a list of addresses and use a somewhat
magical macro to act as a "jump to next function in the list". We also use one register (%esi)
to act as a kind of instruction pointer, pointing to the next function in the list.

I'll just give you a hint of what is to come by saying that a FORTH definition such as:


actually compiles (almost, not precisely but we'll see why in a moment) to a list of
function addresses for DOUBLE, DOUBLE and a special function called EXIT to finish off.


I lied about JMP *(%eax).

INDIRECT THREADED CODE ----------------------------------------------------------------------

It turns out that direct threaded code is interesting but only if you want to just execute
a list of functions written in assembly language. So QUADRUPLE would work only if DOUBLE
was an assembly language function. In the direct threaded code, QUADRUPLE would look like:

| addr of DOUBLE --------------------> (assembly code to do the double)
+------------------+ NEXT
%esi -> | addr of DOUBLE |

We can add an extra indirection to allow us to run both words written in assembly language
(primitives written for speed) and words written in FORTH themselves as lists of addresses.

The extra indirection is the reason for the brackets in JMP *(%eax).

Let's have a look at how QUADRUPLE and DOUBLE really look in FORTH:


| codeword | : DOUBLE DUP + ;
| addr of DOUBLE ---------------> +------------------+
+------------------+ | codeword |
| addr of DOUBLE | +------------------+
+------------------+ | addr of DUP --------------> +------------------+
| addr of EXIT | +------------------+ | codeword -------+
+------------------+ %esi -> | addr of + --------+ +------------------+ |
+------------------+ | | assembly to <-----+
| addr of EXIT | | | implement DUP |
+------------------+ | | .. |
| | .. |
| | NEXT |
| +------------------+
+-----> +------------------+
| codeword -------+
+------------------+ |
| assembly to <------+
| implement + |
| .. |
| .. |
| NEXT |

This is the part where you may need an extra cup of tea/coffee/favourite caffeinated
beverage. What has changed is that I've added an extra pointer to the beginning of
the definitions. In FORTH this is sometimes called the "codeword". The codeword is
a pointer to the interpreter to run the function. For primitives written in
assembly language, the "interpreter" just points to the actual assembly code itself.
They don't need interpreting, they just run.

In words written in FORTH (like QUADRUPLE and DOUBLE), the codeword points to an interpreter

I'll show you the interpreter function shortly, but let's recall our indirect
JMP *(%eax) with the "extra" brackets. Take the case where we're executing DOUBLE
as shown, and DUP has been called. Note that %esi is pointing to the address of +

The assembly code for DUP eventually does a NEXT. That:

(1) reads the address of + into %eax %eax points to the codeword of +
(2) increments %esi by 4
(3) jumps to the indirect %eax jumps to the address in the codeword of +,
ie. the assembly code to implement +

| codeword |
| addr of DOUBLE ---------------> +------------------+
+------------------+ | codeword |
| addr of DOUBLE | +------------------+
+------------------+ | addr of DUP --------------> +------------------+
| addr of EXIT | +------------------+ | codeword -------+
+------------------+ | addr of + --------+ +------------------+ |
+------------------+ | | assembly to <-----+
%esi -> | addr of EXIT | | | implement DUP |
+------------------+ | | .. |
| | .. |
| | NEXT |
| +------------------+
+-----> +------------------+
| codeword -------+
+------------------+ |
now we're | assembly to <-----+
executing | implement + |
this | .. |
function | .. |
| NEXT |

So I hope that I've convinced you that NEXT does roughly what you'd expect. This is
indirect threaded code.

I've glossed over four things. I wonder if you can guess without reading on what they are?


My list of four things are: (1) What does "EXIT" do? (2) which is related to (1) is how do
you call into a function, ie. how does %esi start off pointing at part of QUADRUPLE, but
then point at part of DOUBLE. (3) What goes in the codeword for the words which are written
in FORTH? (4) How do you compile a function which does anything except call other functions
ie. a function which contains a number like : DOUBLE 2 * ; ?

THE INTERPRETER AND RETURN STACK ------------------------------------------------------------

Going at these in no particular order, let's talk about issues (3) and (2), the interpreter
and the return stack.

Words which are defined in FORTH need a codeword which points to a little bit of code to
give them a "helping hand" in life. They don't need much, but they do need what is known
as an "interpreter", although it doesn't really "interpret" in the same way that, say,
Java bytecode used to be interpreted (ie. slowly). This interpreter just sets up a few
machine registers so that the word can then execute at full speed using the indirect
threaded model above.

One of the things that needs to happen when QUADRUPLE calls DOUBLE is that we save the old
%esi ("instruction pointer") and create a new one pointing to the first word in DOUBLE.
Because we will need to restore the old %esi at the end of DOUBLE (this is, after all, like
a function call), we will need a stack to store these "return addresses" (old values of %esi).

As you will have read, when reading the background documentation, FORTH has two stacks,
an ordinary stack for parameters, and a return stack which is a bit more mysterious. But
our return stack is just the stack I talked about in the previous paragraph, used to save
%esi when calling from a FORTH word into another FORTH word.

In this FORTH, we are using the normal stack pointer (%esp) for the parameter stack.
We will use the i386's "other" stack pointer (%ebp, usually called the "frame pointer")
for our return stack.

I've got two macros which just wrap up the details of using %ebp for the return stack.
You use them as for example "PUSHRSP %eax" (push %eax on the return stack) or "POPRSP %ebx"
(pop top of return stack into %ebx).

/* Macros to deal with the return stack. */
.macro PUSHRSP reg
lea -4(%ebp),%ebp // push reg on to return stack
movl \reg,(%ebp)

.macro POPRSP reg
mov (%ebp),\reg // pop top of return stack to reg
lea 4(%ebp),%ebp

And with that we can now talk about the interpreter.

In FORTH the interpreter function is often called DOCOL (I think it means "DO COLON" because
all FORTH definitions start with a colon, as in : DOUBLE DUP + ;

The "interpreter" (it's not really "interpreting") just needs to push the old %esi on the
stack and set %esi to the first word in the definition. Remember that we jumped to the
function using JMP *(%eax)? Well a consequence of that is that conveniently %eax contains
the address of this codeword, so just by adding 4 to it we get the address of the first
data word. Finally after setting up %esi, it just does NEXT which causes that first word
to run.

