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; Copyright (c) 1993, 1994 Richard Kelsey and Jonathan Rees. See file COPYING.
; Type lattice.
; Sorry this is so hairy, but before it was written, type checking
; consumed 15% of compile time.
; f : t1 -> t2 restrictive means:
; if x : t1 then (f x) : t2 (possible error!), else (f x) : error.
; f : t1 -> t2 nonrestrictive means:
; There exists an x : t1 such that (f x) : t2.
(define-record-type meta-type :meta-type
(really-make-type mask more info)
meta-type?
(mask type-mask)
(more type-more)
(info type-info))
(define-record-discloser :meta-type
(lambda (t)
`(type ,(let ((m (type-mask t)))
(or (table-ref mask->name-table m) m))
,(let ((more (type-more t)))
(if (and (pair? more) (eq? (cdr more) t))
'*
more))
,(type-info t))))
(define (make-type mask more info)
(make-immutable!
(really-make-type mask more info)))
(define name->type-table (make-table))
(define mask->name-table (make-table))
(define (name->type x)
(or (table-ref name->type-table x)
(make-other-type x)))
(define (set-type-name! type name)
(table-set! name->type-table name type)
(if (not (or (type-info type)
(type-more type)))
(table-set! mask->name-table (type-mask type) name)))
; Masks
; Top of lattice has mask = -1, bottom has mask = 0.
(define *mask* 1)
(define (new-type-bit)
(let ((m *mask*))
(set! *mask* (arithmetic-shift *mask* 1))
m))
(define (mask->type mask)
(make-type mask #f #f))
(define bottom-type (mask->type 0))
(define error-type bottom-type)
(define (bottom-type? t)
(= (type-mask t) 0))
(set-type-name! bottom-type ':error)
(define (new-atomic-type)
(mask->type (new-type-bit)))
(define (named-atomic-type name)
(let ((t (new-atomic-type)))
(set-type-name! t name)
t))
; --------------------
; Top of the lattice.
(define syntax-type (named-atomic-type ':syntax))
(define other-static-type (new-atomic-type))
; --------------------
; "Rails" are argument sequence or return value sequences.
; Four constructors:
; empty-rail-type
; (rail-type t1 t2)
; (optional-rail-type t1 t2)
; (make-rest-type t)
; If a type's two-or-more? bit is set, then
; more = (head . tail).
; Otherwise, more = #f.
(define empty-rail-type (new-atomic-type))
(define (rail-type t1 t2) ;CONS analog
(cond ((empty-rail-type? t2) t1)
((bottom-type? t1) t1)
((bottom-type? t2) t2)
((and (optional-type? t1)
(rest-type? t2)
(same-type? t1 (head-type t2)))
;; Turn (&opt t &rest t) into (&rest t)
t2)
((or (optional-type? t1)
(optional-type? t2))
(make-type (bitwise-ior (type-mask t1) mask/two-or-more)
(make-immutable! (cons t1 t2))
#f))
(else
(make-type mask/two-or-more
(make-immutable! (cons t1 t2))
(type-info t1)))))
(define (make-optional-type t)
(if (type-more t)
(warn "peculiar type in make-optional-type" t))
(make-type (bitwise-ior (type-mask t) mask/no-values)
#f
(type-info t)))
(define (make-rest-type t)
(if (bottom-type? t)
t
(let* ((z (cons (make-optional-type t) #f))
(t (make-type (bitwise-ior (type-mask t) mask/&rest)
z
(type-info t))))
(set-cdr! z t)
(make-immutable! z)
t)))
(define (head-type t) ;Can return an &opt type
(let ((more (type-more t)))
(if more
(car more)
t)))
(define (head-type-really t) ;Always returns a value type
(let ((h (head-type t)))
(if (optional-type? h)
(make-type (bitwise-and (type-mask h) (bitwise-not mask/no-values))
#f
(type-info h))
h)))
(define (tail-type t)
(if (empty-rail-type? t)
;; bottom-type ?
(warn "rail-type of empty rail" t))
(let ((more (type-more t)))
(if more
(cdr more)
empty-rail-type)))
(define (empty-rail-type? t)
(= (bitwise-and (type-mask t) mask/one-or-more) 0))
(define (rest-type? t) ;For terminating recursions
(let ((more (type-more t)))
(and more
(eq? (cdr more) t))))
(define (optional-type? t)
(> (bitwise-and (type-mask t) mask/no-values) 0))
; The no-values type has one element, the rail of length zero.
