0.8.1.9:

[sbcl.git] / src / code / late-type.lisp

diff --git a/src/code/late-type.lisp b/src/code/late-type.lisp
index 46b983f..5e00418 100644 (file)
--- a/src/code/late-type.lisp
+++ b/src/code/late-type.lisp
@@ -22,14 +22,8 @@
 
 ;;; ### Remaining incorrectnesses:
 ;;;
 
 ;;; ### Remaining incorrectnesses:
 ;;;

-;;; TYPE-UNION (and the OR type) doesn't properly canonicalize an
-;;; exhaustive partition or coalesce contiguous ranges of numeric
-;;; types.
-;;;

 ;;; There are all sorts of nasty problems with open bounds on FLOAT
 ;;; types (and probably FLOAT types in general.)
 ;;; There are all sorts of nasty problems with open bounds on FLOAT
 ;;; types (and probably FLOAT types in general.)

-;;;
-;;; RATIO and BIGNUM are not recognized as numeric types.

 
 ;;; FIXME: This really should go away. Alas, it doesn't seem to be so
 ;;; simple to make it go away.. (See bug 123 in BUGS file.)
 
 ;;; FIXME: This really should go away. Alas, it doesn't seem to be so
 ;;; simple to make it go away.. (See bug 123 in BUGS file.)

@@ -77,15 +71,16 @@
       (values
        ;; FIXME: This old CMU CL code probably deserves a comment
        ;; explaining to us mere mortals how it works...
       (values
        ;; FIXME: This old CMU CL code probably deserves a comment
        ;; explaining to us mere mortals how it works...

-       (and (sb!xc:typep type2 'sb!xc:class)
+       (and (sb!xc:typep type2 'classoid)

            (dolist (x info nil)
              (when (or (not (cdr x))
                        (csubtypep type1 (specifier-type (cdr x))))
                (return
                 (or (eq type2 (car x))
            (dolist (x info nil)
              (when (or (not (cdr x))
                        (csubtypep type1 (specifier-type (cdr x))))
                (return
                 (or (eq type2 (car x))

-                    (let ((inherits (layout-inherits (class-layout (car x)))))
+                    (let ((inherits (layout-inherits
+                                     (classoid-layout (car x)))))

                       (dotimes (i (length inherits) nil)
                       (dotimes (i (length inherits) nil)

-                        (when (eq type2 (layout-class (svref inherits i)))
+                        (when (eq type2 (layout-classoid (svref inherits i)))

                           (return t)))))))))
        t)))
 
                           (return t)))))))))
        t)))
 

@@ -102,15 +97,14 @@
 ;;;
 ;;; WHEN controls when the forms are executed.
 (defmacro !define-superclasses (type-class-name specs when)
 ;;;
 ;;; WHEN controls when the forms are executed.
 (defmacro !define-superclasses (type-class-name specs when)

-  (let ((type-class (gensym "TYPE-CLASS-"))
-       (info (gensym "INFO")))
+  (with-unique-names (type-class info)

     `(,when
        (let ((,type-class (type-class-or-lose ',type-class-name))
             (,info (mapcar (lambda (spec)
                              (destructuring-bind
                                  (super &optional guard)
                                  spec
     `(,when
        (let ((,type-class (type-class-or-lose ',type-class-name))
             (,info (mapcar (lambda (spec)
                              (destructuring-bind
                                  (super &optional guard)
                                  spec

-                               (cons (sb!xc:find-class super) guard)))
+                               (cons (find-classoid super) guard)))

                            ',specs)))
         (setf (type-class-complex-subtypep-arg1 ,type-class)
               (lambda (type1 type2)
                            ',specs)))
         (setf (type-class-complex-subtypep-arg1 ,type-class)
               (lambda (type1 type2)

@@ -156,7 +150,13 @@
   (error "SUBTYPEP is illegal on this type:~%  ~S" (type-specifier type2)))
 
 (!define-type-method (values :unparse) (type)
   (error "SUBTYPEP is illegal on this type:~%  ~S" (type-specifier type2)))
 
 (!define-type-method (values :unparse) (type)

-  (cons 'values (unparse-args-types type)))
+  (cons 'values
+        (let ((unparsed (unparse-args-types type)))
+          (if (or (values-type-optional type)
+                  (values-type-rest type)
+                  (values-type-allowp type))
+              unparsed
+              (nconc unparsed '(&optional))))))

 
 ;;; Return true if LIST1 and LIST2 have the same elements in the same
 ;;; positions according to TYPE=. We return NIL, NIL if there is an
 
 ;;; Return true if LIST1 and LIST2 have the same elements in the same
 ;;; positions according to TYPE=. We return NIL, NIL if there is an

@@ -179,10 +179,7 @@
 (!define-type-method (values :simple-=) (type1 type2)
   (let ((rest1 (args-type-rest type1))
        (rest2 (args-type-rest type2)))
 (!define-type-method (values :simple-=) (type1 type2)
   (let ((rest1 (args-type-rest type1))
        (rest2 (args-type-rest type2)))

-    (cond ((or (args-type-keyp type1) (args-type-keyp type2)
-              (args-type-allowp type1) (args-type-allowp type2))
-          (values nil nil))
-         ((and rest1 rest2 (type/= rest1 rest2))
+    (cond ((and rest1 rest2 (type/= rest1 rest2))

           (type= rest1 rest2))
          ((or rest1 rest2)
           (values nil t))
           (type= rest1 rest2))
          ((or rest1 rest2)
           (values nil t))

@@ -213,10 +210,12 @@
            (type-specifier
             (fun-type-returns type)))))
 
            (type-specifier
             (fun-type-returns type)))))
 

-;;; Since all function types are equivalent to FUNCTION, they are all
-;;; subtypes of each other.
-(!define-type-method
- (function :simple-subtypep) (type1 type2)
+;;; The meaning of this is a little confused. On the one hand, all
+;;; function objects are represented the same way regardless of the
+;;; arglists and return values, and apps don't get to ask things like
+;;; (TYPEP #'FOO (FUNCTION (FIXNUM) *)) in any meaningful way. On the
+;;; other hand, Python wants to reason about function types. So...
+(!define-type-method (function :simple-subtypep) (type1 type2)

  (flet ((fun-type-simple-p (type)
           (not (or (fun-type-rest type)
                    (fun-type-keyp type))))
  (flet ((fun-type-simple-p (type)
           (not (or (fun-type-rest type)
                    (fun-type-keyp type))))

@@ -228,37 +227,41 @@
                     (csubtypep a1 a2)
                   (unless res (return (values res sure-p))))
              finally (return (values t t)))))
                     (csubtypep a1 a2)
                   (unless res (return (values res sure-p))))
              finally (return (values t t)))))

-   (macrolet ((3and (x y)
-                `(multiple-value-bind (val1 win1) ,x
-                   (if (and (not val1) win1)
-                       (values nil t)
-                       (multiple-value-bind (val2 win2) ,y
-                         (if (and val1 val2)
-                             (values t t)
-                             (values nil (or win1 win2))))))))
-     (3and (values-subtypep (fun-type-returns type1)
-                            (fun-type-returns type2))
-           (cond ((fun-type-wild-args type2) (values t t))
-                 ((fun-type-wild-args type1) (values nil t))
-                 ((not (or (fun-type-simple-p type1)
-                           (fun-type-simple-p type2)))
-                  (values nil nil))
-                 (t (multiple-value-bind (min1 max1) (fun-type-nargs type1)
-                      (multiple-value-bind (min2 max2) (fun-type-nargs type2)
-                        (cond ((or (> max1 max2) (< min1 min2))
-                               (values nil t))
-                              ((and (= min1 min2) (= max1 max2))
-                               (3and (every-csubtypep (fun-type-required type1)
-                                                      (fun-type-required type2))
-                                     (every-csubtypep (fun-type-optional type1)
-                                                      (fun-type-optional type2))))
-                              (t (every-csubtypep
-                                  (concatenate 'list
-                                               (fun-type-required type1)
-                                               (fun-type-optional type1))
-                                  (concatenate 'list
-                                               (fun-type-required type2)
-                                               (fun-type-optional type2)))))))))))))
+   (and/type (values-subtypep (fun-type-returns type1)
+                              (fun-type-returns type2))
+             (cond ((fun-type-wild-args type2) (values t t))
+                   ((fun-type-wild-args type1)
+                    (cond ((fun-type-keyp type2) (values nil nil))
+                          ((not (fun-type-rest type2)) (values nil t))
+                          ((not (null (fun-type-required type2)))
+                          (values nil t))
+                          (t (and/type (type= *universal-type*
+                                             (fun-type-rest type2))
+                                       (every/type #'type=
+                                                  *universal-type*
+                                                   (fun-type-optional
+                                                   type2))))))
+                   ((not (and (fun-type-simple-p type1)
+                              (fun-type-simple-p type2)))
+                    (values nil nil))
+                   (t (multiple-value-bind (min1 max1) (fun-type-nargs type1)
+                        (multiple-value-bind (min2 max2) (fun-type-nargs type2)
+                          (cond ((or (> max1 max2) (< min1 min2))
+                                 (values nil t))
+                                ((and (= min1 min2) (= max1 max2))
+                                 (and/type (every-csubtypep
+                                           (fun-type-required type1)
+                                           (fun-type-required type2))
+                                           (every-csubtypep
+                                           (fun-type-optional type1)
+                                           (fun-type-optional type2))))
+                                (t (every-csubtypep
+                                    (concatenate 'list
+                                                 (fun-type-required type1)
+                                                 (fun-type-optional type1))
+                                    (concatenate 'list
+                                                 (fun-type-required type2)
+                                                 (fun-type-optional type2))))))))))))

 
 (!define-superclasses function ((function)) !cold-init-forms)
 
 
 (!define-superclasses function ((function)) !cold-init-forms)
 

@@ -270,10 +273,53 @@
   (declare (ignore type1 type2))
   (specifier-type 'function))
 
   (declare (ignore type1 type2))
   (specifier-type 'function))
 

-;;; ### Not very real, but good enough for redefining transforms
-;;; according to type:
+;;; The union or intersection of a subclass of FUNCTION with a
+;;; FUNCTION type is somewhat complicated.
+(!define-type-method (function :complex-intersection2) (type1 type2)
+  (cond
+    ((type= type1 (specifier-type 'function)) type2)
+    ((csubtypep type1 (specifier-type 'function)) nil)
+    (t :call-other-method)))
+(!define-type-method (function :complex-union2) (type1 type2)
+  (cond
+    ((type= type1 (specifier-type 'function)) type1)
+    (t nil)))
+

 (!define-type-method (function :simple-=) (type1 type2)
 (!define-type-method (function :simple-=) (type1 type2)

-  (values (equalp type1 type2) t))
+  (macrolet ((compare (comparator field)
+               (let ((reader (symbolicate '#:fun-type- field)))
+                 `(,comparator (,reader type1) (,reader type2)))))
+    (and/type (compare type= returns)
+              (cond ((neq (fun-type-wild-args type1) (fun-type-wild-args type2))
+                     (values nil t))
+                    ((eq (fun-type-wild-args type1) t)
+                     (values t t))
+                    (t (and/type
+                        (cond ((null (fun-type-rest type1))
+                               (values (null (fun-type-rest type2)) t))
+                              ((null (fun-type-rest type2))
+                               (values nil t))
+                              (t
+                               (compare type= rest)))
+                        (labels ((type-list-= (l1 l2)
+                                   (cond ((null l1)
+                                          (values (null l2) t))
+                                         ((null l2)
+                                          (values nil t))
+                                         (t (multiple-value-bind (res winp)
+                                                (type= (first l1) (first l2))
+                                              (cond ((not winp)
+                                                     (values nil nil))
+                                                    ((not res)
+                                                     (values nil t))
+                                                    (t
+                                                     (type-list-= (rest l1)
+                                                                  (rest l2)))))))))
+                          (and/type (and/type (compare type-list-= required)
+                                              (compare type-list-= optional))
+                              (if (or (fun-type-keyp type1) (fun-type-keyp type2))
+                                  (values nil nil)
+                                  (values t t))))))))))

