(in-package #:bones.wam)
(named-readtables:in-readtable :fare-quasiquote)
;;;; Utils
(declaim (inline variablep))
(defun* variablep (term)
(:returns boolean)
(keywordp term))
;;;; Registers
(deftype register-type ()
'(member :argument :local :permanent))
(deftype register-number ()
`(integer 0 ,(1- +register-count+)))
(declaim (inline register-type register-number))
(defstruct (register (:constructor make-register (type number)))
(type :local :type register-type)
(number 0 :type register-number))
(defun* make-temporary-register ((number register-number) (arity arity))
(:returns register)
(make-register (if (< number arity) :argument :local)
number))
(defun* make-permanent-register ((number register-number) (arity arity))
(:returns register)
(declare (ignore arity))
(make-register :permanent number))
(defun* register-to-string ((register register))
(format nil "~A~D"
(ecase (register-type register)
(:argument #\A)
(:local #\X)
(:permanent #\Y))
(+ (register-number register)
(if *off-by-one* 1 0))))
(defmethod print-object ((object register) stream)
(print-unreadable-object (object stream :identity nil :type nil)
(format stream (register-to-string object))))
(declaim (inline register-argument-p
register-temporary-p
register-permanent-p))
(defun* register-argument-p ((register register))
(eql (register-type register) :argument))
(defun* register-temporary-p ((register register))
(member (register-type register) '(:argument :local)))
(defun* register-permanent-p ((register register))
(eql (register-type register) :permanent))
(declaim (inline register=))
(defun* register= ((r1 register) (r2 register))
(and (eql (register-type r1)
(register-type r2))
(= (register-number r1)
(register-number r2))))
;;;; Parse Trees
(defclass node () ())
(defclass top-level-node (node)
((functor :accessor node-functor
:type symbol
:initarg :functor)
(arity :accessor node-arity
:type arity
:initarg :arity)
(arguments :accessor node-arguments
:type list
:initarg :arguments)))
(defclass vanilla-node (node)
((register :accessor node-register
:type register
:documentation "The register allocated to store this node.")))
(defclass structure-node (vanilla-node)
((functor :accessor node-functor
:type symbol
:initarg :functor)
(arity :accessor node-arity
:type arity
:initarg :arity)
(arguments :accessor node-arguments
:type list
:initarg :arguments)))
(defclass variable-node (vanilla-node)
((variable :accessor node-variable
:type keyword
:initarg :variable)))
(defclass argument-variable-node (variable-node)
((secondary-register
:accessor node-secondary-register
:type register
:documentation
"The register that actually holds the variable (NOT the argument register).")))
(defclass list-node (vanilla-node)
((head :accessor node-head :type node :initarg :head)
(tail :accessor node-tail :type node :initarg :tail)))
(defun make-top-level-node (functor arity arguments)
(make-instance 'top-level-node
:functor functor
:arity arity
:arguments arguments))
(defun make-structure-node (functor arity arguments)
(make-instance 'structure-node
:functor functor
:arity arity
:arguments arguments))
(defun make-variable-node (variable)
(make-instance 'variable-node :variable variable))
(defun make-argument-variable-node (variable)
(make-instance 'argument-variable-node :variable variable))
(defun make-list-node (head tail)
(make-instance 'list-node :head head :tail tail))
(defgeneric node-children (node)
(:documentation
"Return the children of the given node.
Presumably these will need to be traversed when allocating registers."))
(defmethod node-children ((node vanilla-node))
(list))
(defmethod node-children ((node top-level-node))
(node-arguments node))
(defmethod node-children ((node structure-node))
(node-arguments node))
(defmethod node-children ((node list-node))
(list (node-head node) (node-tail node)))
(defun nil-node-p (node)
"Return whether the given node is the magic nil/0 constant."
(and (typep node 'structure-node)
(eql (node-functor node) nil)
(zerop (node-arity node))))
(defparameter *dump-node-indent* 0)
(defun print-node-register (node stream &optional space-before)
(when (slot-boundp node 'register)
(format stream (if space-before " ~A =" "~A = ") (node-register node))))
(defun print-node-secondary-register (node stream &optional space-before)
(when (slot-boundp node 'secondary-register)
(format stream
(if space-before " ~A =" "~A = ")
(node-secondary-register node))))
(defgeneric dump-node (node))
(defmethod dump-node ((node node))
(format t "~VAAN NODE" *dump-node-indent* ""))
(defmethod dump-node ((node variable-node))
(format t "~VA#<VAR" *dump-node-indent* "")
(print-node-register node t t)
(format t " ~S>" (node-variable node)))
(defmethod dump-node ((node argument-variable-node))
(format t "~VA#<VAR" *dump-node-indent* "")
(print-node-register node t t)
(print-node-secondary-register node t t)
(format t " ~S>" (node-variable node)))
(defmethod dump-node ((node structure-node))
(format t "~VA#<STRUCT " *dump-node-indent* "")
(print-node-register node t)
(format t "~A/~D" (node-functor node) (node-arity node))
(let ((*dump-node-indent* (+ *dump-node-indent* 4)))
(dolist (a (node-arguments node))
(terpri)
(dump-node a)))
(format t ">"))
(defmethod dump-node ((node list-node))
(format t "~VA#<LIST" *dump-node-indent* "")