; The two-or-more type consists of all rails of length two
; or more.
(define mask/no-values (type-mask empty-rail-type))
(define mask/two-or-more (new-type-bit))
(define mask/&rest (bitwise-ior (type-mask empty-rail-type)
mask/two-or-more))
(table-set! mask->name-table mask/no-values ':no-values)
(define value-type (mask->type (bitwise-not (- *mask* 1))))
(set-type-name! value-type ':value)
(define mask/value (type-mask value-type))
(define (value-type? t)
(let ((m (type-mask t)))
(= (bitwise-and m mask/value) m)))
(define any-values-type
(make-rest-type value-type))
(set-type-name! any-values-type ':values)
(define any-arguments-type any-values-type)
(define mask/one-or-more
(bitwise-ior mask/value mask/two-or-more))
; --------------------
; Lattice operations.
; Equivalence
(define (same-type? t1 t2)
(or (eq? t1 t2)
(and (= (type-mask t1) (type-mask t2))
(let ((more1 (type-more t1))
(more2 (type-more t2)))
(if more1
(and more2
(if (eq? (cdr more1) t1)
(eq? (cdr more2) t2)
(if (eq? (cdr more2) t2)
#f
(and (same-type? (car more1) (car more2))
(same-type? (cdr more1) (cdr more2))))))
(not more2)))
(let ((info1 (type-info t1))
(info2 (type-info t2)))
(or (eq? info1 info2)
(and (pair? info1)
(pair? info2)
(same-type? (car info1) (car info2)) ;Procedure
(same-type? (cadr info1) (cadr info2))
(eq? (caddr info1) (caddr info2))))))))
(define (subtype? t1 t2) ;*** optimize later
(same-type? t1 (meet-type t1 t2)))
; (mask->type mask/procedure) represents the TOP of the procedure
; subhierarchy.
(define (meet-type t1 t2)
(if (same-type? t1 t2)
t1
(let ((m (bitwise-and (type-mask t1) (type-mask t2))))
(cond ((> (bitwise-and m mask/two-or-more) 0)
(meet-rail t1 t2))
((eq? (type-info t1) (type-info t2))
(make-type m #f (type-info t1)))
((> (bitwise-and m mask/other) 0)
(let ((i1 (other-type-info t1))
(i2 (other-type-info t2)))
(if (and i1 i2)
(mask->type (bitwise-and m (bitwise-not mask/other)))
(make-type m
#f
(or i1 i2)))))
((> (bitwise-and m mask/procedure) 0)
(meet-procedure m t1 t2))
(else (mask->type m))))))
(define (other-type-info t)
(let ((i (type-info t)))
(if (pair? i) #f i)))
(define (p name x) (write `(,name ,x)) (newline) x)
(define (meet-rail t1 t2)
(let ((t (meet-type (head-type t1) (head-type t2))))
(if (and (rest-type? t1)
(rest-type? t2))
(make-rest-type t)
(rail-type t (meet-type (tail-type t1)
(tail-type t2))))))
; Start with these assumptions:
;
; . (meet? t1 t2) == (not (bottom-type? (meet-type t1 t2)))
; . (subtype? t1 t2) == (same-type? t1 (meet-type t1 t2))
; . (subtype? t1 t2) == (same-type? t2 (join-type t1 t2))
; . We signal a type error if not (intersect? have want).
; . We infer the type of a parameter by intersecting the want-types
; of all definitely-reached points of use.
;
; 1. If both types are nonrestrictive, we have to JOIN both domains
; and codomains (if we are to avoid conjunctive types).
;
; (+ (f 1) (car (f 'a))) [reconstructing type of f by computing meet of all contexts]
; => meet (proc (:integer) :number nonr) (proc (:symbol) :pair nonr)
; => (proc ((join :integer :symbol) (join :number :pair)) nonr), yes?
;
; 2. If both types are restrictive, we need to MEET both domains and
; codomains.
;
; (define (foo) 3), (export (foo (proc (:value) :value)))
; Error - disjoint domains.
;
; (define (foo) 'baz), (export (foo (proc () :number)))
; Error - disjoint codomains.
;
; 3. If one is restrictive and the other isn't then we still need to
; MEET on both sides.
;
; (with-output-to-file "foo" car)
; => meet (proc () :any nonr), (proc (:pair) :value restr)
; => Error - disjoint domains.
;
; (frob (lambda () 'a)) where (define (frob f) (+ (f) 1))
; => meet (proc () :symbol restr), (proc () :number nonr)
; => Error - disjoint codomains.