 
 (!define-type-class constant :inherits values)
 
 
 (!define-type-class constant :inherits values)
 

@@ -284,35 +330,7 @@
   (type= (constant-type-type type1) (constant-type-type type2)))
 
 (!def-type-translator constant-arg (type)
   (type= (constant-type-type type1) (constant-type-type type2)))
 
 (!def-type-translator constant-arg (type)

-  (make-constant-type :type (specifier-type type)))
-
-;;; Given a LAMBDA-LIST-like values type specification and an ARGS-TYPE
-;;; structure, fill in the slots in the structure accordingly. This is
-;;; used for both FUNCTION and VALUES types.
-(declaim (ftype (function (list args-type) (values)) parse-args-types))
-(defun parse-args-types (lambda-list result)
-  (multiple-value-bind (required optional restp rest keyp keys allowp auxp aux)
-      (parse-lambda-list-like-thing lambda-list)
-    (declare (ignore aux)) ; since we require AUXP=NIL
-    (when auxp
-      (error "&AUX in a FUNCTION or VALUES type: ~S." lambda-list))
-    (setf (args-type-required result) (mapcar #'specifier-type required))
-    (setf (args-type-optional result) (mapcar #'specifier-type optional))
-    (setf (args-type-rest result) (if restp (specifier-type rest) nil))
-    (setf (args-type-keyp result) keyp)
-    (collect ((key-info))
-      (dolist (key keys)
-       (unless (proper-list-of-length-p key 2)
-         (error "Keyword type description is not a two-list: ~S." key))
-       (let ((kwd (first key)))
-         (when (find kwd (key-info) :key #'key-info-name)
-           (error "~@<repeated keyword ~S in lambda list: ~2I~_~S~:>"
-                  kwd lambda-list))
-         (key-info (make-key-info :name kwd
-                                  :type (specifier-type (second key))))))
-      (setf (args-type-keywords result) (key-info)))
-    (setf (args-type-allowp result) allowp)
-    (values)))
+  (make-constant-type :type (single-value-specifier-type type)))

 
 ;;; Return the lambda-list-like type specification corresponding
 ;;; to an ARGS-TYPE.
 
 ;;; Return the lambda-list-like type specification corresponding
 ;;; to an ARGS-TYPE.

@@ -344,46 +362,46 @@
     (result)))
 
 (!def-type-translator function (&optional (args '*) (result '*))
     (result)))
 
 (!def-type-translator function (&optional (args '*) (result '*))

-  (let ((res (make-fun-type :returns (values-specifier-type result))))
-    (if (eq args '*)
-       (setf (fun-type-wild-args res) t)
-       (parse-args-types args res))
-    res))
+  (make-fun-type :args args
+                 :returns (coerce-to-values (values-specifier-type result))))

 
 (!def-type-translator values (&rest values)
 
 (!def-type-translator values (&rest values)

-  (let ((res (make-values-type)))
-    (parse-args-types values res)
-    res))
+  (make-values-type :args values))

 \f
 ;;;; VALUES types interfaces
 ;;;;
 ;;;; We provide a few special operations that can be meaningfully used
 ;;;; on VALUES types (as well as on any other type).
 
 \f
 ;;;; VALUES types interfaces
 ;;;;
 ;;;; We provide a few special operations that can be meaningfully used
 ;;;; on VALUES types (as well as on any other type).
 

+(defun type-single-value-p (type)
+  (and (values-type-p type)
+       (not (values-type-rest type))
+       (null (values-type-optional type))
+       (singleton-p (values-type-required type))))
+

 ;;; Return the type of the first value indicated by TYPE. This is used
 ;;; by people who don't want to have to deal with VALUES types.
 #!-sb-fluid (declaim (freeze-type values-type))
 ; (inline single-value-type))
 (defun single-value-type (type)
   (declare (type ctype type))
 ;;; Return the type of the first value indicated by TYPE. This is used
 ;;; by people who don't want to have to deal with VALUES types.
 #!-sb-fluid (declaim (freeze-type values-type))
 ; (inline single-value-type))
 (defun single-value-type (type)
   (declare (type ctype type))

-  (cond ((values-type-p type)
-        (or (car (args-type-required type))
-             (if (args-type-optional type)
-                 (type-union (car (args-type-optional type))
-                            (specifier-type 'null)))
-            (args-type-rest type)
-             (specifier-type 'null)))
-       ((eq type *wild-type*)
-        *universal-type*)
-       (t
-        type)))
+  (cond ((eq type *wild-type*)
+         *universal-type*)
+        ((eq type *empty-type*)
+         *empty-type*)
+        ((not (values-type-p type))
+         type)
+        (t (or (car (args-type-required type))
+               (car (args-type-optional type))
+               (args-type-rest type)
+               (specifier-type 'null)))))

 
 ;;; Return the minimum number of arguments that a function can be
 ;;; called with, and the maximum number or NIL. If not a function
 ;;; type, return NIL, NIL.
 (defun fun-type-nargs (type)
   (declare (type ctype type))
 
 ;;; Return the minimum number of arguments that a function can be
 ;;; called with, and the maximum number or NIL. If not a function
 ;;; type, return NIL, NIL.
 (defun fun-type-nargs (type)
   (declare (type ctype type))

-  (if (fun-type-p type)
+  (if (and (fun-type-p type) (not (fun-type-wild-args type)))

       (let ((fixed (length (args-type-required type))))
        (if (or (args-type-rest type)
                (args-type-keyp type)
       (let ((fixed (length (args-type-required type))))
        (if (or (args-type-rest type)
                (args-type-keyp type)

@@ -398,31 +416,45 @@
 ;;; not fixed, then return NIL and :UNKNOWN.
 (defun values-types (type)
   (declare (type ctype type))
 ;;; not fixed, then return NIL and :UNKNOWN.
 (defun values-types (type)
   (declare (type ctype type))

-  (cond ((eq type *wild-type*)
+  (cond ((or (eq type *wild-type*) (eq type *empty-type*))

         (values nil :unknown))
         (values nil :unknown))

-       ((not (values-type-p type))
-        (values (list type) 1))

        ((or (args-type-optional type)
        ((or (args-type-optional type)

-            (args-type-rest type)
-            (args-type-keyp type)
-            (args-type-allowp type))
+            (args-type-rest type))

         (values nil :unknown))
        (t
         (let ((req (args-type-required type)))
         (values nil :unknown))
        (t
         (let ((req (args-type-required type)))

-          (values (mapcar #'single-value-type req) (length req))))))
+          (values req (length req))))))

 
 ;;; Return two values:
 ;;; 1. A list of all the positional (fixed and optional) types.
 
 ;;; Return two values:
 ;;; 1. A list of all the positional (fixed and optional) types.

-;;; 2. The &REST type (if any). If keywords allowed, *UNIVERSAL-TYPE*.
-;;;    If no keywords or &REST, then the DEFAULT-TYPE.
+;;; 2. The &REST type (if any). If no &REST, then the DEFAULT-TYPE.

 (defun values-type-types (type &optional (default-type *empty-type*))
 (defun values-type-types (type &optional (default-type *empty-type*))

-  (declare (type values-type type))
-  (values (append (args-type-required type)
-                 (args-type-optional type))
-         (cond ((args-type-keyp type) *universal-type*)
-               ((args-type-rest type))
-               (t
-                default-type))))
+  (declare (type ctype type))
+  (if (eq type *wild-type*)
+      (values nil *universal-type*)
+      (values (append (args-type-required type)
+                      (args-type-optional type))
+              (cond ((args-type-rest type))
+                    (t default-type)))))
+
+;;; If COUNT values are supplied, which types should they have?
+(defun values-type-start (type count)
+  (declare (type ctype type) (type unsigned-byte count))
+  (if (eq type *wild-type*)
+      (make-list count :initial-element *universal-type*)
+      (collect ((res))
+        (flet ((process-types (types)
+                 (loop for type in types
+                       while (plusp count)
+                       do (decf count)
+                       do (res type))))
+          (process-types (values-type-required type))
+          (process-types (values-type-optional type))
+          (when (plusp count)
+            (loop with rest = (the ctype (values-type-rest type))
+                  repeat count
+                  do (res rest))))
+        (res))))

 
 ;;; Return a list of OPERATION applied to the types in TYPES1 and
 ;;; TYPES2, padding with REST2 as needed. TYPES1 must not be shorter
 
 ;;; Return a list of OPERATION applied to the types in TYPES1 and
 ;;; TYPES2, padding with REST2 as needed. TYPES1 must not be shorter

@@ -443,13 +475,47 @@
                                       :initial-element rest2)))
            exact)))
 
                                       :initial-element rest2)))
            exact)))
 

-;;; If Type isn't a values type, then make it into one:
-;;;    <type>  ==>  (values type &rest t)
+;;; If TYPE isn't a values type, then make it into one.
+(defun-cached (%coerce-to-values
+               :hash-bits 8
+               :hash-function (lambda (type)
+                                (logand (type-hash-value type)
+                                        #xff)))
+    ((type eq))
+  (cond ((multiple-value-bind (res sure)
+             (csubtypep (specifier-type 'null) type)
+           (and (not res) sure))
+         ;; FIXME: What should we do with (NOT SURE)?
+         (make-values-type :required (list type) :rest *universal-type*))
+        (t
+         (make-values-type :optional (list type) :rest *universal-type*))))
+

 (defun coerce-to-values (type)
   (declare (type ctype type))
 (defun coerce-to-values (type)
   (declare (type ctype type))

-  (if (values-type-p type)
-      type
-      (make-values-type :required (list type) :rest *universal-type*)))
+  (cond ((or (eq type *universal-type*)
+             (eq type *wild-type*))
+         *wild-type*)
+        ((values-type-p type)
+         type)
+        (t (%coerce-to-values type))))
+
+;;; Return type, corresponding to ANSI short form of VALUES type
+;;; specifier.
+(defun make-short-values-type (types)
+  (declare (list types))
+  (let ((last-required (position-if
+                        (lambda (type)
+                          (not/type (csubtypep (specifier-type 'null) type)))
+                        types
+                        :from-end t)))
+    (if last-required
+        (make-values-type :required (subseq types 0 (1+ last-required))
+                          :optional (subseq types (1+ last-required))
+                          :rest *universal-type*)
+        (make-values-type :optional types :rest *universal-type*))))
+
+(defun make-single-value-type (type)
+  (make-values-type :required (list type)))

 
 ;;; Do the specified OPERATION on TYPE1 and TYPE2, which may be any
 ;;; type, including VALUES types. With VALUES types such as:
 
 ;;; Do the specified OPERATION on TYPE1 and TYPE2, which may be any
 ;;; type, including VALUES types. With VALUES types such as:

@@ -474,39 +540,31 @@
 ;;; OPERATION returned true as its second value each time we called
 ;;; it. Since we approximate the intersection of VALUES types, the
 ;;; second value being true doesn't mean the result is exact.
 ;;; OPERATION returned true as its second value each time we called
 ;;; it. Since we approximate the intersection of VALUES types, the
 ;;; second value being true doesn't mean the result is exact.