/* DOCOL - the interpreter! */
.align 4
PUSHRSP %esi // push %esi on to the return stack
addl $4,%eax // %eax points to codeword, so make
movl %eax,%esi // %esi point to first data word

Just to make this absolutely clear, let's see how DOCOL works when jumping from QUADRUPLE
into DOUBLE:

| codeword |
+------------------+ DOUBLE:
| addr of DOUBLE ---------------> +------------------+
+------------------+ %eax -> | addr of DOCOL |
%esi -> | addr of DOUBLE | +------------------+
+------------------+ | addr of DUP |
| addr of EXIT | +------------------+
+------------------+ | etc. |

First, the call to DOUBLE calls DOCOL (the codeword of DOUBLE). DOCOL does this: It
pushes the old %esi on the return stack. %eax points to the codeword of DOUBLE, so we
just add 4 on to it to get our new %esi:

| codeword |
+------------------+ DOUBLE:
| addr of DOUBLE ---------------> +------------------+
top of return +------------------+ %eax -> | addr of DOCOL |
stack points -> | addr of DOUBLE | + 4 = +------------------+
+------------------+ %esi -> | addr of DUP |
| addr of EXIT | +------------------+
+------------------+ | etc. |

Then we do NEXT, and because of the magic of threaded code that increments %esi again
and calls DUP.

Well, it seems to work.

One minor point here. Because DOCOL is the first bit of assembly actually to be defined
in this file (the others were just macros), and because I usually compile this code with the
text segment starting at address 0, DOCOL has address 0. So if you are disassembling the
code and see a word with a codeword of 0, you will immediately know that the word is
written in FORTH (it's not an assembler primitive) and so uses DOCOL as the interpreter.

STARTING UP ----------------------------------------------------------------------

Now let's get down to nuts and bolts. When we start the program we need to set up
a few things like the return stack. But as soon as we can, we want to jump into FORTH
code (albeit much of the "early" FORTH code will still need to be written as
assembly language primitives).

This is what the set up code does. Does a tiny bit of house-keeping, sets up the
separate return stack (NB: Linux gives us the ordinary parameter stack already), then
immediately jumps to a FORTH word called COLD. COLD stands for cold-start. In ISO
FORTH (but not in this FORTH), COLD can be called at any time to completely reset
the state of FORTH, and there is another word called WARM which does a partial reset.

/* ELF entry point. */
.globl _start
mov %esp,var_S0 // Store the initial data stack pointer.
mov $return_stack,%ebp // Initialise the return stack.

mov $cold_start,%esi // Initialise interpreter.
NEXT // Run interpreter!

.section .rodata
cold_start: // High-level code without a codeword.
.int COLD

We also allocate some space for the return stack and some space to store user
definitions. These are static memory allocations using fixed-size buffers, but it
wouldn't be a great deal of work to make them dynamic.

/* FORTH return stack. */
.align 4096
return_stack: // Initial top of return stack.

/* The user definitions area: space for user-defined words and general memory allocations. */
.set USER_DEFS_SIZE,65536
.align 4096

/* This is used as a temporary input buffer when reading from files or the terminal. */
.set BUFFER_SIZE,4096
.align 4096
.int buffer
.int _initbufftop

BUILT-IN WORDS ----------------------------------------------------------------------

Remember our dictionary entries (headers)? Let's bring those together with the codeword
and data words to see how : DOUBLE DUP + ; really looks in memory.

pointer to previous word
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP | + | EXIT |
^ len pad codeword |
| V
LINK in next word points to codeword of DUP

Initially we can't just write ": DOUBLE DUP + ;" (ie. that literal string) here because we
don't yet have anything to read the string, break it up at spaces, parse each word, etc. etc.
So instead we will have to define built-in words using the GNU assembler data constructors
(like .int, .byte, .string, .ascii and so on -- look them up in the gas info page if you are
unsure of them).

The long way would be:
.int <link to previous word>
.byte 6 // len
.ascii "DOUBLE" // string
.byte 0 // padding
DOUBLE: .int DOCOL // codeword
.int DUP // pointer to codeword of DUP
.int PLUS // pointer to codeword of +
.int EXIT // pointer to codeword of EXIT

That's going to get quite tedious rather quickly, so here I define an assembler macro
so that I can just write:

defword "DOUBLE",6,,DOUBLE

and I'll get exactly the same effect.

Don't worry too much about the exact implementation details of this macro - it's complicated!

/* Flags - these are discussed later. */
.set F_IMMED,0x80
.set F_HIDDEN,0x20
.set F_LENMASK,0x1f // length mask

// Store the chain of links.
.set link,0

.macro defword name, namelen, flags=0, label
.section .rodata
.align 4
.globl name_\label
name_\label :
.int link // link
.set link,name_\label
.byte \flags+\namelen // flags + length byte
.ascii "\name" // the name
.align 4
.globl \label
\label :
.int DOCOL // codeword - the interpreter
// list of word pointers follow

Similarly I want a way to write words written in assembly language. There will quite a few
of these to start with because, well, everything has to start in assembly before there's
enough "infrastructure" to be able to start writing FORTH words, but also I want to define
some common FORTH words in assembly language for speed, even though I could write them in FORTH.

This is what DUP looks like in memory:

pointer to previous word
| LINK | 3 | D | U | P | code_DUP ---------------------> points to the assembly
+---------+---+---+---+---+------------+ code used to write DUP,
^ len codeword which ends with NEXT.
LINK in next word

Again, for brevity in writing the header I'm going to write an assembler macro called defcode.