(print-node-register node t t)
(let ((*dump-node-indent* (+ *dump-node-indent* 4)))
(loop :for element = node :then tail
:while (typep element 'list-node)
:for head = (node-head element)
:for tail = (node-tail element)
:do (progn (terpri) (dump-node head))
:finally (when (not (nil-node-p element))
(format t "~%~VA.~%" *dump-node-indent* "")
(dump-node element))))
(format t ">"))
(defmethod dump-node ((node top-level-node))
(format t "#<~A/~D" (node-functor node) (node-arity node))
(let ((*dump-node-indent* 4))
(dolist (n (node-arguments node))
(terpri)
(dump-node n)))
(format t ">"))
(defmethod print-object ((node node) stream)
(let ((*standard-output* stream))
(dump-node node)))
(defun parse-list (contents)
(if contents
(make-list-node (parse (car contents))
(parse-list (cdr contents)))
(make-structure-node 'nil 0 ())))
(defun parse-list* (contents)
(destructuring-bind (next . remaining) contents
(if (null remaining)
(parse next)
(make-list-node (parse next)
(parse-list* remaining)))))
(defun parse (term &optional top-level-argument)
(cond
((keywordp term)
(if top-level-argument
(make-argument-variable-node term)
(make-variable-node term)))
((symbolp term)
(parse (list term))) ; c/0 -> (c/0)
((consp term)
(destructuring-bind (functor . arguments) term
(case functor
(list (parse-list arguments))
(list* (parse-list* arguments))
(t (make-structure-node functor
(length arguments)
(mapcar #'parse arguments))))))))
(defun parse-top-level (term)
(if (symbolp term) ; c/0 -> (c/0)
(parse-top-level (list term))
(destructuring-bind (functor . arguments) term
(make-top-level-node functor (length arguments)
(mapcar (lambda (a) (parse a t))
arguments)))))
;;;; Register Allocation
;;; You might want to grab a coffee for this one.
;;;
;;; Consider this simple Prolog example: `p(A, q(A, r(B)))`. We're going to get
;;; this as a Lisp list: `(p :a (q :a (r b)))`.
;;;
;;; The goal is to turn this list into a set of register assignments. The book
;;; handwaves around how to do this, and it turns out to be pretty complicated.
;;; This example will (maybe, read on) be turned into:
;;;
;;; A0 <- X2
;;; A1 <- (q X2 X3)
;;; X2 <- :a
;;; X3 <- (r X4)
;;; X4 <- :b
;;;
;;; There are a few things to note here. First: like the book says, the
;;; outermost predicate is stripped off and returned separately (later it'll be
;;; used to label the code for a program, or to figure out the procedure to call
;;; for a query).
;;;
;;; The first N registers are designated as argument registers. Structure
;;; assignments can live directly in the argument registers, but variables
;;; cannot. In the example above we can see that A1 contains a structure
;;; assignment. However, the variable `:a` doesn't live in A0 -- it lives in
;;; X2, which A0 points at. The books neglects to explain this little fact.
;;;
;;; The next edge case is permanent variables, which the book does talk about.
;;; Permanent variables are allocated to stack registers, so if `:b` was
;;; permanent in our example we'd get:
;;;
;;; A0 <- X2
;;; A1 <- (q X2 X3)
;;; X2 <- :a
;;; X3 <- (r Y0)
;;; Y0 <- :b
;;;
;;; Note that the mapping of permanent variables to stack register numbers has
;;; to be consistent as we compile all the terms in a clause, so we cheat a bit
;;; here and just always add them all, in order, to the register assignment
;;; produced when parsing. They'll get flattened away later anyway -- it's the
;;; USES that we actually care about. In our example, the `Y0 <- :b` will get
;;; flattened away, but the USE of Y0 in X3 will remain).
;;;
;;; We're almost done, I promise, but there's one more edge case to deal with.
;;;
;;; When we've got a clause with a head and at least one body term, we need the
;;; head term and the first body term to share argument/local registers. For
;;; example, if we have the clause `p(Cats) :- q(A, B, C, Cats)` then when
;;; compiling the head `(p :cats)` we want to get:
;;;
;;; A0 <- X4
;;; A1 <- ???
;;; A2 <- ???
;;; A3 <- ???
;;; X4 <- :cats
;;;
;;; And when compiling `(q :a :b :c :cats)` we need:
;;;
;;; A0 <- X5
;;; A1 <- X6
;;; A2 <- X7
;;; A3 <- X4
;;; X4 <- :cats
;;; X5 <- :a
;;; X6 <- :b
;;; X7 <- :c
;;;
;;; What the hell are those empty argument registers in p? And why did we order
;;; the X registers of q like that?
;;;
;;; The book does not bother to mention this important fact at all, so to find
;;; out that you have to handle this you need to do the following:
;;;
;;; 1. Implement it without this behavior.
;;; 2. Notice your results are wrong.
;;; 3. Figure out the right bytecode on a whiteboard.
;;; 4. Try to puzzle out why that bytecode isn't generated when you do exactly
;;; what the book says.
;;; 5. Scour IRC and the web for scraps of information on what the hell you need
;;; to do here.
;;; 6. Find the answer in a comment squirreled away in a source file somewhere
;;; in a language you don't know.
;;; 7. Drink.
;;;
;;; Perhaps you're reading this comment as part of step 6 right now. If so:
;;; welcome aboard. Email me and we can swap horror stories about this process
;;; over drinks some time.
;;;
;;; Okay, so the clause head and first body term need to share argument/local
;;; registers. Why? To understand this, we need to go back to what Prolog
;;; clauses are supposed to do.