-(defun args-type-op (type1 type2 operation nreq default-type)
-  (declare (type ctype type1 type2 default-type)
+(defun args-type-op (type1 type2 operation nreq)
+  (declare (type ctype type1 type2)

           (type function operation nreq))
           (type function operation nreq))

-  (if (or (values-type-p type1) (values-type-p type2))
-      (let ((type1 (coerce-to-values type1))
-           (type2 (coerce-to-values type2)))
-       (multiple-value-bind (types1 rest1)
-            (values-type-types type1 default-type)
-         (multiple-value-bind (types2 rest2)
-              (values-type-types type2 default-type)
-           (multiple-value-bind (rest rest-exact)
-               (funcall operation rest1 rest2)
-             (multiple-value-bind (res res-exact)
-                 (if (< (length types1) (length types2))
-                     (fixed-values-op types2 types1 rest1 operation)
-                     (fixed-values-op types1 types2 rest2 operation))
-               (let* ((req (funcall nreq
-                                    (length (args-type-required type1))
-                                    (length (args-type-required type2))))
-                      (required (subseq res 0 req))
-                      (opt (subseq res req))
-                      (opt-last (position rest opt :test-not #'type=
-                                          :from-end t)))
-                 (if (find *empty-type* required :test #'type=)
-                     (values *empty-type* t)
-                     (values (make-values-type
-                              :required required
-                              :optional (if opt-last
-                                            (subseq opt 0 (1+ opt-last))
-                                            ())
-                              :rest (if (eq rest default-type) nil rest))
-                             (and rest-exact res-exact)))))))))
-      (funcall operation type1 type2)))
+  (when (eq type1 type2)
+    (values type1 t))
+  (multiple-value-bind (types1 rest1)
+      (values-type-types type1)
+    (multiple-value-bind (types2 rest2)
+        (values-type-types type2)
+      (multiple-value-bind (rest rest-exact)
+          (funcall operation rest1 rest2)
+        (multiple-value-bind (res res-exact)
+            (if (< (length types1) (length types2))
+                (fixed-values-op types2 types1 rest1 operation)
+                (fixed-values-op types1 types2 rest2 operation))
+          (let* ((req (funcall nreq
+                               (length (args-type-required type1))
+                               (length (args-type-required type2))))
+                 (required (subseq res 0 req))
+                 (opt (subseq res req)))
+            (values (make-values-type
+                     :required required
+                     :optional opt
+                     :rest rest)
+                    (and rest-exact res-exact))))))))

 
 ;;; Do a union or intersection operation on types that might be values
 ;;; types. The result is optimized for utility rather than exactness,
 
 ;;; Do a union or intersection operation on types that might be values
 ;;; types. The result is optimized for utility rather than exactness,

@@ -519,27 +577,38 @@
                                 :hash-bits 8
                                 :default nil
                                 :init-wrapper !cold-init-forms)
                                 :hash-bits 8
                                 :default nil
                                 :init-wrapper !cold-init-forms)

-             ((type1 eq) (type2 eq))
+    ((type1 eq) (type2 eq))

   (declare (type ctype type1 type2))
   (cond ((or (eq type1 *wild-type*) (eq type2 *wild-type*)) *wild-type*)
   (declare (type ctype type1 type2))
   (cond ((or (eq type1 *wild-type*) (eq type2 *wild-type*)) *wild-type*)

-       ((eq type1 *empty-type*) type2)
-       ((eq type2 *empty-type*) type1)
-       (t
-        (values (args-type-op type1 type2 #'type-union #'min *empty-type*)))))
+        ((eq type1 *empty-type*) type2)
+        ((eq type2 *empty-type*) type1)
+        (t
+         (values (args-type-op type1 type2 #'type-union #'min)))))
+

 (defun-cached (values-type-intersection :hash-function type-cache-hash
                                        :hash-bits 8
                                        :values 2
                                        :default (values nil :empty)
                                        :init-wrapper !cold-init-forms)
 (defun-cached (values-type-intersection :hash-function type-cache-hash
                                        :hash-bits 8
                                        :values 2
                                        :default (values nil :empty)
                                        :init-wrapper !cold-init-forms)

-             ((type1 eq) (type2 eq))
+    ((type1 eq) (type2 eq))

   (declare (type ctype type1 type2))
   (declare (type ctype type1 type2))

-  (cond ((eq type1 *wild-type*) (values type2 t))
-       ((eq type2 *wild-type*) (values type1 t))
-       (t
-        (args-type-op type1 type2
-                      #'type-intersection
-                      #'max
-                      (specifier-type 'null)))))
+  (cond ((eq type1 *wild-type*) (values (coerce-to-values type2) t))
+        ((or (eq type2 *wild-type*) (eq type2 *universal-type*))
+         (values type1 t))
+        ((or (eq type1 *empty-type*) (eq type2 *empty-type*))
+         *empty-type*)
+        ((and (not (values-type-p type2))
+              (values-type-required type1))
+         (let ((req1 (values-type-required type1)))
+         (make-values-type :required (cons (type-intersection (first req1) type2)
+                                           (rest req1))
+                           :optional (values-type-optional type1)
+                           :rest (values-type-rest type1)
+                           :allowp (values-type-allowp type1))))
+        (t
+         (args-type-op type1 (coerce-to-values type2)
+                       #'type-intersection
+                       #'max))))

 
 ;;; This is like TYPES-EQUAL-OR-INTERSECT, except that it sort of
 ;;; works on VALUES types. Note that due to the semantics of
 
 ;;; This is like TYPES-EQUAL-OR-INTERSECT, except that it sort of
 ;;; works on VALUES types. Note that due to the semantics of

@@ -548,12 +617,12 @@
 (defun values-types-equal-or-intersect (type1 type2)
   (cond ((or (eq type1 *empty-type*) (eq type2 *empty-type*))
         (values t t))
 (defun values-types-equal-or-intersect (type1 type2)
   (cond ((or (eq type1 *empty-type*) (eq type2 *empty-type*))
         (values t t))

-       ((or (values-type-p type1) (values-type-p type2))
+        ((or (eq type1 *wild-type*) (eq type2 *wild-type*))
+         (values t t))
+       (t

         (multiple-value-bind (res win) (values-type-intersection type1 type2)
           (values (not (eq res *empty-type*))
         (multiple-value-bind (res win) (values-type-intersection type1 type2)
           (values (not (eq res *empty-type*))

-                  win)))
-       (t
-        (types-equal-or-intersect type1 type2))))
+                  win)))))

 
 ;;; a SUBTYPEP-like operation that can be used on any types, including
 ;;; VALUES types
 
 ;;; a SUBTYPEP-like operation that can be used on any types, including
 ;;; VALUES types

@@ -562,39 +631,39 @@
                               :values 2
                               :default (values nil :empty)
                               :init-wrapper !cold-init-forms)
                               :values 2
                               :default (values nil :empty)
                               :init-wrapper !cold-init-forms)

-             ((type1 eq) (type2 eq))
+    ((type1 eq) (type2 eq))

   (declare (type ctype type1 type2))
   (declare (type ctype type1 type2))

-  (cond ((eq type2 *wild-type*) (values t t))
-       ((eq type1 *wild-type*)
-        (values (eq type2 *universal-type*) t))
-       ((not (values-types-equal-or-intersect type1 type2))
-        (values nil t))
-       (t
-        (if (or (values-type-p type1) (values-type-p type2))
-            (let ((type1 (coerce-to-values type1))
-                  (type2 (coerce-to-values type2)))
-              (multiple-value-bind (types1 rest1) (values-type-types type1)
-                (multiple-value-bind (types2 rest2) (values-type-types type2)
-                  (cond ((< (length (values-type-required type1))
-                            (length (values-type-required type2)))
-                         (values nil t))
-                        ((< (length types1) (length types2))
-                         (values nil nil))
-                        ((or (values-type-keyp type1)
-                             (values-type-keyp type2))
-                         (values nil nil))
-                        (t
-                         (do ((t1 types1 (rest t1))
-                              (t2 types2 (rest t2)))
-                             ((null t2)
-                              (csubtypep rest1 rest2))
-                           (multiple-value-bind (res win-p)
-                               (csubtypep (first t1) (first t2))
-                             (unless win-p
-                               (return (values nil nil)))
-                             (unless res
-                               (return (values nil t))))))))))
-            (csubtypep type1 type2)))))
+  (cond ((or (eq type2 *wild-type*) (eq type2 *universal-type*)
+             (eq type1 *empty-type*))
+         (values t t))
+        ((eq type1 *wild-type*)
+         (values (eq type2 *wild-type*) t))
+        ((or (eq type2 *empty-type*)
+             (not (values-types-equal-or-intersect type1 type2)))
+         (values nil t))
+        ((and (not (values-type-p type2))
+              (values-type-required type1))
+         (csubtypep (first (values-type-required type1))
+                    type2))
+        (t (setq type2 (coerce-to-values type2))
+           (multiple-value-bind (types1 rest1) (values-type-types type1)
+             (multiple-value-bind (types2 rest2) (values-type-types type2)
+               (cond ((< (length (values-type-required type1))
+                         (length (values-type-required type2)))
+                      (values nil t))
+                     ((< (length types1) (length types2))
+                      (values nil nil))
+                     (t
+                      (do ((t1 types1 (rest t1))
+                           (t2 types2 (rest t2)))
+                          ((null t2)
+                           (csubtypep rest1 rest2))
+                        (multiple-value-bind (res win-p)
+                            (csubtypep (first t1) (first t2))
+                          (unless win-p
+                            (return (values nil nil)))
+                          (unless res
+                            (return (values nil t))))))))))))

 \f
 ;;;; type method interfaces
 
 \f
 ;;;; type method interfaces
 

@@ -608,9 +677,10 @@
   (declare (type ctype type1 type2))
   (cond ((or (eq type1 type2)
             (eq type1 *empty-type*)
   (declare (type ctype type1 type2))
   (cond ((or (eq type1 type2)
             (eq type1 *empty-type*)

-            (eq type2 *wild-type*))
+            (eq type2 *universal-type*))

         (values t t))
         (values t t))

-       ((eq type1 *wild-type*)
+        #+nil
+       ((eq type1 *universal-type*)

         (values nil t))
        (t
         (!invoke-type-method :simple-subtypep :complex-subtypep-arg2
         (values nil t))
        (t
         (!invoke-type-method :simple-subtypep :complex-subtypep-arg2

@@ -618,12 +688,13 @@
                              :complex-arg1 :complex-subtypep-arg1))))
 
 ;;; Just parse the type specifiers and call CSUBTYPE.
                              :complex-arg1 :complex-subtypep-arg1))))
 
 ;;; Just parse the type specifiers and call CSUBTYPE.

-(defun sb!xc:subtypep (type1 type2)
+(defun sb!xc:subtypep (type1 type2 &optional environment)

   #!+sb-doc
   "Return two values indicating the relationship between type1 and type2.
   If values are T and T, type1 definitely is a subtype of type2.
   If values are NIL and T, type1 definitely is not a subtype of type2.
   If values are NIL and NIL, it couldn't be determined."
   #!+sb-doc
   "Return two values indicating the relationship between type1 and type2.
   If values are T and T, type1 definitely is a subtype of type2.
   If values are NIL and T, type1 definitely is not a subtype of type2.
   If values are NIL and NIL, it couldn't be determined."

+  (declare (ignore environment))

   (csubtypep (specifier-type type1) (specifier-type type2)))
 
 ;;; If two types are definitely equivalent, return true. The second
   (csubtypep (specifier-type type1) (specifier-type type2)))
 
 ;;; If two types are definitely equivalent, return true. The second

@@ -715,14 +786,14 @@
   (flet ((1way (x y)
           (!invoke-type-method :simple-intersection2 :complex-intersection2
                                x y
   (flet ((1way (x y)
           (!invoke-type-method :simple-intersection2 :complex-intersection2
                                x y

-                               :default :no-type-method-found)))
+                               :default :call-other-method)))

     (declare (inline 1way))
     (let ((xy (1way type1 type2)))
     (declare (inline 1way))
     (let ((xy (1way type1 type2)))

-      (or (and (not (eql xy :no-type-method-found)) xy)
+      (or (and (not (eql xy :call-other-method)) xy)

          (let ((yx (1way type2 type1)))
          (let ((yx (1way type2 type1)))

-           (or (and (not (eql yx :no-type-method-found)) yx)
-               (cond ((and (eql xy :no-type-method-found)
-                           (eql yx :no-type-method-found))
+           (or (and (not (eql yx :call-other-method)) yx)
+               (cond ((and (eql xy :call-other-method)
+                           (eql yx :call-other-method))

                       *empty-type*)
                      (t
                       (aver (and (not xy) (not yx))) ; else handled above
                       *empty-type*)
                      (t
                       (aver (and (not xy) (not yx))) ; else handled above

@@ -816,71 +887,45 @@
 ;;;; These are fully general operations on CTYPEs: they'll always
 ;;;; return a CTYPE representing the result.
 