.macro defcode name, namelen, flags=0, label
.section .rodata
.align 4
.globl name_\label
name_\label :
.int link // link
.set link,name_\label
.byte \flags+\namelen // flags + length byte
.ascii "\name" // the name
.align 4
.globl \label
\label :
.int code_\label // codeword
.align 4
.globl code_\label
code_\label : // assembler code follows

Now some easy FORTH primitives. These are written in assembly for speed. If you understand
i386 assembly language then it is worth reading these. However if you don't understand assembly
you can skip the details.

defcode "DUP",3,,DUP
pop %eax // duplicate top of stack
push %eax
push %eax

defcode "DROP",4,,DROP
pop %eax // drop top of stack

defcode "SWAP",4,,SWAP
pop %eax // swap top of stack
pop %ebx
push %eax
push %ebx

defcode "OVER",4,,OVER
mov 4(%esp),%eax // get the second element of stack
push %eax // and push it on top

defcode "ROT",3,,ROT
pop %eax
pop %ebx
pop %ecx
push %eax
push %ecx
push %ebx

defcode "-ROT",4,,NROT
pop %eax
pop %ebx
pop %ecx
push %ebx
push %eax
push %ecx

defcode "1+",2,,INCR
incl (%esp) // increment top of stack

defcode "1-",2,,DECR
decl (%esp) // decrement top of stack

defcode "4+",2,,INCR4
addl $4,(%esp) // add 4 to top of stack

defcode "4-",2,,DECR4
subl $4,(%esp) // subtract 4 from top of stack

defcode "+",1,,ADD
pop %eax // get top of stack
addl %eax,(%esp) // and add it to next word on stack

defcode "-",1,,SUB
pop %eax // get top of stack
subl %eax,(%esp) // and subtract it from next word on stack

defcode "*",1,,MUL
pop %eax
pop %ebx
imull %ebx,%eax
push %eax // ignore overflow

In this FORTH, only /MOD is primitive. Later we will define the / and MOD words in
terms of the primitive /MOD.

defcode "/MOD",4,,DIVMOD
xor %edx,%edx
pop %ebx
pop %eax
idivl %ebx
push %edx // push remainder
push %eax // push quotient

defcode "=",1,,EQU // top two words are equal?
pop %eax
pop %ebx
cmp %ebx,%eax
je 1f
pushl $0
1: pushl $1

defcode "<>",2,,NEQU // top two words are not equal?
pop %eax
pop %ebx
cmp %ebx,%eax
je 1f
pushl $1
1: pushl $0

defcode "<",1,,LT
pop %eax
pop %ebx
cmp %eax,%ebx
jl 1f
pushl $0
1: pushl $1

defcode ">",1,,GT
pop %eax
pop %ebx
cmp %eax,%ebx
jg 1f
pushl $0
1: pushl $1

defcode "<=",2,,LE
pop %eax
pop %ebx
cmp %eax,%ebx
jle 1f
pushl $0
1: pushl $1

defcode ">=",2,,GE
pop %eax
pop %ebx
cmp %eax,%ebx
jge 1f
pushl $0
1: pushl $1

defcode "0=",2,,ZEQU // top of stack equals 0?
pop %eax
test %eax,%eax
jz 1f
pushl $0
1: pushl $1

defcode "0<>",3,,ZNEQU // top of stack not 0?
pop %eax
test %eax,%eax
jnz 1f
pushl $0
1: pushl $1

defcode "0<",2,,ZLT // comparisons with 0
pop %eax
test %eax,%eax
jl 1f
pushl $0
1: pushl $1

defcode "0>",2,,ZGT
pop %eax
test %eax,%eax
jg 1f
pushl $0
1: pushl $1

defcode "0<=",3,,ZLE
pop %eax
test %eax,%eax
jle 1f
pushl $0
1: pushl $1

defcode "0>=",3,,ZGE
pop %eax
test %eax,%eax
jge 1f
pushl $0
1: pushl $1

defcode "AND",3,,AND // bitwise AND
pop %eax
andl %eax,(%esp)

defcode "OR",2,,OR // bitwise OR
pop %eax
orl %eax,(%esp)

defcode "XOR",3,,XOR // bitwise XOR
pop %eax
xorl %eax,(%esp)

defcode "INVERT",6,,INVERT // this is the FORTH bitwise "NOT" function (cf. NEGATE)
notl (%esp)

RETURNING FROM FORTH WORDS ----------------------------------------------------------------------

Time to talk about what happens when we EXIT a function. In this diagram QUADRUPLE has called
DOUBLE, and DOUBLE is about to exit (look at where %esi is pointing):

| codeword |
+------------------+ DOUBLE
| addr of DOUBLE ---------------> +------------------+
+------------------+ | codeword |
| addr of DOUBLE | +------------------+
+------------------+ | addr of DUP |
| addr of EXIT | +------------------+
+------------------+ | addr of + |
%esi -> | addr of EXIT |

What happens when the + function does NEXT? Well, the following code is executed.

defcode "EXIT",4,,EXIT
POPRSP %esi // pop return stack into %esi

EXIT gets the old %esi which we saved from before on the return stack, and puts it in %esi.
So after this (but just before NEXT) we get:

| codeword |
+------------------+ DOUBLE
| addr of DOUBLE ---------------> +------------------+
+------------------+ | codeword |
%esi -> | addr of DOUBLE | +------------------+
+------------------+ | addr of DUP |
| addr of EXIT | +------------------+
+------------------+ | addr of + |
| addr of EXIT |

And NEXT just completes the job by, well, in this case just by calling DOUBLE again :-)

LITERALS ----------------------------------------------------------------------

The final point I "glossed over" before was how to deal with functions that do anything
apart from calling other functions. For example, suppose that DOUBLE was defined like this:

: DOUBLE 2 * ;

It does the same thing, but how do we compile it since it contains the literal 2? One way
would be to have a function called "2" (which you'd have to write in assembler), but you'd need
a function for every single literal that you wanted to use.

FORTH solves this by compiling the function using a special word called LIT:

| (usual header of DOUBLE) | DOCOL | LIT | 2 | * | EXIT |

LIT is executed in the normal way, but what it does next is definitely not normal. It
looks at %esi (which now points to the literal 2), grabs it, pushes it on the stack, then
manipulates %esi in order to skip the literal as if it had never been there.

