# FIRST & THIRD (almost FORTH) FORTH is a language mostly familiar to users of "small" machines. FORTH programs are small because they are interpreted--a function call in FORTH takes two bytes. FORTH is an extendable language-- built-in primitives are indistinguishable from user-defined _words_. FORTH interpreters are small because much of the system can be coded in FORTH--only a small number of primitives need to be implemented. Some FORTH interpreters can also compile defined words into machine code, resulting in a fast system. FIRST is an incredibly small language which is sufficient for defining the language THIRD, which is mostly like FORTH. There are some differences, and THIRD is probably just enough like FORTH for those differences to be disturbing to regular FORTH users. The only existing FIRST interpreter is written in obfuscated C, and rings in at under 800 bytes of source code, although through deletion of both whitespace and obfuscation it can be brought to about 650 bytes. This document FIRST defines the FIRST environment and primitives, with relevant design decision explanations. It secondly documents the general strategies we will use to implement THIRD. The THIRD section demonstrates how the complete THIRD system is built up using FIRST. ## Section 1: FIRST ### Environment FIRST implements a virtual machine. The machine has three chunks of memory: "main memory", "the stack", and "string storage". When the virtual machine wishes to do random memory accesses, they come out of main memory--it cannot access the stack or string storage. The stack is simply a standard LIFO data structure that is used implicitly by most of the FIRST primitives. The stack is made up of `int`s, whatever size they are on the host machine. String storage is used to store the names of built-in and defined primitives. Separate storage is used for these because it allows the C code to use C string operations, reducing C source code size. Main memory is a large array of `int`s. When we speak of addresses, we actually mean indices into main memory. Main memory is used for two things, primarily: the return stack and the dictionary. The return stack is a LIFO data structure, independent of the above-mentioned "stack", which is used by FIRST to keep track of function call return addresses. The dictionary is a list of words. Each word contains a header and a data field. In the header is the address of the previous word, an index into the string storage indicating where the name of this word is stored, and a "code pointer". The code pointer is simply an integer which names which "machine-language-primitive" implements this instruction. For example, for defined words the code pointer names the "run some code" primitive, which pushes the current program counter onto the return stack and sets the counter to the address of the data field for this word. There are several important pointers into main memory. There is a pointer to the most recently defined word, which is used to start searches back through memory when compiling words. There is a pointer to the top of the return stack. There is a pointer to the current end of the dictionary, used while compiling. For the last two pointers, namely the return stack pointer and the dictionary pointer, there is an important distinction: the pointers themselves are stored in main memory (in `FIRST`'s main memory). This is critical, because it means FIRST programs can get at them without any further primitives needing to be defined. ### Instructions There are two kinds of FIRST instructions, normal instructions and immediate instructions. Immediate instructions do something significant when they are used. Normal instructions compile a pointer to their executable part onto the end of the dictionary. As we will see, this means that by default FIRST simply compiles things. #### Integer Operations ``` SYMBOL NAME FUNCTION - binary minus pop top 2 elements of stack, subtract, push * multiply pop top 2 elements of stack, multiply, push / divide pop top 2 elements of stack, divide, push <0 less than 0 pop top element of stack, push 1 if < 0 else 0 ``` Note that we can synthesize addition and negation from binary minus, but we cannot synthesize a time efficient divide or multiply from it. `<0` is synthesize-able, but only in a non-portable way. #### Memory Operations ``` SYMBOL NAME FUNCTION @ fetch pop top of stack, treat as address to push contents of ! store top of stack is address, 2nd is value; store to memory and pop both off the stack ``` #### Input/Output Operations ``` NAME FUNCTION echo output top of stack through C's putchar() key push C's getchar() onto top of stack _read read a space-delimited word, find it in the dictionary, and compile a pointer to that word's code pointer onto the current end of the dictionary ``` Although `_read` could be synthesized