 ;;;; These are fully general operations on CTYPEs: they'll always
 ;;;; return a CTYPE representing the result.
 

-;;; shared logic for unions and intersections: Stuff TYPE into the
-;;; vector TYPES, finding pairs of types which can be simplified by
-;;; SIMPLIFY2 (TYPE-UNION2 or TYPE-INTERSECTION2) and replacing them
-;;; by their simplified forms.
-(defun accumulate1-compound-type (type types %compound-type-p simplify2)
-  (declare (type ctype type))
-  (declare (type (vector ctype) types))
-  (declare (type function simplify2))
-  ;; Any input object satisfying %COMPOUND-TYPE-P should've been
-  ;; broken into components before it reached us.
-  (aver (not (funcall %compound-type-p type)))
-  (dotimes (i (length types) (vector-push-extend type types))
-    (let ((simplified2 (funcall simplify2 type (aref types i))))
-      (when simplified2
-       ;; Discard the old (AREF TYPES I).
-       (setf (aref types i) (vector-pop types))
-       ;; Merge the new SIMPLIFIED2 into TYPES, by tail recursing.
-       ;; (Note that the tail recursion is indirect: we go through
-       ;; ACCUMULATE, not ACCUMULATE1, so that if SIMPLIFIED2 is
-       ;; handled properly if it satisfies %COMPOUND-TYPE-P.)
-       (return (accumulate-compound-type simplified2
-                                         types
-                                         %compound-type-p
-                                         simplify2)))))
-  ;; Voila.
-  (values))
-
-;;; shared logic for unions and intersections: Use
-;;; ACCUMULATE1-COMPOUND-TYPE to merge TYPE into TYPES, either
-;;; all in one step or, if %COMPOUND-TYPE-P is satisfied,
-;;; component by component.
-(defun accumulate-compound-type (type types %compound-type-p simplify2)
-  (declare (type function %compound-type-p simplify2))
-  (flet ((accumulate1 (x)
-          (accumulate1-compound-type x types %compound-type-p simplify2)))
-    (declare (inline accumulate1))
-    (if (funcall %compound-type-p type)
-       (map nil #'accumulate1 (compound-type-types type))
-       (accumulate1 type)))
-  (values))
-

 ;;; shared logic for unions and intersections: Return a vector of
 ;;; shared logic for unions and intersections: Return a vector of

-;;; types representing the same types as INPUT-TYPES, but with 
+;;; types representing the same types as INPUT-TYPES, but with

 ;;; COMPOUND-TYPEs satisfying %COMPOUND-TYPE-P broken up into their
 ;;; component types, and with any SIMPLY2 simplifications applied.
 ;;; COMPOUND-TYPEs satisfying %COMPOUND-TYPE-P broken up into their
 ;;; component types, and with any SIMPLY2 simplifications applied.

+(declaim (inline simplified-compound-types))

 (defun simplified-compound-types (input-types %compound-type-p simplify2)
 (defun simplified-compound-types (input-types %compound-type-p simplify2)

-  (let ((simplified-types (make-array (length input-types)
-                                     :fill-pointer 0
-                                     :adjustable t
-                                     :element-type 'ctype
-                                     ;; (This INITIAL-ELEMENT shouldn't
-                                     ;; matter, but helps avoid type
-                                     ;; warnings at compile time.)
-                                     :initial-element *empty-type*)))
-    (dolist (input-type input-types)
-      (accumulate-compound-type input-type
-                               simplified-types
-                               %compound-type-p
-                               simplify2))
-    simplified-types))
+  (declare (function %compound-type-p simplify2))
+  (let ((types (make-array (length input-types)
+                           :fill-pointer 0
+                           :adjustable t
+                           :element-type 'ctype)))
+    (labels ((accumulate-compound-type (type)
+               (if (funcall %compound-type-p type)
+                   (dolist (type (compound-type-types type))
+                     (accumulate1-compound-type type))
+                   (accumulate1-compound-type type)))
+             (accumulate1-compound-type (type)
+               (declare (type ctype type))
+               ;; Any input object satisfying %COMPOUND-TYPE-P should've been
+               ;; broken into components before it reached us.
+               (aver (not (funcall %compound-type-p type)))
+               (dotimes (i (length types) (vector-push-extend type types))
+                 (let ((simplified2 (funcall simplify2 type (aref types i))))
+                   (when simplified2
+                     ;; Discard the old (AREF TYPES I).
+                     (setf (aref types i) (vector-pop types))
+                     ;; Merge the new SIMPLIFIED2 into TYPES, by tail recursing.
+                     ;; (Note that the tail recursion is indirect: we go through
+                     ;; ACCUMULATE, not ACCUMULATE1, so that if SIMPLIFIED2 is
+                     ;; handled properly if it satisfies %COMPOUND-TYPE-P.)
+                     (return (accumulate-compound-type simplified2)))))))
+      (dolist (input-type input-types)
+        (accumulate-compound-type input-type)))
+    types))

 
 ;;; shared logic for unions and intersections: Make a COMPOUND-TYPE
 ;;; object whose components are the types in TYPES, or skip to special
 ;;; cases when TYPES is short.
 
 ;;; shared logic for unions and intersections: Make a COMPOUND-TYPE
 ;;; object whose components are the types in TYPES, or skip to special
 ;;; cases when TYPES is short.

-(defun make-compound-type-or-something (constructor types enumerable identity)
+(defun make-probably-compound-type (constructor types enumerable identity)

   (declare (type function constructor))
   (declare (type (vector ctype) types))
   (declare (type ctype identity))
   (declare (type function constructor))
   (declare (type (vector ctype) types))
   (declare (type ctype identity))

@@ -894,7 +939,7 @@
                ;; brain-dead, so that would generate a full call to
                ;; SPECIFIER-TYPE at runtime, so we get into bootstrap
                ;; problems in cold init because 'LIST is a compound
                ;; brain-dead, so that would generate a full call to
                ;; SPECIFIER-TYPE at runtime, so we get into bootstrap
                ;; problems in cold init because 'LIST is a compound

-               ;; type, so we need to MAKE-COMPOUND-TYPE-OR-SOMETHING
+               ;; type, so we need to MAKE-PROBABLY-COMPOUND-TYPE

                ;; before we know what 'LIST is. Once the COERCE
                ;; optimizer is less brain-dead, we can make this
                ;; (COERCE TYPES 'LIST) again.
                ;; before we know what 'LIST is. Once the COERCE
                ;; optimizer is less brain-dead, we can make this
                ;; (COERCE TYPES 'LIST) again.

@@ -912,6 +957,11 @@
        nil)))
 
 (defun type-intersection (&rest input-types)
        nil)))
 
 (defun type-intersection (&rest input-types)

+  (%type-intersection input-types))
+(defun-cached (%type-intersection :hash-bits 8
+                                  :hash-function (lambda (x)
+                                                   (logand (sxhash x) #xff)))
+    ((input-types equal))

   (let ((simplified-types (simplified-compound-types input-types
                                                     #'intersection-type-p
                                                     #'type-intersection2)))
   (let ((simplified-types (simplified-compound-types input-types
                                                     #'intersection-type-p
                                                     #'type-intersection2)))

@@ -927,26 +977,35 @@
     (if (and (> (length simplified-types) 1)
             (some #'union-type-p simplified-types))
        (let* ((first-union (find-if #'union-type-p simplified-types))
     (if (and (> (length simplified-types) 1)
             (some #'union-type-p simplified-types))
        (let* ((first-union (find-if #'union-type-p simplified-types))

-              (other-types (coerce (remove first-union simplified-types) 'list))
-              (distributed (maybe-distribute-one-union first-union other-types)))
+              (other-types (coerce (remove first-union simplified-types)
+                                   'list))
+              (distributed (maybe-distribute-one-union first-union
+                                                       other-types)))

          (if distributed
              (apply #'type-union distributed)
              (make-hairy-type
          (if distributed
              (apply #'type-union distributed)
              (make-hairy-type

-              :specifier `(and ,@(map 'list #'type-specifier simplified-types)))))
-       (make-compound-type-or-something #'%make-intersection-type
-                                        simplified-types
-                                        (some #'type-enumerable
-                                              simplified-types)
-                                        *universal-type*))))
+              :specifier `(and ,@(map 'list
+                                      #'type-specifier
+                                      simplified-types)))))
+       (make-probably-compound-type #'%make-intersection-type
+                                    simplified-types
+                                    (some #'type-enumerable
+                                          simplified-types)
+                                    *universal-type*))))

 
 (defun type-union (&rest input-types)
 
 (defun type-union (&rest input-types)

+  (%type-union input-types))
+(defun-cached (%type-union :hash-bits 8
+                           :hash-function (lambda (x)
+                                            (logand (sxhash x) #xff)))
+    ((input-types equal))

   (let ((simplified-types (simplified-compound-types input-types
                                                     #'union-type-p
                                                     #'type-union2)))
   (let ((simplified-types (simplified-compound-types input-types
                                                     #'union-type-p
                                                     #'type-union2)))

-    (make-compound-type-or-something #'%make-union-type
-                                    simplified-types
-                                    (every #'type-enumerable simplified-types)
-                                    *empty-type*)))
+    (make-probably-compound-type #'make-union-type
+                                simplified-types
+                                (every #'type-enumerable simplified-types)
+                                *empty-type*)))

 \f
 ;;;; built-in types
 
 \f
 ;;;; built-in types
 

@@ -956,18 +1015,18 @@
 (defvar *empty-type*)
 (defvar *universal-type*)
 (defvar *universal-fun-type*)
 (defvar *empty-type*)
 (defvar *universal-type*)
 (defvar *universal-fun-type*)

+

 (!cold-init-forms
  (macrolet ((frob (name var)
              `(progn
 (!cold-init-forms
  (macrolet ((frob (name var)
              `(progn

-                (setq ,var (make-named-type :name ',name))
-                (setf (info :type :kind ',name) #+sb-xc-host :defined #-sb-xc-host :primitive)
+                 (setq ,var (make-named-type :name ',name))
+                (setf (info :type :kind ',name)
+                      #+sb-xc-host :defined #-sb-xc-host :primitive)

                 (setf (info :type :builtin ',name) ,var))))
    ;; KLUDGE: In ANSI, * isn't really the name of a type, it's just a
    ;; special symbol which can be stuck in some places where an
    ;; ordinary type can go, e.g. (ARRAY * 1) instead of (ARRAY T 1).
                 (setf (info :type :builtin ',name) ,var))))
    ;; KLUDGE: In ANSI, * isn't really the name of a type, it's just a
    ;; special symbol which can be stuck in some places where an
    ;; ordinary type can go, e.g. (ARRAY * 1) instead of (ARRAY T 1).

-   ;; At some point, in order to become more standard, we should
-   ;; convert all the classic CMU CL legacy *s and *WILD-TYPE*s into
-   ;; Ts and *UNIVERSAL-TYPE*s.
+   ;; In SBCL it also used to denote universal VALUES type.

    (frob * *wild-type*)
    (frob nil *empty-type*)
    (frob t *universal-type*))
    (frob * *wild-type*)
    (frob nil *empty-type*)
    (frob t *universal-type*))

@@ -976,12 +1035,26 @@
                      :returns *wild-type*)))
 
 (!define-type-method (named :simple-=) (type1 type2)
                      :returns *wild-type*)))
 
 (!define-type-method (named :simple-=) (type1 type2)

-  ;; FIXME: BUG 85: This assertion failed when I added it in
-  ;; sbcl-0.6.11.13. It probably shouldn't fail; but for now it's
-  ;; just commented out.