;;;
;;; Imagine we have:
;;;
;;; p(f(X)) :- q(X), ...other goals.
;;;
;;; When we want to check if `p(SOMETHING)` is true, we need to first unify
;;; SOMETHING with `f(X)`. Then we search all of the goals in the body, AFTER
;;; substituting in any X's in those goals with the X from the result of the
;;; unification.
;;;
;;; This substitution is why we need the head and the first term in the body to
;;; share the same argument/local registers. By sharing the registers, when the
;;; body term builds a representation of itself on the stack before calling its
;;; predicate any references to X will be point at the (unified) results instead
;;; of fresh ones (because they'll be compiled as `put_value` instead of
;;; `put_variable`).
;;;
;;; But wait: don't we need to substitute into ALL the body terms, not just the
;;; first one? Yes we do, but the trick is that any variables in the REST of
;;; the body that would need to be substituted must, by definition, be permanent
;;; variables! So the substitution process for the rest of the body is handled
;;; automatically with the stack machinery.
;;;
;;; In theory, you could eliminate this edge case by NOT treating the head and
;;; first goal as a single term when searching for permanent variables. Then
;;; all substitution would happen elegantly through the stack. But this
;;; allocates more variables on the stack than you really need (especially for
;;; rules with just a single term in the body (which is many of them)), so we
;;; have this extra corner case to optimize it away.
;;;
;;; In the following code these variables will be called "nead variables"
;;; because:
;;;
;;; 1. They're present in the head of the clause.
;;; 2. They're present in the first term of the body (the "neck", as referred to
;;; in "neck cut" and such).
;;; 3. https://www.urbandictionary.com/define.php?term=nead&defid=1488946
;;;
;;; We now return you to your regularly scheduled Lisp code.
(defstruct allocation-state
local-registers
stack-registers
permanent-variables
reserved-variables
reserved-arity
actual-arity)
(defun find-variable (state variable)
"Return the register that already contains this variable, or `nil` otherwise."
(or (when-let (r (position variable (allocation-state-local-registers state)))
(make-temporary-register r (allocation-state-actual-arity state)))
(when-let (s (position variable (allocation-state-stack-registers state)))
(make-permanent-register s (allocation-state-actual-arity state)))
nil))
(defun store-variable (state variable)
"Assign `variable` to the next available local register.
It is assumed that `variable` is not already assigned to another register
(check that with `find-variable` first).
It is also assumed that this will be a non-argument register, because as
mentioned above variables cannot live directly inside argument registers.
"
(make-register
:local
(vector-push-extend variable (allocation-state-local-registers state))))
(defun ensure-variable (state variable)
(or (find-variable state variable)
(store-variable state variable)))
(defmacro set-when-unbound (instance slot value-form)
(once-only (instance slot)
`(when (not (slot-boundp ,instance ,slot))
(setf (slot-value ,instance ,slot) ,value-form))))
(defun allocate-nonvariable-register (state)
"Allocate and return a register for something that's not a variable."
;; We need to allocate registers for things like structures and lists, but we
;; never need to look them up later (like we do with variables), so we'll just
;; shove a nil into the local registers array as a placeholder.
(make-temporary-register
(vector-push-extend nil (allocation-state-local-registers state))
(allocation-state-actual-arity state)))
(defgeneric allocate-register (node allocation-state))
(defmethod allocate-register ((node top-level-node) state)
(declare (ignore node state))
(values))
(defmethod allocate-register ((node variable-node) state)
(set-when-unbound node 'register
(ensure-variable state (node-variable node))))
(defmethod allocate-register ((node argument-variable-node) state)
(set-when-unbound node 'secondary-register
(ensure-variable state (node-variable node))))
(defmethod allocate-register ((node structure-node) state)
(set-when-unbound node 'register
(allocate-nonvariable-register state)))
(defmethod allocate-register ((node list-node) state)
(set-when-unbound node 'register
(allocate-nonvariable-register state)))
(defun allocate-argument-registers (node)
(loop :for argument :in (node-arguments node)
:for i :from 0
:do (setf (node-register argument)
(make-register :argument i)))
(values))
(defun allocate-nonargument-registers
(node permanent-variables reserved-variables reserved-arity)
;; JESUS TAKE THE WHEEL
(let*
((actual-arity (node-arity node))
;; Preallocate enough registers for all of the arguments. We'll fill
;; them in later. Note that things are more complicated in the head and
;; first body term of a clause (see above).
(local-registers (make-array 64
:fill-pointer (or reserved-arity actual-arity)
:adjustable t
:initial-element nil))
;; We essentially "preallocate" all the permanent variables up front
;; because we need them to always be in the same stack registers across
;; all the terms of our clause.
;;
;; The ones that won't get used in this term will end up getting
;; flattened away anyway.
(stack-registers (make-array (length permanent-variables)
:initial-contents permanent-variables))
(allocation-state (make-allocation-state
:local-registers local-registers
:stack-registers stack-registers
:permanent-variables permanent-variables
:reserved-variables reserved-variables
:reserved-arity reserved-arity
:actual-arity actual-arity)))
;; Actually reserve the reserved (but non-permanent, see above) variables.
;; They need to live in consistent spots for the head and first body term.