What's neat is that the whole grab/manipulate can be done using a single byte single
i386 instruction, our old friend LODSL. Rather than me drawing more ASCII-art diagrams,
see if you can find out how LIT works:

defcode "LIT",3,,LIT
// %esi points to the next command, but in this case it points to the next
// literal 32 bit integer. Get that literal into %eax and increment %esi.
// On x86, it's a convenient single byte instruction! (cf. NEXT macro)
push %eax // push the literal number on to stack

MEMORY ----------------------------------------------------------------------

As important point about FORTH is that it gives you direct access to the lowest levels
of the machine. Manipulating memory directly is done frequently in FORTH, and these are
the primitive words for doing it.

defcode "!",1,,STORE
pop %ebx // address to store at
pop %eax // data to store there
mov %eax,(%ebx) // store it

defcode "@",1,,FETCH
pop %ebx // address to fetch
mov (%ebx),%eax // fetch it
push %eax // push value onto stack

defcode "+!",2,,ADDSTORE
pop %ebx // address
pop %eax // the amount to add
addl %eax,(%ebx) // add it

defcode "-!",2,,SUBSTORE
pop %ebx // address
pop %eax // the amount to subtract
subl %eax,(%ebx) // add it

! and @ (STORE and FETCH) store 32-bit words. It's also useful to be able to read and write bytes
so we also define standard words C@ and C!.

Byte-oriented operations only work on architectures which permit them (i386 is one of those).

defcode "C!",2,,STOREBYTE
pop %ebx // address to store at
pop %eax // data to store there
movb %al,(%ebx) // store it

defcode "C@",2,,FETCHBYTE
pop %ebx // address to fetch
xor %eax,%eax
movb (%ebx),%al // fetch it
push %eax // push value onto stack

BUILT-IN VARIABLES ----------------------------------------------------------------------

These are some built-in variables and related standard FORTH words. Of these, the only one that we
have discussed so far was LATEST, which points to the last (most recently defined) word in the
FORTH dictionary. LATEST is also a FORTH word which pushes the address of LATEST (the variable)
on to the stack, so you can read or write it using @ and ! operators. For example, to print
the current value of LATEST (and this can apply to any FORTH variable) you would do:


To make defining variables shorter, I'm using a macro called defvar, similar to defword and
defcode above. (In fact the defvar macro uses defcode to do the dictionary header).

.macro defvar name, namelen, flags=0, label, initial=0
defcode \name,\namelen,\flags,\label
push $var_\name
.align 4
var_\name :
.int \initial

The built-in variables are:

STATE Is the interpreter executing code (0) or compiling a word (non-zero)?
LATEST Points to the latest (most recently defined) word in the dictionary.
HERE Points to the next free byte of memory. When compiling, compiled words go here.
_X These are three scratch variables, used by some standard dictionary words.
S0 Stores the address of the top of the parameter stack.
BASE The current base for printing and reading numbers.

defvar "STATE",5,,STATE
defvar "HERE",4,,HERE,user_defs_start
defvar "LATEST",6,,LATEST,name_SYSEXIT // SYSEXIT must be last in built-in dictionary
defvar "_X",2,,TX
defvar "_Y",2,,TY
defvar "_Z",2,,TZ
defvar "S0",2,,SZ
defvar "BASE",4,,BASE,10

BUILT-IN CONSTANTS ----------------------------------------------------------------------

It's also useful to expose a few constants to FORTH. When the word is executed it pushes a
constant value on the stack.

The built-in constants are:

VERSION Is the current version of this FORTH.
R0 The address of the top of the return stack.
DOCOL Pointer to DOCOL.
F_IMMED The IMMEDIATE flag's actual value.
F_HIDDEN The HIDDEN flag's actual value.
F_LENMASK The length mask in the flags/len byte.

.macro defconst name, namelen, flags=0, label, value
defcode \name,\namelen,\flags,\label
push $\value

defconst "R0",2,,RZ,return_stack
defconst "DOCOL",5,,__DOCOL,DOCOL
defconst "F_IMMED",7,,__F_IMMED,F_IMMED
defconst "F_HIDDEN",8,,__F_HIDDEN,F_HIDDEN

RETURN STACK ----------------------------------------------------------------------

These words allow you to access the return stack. Recall that the register %ebp always points to
the top of the return stack.

defcode ">R",2,,TOR
pop %eax // pop parameter stack into %eax
PUSHRSP %eax // push it on to the return stack

defcode "R>",2,,FROMR
POPRSP %eax // pop return stack on to %eax
push %eax // and push on to parameter stack

defcode "RSP@",4,,RSPFETCH
push %ebp

defcode "RSP!",4,,RSPSTORE
pop %ebp

defcode "RDROP",5,,RDROP
lea 4(%ebp),%ebp // pop return stack and throw away

PARAMETER (DATA) STACK ----------------------------------------------------------------------

These functions allow you to manipulate the parameter stack. Recall that Linux sets up the parameter
stack for us, and it is accessed through %esp.

defcode "DSP@",4,,DSPFETCH
mov %esp,%eax
push %eax

defcode "DSP!",4,,DSPSTORE
pop %esp

INPUT AND OUTPUT ----------------------------------------------------------------------

These are our first really meaty/complicated FORTH primitives. I have chosen to write them in
assembler, but surprisingly in "real" FORTH implementations these are often written in terms
of more fundamental FORTH primitives. I chose to avoid that because I think that just obscures
the implementation. After all, you may not understand assembler but you can just think of it
as an opaque block of code that does what it says.

Let's discuss input first.

The FORTH word KEY reads the next byte from stdin (and pushes it on the parameter stack).
So if KEY is called and someone hits the space key, then the number 32 (ASCII code of space)
is pushed on the stack.

In FORTH there is no distinction between reading code and reading input. We might be reading
and compiling code, we might be reading words to execute, we might be asking for the user
to type their name -- ultimately it all comes in through KEY.

The implementation of KEY uses an input buffer of a certain size (defined at the end of the
program). It calls the Linux read(2) system call to fill this buffer and tracks its position
in the buffer using a couple of variables, and if it runs out of input buffer then it refills
it automatically. The other thing that KEY does is if it detects that stdin has closed, it
exits the program, which is why when you hit ^D the FORTH system cleanly exits.