   ;;(aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (values (eq type1 type2) t))
 
   ;;(aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (values (eq type1 type2) t))
 

+(!define-type-method (named :complex-=) (type1 type2)
+  (cond
+    ((and (eq type2 *empty-type*)
+         (intersection-type-p type1)
+         ;; not allowed to be unsure on these... FIXME: keep the list
+         ;; of CL types that are intersection types once and only
+         ;; once.
+         (not (or (type= type1 (specifier-type 'ratio))
+                  (type= type1 (specifier-type 'keyword)))))
+     ;; things like (AND (EQL 0) (SATISFIES ODDP)) or (AND FUNCTION
+     ;; STREAM) can get here.  In general, we can't really tell
+     ;; whether these are equal to NIL or not, so
+     (values nil nil))
+    ((type-might-contain-other-types-p type1)
+     (invoke-complex-=-other-method type1 type2))
+    (t (values nil t))))
+

 (!define-type-method (named :simple-subtypep) (type1 type2)
   (aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (values (or (eq type1 *empty-type*) (eq type2 *wild-type*)) t))
 (!define-type-method (named :simple-subtypep) (type1 type2)
   (aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (values (or (eq type1 *empty-type*) (eq type2 *wild-type*)) t))

@@ -1012,7 +1085,7 @@
         (values nil nil))
        (t
         ;; By elimination, TYPE1 is the universal type.
         (values nil nil))
        (t
         ;; By elimination, TYPE1 is the universal type.

-        (aver (or (eq type1 *wild-type*) (eq type1 *universal-type*)))
+        (aver (eq type1 *universal-type*))

         ;; This case would have been picked off by the SIMPLE-SUBTYPEP
         ;; method, and so shouldn't appear here.
         (aver (not (eq type2 *universal-type*)))
         ;; This case would have been picked off by the SIMPLE-SUBTYPEP
         ;; method, and so shouldn't appear here.
         (aver (not (eq type2 *universal-type*)))

@@ -1024,11 +1097,13 @@
   (aver (not (eq type2 *wild-type*))) ; * isn't really a type.
   (cond ((eq type2 *universal-type*)
         (values t t))
   (aver (not (eq type2 *wild-type*))) ; * isn't really a type.
   (cond ((eq type2 *universal-type*)
         (values t t))

-       ((hairy-type-p type1)
+       ((type-might-contain-other-types-p type1)
+        ;; those types can be *EMPTY-TYPE* or *UNIVERSAL-TYPE* in
+        ;; disguise.  So we'd better delegate.

         (invoke-complex-subtypep-arg1-method type1 type2))
        (t
         ;; FIXME: This seems to rely on there only being 2 or 3
         (invoke-complex-subtypep-arg1-method type1 type2))
        (t
         ;; FIXME: This seems to rely on there only being 2 or 3

-        ;; HAIRY-TYPE values, and the exclusion of various
+        ;; NAMED-TYPE values, and the exclusion of various

         ;; possibilities above. It would be good to explain it and/or
         ;; rewrite it so that it's clearer.
         (values (not (eq type2 *empty-type*)) t))))
         ;; possibilities above. It would be good to explain it and/or
         ;; rewrite it so that it's clearer.
         (values (not (eq type2 *empty-type*)) t))))

@@ -1051,150 +1126,44 @@
 
 (!define-type-method (hairy :unparse) (x)
   (hairy-type-specifier x))
 
 (!define-type-method (hairy :unparse) (x)
   (hairy-type-specifier x))

-    
+

 (!define-type-method (hairy :simple-subtypep) (type1 type2)
   (let ((hairy-spec1 (hairy-type-specifier type1))
        (hairy-spec2 (hairy-type-specifier type2)))
 (!define-type-method (hairy :simple-subtypep) (type1 type2)
   (let ((hairy-spec1 (hairy-type-specifier type1))
        (hairy-spec2 (hairy-type-specifier type2)))

-    (cond ((and (consp hairy-spec1) (eq (car hairy-spec1) 'not)
-               (consp hairy-spec2) (eq (car hairy-spec2) 'not))
-          (csubtypep (specifier-type (cadr hairy-spec2))
-                     (specifier-type (cadr hairy-spec1))))
-         ((equal hairy-spec1 hairy-spec2)
+    (cond ((equal-but-no-car-recursion hairy-spec1 hairy-spec2)

           (values t t))
          (t
           (values nil nil)))))
 
 (!define-type-method (hairy :complex-subtypep-arg2) (type1 type2)
           (values t t))
          (t
           (values nil nil)))))
 
 (!define-type-method (hairy :complex-subtypep-arg2) (type1 type2)

-  (let ((hairy-spec (hairy-type-specifier type2)))
-    (cond ((and (consp hairy-spec) (eq (car hairy-spec) 'not))
-          (let* ((complement-type2 (specifier-type (cadr hairy-spec)))
-                 (intersection2 (type-intersection2 type1
-                                                    complement-type2)))
-            (if intersection2
-                (values (eq intersection2 *empty-type*) t)
-                (invoke-complex-subtypep-arg1-method type1 type2))))
-         (t
-          (invoke-complex-subtypep-arg1-method type1 type2)))))
+  (invoke-complex-subtypep-arg1-method type1 type2))

 
 (!define-type-method (hairy :complex-subtypep-arg1) (type1 type2)
 
 (!define-type-method (hairy :complex-subtypep-arg1) (type1 type2)

-  ;; "Incrementally extended heuristic algorithms tend inexorably toward the
-  ;; incomprehensible." -- http://www.unlambda.com/~james/lambda/lambda.txt
-  (let ((hairy-spec (hairy-type-specifier type1)))
-     (cond ((and (consp hairy-spec) (eq (car hairy-spec) 'not))
-           ;; You may not believe this. I couldn't either. But then I
-           ;; sat down and drew lots of Venn diagrams. Comments
-           ;; involving a and b refer to the call (subtypep '(not a)
-           ;; 'b) -- CSR, 2002-02-27.
-           (block nil
-             ;; (Several logical truths in this block are true as
-             ;; long as b/=T. As of sbcl-0.7.1.28, it seems
-             ;; impossible to construct a case with b=T where we
-             ;; actually reach this type method, but we'll test for
-             ;; and exclude this case anyway, since future
-             ;; maintenance might make it possible for it to end up
-             ;; in this code.)
-             (multiple-value-bind (equal certain)
-                 (type= type2 (specifier-type t))
-               (unless certain
-                 (return (values nil nil)))
-               (when equal
-                 (return (values t t))))
-             (let ((complement-type1 (specifier-type (cadr hairy-spec))))
-               ;; Do the special cases first, in order to give us a
-               ;; chance if subtype/supertype relationships are hairy.
-               (multiple-value-bind (equal certain) 
-                   (type= complement-type1 type2)
-                 ;; If a = b, ~a is not a subtype of b (unless b=T,
-                 ;; which was excluded above).
-                 (unless certain
-                   (return (values nil nil)))
-                 (when equal
-                   (return (values nil t))))
-               ;; KLUDGE: ANSI requires that the SUBTYPEP result
-               ;; between any two built-in atomic type specifiers
-               ;; never be uncertain. This is hard to do cleanly for
-               ;; the built-in types whose definitions include
-               ;; (NOT FOO), i.e. CONS and RATIO. However, we can do
-               ;; it with this hack, which uses our global knowledge
-               ;; that our implementation of the type system uses
-               ;; disjoint implementation types to represent disjoint
-               ;; sets (except when types are contained in other types).
-               ;; (This is a KLUDGE because it's fragile. Various
-               ;; changes in internal representation in the type
-               ;; system could make it start confidently returning
-               ;; incorrect results.) -- WHN 2002-03-08
-               (unless (or (type-might-contain-other-types-p complement-type1)
-                           (type-might-contain-other-types-p type2))
-                 ;; Because of the way our types which don't contain
-                 ;; other types are disjoint subsets of the space of
-                 ;; possible values, (SUBTYPEP '(NOT AA) 'B)=NIL when
-                 ;; AA and B are simple (and B is not T, as checked above).
-                 (return (values nil t)))
-               ;; The old (TYPE= TYPE1 TYPE2) branch would never be
-               ;; taken, as TYPE1 and TYPE2 will only be equal if
-               ;; they're both NOT types, and then the
-               ;; :SIMPLE-SUBTYPEP method would be used instead.
-               ;; But a CSUBTYPEP relationship might still hold:
-               (multiple-value-bind (equal certain)
-                   (csubtypep complement-type1 type2)
-                 ;; If a is a subtype of b, ~a is not a subtype of b
-                 ;; (unless b=T, which was excluded above).
-                 (unless certain
-                   (return (values nil nil)))
-                 (when equal
-                   (return (values nil t))))
-               (multiple-value-bind (equal certain)
-                   (csubtypep type2 complement-type1)
-                 ;; If b is a subtype of a, ~a is not a subtype of b.
-                 ;; (FIXME: That's not true if a=T. Do we know at
-                 ;; this point that a is not T?)
-                 (unless certain
-                   (return (values nil nil)))
-                 (when equal
-                   (return (values nil t))))
-               ;; old CSR comment ca. 0.7.2, now obsoleted by the
-               ;; SIMPLE-CTYPE? KLUDGE case above:
-               ;;   Other cases here would rely on being able to catch
-               ;;   all possible cases, which the fragility of this
-               ;;   type system doesn't inspire me; for instance, if a
-               ;;   is type= to ~b, then we want T, T; if this is not
-               ;;   the case and the types are disjoint (have an
-               ;;   intersection of *empty-type*) then we want NIL, T;
-               ;;   else if the union of a and b is the
-               ;;   *universal-type* then we want T, T. So currently we
-               ;;   still claim to be unsure about e.g. (subtypep '(not
-               ;;   fixnum) 'single-float).
-               )))
-          (t
-           (values nil nil)))))
+  (declare (ignore type1 type2))
+  (values nil nil))

 
 (!define-type-method (hairy :complex-=) (type1 type2)
   (declare (ignore type1 type2))
   (values nil nil))
 
 
 (!define-type-method (hairy :complex-=) (type1 type2)
   (declare (ignore type1 type2))
   (values nil nil))
 

-(!define-type-method (hairy :simple-intersection2 :complex-intersection2)
+(!define-type-method (hairy :simple-intersection2 :complex-intersection2) 
+                    (type1 type2)
+  (if (type= type1 type2)
+      type1
+      nil))
+
+(!define-type-method (hairy :simple-union2) 

                     (type1 type2)
   (if (type= type1 type2)
       type1
       nil))
 
 (!define-type-method (hairy :simple-=) (type1 type2)
                     (type1 type2)
   (if (type= type1 type2)
       type1
       nil))
 
 (!define-type-method (hairy :simple-=) (type1 type2)

-  (if (equal (hairy-type-specifier type1)
-            (hairy-type-specifier type2))
+  (if (equal-but-no-car-recursion (hairy-type-specifier type1)
+                                 (hairy-type-specifier type2))

       (values t t)
       (values nil nil)))
 
       (values t t)
       (values nil nil)))
 

-(!def-type-translator not (&whole whole type)
-  (declare (ignore type))
-  ;; Check legality of arguments.
-  (destructuring-bind (not typespec) whole
-    (declare (ignore not))
-    (let ((spec (type-specifier (specifier-type typespec)))) ; must be legal typespec
-      (if (and (listp spec) (eq (car spec) 'not))
-         ;; canonicalize (not (not foo))
-         (specifier-type (cadr spec))
-         (make-hairy-type :specifier whole)))))
-

 (!def-type-translator satisfies (&whole whole fun)
   (declare (ignore fun))
   ;; Check legality of arguments.
 (!def-type-translator satisfies (&whole whole fun)
   (declare (ignore fun))
   ;; Check legality of arguments.