(loop :for variable :in reserved-variables
:do (vector-push-extend variable local-registers))
(recursively ((remaining (list node)))
(when remaining
(destructuring-bind (node . remaining) remaining
(allocate-register node allocation-state)
(recur (append remaining (node-children node)))))))
(values))
(defun allocate-registers
(node permanent-variables &optional reserved-variables reserved-arity)
(allocate-argument-registers node)
(allocate-nonargument-registers
node permanent-variables reserved-variables reserved-arity)
(values))
;;;; Flattening
;;; "Flattening" is the process of turning a parse tree (with register
;;; assignments) into a flat list of nodes, which will then be turned into
;;; a series of instructions.
;;;
;;; The order of this list depends on whether we're compiling a query term or
;;; a program term.
;;;
;;; Turns:
;;;
;;; X0 <- p(X1, X2)
;;; X1 <- A
;;; X2 <- q(X1, X3)
;;; X3 <- B
;;;
;;; into something like:
;;;
;;; X2 <- q(X1, X3)
;;; X0 <- p(X1, X2)
(defclass register-assignment ()
((register :accessor assignment-register :type register :initarg :register)))
(defclass structure-assignment (register-assignment)
((functor :accessor assignment-functor :type symbol :initarg :functor)
(arity :accessor assignment-arity :type arity :initarg :arity)
(arguments :accessor assignment-arguments :type list :initarg :arguments)))
(defclass argument-variable-assignment (register-assignment)
((target :accessor assignment-target :type register :initarg :target)))
(defclass list-assignment (register-assignment)
((head :accessor assignment-head :type register :initarg :head)
(tail :accessor assignment-tail :type register :initarg :tail)))
(defmethod print-object ((assignment structure-assignment) stream)
(print-unreadable-object (assignment stream :type nil :identity nil)
(format stream "~A = ~A/~D(~{~A~^, ~})"
(register-to-string (assignment-register assignment))
(assignment-functor assignment)
(assignment-arity assignment)
(mapcar #'register-to-string (assignment-arguments assignment)))))
(defmethod print-object ((assignment argument-variable-assignment) stream)
(print-unreadable-object (assignment stream :type nil :identity nil)
(format stream "~A = ~A"
(register-to-string (assignment-register assignment))
(register-to-string (assignment-target assignment)))))
(defmethod print-object ((assignment list-assignment) stream)
(print-unreadable-object (assignment stream :type nil :identity nil)
(format stream "~A = [~A | ~A]"
(register-to-string (assignment-register assignment))
(register-to-string (assignment-head assignment))
(register-to-string (assignment-tail assignment)))))
(defgeneric node-flatten (node))
(defmethod node-flatten (node)
nil)
(defmethod node-flatten ((node structure-node))
(make-instance 'structure-assignment
:register (node-register node)
:functor (node-functor node)
:arity (node-arity node)
:arguments (mapcar #'node-register (node-arguments node))))
(defmethod node-flatten ((node argument-variable-node))
(make-instance 'argument-variable-assignment
:register (node-register node)
:target (node-secondary-register node)))
(defmethod node-flatten ((node list-node))
(make-instance 'list-assignment
:register (node-register node)
:head (node-register (node-head node))
:tail (node-register (node-tail node))))
(defun flatten-breadth-first (tree)
(let ((results nil))
(recursively ((node tree))
(when-let (assignment (node-flatten node))
(push assignment results))
(mapcar #'recur (node-children node)))
(nreverse results)))
(defun flatten-depth-first-post-order (tree)
(let ((results nil))
(recursively ((node tree))
(mapcar #'recur (node-children node))
(when-let (assignment (node-flatten node))
(push assignment results)))
(nreverse results)))
(defun flatten-query (tree)
(flatten-depth-first-post-order tree))
(defun flatten-program (tree)
(flatten-breadth-first tree))
;;;; Tokenization
;;; Tokenizing takes a flattened set of assignments and turns it into a stream
;;; of structure assignments and bare registers.
;;;
;;; It turns:
;;;
;;; X2 <- q(X1, X3)
;;; X0 <- p(X1, X2)
;;; A3 <- X4
;;;
;;; into something like:
;;;
;;; (X2 = q/2), X1, X3, (X0 = p/2), X1, X2, (A3 = X4)
(defclass token () ())
(defclass register-token (token)
((register :accessor token-register :type register :initarg :register)))
(defclass structure-token (register-token)
((functor :accessor token-functor :type symbol :initarg :functor)
(arity :accessor token-arity :type arity :initarg :arity)))
(defclass argument-variable-token (register-token)
((target :accessor token-target :type register :initarg :target)))
(defclass list-token (register-token) ())
(defclass call-token (token)
((functor :accessor token-functor :type symbol :initarg :functor)
(arity :accessor token-arity :type arity :initarg :arity)))
(defclass cut-token (token) ())
(defun make-register-token (register)
(make-instance 'register-token :register register))
(defmethod print-object ((token register-token) stream)
(print-object (token-register token) stream))
(defmethod print-object ((token structure-token) stream)
(print-unreadable-object (token stream :identity nil :type nil)
(format stream "~A = ~A/~D"
(register-to-string (token-register token))
(token-functor token)
(token-arity token))))
(defmethod print-object ((token argument-variable-token) stream)
(print-unreadable-object (token stream :identity nil :type nil)
(format stream "~A = ~A"
(register-to-string (token-register token))
(register-to-string (token-target token)))))
(defmethod print-object ((token list-token) stream)
(print-unreadable-object (token stream :identity nil :type nil)
(format stream "~A = LIST" (register-to-string (token-register token)))))
(defmethod print-object ((token call-token) stream)
(print-unreadable-object (token stream :identity nil :type nil)
(format stream "CALL ~A/~D"
(token-functor token)
(token-arity token))))
(defmethod print-object ((token cut-token) stream)
(print-unreadable-object (token stream :identity nil :type nil)
(format stream "CUT!")))