;
; Does export checking look for (intersect? want have), or for
; (subtype? want have) ? We should be able to narrow something as we
; export it, but not widen it.
;
; (define (foo . x) 3), (export (foo (proc (value) value)))
; No problem, since the domain of the first contains the domain of the second.
;
; (define (foo x . x) (+ x 3)), (export (foo (proc (value) value)))
; Dubious; the domains intersect but are incomparable. The meet
; should be (proc (number) number).
;
; (define (foo x) (numerator x)), (export (foo (proc (real) integer)))
; This is dubious, since the stated domain certainly contains values
; that will be rejected. (But then, what about divide by zero, or
; vector indexing?)
;
; (define (foo x) (numerator x)), (export (foo (proc (integer) integer)))
; This should definitely be OK.
(define (meet-procedure m t1 t2)
(let ((dom1 (procedure-type-domain t1))
(dom2 (procedure-type-domain t2))
(cod1 (procedure-type-codomain t1))
(cod2 (procedure-type-codomain t2)))
(cond ((or (restrictive? t1) (restrictive? t2))
(let ((dom (meet-type dom1 dom2))
(cod (meet-type cod1 cod2)))
(if (or (bottom-type? dom)
(and (bottom-type? cod)
(not (bottom-type? cod1)) ;uck
(not (bottom-type? cod2))))
(mask->type (bitwise-and m (bitwise-not mask/procedure)))
(make-procedure-type m
dom
cod
#t))))
((and (subtype? dom2 dom1) (subtype? cod2 cod1))
;; exists x : dom1 s.t. (f x) : cod1 adds no info
(make-procedure-type m dom2 cod2 #f))
(else
;; Arbitrary choice.
(make-procedure-type m dom1 cod1 #f)))))
; MEET? is the operation used all the time by the compiler. We want
; getting a yes answer to be as fast as possible. We could do
;
; (define (meet? t1 t2) (not (bottom-type? (meet-type t1 t2))))
;
; but that would be too slow.
(define (meet? t1 t2)
(or (eq? t1 t2)
(let ((m (bitwise-and (type-mask t1) (type-mask t2))))
(cond ((= m mask/two-or-more)
(and (meet? (head-type t1) (head-type t2))
(meet? (tail-type t1) (tail-type t2))))
((= m 0) #f)
((eq? (type-info t1) (type-info t2)) #t)
((= m mask/other)
(not (and (other-type-info t1) (other-type-info t2))))
((= m mask/procedure) (meet-procedure? t1 t2))
(else #t)))))
(define (meet-procedure? t1 t2)
(if (or (restrictive? t1) (restrictive? t2))
(and (meet? (procedure-type-domain t1) (procedure-type-domain t2))
(meet? (procedure-type-codomain t1) (procedure-type-codomain t2)))
#t))
; Join
(define (join-type t1 t2)
(if (same-type? t1 t2)
t1
(let ((m (bitwise-ior (type-mask t1) (type-mask t2))))
(if (> (bitwise-and m mask/two-or-more) 0)
(join-rail t1 t2)
(let ((info1 (type-info t1)) (info2 (type-info t2)))
(cond ((equal? info1 info2)
(make-type m #f (type-info t1)))
((> (bitwise-and m mask/other) 0)
(make-type m #f #f))
((> (bitwise-and m mask/procedure) 0)
(join-procedure m t1 t2))
(else
(error "This shouldn't happen" t1 t2))))))))
(define (join-rail t1 t2)
(let ((t (join-type (head-type t1) (head-type t2))))
(if (and (rest-type? t1)
(rest-type? t2))
(make-rest-type t)
(rail-type t
(if (type-more t1)
(if (type-more t2)
(join-type (tail-type t1)
(tail-type t2))
(tail-type t1))
(tail-type t2))))))
; This is pretty gross.
(define (join-procedure m t1 t2)
(if (procedure-type? t1)
(if (procedure-type? t2)
(let ((dom1 (procedure-type-domain t1))
(dom2 (procedure-type-domain t2))
(cod1 (procedure-type-codomain t1))
(cod2 (procedure-type-codomain t2)))
(make-procedure-type m
(join-type dom1 dom2) ;Error when outside here
(join-type cod1 cod2)
(and (restrictive? t1) (restrictive? t2))))
(make-type m #f (type-info t1)))
(make-type m #f (type-info t2))))
; --------------------
; Value types.
; First, the ten indivisible number types.