from key, we need `_read` to be able to compile words to be able to start any syntheses. #### Execution Operations ``` NAME FUNCTION exit leave the current function: pop the return stack into the program counter ``` #### Immediate (compilation) Operations ``` SYMBOL NAME FUNCTION : define read in the next space-delimited word, add it to the end of our string storage, and generate a header for the new word so that when it is typed it compiles a pointer to itself so that it can be executed. immediate immediate when used immediately after a name following a ':', it makes the word being defined run whenever it is typed. ``` `:` cannot be synthesized, because we could not synthesize anything. `immediate` has to be an immediate operation, so it could not be synthesized unless by default operations were immediate; but that would preclude our being able to do any useful compilation. #### Stack Operations ``` NAME FUNCTION pick pop top of stack, use as index into stack and copy up that element ``` If the data stack were stored in main memory, we could synthesize `pick`; but putting the stack and stack pointer in main memory would significantly increase the C source code size. There are three more primitives, but they are "internal only"-- they have no names and no dictionary entries. The first is `pushint`. It takes the next integer out of the instruction stream and pushes it on the stack. This could be synthesized, but probably not without using integer constants. It is generated by `_read` when the input is not a known word. The second is `compile me`. When this instruction is executed, a pointer to the word's data field is appended to the dictionary. The third is `run me`--the word's data field is taken to be a stream of pointers to words, and is executed. One last note about the environment: FIRST builds a very small word internally that it executes as its main loop. This word calls `_read` and then calls itself. Each time it calls itself, it uses up a word on the return stack, so it will eventually trash things. This is discussed some more in section 2. Here's a handy summary of all the FIRST words: ``` WORD DESCRIPTION - * / binary integer operations on the stack <0 is top of stack less than 0? @ ! read from or write to memory echo key output or input one character _read read a word from input and compile a pointer to it exit stop running the current function : compile the header of a definition immediate modify the header to create an immediate word ``` Here is a sample FIRST program. I'm assuming you're using the ASCII character set. FIRST does not depend upon ASCII, but since FIRST has no syntax for character constants, one normally has to use decimal values. This can be avoided using `getchar(3)`, though. Oh. One other odd thing. FIRST initially builds its symbol table by calling `:` several times, so it needs to get the names of the base symbols as its first 13 words of input. You could even name them differently if you wanted. These FIRST programs have FORTH comments in them: they are contained inside parentheses. FIRST programs cannot have FORTH comments; but I need some device to indicate what's going on. (THIRD programs are an entirely different subject.) ``` ( Our first line gives the symbols for the built-ins ) : immediate _read @ ! - * / <0 exit echo key _pick ( now we define a simple word that will print out a couple characters ) : L ( define a word named 'L' ) 108 echo ( output an ascii 'l' ) exit : hello ( define a word named 'hello') 72 echo ( output an ascii 'H' ) 101 echo ( output an ascii 'e' ) 111 ( push ascii 'o' onto the stack ) L L ( output two ascii 'l's ) echo ( output the 'o' we pushed on the stack before ) 10 echo ( print a newline ) exit ( stop running this routine ) : test immediate ( define a word named 'test' that runs whenever typed ) hello ( call hello ) exit test ( The result of running this program should be: Hello ) ``` ## Section 2: Motivating THIRD What is missing from FIRST? There are a large number of important primitives that aren't implemented, but which are easy to implement. `drop`, which throws away the top of the stack, can be implemented as `{ 0 * + }` -- that is, multiply the top of the stack by `0` (which turns the top of the stack into a `0`), and then add the top two elements of the stack. `dup`, which copies the top of the stack, can be easily implemented using temporary storage locations. Conveniently, FIRST leaves memory locations `3`, `4`, and `5` unused. So we can implement `dup` by writing the top of stack into `3`, and then reading it out twice: `{ 3 ! 