(defgeneric tokenize-assignment (assignment))
(defmethod tokenize-assignment ((assignment structure-assignment))
(list* (make-instance 'structure-token
:register (assignment-register assignment)
:functor (assignment-functor assignment)
:arity (assignment-arity assignment))
(mapcar #'make-register-token (assignment-arguments assignment))))
(defmethod tokenize-assignment ((assignment argument-variable-assignment))
(list (make-instance 'argument-variable-token
:register (assignment-register assignment)
:target (assignment-target assignment))))
(defmethod tokenize-assignment ((assignment list-assignment))
(list (make-instance 'list-token :register (assignment-register assignment))
(make-register-token (assignment-head assignment))
(make-register-token (assignment-tail assignment))))
(defun tokenize-assignments (assignments)
"Tokenize a flattened set of register assignments into a stream."
(mapcan #'tokenize-assignment assignments))
(defun tokenize-program-term
(term permanent-variables nead-variables nead-arity)
"Tokenize `term` as a program term, returning its tokens."
(let ((tree (parse-top-level term)))
(allocate-registers tree permanent-variables nead-variables nead-arity)
(-> tree flatten-program tokenize-assignments)))
(defun tokenize-query-term
(term permanent-variables &optional nead-variables nead-arity)
"Tokenize `term` as a query term, returning its tokens."
(let ((tree (parse-top-level term)))
(allocate-registers tree permanent-variables nead-variables nead-arity)
(-<> tree
flatten-query
tokenize-assignments
;; We need to shove a CALL token onto the end.
(append <> (list (make-instance 'call-token
:functor (node-functor tree)
:arity (node-arity tree)))))))
;;;; Precompilation
;;; Once we have a tokenized stream we can generate the machine instructions
;;; from it.
;;;
;;; We don't generate the ACTUAL bytecode immediately, because we want to run
;;; a few optimization passes on it first, and it's easier to work with if we
;;; have a friendlier format.
;;;
;;; So we turn a stream of tokens:
;;;
;;; (X2 = q/2), X1, X3, (X0 = p/2), X1, X2
;;;
;;; into a list of instructions, each of which is a list:
;;;
;;; (:put-structure X2 q 2)
;;; (:set-variable X1)
;;; (:set-variable X3)
;;; (:put-structure X0 p 2)
;;; (:set-value X1)
;;; (:set-value X2)
;;;
;;; The opcodes are keywords and the register arguments remain register objects.
;;; They get converted down to the raw bytes in the final "rendering" step.
;;;
;;; # Cut
;;;
;;; A quick note on cut (!): the book and original WAM do some nutty things to
;;; save one stack word per frame. They store the cut register for non-neck
;;; cuts in a "pseudovariable" on the stack, so they only have to allocate that
;;; extra stack word for things that actually USE non-neck cuts.
;;;
;;; We're going to just eat the extra stack word and store the cut register in
;;; every frame instead. This massively simplifies the implementation and lets
;;; me keep my sanity, and it MIGHT even end up being faster because there's
;;; one fewer opcode, less fucking around in the compiler, etc. But regardless:
;;; I don't want to go insane, and my laptop has sixteen gigabytes of RAM, so
;;; let's just store the damn word.
;;;
;;; # "Seen" Registers
;;;
;;; The book neglects to mention some REALLY important information about how you
;;; have to handle registers when compiling a stream of tokens. But if you've
;;; made it this far, you should be pretty used to the book omitting vital
;;; information. So hop in the clown car and take a ride with me.
;;;
;;; From the very beginning,the book mentions that certain instructions come in
;;; pairs, the first of which is used the first time the register is "seen" or
;;; "encountered", and the second used of which is used subsequent times.
;;;
;;; For example, a simple query like `p(A, A, A)` would result in:
;;;
;;; put-variable A0 X3
;;; put-value A1 X3
;;; put-value A2 X3
;;; call p/3
;;;
;;; This is all fine and dandy and works for single goals, but if you have
;;; a clause with MULTIPLE body goals you need to "reset" the list of
;;; already-seen registers after each goal. For example, consider:
;;;
;;; p() :-
;;; f(X, X),
;;; g(Y, Y).
;;;
;;; If you just apply what the book says without resetting the already-seen
;;; register list, you get:
;;;
;;; put-variable A0 X2
;;; put-value A1 X2
;;; call f/2
;;; put-value A0 X2 <--- wrong!
;;; put-value A1 X2
;;; call g/2
;;;
;;; But the variable in `g/2` is DIFFERENT than the one used in `f/2`, so that
;;; second `put-value` instruction is wrong! What we need instead is this:
;;;
;;; put-variable A0 X2
;;; put-value A1 X2
;;; call f/2
;;; put-variable A0 X2 <--- right!
;;; put-value A1 X2
;;; call g/2
;;;
;;; So the list of seen registers needs to get cleared after each body goal.
;;;
;;; But be careful: it's only TEMPORARY registers that need to get cleared! If
;;; the variables in our example WEREN'T different (`p() :- f(X, X), g(X, X)`)
;;; the instructions would be assigning to stack registers, and we WANT to do
;;; one `put-variable` and have the rest be `put-value`s.