#include <asm-i386/unistd.h>

defcode "KEY",3,,KEY
call _KEY
push %eax // push return value on stack
mov (currkey),%ebx
cmp (bufftop),%ebx
jge 1f
xor %eax,%eax
mov (%ebx),%al
inc %ebx
mov %ebx,(currkey)

1: // out of input; use read(2) to fetch more input from stdin
xor %ebx,%ebx // 1st param: stdin
mov $buffer,%ecx // 2nd param: buffer
mov %ecx,currkey
mov $buffend-buffer,%edx // 3rd param: max length
mov $__NR_read,%eax // syscall: read
int $0x80
test %eax,%eax // If %eax <= 0, then exit.
jbe 2f
addl %eax,%ecx // buffer+%eax = bufftop
mov %ecx,bufftop
jmp _KEY

2: // error or out of input: exit
xor %ebx,%ebx
mov $__NR_exit,%eax // syscall: exit
int $0x80

By contrast, output is much simpler. The FORTH word EMIT writes out a single byte to stdout.
This implementation just uses the write system call. No attempt is made to buffer output, but
it would be a good exercise to add it.

defcode "EMIT",4,,EMIT
pop %eax
call _EMIT
mov $1,%ebx // 1st param: stdout

// write needs the address of the byte to write
mov %al,(2f)
mov $2f,%ecx // 2nd param: address

mov $1,%edx // 3rd param: nbytes = 1

mov $__NR_write,%eax // write syscall
int $0x80

2: .space 1 // scratch used by EMIT

Back to input, WORD is a FORTH word which reads the next full word of input.

What it does in detail is that it first skips any blanks (spaces, tabs, newlines and so on).
Then it calls KEY to read characters into an internal buffer until it hits a blank. Then it
calculates the length of the word it read and returns the address and the length as
two words on the stack (with address at the top).

Notice that WORD has a single internal buffer which it overwrites each time (rather like
a static C string). Also notice that WORD's internal buffer is just 32 bytes long and
there is NO checking for overflow. 31 bytes happens to be the maximum length of a
FORTH word that we support, and that is what WORD is used for: to read FORTH words when
we are compiling and executing code. The returned strings are not NUL-terminated, so
in some crazy-world you could define FORTH words containing ASCII NULs, although why
you'd want to is a bit beyond me.

WORD is not suitable for just reading strings (eg. user input) because of all the above
peculiarities and limitations.

Note that when executing, you'll see:
which puts "FOO" and length 3 on the stack, but when compiling:
is an error (or at least it doesn't do what you might expect). Later we'll talk about compiling
and immediate mode, and you'll understand why.

defcode "WORD",4,,WORD
call _WORD
push %ecx // push length
push %edi // push base address

/* Search for first non-blank character. Also skip \ comments. */
call _KEY // get next key, returned in %eax
cmpb $'\\',%al // start of a comment?
je 3f // if so, skip the comment
cmpb $' ',%al
jbe 1b // if so, keep looking

/* Search for the end of the word, storing chars as we go. */
mov $5f,%edi // pointer to return buffer
stosb // add character to return buffer
call _KEY // get next key, returned in %al
cmpb $' ',%al // is blank?
ja 2b // if not, keep looping

/* Return the word (well, the static buffer) and length. */
sub $5f,%edi
mov %edi,%ecx // return length of the word
mov $5f,%edi // return address of the word

/* Code to skip \ comments to end of the current line. */
call _KEY
cmpb $'\n',%al // end of line yet?
jne 3b
jmp 1b

// A static buffer where WORD returns. Subsequent calls
// overwrite this buffer. Maximum word length is 32 chars.
5: .space 32

As well as reading in words we'll need to read in numbers and for that we are using a function
called SNUMBER. This parses a numeric string such as one returned by WORD and pushes the
number on the parameter stack.

This function does absolutely no error checking, and in particular the length of the string
must be >= 1 bytes, and should contain only digits 0-9. If it doesn't you'll get random results.

This function is only used when reading literal numbers in code, and shouldn't really be used
in user code at all.
defcode "SNUMBER",7,,SNUMBER
pop %edi
pop %ecx
push %eax
xor %eax,%eax
xor %ebx,%ebx
imull $10,%eax // %eax *= 10
movb (%edi),%bl
inc %edi
subb $'0',%bl // ASCII -> digit
add %ebx,%eax
dec %ecx
jnz 1b

DICTIONARY LOOK UPS ----------------------------------------------------------------------

We're building up to our prelude on how FORTH code is compiled, but first we need yet more infrastructure.

The FORTH word FIND takes a string (a word as parsed by WORD -- see above) and looks it up in the
dictionary. What it actually returns is the address of the dictionary header, if it finds it,
or 0 if it didn't.

So if DOUBLE is defined in the dictionary, then WORD DOUBLE FIND returns the following pointer:

pointer to this
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP | + | EXIT |

See also >CFA and >DFA.

FIND doesn't find dictionary entries which are flagged as HIDDEN. See below for why.

defcode "FIND",4,,FIND
pop %edi // %edi = address
pop %ecx // %ecx = length
call _FIND
push %eax

push %esi // Save %esi so we can use it in string comparison.

// Now we start searching backwards through the dictionary for this word.
mov var_LATEST,%edx // LATEST points to name header of the latest word in the dictionary
test %edx,%edx // NULL pointer? (end of the linked list)
je 4f

// Compare the length expected and the length of the word.
// Note that if the F_HIDDEN flag is set on the word, then by a bit of trickery
// this won't pick the word (the length will appear to be wrong).
xor %eax,%eax
movb 4(%edx),%al // %al = flags+length field
andb $(F_HIDDEN|F_LENMASK),%al // %al = name length
cmpb %cl,%al // Length is the same?
jne 2f

// Compare the strings in detail.
push %ecx // Save the length
push %edi // Save the address (repe cmpsb will move this pointer)
lea 5(%edx),%esi // Dictionary string we are checking against.
repe cmpsb // Compare the strings.
pop %edi
pop %ecx
jne 2f // Not the same.

// The strings are the same - return the header pointer in %eax
pop %esi
mov %edx,%eax

mov (%edx),%edx // Move back through the link field to the previous word
jmp 1b // .. and loop.