3 @ 3 @ }`. We will never use the FIRST primitive `pick` in building THIRD, just to show that it can be done; `pick` is only provided because `pick` itself cannot be built out of the rest of `FIRST`'s building blocks. So, instead of worrying about stack primitives and the like, what else is missing from FIRST? We get recursion, but no control flow--no conditional operations. We cannot at the moment write a looping routine which terminates. Another glaring dissimilarity between FIRST and FORTH is that there is no "command mode"--you cannot be outside of a `:` definition and issue some straight commands to be executed. Also, as we noted above, we cannot do comments. FORTH also provides a system for defining new data types, using the words (in one version of FORTH) `builds and does`. We would like to implement these words as well. As the highest priority thing, we will build control flow structures first. Once we have control structures, we can write recursive routines that terminate, and we are ready to tackle tasks like parsing, and the building of a command mode. By the way, location `0` holds the dictionary pointer, location `1` holds the return stack pointer, and location `2` should always be `0`--it's a fake dictionary entry that means `pushint`. ## Section 3: Building THIRD In this section we'll eventually have real comments. The first thing we have to do is give the symbols for our built-ins. ``` : immediate _read @ ! - * / < exit echo key _pick ``` Next we want to be mildly self commenting, so we define the word `r` to push the *address of the return stack pointer* onto the stack--NOT the value of the return stack pointer. (In fact, when we run `r`, the value of the return stack pointer is temporarily changed.) ``` : r 1 exit ``` Next, we're currently executing a short loop that contains `_read` and recursion, which is slowly blowing up the return stack. So let's define a new word, from which you can never return. What it does is drops the top value off the return stack, calls `_read`, then calls itself. Because it kills the top of the return stack, it can recurse indefinitely. ``` : ] r @ Get the value of the return stack pointer 1 - Subtract one r ! Store it back into the return stack pointer _read Read and compile one word ] Start over ``` Notice that we don't need to exit, since we never come back. Also, it's possible that an immediate word may get run during `_read`, and that `_read` will never return! Now let's get compile running. ``` : main immediate ] main ``` Next off, I'm going to do this the easy but non-portable way, and put some character constant definitions in. I wanted them at the top of the file, but that would have burned too much of the return stack. ``` : '"' 34 exit : ')' 41 exit : '\n' 10 exit : 'space' 32 exit : '0' 48 exit : '-' 45 exit : cr '\n' echo exit ``` Next, we want to define some temporary variables for locations `3`, `4`, and `5`, since this'll make our code look clearer. ``` : _x 3 @ exit : _x! 3 ! exit : _y 4 @ exit : _y! 4 ! exit ``` OK. Now, we want to make THIRD look vaguely like FORTH, so we're going to define `;`. What `;` ought to do is terminate a compilation, and turn control over to the command-mode handler. We don't have one, so all we want `;` to do for now is compile `exit` at the end of the current word. To do this we'll need several other words. Swap by writing out the top two elements into temps, and then reading them back in the other order. ``` : swap _x! _y! _x _y exit ``` Take another look and make sure you see why that works, since it LOOKS like I'm reading them back in the same order--in fact, it not only looks like it, but I AM! Addition might be nice to have. To add, we need to negate the top element of the stack, and then subtract. To negate, we subtract from `0`. ``` : + 0 swap - - exit ``` Create a copy of the top of stack. ``` : dup _x! _x _x exit ``` Get a mnemonic name for our dictionary pointer--we need to compile stuff, so it goes through this. ``` : h 0 exit ``` We're going to need to advance that pointer, so let's make a generic pointer-advancing function. Given a pointer to a memory location, increment the value at that memory location. ``` : inc dup @ Get another copy of the address, and get the value so now we have value, address on top of stack. 1 + Add one to the value swap Swap to put the address on top of the stack ! exit Write it to memory ``` `,` is a standard FORTH word. It should write the top of stack into the dictionary, and advance the pointer ``` : , h @ Get the value of the dictionary pointer ! Write the top of stack there h inc And increment the dictionary pointer exit ``` `'` is a standard FORTH word. It should push the address of the word that follows it onto the stack. We could do this by making `'` immediate, but then it'd need to parse the next word. Instead, we compile the next word as normal. When `'` is executed, the top of the return stack will point into the instruction stream immediately after the `'`. We push the word there, and advance the return stack pointer so that we don't execute it. ``` : ' r @ Get the address of the