;;;
;;; And there's one more edge case you're probably wondering about: what happens
;;; after the HEAD of a clause? Do we need to reset? The answer is: no,
;;; because the head and first body goal share registers, which is what performs
;;; the "substitution" for the first body goal (see the comment earlier for more
;;; on that rabbit hole).
(defun find-opcode (opcode newp mode &optional register)
(flet ((find-variant (register)
(when register
(if (register-temporary-p register)
:local
:stack))))
(eswitch ((list opcode newp mode (find-variant register)) :test #'equal)
('(:argument t :program :local) :get-variable-local)
('(:argument t :program :stack) :get-variable-stack)
('(:argument t :query :local) :put-variable-local)
('(:argument t :query :stack) :put-variable-stack)
('(:argument nil :program :local) :get-value-local)
('(:argument nil :program :stack) :get-value-stack)
('(:argument nil :query :local) :put-value-local)
('(:argument nil :query :stack) :put-value-stack)
;; Structures and lists can only live locally, they never go on the stack
('(:structure nil :program :local) :get-structure)
('(:structure nil :query :local) :put-structure)
('(:list nil :program :local) :get-list)
('(:list nil :query :local) :put-list)
('(:register t :program :local) :unify-variable-local)
('(:register t :program :stack) :unify-variable-stack)
('(:register t :query :local) :set-variable-local)
('(:register t :query :stack) :set-variable-stack)
('(:register nil :program :local) :unify-value-local)
('(:register nil :program :stack) :unify-value-stack)
('(:register nil :query :local) :set-value-local)
('(:register nil :query :stack) :set-value-stack))))
(defun precompile-tokens (wam head-tokens body-tokens)
"Generate a series of machine instructions from a stream of head and body
tokens.
The `head-tokens` should be program-style tokens, and are compiled in program
mode. The `body-tokens` should be query-style tokens, and are compiled in
query mode.
Actual queries are a special case where the `head-tokens` stream is `nil`
The compiled instructions will be returned as a circle.
"
(let ((seen (list))
(mode nil)
(instructions (make-empty-circle)))
(labels
((push-instruction (&rest instruction)
(circle-insert-end instructions instruction))
(reset-seen ()
;; Reset the list of seen registers (grep for "clown car" above)
(setf seen (remove-if #'register-temporary-p seen)))
(handle-argument (argument-register source-register)
;; OP X_n A_i
(let ((newp (push-if-new source-register seen :test #'register=)))
(push-instruction (find-opcode :argument newp mode source-register)
source-register
argument-register)))
(handle-structure (destination-register functor arity)
;; OP functor reg
(push destination-register seen)
(push-instruction (find-opcode :structure nil mode destination-register)
(wam-ensure-functor-index wam (cons functor arity))
destination-register))
(handle-list (register)
(push register seen)
(push-instruction (find-opcode :list nil mode register)
register))
(handle-cut ()
(push-instruction :cut))
(handle-call (functor arity)
;; CALL functor
(push-instruction :call
(wam-ensure-functor-index wam (cons functor arity)))
;; This is a little janky, but at this point the body goals have been
;; turned into one single stream of tokens, so we don't have a nice
;; clean way to tell when one ends. But in practice, a body goal is
;; going to end with a CALL instruction, so we can use this as
;; a kludge to know when to reset.
;;
;; TODO: We should probably dekludge this by emitting an extra "end
;; body goal" token, especially once we add some special forms that
;; might need to do some resetting but not end in a CALL.
(reset-seen))
(handle-register (register)
;; OP reg
(let ((newp (push-if-new register seen :test #'register=)))
(push-instruction (find-opcode :register newp mode register)
register)))
(handle-token (token)
(etypecase token
(argument-variable-token
(handle-argument (token-register token)
(token-target token)))
(structure-token
(handle-structure (token-register token)
(token-functor token)
(token-arity token)))
(list-token
(handle-list (token-register token)))
(cut-token
(handle-cut))
(call-token
(handle-call (token-functor token)
(token-arity token)))
(register-token
(handle-register (token-register token)))))
(handle-stream (tokens)
(map nil #'handle-token tokens)))
(when head-tokens
(setf mode :program)
(handle-stream head-tokens))
(setf mode :query)
(handle-stream body-tokens)
instructions)))
(defun find-variables (terms)
"Return the set of variables in `terms`."
(remove-duplicates (tree-collect #'variablep terms)))
(defun find-shared-variables (terms)
"Return the set of all variables shared by two or more terms."
(labels
((count-uses (variable)
(count-if (curry #'tree-member-p variable) terms))
(shared-p (variable)
(> (count-uses variable) 1)))
(remove-if-not #'shared-p (find-variables terms))))
(defun find-permanent-variables (clause)
"Return a list of all the permanent variables in `clause`.
Permanent variables are those that appear in more than one goal of the clause,
where the head of the clause is considered to be a part of the first goal.
"
(if (<= (length clause) 2)
(list) ; Facts and chain rules have no permanent variables at all
(destructuring-bind (head body-first . body-rest) clause
;; The head is treated as part of the first goal for the purposes of
;; finding permanent variables.
(find-shared-variables (cons (cons head body-first) body-rest)))))
(defun find-nead-variables (clause)
"Return a list of all variables in the nead of `clause`.
The head and neck (first term in the body) are the 'nead'.
"
(if (<= (length clause) 1)
(list)
(destructuring-bind (head body-first . body-rest) clause
(declare (ignore body-rest))
(find-variables (list head body-first)))))
(defun precompile-clause (wam head body)
"Precompile the clause.