(define number-hierarchy
'(:integer :rational :real :complex :number))
(let loop ((names number-hierarchy)
(exact bottom-type)
(inexact bottom-type))
(if (null? names)
(begin (set-type-name! exact ':exact)
(set-type-name! inexact ':inexact))
(let* ((exact (join-type exact (new-atomic-type)))
(inexact (join-type inexact (new-atomic-type))))
(set-type-name! (join-type exact inexact)
(car names))
(loop (cdr names)
exact
inexact))))
(define integer-type (name->type ':integer))
(define rational-type (name->type ':rational))
(define real-type (name->type ':real))
(define complex-type (name->type ':complex))
(define number-type (name->type ':number))
(define exact-type (name->type ':exact))
(define inexact-type (name->type ':inexact))
(define exact-integer-type (meet-type integer-type exact-type))
(set-type-name! exact-integer-type ':exact-integer)
; Next, all the others.
(define boolean-type (named-atomic-type ':boolean))
(define pair-type (named-atomic-type ':pair))
(define null-type (named-atomic-type ':null))
(define record-type (named-atomic-type ':record))
(define any-procedure-type (named-atomic-type ':procedure))
; ???
; (define procedure-nonbottom-type (new-atomic-type))
; (define procedure-bottom-type (new-atomic-type))
; (define mask/procedure (meet procedure-nonbottom-type procedure-bottom-type))
; OTHER-VALUE-TYPE is a catchall for all the other ones we don't
; anticipate (for now including string, vector, char, etc.).
(define other-value-type (named-atomic-type ':other))
(define mask/other (type-mask other-value-type))
(define (make-other-type id)
(let ((t (make-type mask/other #f id)))
(set-type-name! t id)
t))
(define char-type (make-other-type ':char))
(define unspecific-type (make-other-type ':unspecific))
(define string-type (make-other-type ':string))
(define symbol-type (make-other-type ':symbol))
(define vector-type (make-other-type ':vector))
(define escape-type (make-other-type ':escape))
(define structure-type (make-other-type ':structure))
; --------------------
; Procedures.
(define mask/procedure (type-mask any-procedure-type))
(define (procedure-type dom cod r?)
(make-procedure-type mask/procedure dom cod r?))
(define (make-procedure-type m dom cod r?)
(make-type m
#f
(if (and (not r?)
(same-type? dom value-type)
(same-type? cod value-type))
#f ;LUB of all procedure types
(list dom cod r?))))
(define (procedure-type-domain t)
(let ((info (type-info t)))
(if (pair? info)
(car info)
any-values-type)))
(define (procedure-type-codomain t)
(let ((info (type-info t)))
(if (pair? info)
(cadr info)
any-values-type)))
(define (restrictive? t)
(let ((info (type-info t)))
(if (pair? info)
(caddr info)
#f)))
; --------------------
; Conversion to and from S-expression.
(define (sexp->type x r?)
(cond ((symbol? x)
(name->type x))
((pair? x)
(case (car x)
((some-values)
(sexp->values-type (cdr x) #t r?))
((proc)
(let ((r? (if (or (null? (cdddr x))
(eq? (cadddr x) r?))
r?
(not r?))))
(procedure-type (sexp->values-type (cadr x) #t (not r?))
(sexp->type (caddr x) r?)
r?)))
((meet)
(if (null? (cdr x))
bottom-type
(let ((l (map (lambda (x) (sexp->type x r?)) (cdr x))))
(reduce meet-type (car l) (cdr l)))))
((join)
(let ((l (map (lambda (x) (sexp->type x r?)) (cdr x))))
(reduce join-type (car l) (cdr l))))
((mask->type)
(mask->type (cadr x)))
(else (error "unrecognized type" x))))
(else (error "unrecognized type" x))))
(define (sexp->values-type l req? r?)
(cond ((null? l) empty-rail-type)
((eq? (car l) '&rest)
(make-rest-type (sexp->type (cadr l) r?)))
((eq? (car l) '&opt)
(sexp->values-type (cdr l) #f r?))
(else
(let ((t (sexp->type (car l) r?)))
(rail-type (if req? t (make-optional-type t))
(sexp->values-type (cdr l)
req?
r?))))))
; Convert type to S-expression
(define (type->sexp t r?)
(if (> (bitwise-and (type-mask t) mask/&rest) 0)
(if (same-type? t any-values-type)
':values
`(some-values ,@(rail-type->sexp t r?)))
(let ((j (disjoin-type t)))
(cond ((null? j) ':error)
((null? (cdr j))
(atomic-type->sexp (car j) r?))