@@ -1204,11 +1173,283 @@
       (error 'simple-type-error
             :datum predicate-name
             :expected-type 'symbol
       (error 'simple-type-error
             :datum predicate-name
             :expected-type 'symbol

-            :format-control "~S is not a symbol."
+            :format-control "The SATISFIES predicate name is not a symbol: ~S"

             :format-arguments (list predicate-name))))
   ;; Create object.
   (make-hairy-type :specifier whole))
 \f
             :format-arguments (list predicate-name))))
   ;; Create object.
   (make-hairy-type :specifier whole))
 \f

+;;;; negation types
+
+(!define-type-method (negation :unparse) (x)
+  `(not ,(type-specifier (negation-type-type x))))
+
+(!define-type-method (negation :simple-subtypep) (type1 type2)
+  (csubtypep (negation-type-type type2) (negation-type-type type1)))
+
+(!define-type-method (negation :complex-subtypep-arg2) (type1 type2)
+  (let* ((complement-type2 (negation-type-type type2))
+        (intersection2 (type-intersection2 type1
+                                           complement-type2)))
+    (if intersection2
+       ;; FIXME: if uncertain, maybe try arg1?
+       (type= intersection2 *empty-type*)
+       (invoke-complex-subtypep-arg1-method type1 type2))))
+
+(!define-type-method (negation :complex-subtypep-arg1) (type1 type2)
+  ;; "Incrementally extended heuristic algorithms tend inexorably toward the
+  ;; incomprehensible." -- http://www.unlambda.com/~james/lambda/lambda.txt
+  ;;
+  ;; You may not believe this. I couldn't either. But then I sat down
+  ;; and drew lots of Venn diagrams. Comments involving a and b refer
+  ;; to the call (subtypep '(not a) 'b) -- CSR, 2002-02-27.
+  (block nil
+    ;; (Several logical truths in this block are true as long as
+    ;; b/=T. As of sbcl-0.7.1.28, it seems impossible to construct a
+    ;; case with b=T where we actually reach this type method, but
+    ;; we'll test for and exclude this case anyway, since future
+    ;; maintenance might make it possible for it to end up in this
+    ;; code.)
+    (multiple-value-bind (equal certain)
+       (type= type2 *universal-type*)
+      (unless certain
+       (return (values nil nil)))
+      (when equal
+       (return (values t t))))
+    (let ((complement-type1 (negation-type-type type1)))
+      ;; Do the special cases first, in order to give us a chance if
+      ;; subtype/supertype relationships are hairy.
+      (multiple-value-bind (equal certain)
+         (type= complement-type1 type2)
+       ;; If a = b, ~a is not a subtype of b (unless b=T, which was
+       ;; excluded above).
+       (unless certain
+         (return (values nil nil)))
+       (when equal
+         (return (values nil t))))
+      ;; KLUDGE: ANSI requires that the SUBTYPEP result between any
+      ;; two built-in atomic type specifiers never be uncertain. This
+      ;; is hard to do cleanly for the built-in types whose
+      ;; definitions include (NOT FOO), i.e. CONS and RATIO. However,
+      ;; we can do it with this hack, which uses our global knowledge
+      ;; that our implementation of the type system uses disjoint
+      ;; implementation types to represent disjoint sets (except when
+      ;; types are contained in other types).  (This is a KLUDGE
+      ;; because it's fragile. Various changes in internal
+      ;; representation in the type system could make it start
+      ;; confidently returning incorrect results.) -- WHN 2002-03-08
+      (unless (or (type-might-contain-other-types-p complement-type1)
+                 (type-might-contain-other-types-p type2))
+       ;; Because of the way our types which don't contain other
+       ;; types are disjoint subsets of the space of possible values,
+       ;; (SUBTYPEP '(NOT AA) 'B)=NIL when AA and B are simple (and B
+       ;; is not T, as checked above).
+       (return (values nil t)))
+      ;; The old (TYPE= TYPE1 TYPE2) branch would never be taken, as
+      ;; TYPE1 and TYPE2 will only be equal if they're both NOT types,
+      ;; and then the :SIMPLE-SUBTYPEP method would be used instead.
+      ;; But a CSUBTYPEP relationship might still hold:
+      (multiple-value-bind (equal certain)
+         (csubtypep complement-type1 type2)
+       ;; If a is a subtype of b, ~a is not a subtype of b (unless
+       ;; b=T, which was excluded above).
+       (unless certain
+         (return (values nil nil)))
+       (when equal
+         (return (values nil t))))
+      (multiple-value-bind (equal certain)
+         (csubtypep type2 complement-type1)
+       ;; If b is a subtype of a, ~a is not a subtype of b.  (FIXME:
+       ;; That's not true if a=T. Do we know at this point that a is
+       ;; not T?)
+       (unless certain
+         (return (values nil nil)))
+       (when equal
+         (return (values nil t))))
+      ;; old CSR comment ca. 0.7.2, now obsoleted by the SIMPLE-CTYPE?
+      ;; KLUDGE case above: Other cases here would rely on being able
+      ;; to catch all possible cases, which the fragility of this type
+      ;; system doesn't inspire me; for instance, if a is type= to ~b,
+      ;; then we want T, T; if this is not the case and the types are
+      ;; disjoint (have an intersection of *empty-type*) then we want
+      ;; NIL, T; else if the union of a and b is the *universal-type*
+      ;; then we want T, T. So currently we still claim to be unsure
+      ;; about e.g. (subtypep '(not fixnum) 'single-float).
+      ;;
+      ;; OTOH we might still get here:
+      (values nil nil))))
+
+(!define-type-method (negation :complex-=) (type1 type2)
+  ;; (NOT FOO) isn't equivalent to anything that's not a negation
+  ;; type, except possibly a type that might contain it in disguise.
+  (declare (ignore type2))
+  (if (type-might-contain-other-types-p type1)
+      (values nil nil)
+      (values nil t)))
+
+(!define-type-method (negation :simple-intersection2) (type1 type2)
+  (let ((not1 (negation-type-type type1))
+       (not2 (negation-type-type type2)))
+    (cond
+      ((csubtypep not1 not2) type2)
+      ((csubtypep not2 not1) type1)
+      ;; Why no analagous clause to the disjoint in the SIMPLE-UNION2
+      ;; method, below?  The clause would read
+      ;;
+      ;; ((EQ (TYPE-UNION NOT1 NOT2) *UNIVERSAL-TYPE*) *EMPTY-TYPE*)
+      ;;
+      ;; but with proper canonicalization of negation types, there's
+      ;; no way of constructing two negation types with union of their
+      ;; negations being the universal type.
+      (t
+       (aver (not (eq (type-union not1 not2) *universal-type*)))
+       nil))))
+
+(!define-type-method (negation :complex-intersection2) (type1 type2)
+  (cond
+    ((csubtypep type1 (negation-type-type type2)) *empty-type*)
+    ((eq (type-intersection type1 (negation-type-type type2)) *empty-type*)
+     type1)
+    (t nil)))
+
+(!define-type-method (negation :simple-union2) (type1 type2)
+  (let ((not1 (negation-type-type type1))
+       (not2 (negation-type-type type2)))
+    (cond
+      ((csubtypep not1 not2) type1)
+      ((csubtypep not2 not1) type2)
+      ((eq (type-intersection not1 not2) *empty-type*)
+       *universal-type*)
+      (t nil))))
+
+(!define-type-method (negation :complex-union2) (type1 type2)
+  (cond
+    ((csubtypep (negation-type-type type2) type1) *universal-type*)
+    ((eq (type-intersection type1 (negation-type-type type2)) *empty-type*)
+     type2)
+    (t nil)))
+
+(!define-type-method (negation :simple-=) (type1 type2)
+  (type= (negation-type-type type1) (negation-type-type type2)))
+
+(!def-type-translator not (typespec)
+  (let* ((not-type (specifier-type typespec))
+        (spec (type-specifier not-type)))
+    (cond
+      ;; canonicalize (NOT (NOT FOO))
+      ((and (listp spec) (eq (car spec) 'not))
+       (specifier-type (cadr spec)))
+      ;; canonicalize (NOT NIL) and (NOT T)
+      ((eq not-type *empty-type*) *universal-type*)
+      ((eq not-type *universal-type*) *empty-type*)
+      ((and (numeric-type-p not-type)
+           (null (numeric-type-low not-type))
+           (null (numeric-type-high not-type)))
+       (make-negation-type :type not-type))
+      ((numeric-type-p not-type)
+       (type-union
+       (make-negation-type
+        :type (modified-numeric-type not-type :low nil :high nil))
+       (cond
+         ((null (numeric-type-low not-type))
+          (modified-numeric-type
+           not-type
+           :low (let ((h (numeric-type-high not-type)))
+                  (if (consp h) (car h) (list h)))
+           :high nil))
+         ((null (numeric-type-high not-type))
+          (modified-numeric-type
+           not-type
+           :low nil
+           :high (let ((l (numeric-type-low not-type)))
+                   (if (consp l) (car l) (list l)))))
+         (t (type-union
+             (modified-numeric-type
+              not-type
+              :low nil
+              :high (let ((l (numeric-type-low not-type)))
+                      (if (consp l) (car l) (list l))))
+             (modified-numeric-type
+              not-type
+              :low (let ((h (numeric-type-high not-type)))
+                     (if (consp h) (car h) (list h)))
+              :high nil))))))
+      ((intersection-type-p not-type)
+       (apply #'type-union
+             (mapcar #'(lambda (x)
+                         (specifier-type `(not ,(type-specifier x))))
+                     (intersection-type-types not-type))))
+      ((union-type-p not-type)
+       (apply #'type-intersection
+             (mapcar #'(lambda (x)
+                         (specifier-type `(not ,(type-specifier x))))
+                     (union-type-types not-type))))
+      ((member-type-p not-type)
+       (let ((members (member-type-members not-type)))
+        (if (some #'floatp members)
+            (let (floats)
+              (dolist (pair `((0.0f0 . ,(load-time-value (make-unportable-float :single-float-negative-zero)))
+                              (0.0d0 . ,(load-time-value (make-unportable-float :double-float-negative-zero)))
+                              #!+long-float
+                              (0.0l0 . ,(load-time-value (make-unportable-float :long-float-negative-zero)))))
+                (when (member (car pair) members)
+                  (aver (not (member (cdr pair) members)))
+                  (push (cdr pair) floats)
+                  (setf members (remove (car pair) members)))
+                (when (member (cdr pair) members)
+                  (aver (not (member (car pair) members)))
+                  (push (car pair) floats)
+                  (setf members (remove (cdr pair) members))))
+              (apply #'type-intersection
+                     (if (null members)
+                         *universal-type*
+                         (make-negation-type
+                          :type (make-member-type :members members)))
+                     (mapcar
+                      (lambda (x)
+                        (let ((type (ctype-of x)))
+                          (type-union
+                           (make-negation-type
+                            :type (modified-numeric-type type
+                                                         :low nil :high nil))
+                           (modified-numeric-type type
+                                                  :low nil :high (list x))
+                           (make-member-type :members (list x))
+                           (modified-numeric-type type
+                                                  :low (list x) :high nil))))
+                      floats)))
+            (make-negation-type :type not-type))))
+      ((and (cons-type-p not-type)
+           (eq (cons-type-car-type not-type) *universal-type*)
+           (eq (cons-type-cdr-type not-type) *universal-type*))
+       (make-negation-type :type not-type))
+      ((cons-type-p not-type)
+       (type-union
+       (make-negation-type :type (specifier-type 'cons))
+       (cond
+         ((and (not (eq (cons-type-car-type not-type) *universal-type*))
+               (not (eq (cons-type-cdr-type not-type) *universal-type*)))
+          (type-union
+           (make-cons-type
+            (specifier-type `(not ,(type-specifier
+                                    (cons-type-car-type not-type))))
+            *universal-type*)
+           (make-cons-type
+            *universal-type*
+            (specifier-type `(not ,(type-specifier
+                                    (cons-type-cdr-type not-type)))))))
+         ((not (eq (cons-type-car-type not-type) *universal-type*))
+          (make-cons-type
+           (specifier-type `(not ,(type-specifier
+                                   (cons-type-car-type not-type))))
+           *universal-type*))
+         ((not (eq (cons-type-cdr-type not-type) *universal-type*))
+          (make-cons-type
+           *universal-type*
+           (specifier-type `(not ,(type-specifier
+                                   (cons-type-cdr-type not-type))))))
+         (t (bug "Weird CONS type ~S" not-type)))))
+      (t (make-negation-type :type not-type)))))
+\f

 ;;;; numeric types
 
 (!define-type-class number)
 ;;;; numeric types
 
 (!define-type-class number)

@@ -1218,8 +1459,8 @@
    (and (eq (numeric-type-class type1) (numeric-type-class type2))
        (eq (numeric-type-format type1) (numeric-type-format type2))
        (eq (numeric-type-complexp type1) (numeric-type-complexp type2))
    (and (eq (numeric-type-class type1) (numeric-type-class type2))
        (eq (numeric-type-format type1) (numeric-type-format type2))
        (eq (numeric-type-complexp type1) (numeric-type-complexp type2))

-       (equal (numeric-type-low type1) (numeric-type-low type2))
-       (equal (numeric-type-high type1) (numeric-type-high type2)))
+       (equalp (numeric-type-low type1) (numeric-type-low type2))
+       (equalp (numeric-type-high type1) (numeric-type-high type2)))

    t))
 
 (!define-type-method (number :unparse) (type)
    t))
 
 (!define-type-method (number :unparse) (type)

@@ -1279,7 +1520,6 @@
 ;;;
 ;;; This is for comparing bounds of the same kind, e.g. upper and
 ;;; upper. Use NUMERIC-BOUND-TEST* for different kinds of bounds.
 ;;;
 ;;; This is for comparing bounds of the same kind, e.g. upper and
 ;;; upper. Use NUMERIC-BOUND-TEST* for different kinds of bounds.