`head` should be the head of the clause for program clauses, or `nil` for
query clauses.
`body` is the body of the clause, or `nil` for facts.
Returns a circle of instructions and the permanent variables.
"
(let* ((basic-clause
(remove '! (cons head body))) ; gross
(permanent-variables
(if (null head)
;; For query clauses we cheat a bit and make ALL variables
;; permanent, so we can extract their bindings as results later.
(find-variables body)
(find-permanent-variables basic-clause)))
;; grep above to see what the hell the nead is.
(nead-variables
(set-difference (find-nead-variables basic-clause)
permanent-variables))
(nead-arity
(max (1- (length head))
(1- (length (second basic-clause)))))
(head-tokens
(when head
(tokenize-program-term head
permanent-variables
nead-variables
nead-arity)))
(body-tokens
(when body
(loop
:with first = t
:for goal :in body
:append
(cond
;; cut just gets emitted straight, but DOESN'T flip `first`...
;; TODO: fix the cut layering violation here...
((eql goal '!) ; gross
(list (make-instance 'cut-token)))
(first
(setf first nil)
(tokenize-query-term goal
permanent-variables
nead-variables
nead-arity))
(t
(tokenize-query-term goal permanent-variables)))))))
(let ((instructions (precompile-tokens wam head-tokens body-tokens))
(variable-count (length permanent-variables)))
;; We need to compile facts and rules differently. Facts end with
;; a PROCEED and rules are wrapped in ALOC/DEAL.
(cond
((and head body) ; a full-ass rule
(circle-insert-beginning instructions `(:allocate ,variable-count))
(circle-insert-end instructions `(:deallocate)))
((and head (null body)) ; a bare fact
(circle-insert-end instructions `(:proceed)))
(t ; a query
;; The book doesn't have this ALOC here, but we do it to aid in result
;; extraction. Basically, to make extracting th results of a query
;; easier we allocate all of its variables on the stack, so we need
;; push a stack frame for them before we get started. We don't DEAL
;; because we want the frame to be left on the stack at the end so we
;; can poke at it.
(circle-insert-beginning instructions `(:allocate ,variable-count))
(circle-insert-end instructions `(:done))))
(values instructions permanent-variables))))
(defun precompile-query (wam query)
"Compile `query`, returning the instructions and permanent variables.
`query` should be a list of goal terms.
"
(precompile-clause wam nil query))
(defun find-arity (rule)
(let ((head (first rule)))
(cond
((null head) (error "Rule ~S has a NIL head." rule))
((atom head) 0) ; constants are 0-arity
(t (1- (length head))))))
(defun check-rules (rules)
;; TODO: fix constant handling here...
(let* ((predicates (mapcar #'caar rules))
(arities (mapcar #'find-arity rules))
(functors (zip predicates arities)))
(assert (= 1 (length (remove-duplicates functors :test #'equal))) ()
"Must add exactly 1 predicate at a time (got: ~S)."
functors)
(values (first predicates) (first arities))))
(defun precompile-rules (wam rules)
"Compile `rules` into a list of instructions.
Each rule in `rules` should be a clause consisting of a head term and zero or
more body terms. A rule with no body is called a fact.
Returns the circle of compiled instructions, as well as the functor and arity
of the rules being compiled.
"
(assert rules () "Cannot compile an empty program.")
(multiple-value-bind (functor arity) (check-rules rules)
(values
(if (= 1 (length rules))
;; Single-clause rules don't need to bother setting up a choice point.
(destructuring-bind ((head . body)) rules
(precompile-clause wam head body))
;; Otherwise we need to loop through each of the clauses, pushing their
;; choice point instruction first, then their actual code.
;;
;; The `nil` clause addresses will get filled in later, during rendering.
(loop :with instructions = (make-empty-circle)
:for ((head . body) . remaining) :on rules
:for first-p = t :then nil
:for last-p = (null remaining)
:for clause-instructions = (precompile-clause wam head body)
:do (progn
(circle-insert-end instructions
(cond (first-p '(:try nil))
(last-p '(:trust))
(t '(:retry nil))))
(circle-append-circle instructions clause-instructions))
:finally (return instructions)))
functor
arity)))
;;;; Optimization
;;; Optimization of the WAM instructions happens between the precompilation
;;; phase and the rendering phase. We perform a number of passes over the
;;; circle of instructions, doing one optimization each time.
(defun optimize-get-constant (node constant register)
;; 1. get_structure c/0, Ai -> get_constant c, Ai
(circle-replace node `(:get-constant ,constant ,register)))
(defun optimize-put-constant (node constant register)
;; 2. put_structure c/0, Ai -> put_constant c, Ai
(circle-replace node `(:put-constant ,constant ,register)))
(defun optimize-set-constant (node constant register)
;; 3. put_structure c/0, Xi *** WE ARE HERE
;; ...
;; set_value Xi -> set_constant c
(loop
:with previous = (circle-prev node)
;; Search forward for the corresponding set-value instruction
:for n = (circle-forward-remove node) :then (circle-forward n)
:while n
:for (opcode . arguments) = (circle-value n)
:when (and (eql opcode :set-value-local)
(register= register (first arguments)))
:do
(circle-replace n `(:set-constant ,constant))
(return previous)))
(defun optimize-unify-constant (node constant register)
;; 4. unify_variable Xi -> unify_constant c
;; ...