top of return stack We currently have a pointer to the top of return stack @ Get the value from there We currently have a pointer to the instruction stream dup Get another copy of it--the bottom copy will stick around until the end of this word 1 + Increment the pointer, pointing to the NEXT instruction r @ ! Write it back onto the top of the return stack We currently have our first copy of the old pointer to the instruction stream @ Get the value there--the address of the "next word" exit ``` Now we're set. `;` should be an immediate word that pushes the address of `exit` onto the stack, then writes it out. ``` : ; immediate ' exit Get the address of exit , Compile it exit And we should return ``` Now let's test out `;` by defining a useful word: ``` : drop 0 * + ; ``` Since we have `inc`, we ought to make `dec`: ``` : dec dup @ 1 - swap ! ; ``` Our next goal, now that we have `;`, is to implement `if-then`. To do this, we'll need to play fast and loose with the return stack, so let's make some words to save us some effort. First we want a word that pops off the top of the normal stack and pushes it on top of the return stack. We'll call this `tor`, for TO-Return-stack. It sounds easy, but when `tor` is running, there's an extra value on the return stack--`tor`'s return address! So we have to pop that off first... We better just bite the bullet and code it out--but we can't really break it into smaller words, because that'll trash the return stack. ``` : tor r @ @ Get the value off the top of the return stack swap Bring the value to be pushed to the top of stack r @ ! Write it over the current top of return stack r @ 1 + r ! Increment the return stack pointer--but can't use inc r @ ! Store our return address back on the return stack ; ``` Next we want the opposite routine, which pops the top of the return stack, and puts it on the normal stack. ``` : fromr r @ @ Save old value r @ 1 - r ! Decrement pointer r @ @ Get value that we want off swap Bring return address to top r @ ! Store it and return ; ``` Now, if we have a routine that's recursing, and we want to be polite about the return stack, right before we recurse we can run `{ fromr drop }` so the stack won't blow up. This means, though, that the first time we enter this recursive routine, we blow our *real* return address--so when we're done, we'll return up two levels. To save a little, we make `tail` mean `{ fromr drop }`; however, it's more complex since there's a new value on top of the return stack. ``` : tail fromr fromr drop tor ; ``` Now, we want to do `if`. To do this, we need to convert values to boolean values. The next few words set this up. `minus` gives us unary negation. ``` : minus 0 swap - ; ``` If top of stack is boolean, `bnot` gives us inverse ``` : bnot 1 swap - ; ``` To compare two numbers, subtract and compare to `0`. ``` : < - <0 ; ``` `logical` turns the top of stack into either `0` or `1`. ``` : logical dup Get two copies of it 0 < 1 if < 0, 0 otherwise swap minus Swap number back up, and take negative 0 < 1 if original was > 0, 0 otherwise + Add them up--has to be 0 or 1! ; ``` `not` returns 1 if top of stack is 0, and 0 otherwise ``` : not logical bnot ; ``` We can test equality by subtracting and comparing to `0`. ``` : = - not ; ``` Just to show how you compute a branch: Suppose you've compiled a call to branch, and immediately after it is an integer constant with the offset of how far to branch. To branch, we use the return stack to read the offset, and add that on to the top of the return stack, and return. ``` : branch r @ Address of top of return stack @ Our return address @ Value from there: the branch offset r @ @ Our return address again + The address we want to execute at r @ ! Store it back onto the return stack ; ``` For conditional branches, we want to branch by a certain amount if true, otherwise we want to skip over the branch offset constant--that is, branch by one. Assuming that the top of the stack is the branch offset, and the second on the stack is `1` if we should branch, and `0` if not, the following computes the correct branch offset. ``` : computebranch 1 - * 1 + ; ``` Branch if the value on top of the stack is `0`. ``` : notbranch not r @ @ @ Get the branch offset computebranch Adjust as necessary r @ @ + Calculate the new address r @ ! Store it ; ``` `here` is a standard FORTH word which returns a pointer to the current dictionary address--that is, the value of the dictionary pointer. ``` : here h @ ; ``` We're ALL SET to compile `if...else...then` constructs! Here's what we do. When we get `if`, we compile a call to `notbranch`, and then compile a dummy offset, because we don't know where the `then` will be. On the *stack* we leave the address where we compiled the dummy offset. `then` will calculate the offset and fill it in for us. ``` : if immediate ' notbranch , Compile notbranch here Save the current dictionary address 0 , Compile a dummy value ; ``` `then` expects the address to `fixup` to be on the stack. ``` : then immediate dup Make another copy of the address here Find the current location, where to branch to swap - Calculate the difference between them swap ! Bring the address to the top, and store it. ; ``` Now that we can do `if...then` statements, we can do some parsing! Let's introduce real FORTH comments. `find-)` will scan the input until it finds a `)`, and exit. ``` : find-) key Read in a character ')' = Compare it to close parentheses not if If it's not equal tail find-) repeat (popping R stack) then Otherwise branch here and exit ; : ( immediate find-) ; ( we should be able to do FORTH-style comments now ) ( now that we've got comments, we can comment the rest of the code in a legitimate [self parsing] fashion. Note that you can't nest parentheses... ) : else immediate ' branch , ( compile a definite branch ) here ( push the backpatching address ) 0 , ( compile a dummy offset for branch ) swap ( bring old backpatch address to top ) dup here swap - ( calculate the offset from old address ) swap ! ( put the address on top and store it ) ; : over _x! _y! _y _x _y ; : add _x! ( save the pointer in a temp variable ) _x @ ( get the value pointed to ) + ( add the incremement from on top of the stack ) _x ! ( and save it ) ; : allot h add ; : maybebranch logical ( force the TOS to be 0 or 1 ) r @ @ @ ( load the branch offset ) computebranch ( calculate the condition offset [either TOS or 1]) r @ @ + ( add it to the return address ) r @ ! ( store it to our return address and return ) ; : mod _x! _y! ( get x then y off of stack ) _y _y _x / _x * ( y - y / x * x ) - ; : printnum dup 10 mod '0' + swap 10 / dup if printnum echo else drop echo then ; : . dup 0 < if '-' echo minus then printnum 'space' echo ; : debugprint dup . cr ; ( the following routine takes a pointer to a string, and prints it, except for the trailing quote. returns a pointer to the next word after the trailing quote ) : _print dup 1 + swap @ dup '"' = if drop exit then echo tail _print ; : print _print ; ( print the next thing from the instruction stream ) : immprint r @ @ print r @ ! ; : find-" key dup , '"' = if exit then tail find-" ; : " immediate key drop ' immprint , find-" ; : do immediate ' swap , ( compile 'swap' to swap the limit and start ) ' tor , ( compile to push the limit onto the return stack ) ' tor , ( compile to push the start on the return stack ) here ( save this address so we can branch back to it ) ; : i r @ 1 - @ ; : j r @ 3 - @ ; : > swap < ; : <= 1 + < ; : >= swap <= ; : inci r @ 1 - ( get the pointer to i ) inc ( add one to it ) r @ 1 - @ ( find the value again ) r @ 2 - @ ( find the limit value ) <= if r @ @ @ r @ @ + r @ ! exit ( branch ) then fromr 1 + fromr drop fromr drop tor ; : loop immediate ' inci @ here - , ; : loopexit fromr drop ( pop off our return address ) fromr drop ( pop off i ) fromr drop ( pop off the limit of i ) ; ( and return to the caller's caller routine ) : execute 8 ! ' exit 9 ! 8 tor ; : :: ; ( :: is going to be a word that does ':' at runtime ) : fix-:: immediate 3 ' :: ! ; fix-:: ( Override old definition of ':' with a new one that invokes ] ) : : immediate :: ] ; : command here 5 ! ( store dict pointer in temp variable ) _read ( compile a word ) ( if we get control back: ) here 5 @ = if tail command ( we didn't compile anything ) then here 1 - h ! ( decrement the dictionary pointer ) here 5 @ ( get the original value ) = if here @ ( get the word that was compiled ) execute ( and run it ) else here @ ( else it was an integer constant, so push it ) here 1 - h ! ( and decrement the dictionary pointer again ) then tail command ; : make-immediate ( make a word just compiled immediate ) here 1 - ( back up a word in the dictionary ) dup dup ( save the pointer to here ) h ! ( store as the current dictionary pointer ) @ ( get the run-time code pointer ) swap ( get the dict pointer again ) 1 - ( point to the compile-time code pointer ) ! ( write run-time code pointer on compile-time pointer ) ; : ) ' , , ( compile a push that address onto dictionary ) ; : does> immediate ' command , ( jump back into command mode at runtime ) here swap ! ( backpatch the build> to point to here ) 2 , ( compile run-code primitive so we look like a word ) ' fromr , ( compile fromr, which leaves var address on stack ) ; : _dump ( dump out the definition of a word, sort of ) dup " (" . " , " dup @ ( save the pointer and get the contents ) dup ' exit = if " ;)" cr exit then . " ), " 1 + tail _dump ; : dump _dump ; : # . cr ; : var ; : constant @ ; : array + ; : [ immediate command ; : _welcome " Welcome to THIRD. Ok. " ; : ; immediate ' exit , command exit [ _welcome ```
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