4: // Not found.
pop %esi
xor %eax,%eax // Return zero to indicate not found.

FIND returns the dictionary pointer, but when compiling we need the codeword pointer (recall
that FORTH definitions are compiled into lists of codeword pointers). The standard FORTH
word >CFA turns a dictionary pointer into a codeword pointer.

The example below shows the result of:


FIND returns a pointer to this
| >CFA converts it to a pointer to this
| |
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP | + | EXIT |


Because names vary in length, this isn't just a simple increment.

In this FORTH you cannot easily turn a codeword pointer back into a dictionary entry pointer, but
that is not true in most FORTH implementations where they store a back pointer in the definition
(with an obvious memory/complexity cost). The reason they do this is that it is useful to be
able to go backwards (codeword -> dictionary entry) in order to decompile FORTH definitions.

What does CFA stand for? My best guess is "Code Field Address".

defcode ">CFA",4,,TCFA
pop %edi
call _TCFA
push %edi
xor %eax,%eax
add $4,%edi // Skip link pointer.
movb (%edi),%al // Load flags+len into %al.
inc %edi // Skip flags+len byte.
andb $F_LENMASK,%al // Just the length, not the flags.
add %eax,%edi // Skip the name.
addl $3,%edi // The codeword is 4-byte aligned.
andl $~3,%edi

Related to >CFA is >DFA which takes a dictionary entry address as returned by FIND and
returns a pointer to the first data field.

FIND returns a pointer to this
| >CFA converts it to a pointer to this
| |
| | >DFA converts it to a pointer to this
| | |
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP | + | EXIT |

(Note to those following the source of FIG-FORTH / ciforth: My >DFA definition is
different from theirs, because they have an extra indirection).

You can see that >DFA is easily defined in FORTH just by adding 4 to the result of >CFA.

defword ">DFA",4,,TDFA
.int TCFA // >CFA (get code field address)
.int INCR4 // 4+ (add 4 to it to get to next word)
.int EXIT // EXIT (return from FORTH word)

COMPILING ----------------------------------------------------------------------

Now we'll talk about how FORTH compiles words. Recall that a word definition looks like this:


and we have to turn this into:

pointer to previous word
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP | + | EXIT |
^ len pad codeword |
| V
LATEST points here points to codeword of DUP

There are several problems to solve. Where to put the new word? How do we read words? How
do we define the words : (COLON) and ; (SEMICOLON)?

FORTH solves this rather elegantly and as you might expect in a very low-level way which
allows you to change how the compiler works on your own code.

FORTH has an INTERPRETER function (a true interpreter this time, not DOCOL) which runs in a
loop, reading words (using WORD), looking them up (using FIND), turning them into codeword
pointers (using >CFA) and deciding what to do with them.

What it does depends on the mode of the interpreter (in variable STATE).

When STATE is zero, the interpreter just runs each word as it looks them up. This is known as
immediate mode.

The interesting stuff happens when STATE is non-zero -- compiling mode. In this mode the
interpreter appends the codeword pointer to user memory (the HERE variable points to the next
free byte of user memory).

So you may be able to see how we could define : (COLON). The general plan is:

(1) Use WORD to read the name of the function being defined.

(2) Construct the dictionary entry -- just the header part -- in user memory:

pointer to previous word (from LATEST) +-- Afterwards, HERE points here, where
^ | the interpreter will start appending
| V codewords.
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL |
len pad codeword

(3) Set LATEST to point to the newly defined word, ...

(4) .. and most importantly leave HERE pointing just after the new codeword. This is where
the interpreter will append codewords.

(5) Set STATE to 1. This goes into compile mode so the interpreter starts appending codewords to
our partially-formed header.

After : has run, our input is here:

Next byte returned by KEY will be the 'D' character of DUP

so the interpreter (now it's in compile mode, so I guess it's really the compiler) reads "DUP",
looks it up in the dictionary, gets its codeword pointer, and appends it:

+-- HERE updated to point here.
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP |
len pad codeword

Next we read +, get the codeword pointer, and append it:

+-- HERE updated to point here.
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP | + |
len pad codeword

The issue is what happens next. Obviously what we _don't_ want to happen is that we
read ";" and compile it and go on compiling everything afterwards.

At this point, FORTH uses a trick. Remember the length byte in the dictionary definition
isn't just a plain length byte, but can also contain flags. One flag is called the
IMMEDIATE flag (F_IMMED in this code). If a word in the dictionary is flagged as
IMMEDIATE then the interpreter runs it immediately _even if it's in compile mode_.

This is how the word ; (SEMICOLON) works -- as a word flagged in the dictionary as IMMEDIATE.
And all it does is append the codeword for EXIT on to the current definition and switch
back to immediate mode (set STATE back to 0). Shortly we'll see the actual definition
of ; and we'll see that it's really a very simple definition, declared IMMEDIATE.

After the interpreter reads ; and executes it 'immediately', we get this:

| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL | DUP | + | EXIT |
len pad codeword ^

STATE is set to 0.

And that's it, job done, our new definition is compiled, and we're back in immediate mode
just reading and executing words, perhaps including a call to test our new word DOUBLE.

The only last wrinkle in this is that while our word was being compiled, it was in a
half-finished state. We certainly wouldn't want DOUBLE to be called somehow during
this time. There are several ways to stop this from happening, but in FORTH what we
do is flag the word with the HIDDEN flag (F_HIDDEN in this code) just while it is
being compiled. This prevents FIND from finding it, and thus in theory stops any
chance of it being called.

The above explains how compiling, : (COLON) and ; (SEMICOLON) works and in a moment I'm
going to define them. The : (COLON) function can be made a little bit more general by writing
it in two parts. The first part, called CREATE, makes just the header:

+-- Afterwards, HERE points here.
| LINK | 6 | D | O | U | B | L | E | 0 |
len pad

and the second part, the actual definition of : (COLON), calls CREATE and appends the
DOCOL codeword, so leaving:

+-- Afterwards, HERE points here.
| LINK | 6 | D | O | U | B | L | E | 0 | DOCOL |
len pad codeword

CREATE is a standard FORTH word and the advantage of this split is that we can reuse it to
create other types of words (not just ones which contain code, but words which contain variables,
constants and other data).

defcode "CREATE",6,,CREATE

// Get the word.
call _WORD // Returns %ecx = length, %edi = pointer to word.
mov %edi,%ebx // %ebx = address of the word

// Link pointer.
movl var_HERE,%edi // %edi is the address of the header
movl var_LATEST,%eax // Get link pointer
stosl // and store it in the header.