-#!-negative-zero-is-not-zero

 (defmacro numeric-bound-test (x y closed open)
   `(cond ((not ,y) t)
         ((not ,x) nil)
 (defmacro numeric-bound-test (x y closed open)
   `(cond ((not ,y) t)
         ((not ,x) nil)

@@ -1292,32 +1532,12 @@
              (,open ,x (car ,y))
              (,closed ,x ,y)))))
 
              (,open ,x (car ,y))
              (,closed ,x ,y)))))
 

-#!+negative-zero-is-not-zero
-(defmacro numeric-bound-test-zero (op x y)
-  `(if (and (zerop ,x) (zerop ,y) (floatp ,x) (floatp ,y))
-       (,op (float-sign ,x) (float-sign ,y))
-       (,op ,x ,y)))
-
-#!+negative-zero-is-not-zero
-(defmacro numeric-bound-test (x y closed open)
-  `(cond ((not ,y) t)
-        ((not ,x) nil)
-        ((consp ,x)
-         (if (consp ,y)
-             (numeric-bound-test-zero ,closed (car ,x) (car ,y))
-             (numeric-bound-test-zero ,closed (car ,x) ,y)))
-        (t
-         (if (consp ,y)
-             (numeric-bound-test-zero ,open ,x (car ,y))
-             (numeric-bound-test-zero ,closed ,x ,y)))))
-

 ;;; This is used to compare upper and lower bounds. This is different
 ;;; from the same-bound case:
 ;;; -- Since X = NIL is -infinity, whereas y = NIL is +infinity, we
 ;;;    return true if *either* arg is NIL.
 ;;; -- an open inner bound is "greater" and also squeezes the interval,
 ;;;    causing us to use the OPEN test for those cases as well.
 ;;; This is used to compare upper and lower bounds. This is different
 ;;; from the same-bound case:
 ;;; -- Since X = NIL is -infinity, whereas y = NIL is +infinity, we
 ;;;    return true if *either* arg is NIL.
 ;;; -- an open inner bound is "greater" and also squeezes the interval,
 ;;;    causing us to use the OPEN test for those cases as well.

-#!-negative-zero-is-not-zero

 (defmacro numeric-bound-test* (x y closed open)
   `(cond ((not ,y) t)
         ((not ,x) t)
 (defmacro numeric-bound-test* (x y closed open)
   `(cond ((not ,y) t)
         ((not ,x) t)

@@ -1330,19 +1550,6 @@
              (,open ,x (car ,y))
              (,closed ,x ,y)))))
 
              (,open ,x (car ,y))
              (,closed ,x ,y)))))
 

-#!+negative-zero-is-not-zero
-(defmacro numeric-bound-test* (x y closed open)
-  `(cond ((not ,y) t)
-        ((not ,x) t)
-        ((consp ,x)
-         (if (consp ,y)
-             (numeric-bound-test-zero ,open (car ,x) (car ,y))
-             (numeric-bound-test-zero ,open (car ,x) ,y)))
-        (t
-         (if (consp ,y)
-             (numeric-bound-test-zero ,open ,x (car ,y))
-             (numeric-bound-test-zero ,closed ,x ,y)))))
-

 ;;; Return whichever of the numeric bounds X and Y is "maximal"
 ;;; according to the predicates CLOSED (e.g. >=) and OPEN (e.g. >).
 ;;; This is only meaningful for maximizing like bounds, i.e. upper and
 ;;; Return whichever of the numeric bounds X and Y is "maximal"
 ;;; according to the predicates CLOSED (e.g. >=) and OPEN (e.g. >).
 ;;; This is only meaningful for maximizing like bounds, i.e. upper and

@@ -1376,11 +1583,13 @@
                    (null complexp2)))
           (values nil t))
          ;; If the classes are specified and different, the types are
                    (null complexp2)))
           (values nil t))
          ;; If the classes are specified and different, the types are

-         ;; disjoint unless type2 is rational and type1 is integer.
+         ;; disjoint unless type2 is RATIONAL and type1 is INTEGER.
+         ;; [ or type1 is INTEGER and type2 is of the form (RATIONAL
+         ;; X X) for integral X, but this is dealt with in the
+         ;; canonicalization inside MAKE-NUMERIC-TYPE ]

          ((not (or (eq class1 class2)
                    (null class2)
          ((not (or (eq class1 class2)
                    (null class2)

-                   (and (eq class1 'integer)
-                        (eq class2 'rational))))
+                   (and (eq class1 'integer) (eq class2 'rational))))

           (values nil t))
          ;; If the float formats are specified and different, the types
          ;; are disjoint.
           (values nil t))
          ;; If the float formats are specified and different, the types
          ;; are disjoint.

@@ -1404,28 +1613,43 @@
     (cond ((not (and low-bound high-bound)) nil)
          ((and (consp low-bound) (consp high-bound)) nil)
          ((consp low-bound)
     (cond ((not (and low-bound high-bound)) nil)
          ((and (consp low-bound) (consp high-bound)) nil)
          ((consp low-bound)

-          #!-negative-zero-is-not-zero

           (let ((low-value (car low-bound)))
             (or (eql low-value high-bound)
           (let ((low-value (car low-bound)))
             (or (eql low-value high-bound)

-                (and (eql low-value -0f0) (eql high-bound 0f0))
-                (and (eql low-value 0f0) (eql high-bound -0f0))
-                (and (eql low-value -0d0) (eql high-bound 0d0))
-                (and (eql low-value 0d0) (eql high-bound -0d0))))
-          #!+negative-zero-is-not-zero
-          (eql (car low-bound) high-bound))
+                (and (eql low-value
+                          (load-time-value (make-unportable-float
+                                            :single-float-negative-zero)))
+                     (eql high-bound 0f0))
+                (and (eql low-value 0f0)
+                     (eql high-bound
+                          (load-time-value (make-unportable-float
+                                            :single-float-negative-zero))))
+                (and (eql low-value
+                          (load-time-value (make-unportable-float
+                                            :double-float-negative-zero)))
+                     (eql high-bound 0d0))
+                (and (eql low-value 0d0)
+                     (eql high-bound
+                          (load-time-value (make-unportable-float
+                                            :double-float-negative-zero)))))))

          ((consp high-bound)
          ((consp high-bound)

-          #!-negative-zero-is-not-zero

           (let ((high-value (car high-bound)))
             (or (eql high-value low-bound)
           (let ((high-value (car high-bound)))
             (or (eql high-value low-bound)

-                (and (eql high-value -0f0) (eql low-bound 0f0))
-                (and (eql high-value 0f0) (eql low-bound -0f0))
-                (and (eql high-value -0d0) (eql low-bound 0d0))
-                (and (eql high-value 0d0) (eql low-bound -0d0))))
-          #!+negative-zero-is-not-zero
-          (eql (car high-bound) low-bound))
-         #!+negative-zero-is-not-zero
-         ((or (and (eql low-bound -0f0) (eql high-bound 0f0))
-              (and (eql low-bound -0d0) (eql high-bound 0d0))))
+                (and (eql high-value
+                          (load-time-value (make-unportable-float
+                                            :single-float-negative-zero)))
+                     (eql low-bound 0f0))
+                (and (eql high-value 0f0)
+                     (eql low-bound
+                          (load-time-value (make-unportable-float
+                                            :single-float-negative-zero))))
+                (and (eql high-value
+                          (load-time-value (make-unportable-float
+                                            :double-float-negative-zero)))
+                     (eql low-bound 0d0))
+                (and (eql high-value 0d0)
+                     (eql low-bound
+                          (load-time-value (make-unportable-float
+                                            :double-float-negative-zero)))))))

          ((and (eq (numeric-type-class low) 'integer)
                (eq (numeric-type-class high) 'integer))
           (eql (1+ low-bound) high-bound))
          ((and (eq (numeric-type-class low) 'integer)
                (eq (numeric-type-class high) 'integer))
           (eql (1+ low-bound) high-bound))

@@ -1434,8 +1658,10 @@
 
 ;;; Return a numeric type that is a supertype for both TYPE1 and TYPE2.
 ;;;
 
 ;;; Return a numeric type that is a supertype for both TYPE1 and TYPE2.
 ;;;

-;;; ### Note: we give up early to keep from dropping lots of information on
-;;; the floor by returning overly general types.
+;;; Old comment, probably no longer applicable:
+;;;
+;;;   ### Note: we give up early to keep from dropping lots of
+;;;   information on the floor by returning overly general types.

 (!define-type-method (number :simple-union2) (type1 type2)
   (declare (type numeric-type type1 type2))
   (cond ((csubtypep type1 type2) type2)
 (!define-type-method (number :simple-union2) (type1 type2)
   (declare (type numeric-type type1 type2))
   (cond ((csubtypep type1 type2) type2)

@@ -1447,25 +1673,69 @@
               (class2 (numeric-type-class type2))
               (format2 (numeric-type-format type2))
               (complexp2 (numeric-type-complexp type2)))
               (class2 (numeric-type-class type2))
               (format2 (numeric-type-format type2))
               (complexp2 (numeric-type-complexp type2)))

-          (when (and (eq class1 class2)
-                     (eq format1 format2)
-                     (eq complexp1 complexp2)
-                     (or (numeric-types-intersect type1 type2)
-                         (numeric-types-adjacent type1 type2)
-                         (numeric-types-adjacent type2 type1)))
-            (make-numeric-type
-             :class class1
-             :format format1
-             :complexp complexp1
-             :low (numeric-bound-max (numeric-type-low type1)
-                                     (numeric-type-low type2)
-                                     <= < t)
-             :high (numeric-bound-max (numeric-type-high type1)
-                                      (numeric-type-high type2)
-                                      >= > t)))))))
+          (cond
+            ((and (eq class1 class2)
+                  (eq format1 format2)
+                  (eq complexp1 complexp2)
+                  (or (numeric-types-intersect type1 type2)
+                      (numeric-types-adjacent type1 type2)
+                      (numeric-types-adjacent type2 type1)))
+             (make-numeric-type
+              :class class1
+              :format format1
+              :complexp complexp1
+              :low (numeric-bound-max (numeric-type-low type1)
+                                      (numeric-type-low type2)
+                                      <= < t)
+              :high (numeric-bound-max (numeric-type-high type1)
+                                       (numeric-type-high type2)
+                                       >= > t)))
+            ;; FIXME: These two clauses are almost identical, and the
+            ;; consequents are in fact identical in every respect.
+            ((and (eq class1 'rational)
+                  (eq class2 'integer)
+                  (eq format1 format2)
+                  (eq complexp1 complexp2)
+                  (integerp (numeric-type-low type2))
+                  (integerp (numeric-type-high type2))
+                  (= (numeric-type-low type2) (numeric-type-high type2))
+                  (or (numeric-types-adjacent type1 type2)
+                      (numeric-types-adjacent type2 type1)))
+             (make-numeric-type
+              :class 'rational
+              :format format1
+              :complexp complexp1
+              :low (numeric-bound-max (numeric-type-low type1)
+                                      (numeric-type-low type2)
+                                      <= < t)
+              :high (numeric-bound-max (numeric-type-high type1)
+                                       (numeric-type-high type2)
+                                       >= > t)))
+            ((and (eq class1 'integer)
+                  (eq class2 'rational)
+                  (eq format1 format2)
+                  (eq complexp1 complexp2)
+                  (integerp (numeric-type-low type1))
+                  (integerp (numeric-type-high type1))
+                  (= (numeric-type-low type1) (numeric-type-high type1))
+                  (or (numeric-types-adjacent type1 type2)
+                      (numeric-types-adjacent type2 type1)))
+             (make-numeric-type
+              :class 'rational
+              :format format1
+              :complexp complexp1
+              :low (numeric-bound-max (numeric-type-low type1)
+                                      (numeric-type-low type2)
+                                      <= < t)
+              :high (numeric-bound-max (numeric-type-high type1)
+                                       (numeric-type-high type2)
+                                       >= > t)))
+            (t nil))))))
+