(else
`(join ,@(map (lambda (t)
(atomic-type->sexp t r?))
j)))))))
(define (atomic-type->sexp t r?)
(let ((m (type-mask t)))
(cond ((and (not (type-info t))
(table-ref mask->name-table m)))
((= m mask/other)
(or (type-info t) ':value)) ;not quite
((= m mask/procedure)
(let ((r (restrictive? t)))
`(proc ,(rail-type->sexp (procedure-type-domain t)
(not r))
,(type->sexp (procedure-type-codomain t) r)
,@(if (eq? r r?)
'()
`(,r)))))
((type-info t)
`(ill-formed ,(type-mask t) ,(type-info t)))
((subtype? t exact-type)
`(meet :exact
,(type->sexp (mask->type (let ((m (type-mask t)))
(bitwise-ior m (arithmetic-shift m 1))))
#t)))
((subtype? t inexact-type)
`(meet :inexact
,(type->sexp (mask->type (let ((m (type-mask t)))
(bitwise-ior m (arithmetic-shift m -1))))
#t)))
;; ((meet? t number-type) ...)
(else
`(mask->type ,(type-mask t))))))
(define (rail-type->sexp t r?)
(let recur ((t t) (prev-req? #t) (r? r?))
(cond ((empty-rail-type? t) '())
((rest-type? t)
`(&rest ,(type->sexp (head-type-really t) r?)))
((optional-type? t)
(let ((tail (cons (type->sexp (head-type-really t) r?)
(recur (tail-type t) #f r?))))
(if prev-req?
`(&opt ,@tail)
tail)))
(else
(cons (type->sexp (head-type t) r?)
(recur (tail-type t) #t r?))))))
; Decompose a type into components
(define (disjoin-type t)
(cond ((bottom-type? t) '())
((and (not (type-info t))
(table-ref mask->name-table (type-mask t)))
(list t))
((meet? t other-value-type)
(cons (meet-type t other-value-type)
(disjoin-rest t mask/other)))
((meet? t any-procedure-type)
(cons (meet-type t any-procedure-type)
(disjoin-rest t mask/procedure)))
((meet? t number-type)
(cons (meet-type t number-type)
(disjoin-rest t mask/number)))
(else
(do ((i 1 (arithmetic-shift i 1)))
((> (bitwise-and (type-mask t) i) 0)
(cons (mask->type i)
(disjoin-rest t i)))))))
(define (disjoin-rest t mask)
(disjoin-type (mask->type (bitwise-and (type-mask t)
(bitwise-not mask)))))
(define mask/number (type-mask number-type))
; --------------------
; obsolescent? see lambda and values reconstructors in recon.scm
(define (make-some-values-type types)
(if (null? types)
empty-rail-type
(rail-type (car types) (make-some-values-type (cdr types)))))
(define-syntax proc
(syntax-rules ()
((proc (?type ...) ?cod)
(procedure-type (some-values ?type ...) ?cod #t))
((proc (?type ...) ?cod ?r)
(procedure-type (some-values ?type ...) ?cod ?r))))
(define-syntax some-values
(syntax-rules (&opt &rest)
((some-values) empty-rail-type)
((some-values &opt) empty-rail-type)
((some-values ?t) ?t)
((some-values &rest ?t) (make-rest-type ?t))
((some-values &opt &rest ?t) (make-rest-type ?t))
((some-values &opt ?t1 . ?ts)
(rail-type (make-optional-type ?t1)
(some-values &opt . ?ts)))
((some-values ?t1 . ?ts)
(rail-type ?t1 (some-values . ?ts)))))
(define (procedure-type? t)
(= (type-mask t) mask/procedure))
(define (fixed-arity-procedure-type? t)
(and (procedure-type? t)
(let loop ((d (procedure-type-domain t)))
(cond ((empty-rail-type? d) #t)
((optional-type? d) #f)
(else (loop (tail-type d)))))))
(define (procedure-type-arity t)
(do ((d (procedure-type-domain t) (tail-type d))
(i 0 (+ i 1)))
((empty-rail-type? d) i)
(if (optional-type? d)
(error "this shouldn't happen" t d))))
(define (procedure-type-argument-types t)
(let recur ((d (procedure-type-domain t)))
(cond ((empty-rail-type? d) '())
((optional-type? d)
(call-error "lossage" procedure-type-argument-types t))
(else
(cons (head-type d)
(recur (tail-type d)))))))
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