// Length byte and the word itself.
mov %cl,%al // Get the length.
stosb // Store the length/flags byte.
push %esi
mov %ebx,%esi // %esi = word
rep movsb // Copy the word
pop %esi
addl $3,%edi // Align to next 4 byte boundary.
andl $~3,%edi

// Update LATEST and HERE.
movl var_HERE,%eax
movl %eax,var_LATEST
movl %edi,var_HERE

Because I want to define : (COLON) in FORTH, not assembler, we need a few more FORTH words
to use.

The first is , (COMMA) which is a standard FORTH word which appends a 32 bit integer to the user
data area pointed to by HERE, and adds 4 to HERE. So the action of , (COMMA) is:

previous value of HERE
+---------+---+---+---+---+---+---+---+---+-- - - - - --+------------+
| LINK | 6 | D | O | U | B | L | E | 0 | | <data> |
+---------+---+---+---+---+---+---+---+---+-- - - - - --+------------+
len pad ^
new value of HERE

and <data> is whatever 32 bit integer was at the top of the stack.

, (COMMA) is quite a fundamental operation when compiling. It is used to append codewords
to the current word that is being compiled.

defcode ",",1,,COMMA
pop %eax // Code pointer to store.
call _COMMA
movl var_HERE,%edi // HERE
stosl // Store it.
movl %edi,var_HERE // Update HERE (incremented)

Our definitions of : (COLON) and ; (SEMICOLON) will need to switch to and from compile mode.

Immediate mode vs. compile mode is stored in the global variable STATE, and by updating this
variable we can switch between the two modes.

For various reasons which may become apparent later, FORTH defines two standard words called
[ and ] (LBRAC and RBRAC) which switch between modes:

Word Assembler Action Effect
[ LBRAC STATE := 0 Switch to immediate mode.
] RBRAC STATE := 1 Switch to compile mode.

[ (LBRAC) is an IMMEDIATE word. The reason is as follows: If we are in compile mode and the
interpreter saw [ then it would compile it rather than running it. We would never be able to
switch back to immediate mode! So we flag the word as IMMEDIATE so that even in compile mode
the word runs immediately, switching us back to immediate mode.

defcode "[",1,F_IMMED,LBRAC
xor %eax,%eax
movl %eax,var_STATE // Set STATE to 0.

defcode "]",1,,RBRAC
movl $1,var_STATE // Set STATE to 1.

Now we can define : (COLON) using CREATE. It just calls CREATE, appends DOCOL (the codeword), sets
the word HIDDEN and goes into compile mode.

defword ":",1,,COLON
.int CREATE // CREATE the dictionary entry / header
.int LIT, DOCOL, COMMA // Append DOCOL (the codeword).
.int LATEST, FETCH, HIDDEN // Make the word hidden (see below for definition).
.int RBRAC // Go into compile mode.
.int EXIT // Return from the function.

; (SEMICOLON) is also elegantly simple. Notice the F_IMMED flag.

defword ";",1,F_IMMED,SEMICOLON
.int LIT, EXIT, COMMA // Append EXIT (so the word will return).
.int LATEST, FETCH, HIDDEN // Toggle hidden flag -- unhide the word (see below for definition).
.int LBRAC // Go back to IMMEDIATE mode.
.int EXIT // Return from the function.

EXTENDING THE COMPILER ----------------------------------------------------------------------

Words flagged with IMMEDIATE (F_IMMED) aren't just for the FORTH compiler to use. You can define
your own IMMEDIATE words too, and this is a crucial aspect when extending basic FORTH, because
it allows you in effect to extend the compiler itself. Does gcc let you do that?

Standard FORTH words like IF, WHILE, ." and so on are all written as extensions to the basic
compiler, and are all IMMEDIATE words.

The IMMEDIATE word toggles the F_IMMED (IMMEDIATE flag) on the most recently defined word,
or on the current word if you call it in the middle of a definition.

Typical usage is:


but some FORTH programmers write this instead:


The two usages are equivalent, to a first approximation.

movl var_LATEST,%edi // LATEST word.
addl $4,%edi // Point to name/flags byte.
xorb $F_IMMED,(%edi) // Toggle the IMMED bit.

'addr HIDDEN' toggles the hidden flag (F_HIDDEN) of the word defined at addr. To hide the
most recently defined word (used above in : and ; definitions) you would do:


Setting this flag stops the word from being found by FIND, and so can be used to make 'private'
words. For example, to break up a large word into smaller parts you might do:

: SUB1 ... subword ... ;
: SUB2 ... subword ... ;
: SUB3 ... subword ... ;
: MAIN ... defined in terms of SUB1, SUB2, SUB3 ... ;

After this, only MAIN is 'exported' or seen by the rest of the program.

defcode "HIDDEN",6,,HIDDEN
pop %edi // Dictionary entry.
addl $4,%edi // Point to name/flags byte.
xorb $F_HIDDEN,(%edi) // Toggle the HIDDEN bit.

' (TICK) is a standard FORTH word which returns the codeword pointer of the next word.

The common usage is:

' FOO ,

which appends the codeword of FOO to the current word we are defining (this only works in compiled code).

You tend to use ' in IMMEDIATE words. For example an alternate (and rather useless) way to define
a literal 2 might be:

' LIT , \ Appends LIT to the currently-being-defined word
2 , \ Appends the number 2 to the currently-being-defined word

So you could do:


(If you don't understand how LIT2 works, then you should review the material about compiling words
and immediate mode).

This definition of ' uses a cheat which I copied from buzzard92. As a result it only works in
compiled code. It is possible to write a version of ' based on WORD, FIND, >CFA which works in
immediate mode too.
defcode "'",1,,TICK
lodsl // Get the address of the next word and skip it.
pushl %eax // Push it on the stack.