;; get_structure c/0, Xi *** WE ARE HERE
(loop
;; Search backward for the corresponding unify-variable instruction
:for n = (circle-backward node) :then (circle-backward n)
:while n
:for (opcode . arguments) = (circle-value n)
:when (and (eql opcode :unify-variable-local)
(register= register (first arguments)))
:do
(circle-replace n `(:unify-constant ,constant))
(return (circle-backward-remove node))))
(defun optimize-constants (wam instructions)
;; From the book and the erratum, there are four optimizations we can do for
;; constants (0-arity structures).
(flet ((constant-p (functor)
(zerop (wam-functor-arity wam functor))))
(loop :for node = (circle-forward instructions) :then (circle-forward node)
:while node
:for (opcode . arguments) = (circle-value node)
:do
(match (circle-value node)
((guard `(:put-structure ,functor ,register)
(constant-p functor))
(setf node
(if (register-argument-p register)
(optimize-put-constant node functor register)
(optimize-set-constant node functor register))))
((guard `(:get-structure ,functor ,register)
(constant-p functor))
(setf node
(if (register-argument-p register)
(optimize-get-constant node functor register)
(optimize-unify-constant node functor register))))))
instructions))
(defun optimize-instructions (wam instructions)
(optimize-constants wam instructions))
;;;; Rendering
;;; Rendering is the act of taking the friendly list-of-instructions format and
;;; actually converting it to raw-ass bytes and storing it in an array.
(defun render-opcode (opcode)
(ecase opcode
(:get-structure +opcode-get-structure+)
(:unify-variable-local +opcode-unify-variable-local+)
(:unify-variable-stack +opcode-unify-variable-stack+)
(:unify-value-local +opcode-unify-value-local+)
(:unify-value-stack +opcode-unify-value-stack+)
(:get-variable-local +opcode-get-variable-local+)
(:get-variable-stack +opcode-get-variable-stack+)
(:get-value-local +opcode-get-value-local+)
(:get-value-stack +opcode-get-value-stack+)
(:put-structure +opcode-put-structure+)
(:set-variable-local +opcode-set-variable-local+)
(:set-variable-stack +opcode-set-variable-stack+)
(:set-value-local +opcode-set-value-local+)
(:set-value-stack +opcode-set-value-stack+)
(:put-variable-local +opcode-put-variable-local+)
(:put-variable-stack +opcode-put-variable-stack+)
(:put-value-local +opcode-put-value-local+)
(:put-value-stack +opcode-put-value-stack+)
(:put-constant +opcode-put-constant+)
(:get-constant +opcode-get-constant+)
(:set-constant +opcode-set-constant+)
(:get-list +opcode-get-list+)
(:put-list +opcode-put-list+)
(:unify-constant +opcode-unify-constant+)
(:call +opcode-call+)
(:proceed +opcode-proceed+)
(:allocate +opcode-allocate+)
(:deallocate +opcode-deallocate+)
(:done +opcode-done+)
(:try +opcode-try+)
(:retry +opcode-retry+)
(:trust +opcode-trust+)
(:cut +opcode-cut+)))
(defun render-argument (argument)
(etypecase argument
(null 0) ; ugly choice point args that'll be filled later...
(register (register-number argument)) ; bytecode just needs register numbers
(number argument))) ; just a numeric argument, e.g. alloc 0
(defun render-bytecode (code instructions)
"Render `instructions` (a circle) into `code` (a bytecode array)."
(let ((previous-jump nil))
(flet
((fill-previous-jump (address)
(when previous-jump
(setf (aref code (1+ previous-jump)) address))
(setf previous-jump address)))
(loop
:for (opcode . arguments) :in (circle-to-list instructions)
:for address = (code-push-instruction! code
(render-opcode opcode)
(mapcar #'render-argument arguments))
;; We need to fill in the addresses for the choice point jumping
;; instructions. For example, when we have TRY ... TRUST, the TRUST
;; needs to patch its address into the TRY instruction.
;;
;; I know, this is ugly, sorry.
:when (member opcode '(:try :retry :trust))
:do (fill-previous-jump address)))))
(defun make-query-code-store ()
(make-array 512
:fill-pointer 0
:adjustable t
:element-type 'code-word))
(defun render-query (instructions)
(let ((code (make-query-code-store)))
(render-bytecode code instructions)
code))
(defun mark-label (wam functor arity address)
"Set the code label `functor`/`arity` to point at `address`."
(setf (wam-code-label wam functor arity) address))
(defun render-rules (wam functor arity instructions)
;; Before we render the instructions, make the label point at where they're
;; about to go.
(mark-label wam functor arity (fill-pointer (wam-code wam)))
(render-bytecode (wam-code wam) instructions))
;;;; Compilation
;;; The compilation phase wraps everything else up into a sane UI.
(defun compile-query (wam query)
"Compile `query` into a fresh array of bytecode.
`query` should be a list of goal terms.
Returns the fresh code array and the permanent variables.
"
(multiple-value-bind (instructions permanent-variables)
(precompile-query wam query)
(optimize-instructions wam instructions)
(values
(render-query instructions)
permanent-variables)))
(defun compile-rules (wam rules)
"Compile `rules` into the WAM's code store.
Each rule in `rules` should be a clause consisting of a head term and zero or
more body terms. A rule with no body is called a fact.
"
(multiple-value-bind (instructions functor arity)
(precompile-rules wam rules)
(optimize-instructions wam instructions)
(render-rules wam functor arity instructions)))