BRANCHING ----------------------------------------------------------------------

It turns out that all you need in order to define looping constructs, IF-statements, etc.
are two primitives.

BRANCH is an unconditional branch. 0BRANCH is a conditional branch (it only branches if the
top of stack is zero).

The diagram below shows how BRANCH works in some imaginary compiled word. When BRANCH executes,
%esi starts by pointing to the offset field (compare to LIT above):

+---------------------+-------+---- - - ---+------------+------------+---- - - - ----+------------+
| (Dictionary header) | DOCOL | | BRANCH | offset | (skipped) | word |
+---------------------+-------+---- - - ---+------------+-----|------+---- - - - ----+------------+
^ | ^
| | |
| +-----------------------+
%esi added to offset

The offset is added to %esi to make the new %esi, and the result is that when NEXT runs, execution
continues at the branch target. Negative offsets work as expected.

0BRANCH is the same except the branch happens conditionally.

Now standard FORTH words such as IF, THEN, ELSE, WHILE, REPEAT, etc. can be implemented entirely
in FORTH. They are IMMEDIATE words which append various combinations of BRANCH or 0BRANCH
into the word currently being compiled.

As an example, code written like this:

condition-code IF true-part THEN rest-code

compiles to:

condition-code 0BRANCH OFFSET true-part rest-code
| ^
| |

defcode "BRANCH",6,,BRANCH
add (%esi),%esi // add the offset to the instruction pointer

defcode "0BRANCH",7,,ZBRANCH
pop %eax
test %eax,%eax // top of stack is zero?
jz code_BRANCH // if so, jump back to the branch function above
lodsl // otherwise we need to skip the offset

PRINTING STRINGS ----------------------------------------------------------------------

LITSTRING and EMITSTRING are primitives used to implement the ." and S" operators
(which are written in FORTH). See the definition of those operators below.

lodsl // get the length of the string
push %eax // push it on the stack
push %esi // push the address of the start of the string
addl %eax,%esi // skip past the string
addl $3,%esi // but round up to next 4 byte boundary
andl $~3,%esi

mov $1,%ebx // 1st param: stdout
pop %ecx // 2nd param: address of string
pop %edx // 3rd param: length of string
mov $__NR_write,%eax // write syscall
int $0x80

COLD START AND INTERPRETER ----------------------------------------------------------------------

COLD is the first FORTH function called, almost immediately after the FORTH system "boots".

INTERPRETER is the FORTH interpreter ("toploop", "toplevel" or "REPL" might be a more accurate
description -- see: http://en.wikipedia.org/wiki/REPL).

// COLD must not return (ie. must not call EXIT).
defword "COLD",4,,COLD
.int INTERPRETER // call the interpreter loop (never returns)
.int LIT,1,SYSEXIT // hmmm, but in case it does, exit(1).

/* This interpreter is pretty simple, but remember that in FORTH you can always override
* it later with a more powerful one!

call _WORD // Returns %ecx = length, %edi = pointer to word.

// Is it in the dictionary?
xor %eax,%eax
movl %eax,interpret_is_lit // Not a literal number (not yet anyway ...)
call _FIND // Returns %eax = pointer to header or 0 if not found.
test %eax,%eax // Found?
jz 1f

// In the dictionary. Is it an IMMEDIATE codeword?
mov %eax,%edi // %edi = dictionary entry
movb 4(%edi),%al // Get name+flags.
push %ax // Just save it for now.
call _TCFA // Convert dictionary entry (in %edi) to codeword pointer.
pop %ax
andb $F_IMMED,%al // Is IMMED flag set?
mov %edi,%eax
jnz 4f // If IMMED, jump straight to executing.

jmp 2f

1: // Not in the dictionary (not a word) so assume it's a literal number.
incl interpret_is_lit
call _SNUMBER // Returns the parsed number in %eax
mov %eax,%ebx
mov $LIT,%eax // The word is LIT

2: // Are we compiling or executing?
movl var_STATE,%edx
test %edx,%edx
jz 4f // Jump if executing.

// Compiling - just append the word to the current dictionary definition.
call _COMMA
mov interpret_is_lit,%ecx // Was it a literal?
test %ecx,%ecx
jz 3f
mov %ebx,%eax // Yes, so LIT is followed by a number.
call _COMMA

4: // Executing - run it!
mov interpret_is_lit,%ecx // Literal?
test %ecx,%ecx // Literal?
jnz 5f

// Not a literal, execute it now. This never returns, but the codeword will
// eventually call NEXT which will reenter the loop in INTERPRETER.
jmp *(%eax)

5: // Executing a literal, which means push it on the stack.
push %ebx

.align 4
.int 0 // Flag used to record if reading a literal

ODDS AND ENDS ----------------------------------------------------------------------

CHAR puts the ASCII code of the first character of the following word on the stack. For example
CHAR A puts 65 on the stack.

SYSEXIT exits the process using Linux exit syscall.

In this FORTH, SYSEXIT must be the last word in the built-in (assembler) dictionary because we
initialise the LATEST variable to point to it. This means that if you want to extend the assembler
part, you must put new words before SYSEXIT, or else change how LATEST is initialised.

defcode "CHAR",4,,CHAR
call _WORD // Returns %ecx = length, %edi = pointer to word.
xor %eax,%eax
movb (%edi),%al // Get the first character of the word.
push %eax // Push it onto the stack.

// NB: SYSEXIT must be the last entry in the built-in dictionary.
pop %ebx
mov $__NR_exit,%eax
int $0x80

START OF FORTH CODE ----------------------------------------------------------------------

We've now reached the stage where the FORTH system is running and self-hosting. All further
words can be written as FORTH itself, including words like IF, THEN, .", etc which in most
languages would be considered rather fundamental.

I used to append this here in the assembly file, but I got sick of fighting against gas's
stupid (lack of) multiline string syntax. So now that is in a separate file called jonesforth.f

If you don't already have that file, download it from http://annexia.org/forth in order
to continue the tutorial.

/* END OF jonesforth.S */