 
 (!cold-init-forms
 
 (!cold-init-forms

-  (setf (info :type :kind 'number) #+sb-xc-host :defined #-sb-xc-host :primitive)
+  (setf (info :type :kind 'number)
+       #+sb-xc-host :defined #-sb-xc-host :primitive)

   (setf (info :type :builtin 'number)
        (make-numeric-type :complexp nil)))
 
   (setf (info :type :builtin 'number)
        (make-numeric-type :complexp nil)))
 

@@ -1571,9 +1841,6 @@
         (h (canonicalized-bound high 'integer))
         (hb (if (consp h) (1- (car h)) h)))
     (if (and hb lb (< hb lb))
         (h (canonicalized-bound high 'integer))
         (hb (if (consp h) (1- (car h)) h)))
     (if (and hb lb (< hb lb))

-       ;; previously we threw an error here:
-       ;; (error "Lower bound ~S is greater than upper bound ~S." l h))
-       ;; but ANSI doesn't say anything about that, so:

        *empty-type*
       (make-numeric-type :class 'integer
                         :complexp :real
        *empty-type*
       (make-numeric-type :class 'integer
                         :complexp :real

@@ -1586,11 +1853,11 @@
      (let ((lb (canonicalized-bound low ',type))
           (hb (canonicalized-bound high ',type)))
        (if (not (numeric-bound-test* lb hb <= <))
      (let ((lb (canonicalized-bound low ',type))
           (hb (canonicalized-bound high ',type)))
        (if (not (numeric-bound-test* lb hb <= <))

-          ;; as above, previously we did
-          ;; (error "Lower bound ~S is not less than upper bound ~S." low high))
-          ;; but it is correct to do

           *empty-type*
           *empty-type*

-        (make-numeric-type :class ',class :format ',format :low lb :high hb)))))
+        (make-numeric-type :class ',class
+                           :format ',format
+                           :low lb
+                           :high hb)))))

 
 (!def-bounded-type rational rational nil)
 
 
 (!def-bounded-type rational rational nil)
 

@@ -2027,7 +2294,10 @@
                             (mapcar (lambda (x y) (if (eq x '*) y x))
                                     dims1 dims2)))
          :complexp (if (eq complexp1 :maybe) complexp2 complexp1)
                             (mapcar (lambda (x y) (if (eq x '*) y x))
                                     dims1 dims2)))
          :complexp (if (eq complexp1 :maybe) complexp2 complexp1)

-         :element-type (if (eq eltype1 *wild-type*) eltype2 eltype1))))
+         :element-type (cond
+                         ((eq eltype1 *wild-type*) eltype2)
+                         ((eq eltype2 *wild-type*) eltype1)
+                         (t (type-intersection eltype1 eltype2))))))

       *empty-type*))
 
 ;;; Check a supplied dimension list to determine whether it is legal,
       *empty-type*))
 
 ;;; Check a supplied dimension list to determine whether it is legal,

@@ -2095,7 +2365,7 @@
                 *empty-type*))))))
 
 (!define-type-method (member :complex-intersection2) (type1 type2)
                 *empty-type*))))))
 
 (!define-type-method (member :complex-intersection2) (type1 type2)

-  (block punt               
+  (block punt

     (collect ((members))
       (let ((mem2 (member-type-members type2)))
         (dolist (member mem2)
     (collect ((members))
       (let ((mem2 (member-type-members type2)))
         (dolist (member mem2)

@@ -2136,8 +2406,20 @@
 
 (!def-type-translator member (&rest members)
   (if members
 
 (!def-type-translator member (&rest members)
   (if members

-    (make-member-type :members (remove-duplicates members))
-    *empty-type*))
+      (let (ms numbers)
+       (dolist (m (remove-duplicates members))
+         (typecase m
+           (float (if (zerop m)
+                      (push m ms)
+                      (push (ctype-of m) numbers)))
+           (number (push (ctype-of m) numbers))
+           (t (push m ms))))
+       (apply #'type-union
+              (if ms
+                  (make-member-type :members ms)
+                  *empty-type*)
+              (nreverse numbers)))
+      *empty-type*))

 \f
 ;;;; intersection types
 ;;;;
 \f
 ;;;; intersection types
 ;;;;

@@ -2164,21 +2446,19 @@
 ;;; mechanically unparsed.
 (!define-type-method (intersection :unparse) (type)
   (declare (type ctype type))
 ;;; mechanically unparsed.
 (!define-type-method (intersection :unparse) (type)
   (declare (type ctype type))

-  (or (find type '(ratio bignum keyword) :key #'specifier-type :test #'type=)
+  (or (find type '(ratio keyword) :key #'specifier-type :test #'type=)

       `(and ,@(mapcar #'type-specifier (intersection-type-types type)))))
 
 ;;; shared machinery for type equality: true if every type in the set
 ;;; TYPES1 matches a type in the set TYPES2 and vice versa
 (defun type=-set (types1 types2)
       `(and ,@(mapcar #'type-specifier (intersection-type-types type)))))
 
 ;;; shared machinery for type equality: true if every type in the set
 ;;; TYPES1 matches a type in the set TYPES2 and vice versa
 (defun type=-set (types1 types2)

-  (flet (;; true if every type in the set X matches a type in the set Y
-        (type<=-set (x y)
+  (flet ((type<=-set (x y)

           (declare (type list x y))
           (declare (type list x y))

-          (every (lambda (xelement)
-                   (position xelement y :test #'type=))
-                 x)))
-    (values (and (type<=-set types1 types2)
-                (type<=-set types2 types1))
-           t)))
+          (every/type (lambda (x y-element)
+                         (any/type #'type= y-element x))
+                       x y)))
+    (and/type (type<=-set types1 types2)
+              (type<=-set types2 types1))))

 
 ;;; Two intersection types are equal if their subtypes are equal sets.
 ;;;
 
 ;;; Two intersection types are equal if their subtypes are equal sets.
 ;;;

@@ -2192,21 +2472,94 @@
             (intersection-type-types type2)))
 
 (defun %intersection-complex-subtypep-arg1 (type1 type2)
             (intersection-type-types type2)))
 
 (defun %intersection-complex-subtypep-arg1 (type1 type2)

-  (any/type (swapped-args-fun #'csubtypep)
-           type2
-           (intersection-type-types type1)))
+  (type= type1 (type-intersection type1 type2)))

 
 

-(!define-type-method (intersection :simple-subtypep) (type1 type2)
+(defun %intersection-simple-subtypep (type1 type2)

   (every/type #'%intersection-complex-subtypep-arg1
              type1
              (intersection-type-types type2)))
 
   (every/type #'%intersection-complex-subtypep-arg1
              type1
              (intersection-type-types type2)))
 

+(!define-type-method (intersection :simple-subtypep) (type1 type2)
+  (%intersection-simple-subtypep type1 type2))
+  

 (!define-type-method (intersection :complex-subtypep-arg1) (type1 type2)
   (%intersection-complex-subtypep-arg1 type1 type2))
 
 (!define-type-method (intersection :complex-subtypep-arg1) (type1 type2)
   (%intersection-complex-subtypep-arg1 type1 type2))
 

-(!define-type-method (intersection :complex-subtypep-arg2) (type1 type2)
+(defun %intersection-complex-subtypep-arg2 (type1 type2)

   (every/type #'csubtypep type1 (intersection-type-types type2)))
 
   (every/type #'csubtypep type1 (intersection-type-types type2)))
 

+(!define-type-method (intersection :complex-subtypep-arg2) (type1 type2)
+  (%intersection-complex-subtypep-arg2 type1 type2))
+
+;;; FIXME: This will look eeriely familiar to readers of the UNION
+;;; :SIMPLE-INTERSECTION2 :COMPLEX-INTERSECTION2 method.  That's
+;;; because it was generated by cut'n'paste methods.  Given that
+;;; intersections and unions have all sorts of symmetries known to
+;;; mathematics, it shouldn't be beyond the ken of some programmers to
+;;; reflect those symmetries in code in a way that ties them together
+;;; more strongly than having two independent near-copies :-/
+(!define-type-method (intersection :simple-union2 :complex-union2)
+                    (type1 type2)
+  ;; Within this method, type2 is guaranteed to be an intersection
+  ;; type:
+  (aver (intersection-type-p type2))
+  ;; Make sure to call only the applicable methods...
+  (cond ((and (intersection-type-p type1)
+             (%intersection-simple-subtypep type1 type2)) type2)
+       ((and (intersection-type-p type1)
+             (%intersection-simple-subtypep type2 type1)) type1)
+       ((and (not (intersection-type-p type1))
+             (%intersection-complex-subtypep-arg2 type1 type2))
+        type2)
+       ((and (not (intersection-type-p type1))
+             (%intersection-complex-subtypep-arg1 type2 type1))
+        type1)
+       ;; KLUDGE: This special (and somewhat hairy) magic is required
+       ;; to deal with the RATIONAL/INTEGER special case.  The UNION
+       ;; of (INTEGER * -1) and (AND (RATIONAL * -1/2) (NOT INTEGER))
+       ;; should be (RATIONAL * -1/2) -- CSR, 2003-02-28
+       ((and (csubtypep type2 (specifier-type 'ratio))
+             (numeric-type-p type1)
+             (csubtypep type1 (specifier-type 'integer))
+             (csubtypep type2
+                        (make-numeric-type
+                         :class 'rational
+                         :complexp nil
+                         :low (if (null (numeric-type-low type1))
+                                  nil
+                                  (list (1- (numeric-type-low type1))))
+                         :high (if (null (numeric-type-high type1))
+                                   nil
+                                   (list (1+ (numeric-type-high type1)))))))
+        (type-union type1
+                    (apply #'type-intersection
+                           (remove (specifier-type '(not integer))
+                                   (intersection-type-types type2)
+                                   :test #'type=))))
+       (t
+        (let ((accumulator *universal-type*))
+          (do ((t2s (intersection-type-types type2) (cdr t2s)))
+              ((null t2s) accumulator)
+            (let ((union (type-union type1 (car t2s))))
+              (when (union-type-p union)
+                ;; we have to give up here -- there are all sorts of
+                ;; ordering worries, but it's better than before.
+                ;; Doing exactly the same as in the UNION
+                ;; :SIMPLE/:COMPLEX-INTERSECTION2 method causes stack
+                ;; overflow with the mutual recursion never bottoming
+                ;; out.
+                (if (and (eq accumulator *universal-type*)
+                         (null (cdr t2s)))
+                    ;; KLUDGE: if we get here, we have a partially
+                    ;; simplified result.  While this isn't by any
+                    ;; means a universal simplification, including
+                    ;; this logic here means that we can get (OR
+                    ;; KEYWORD (NOT KEYWORD)) canonicalized to T.
+                    (return union)
+                    (return nil)))
+              (setf accumulator
+                    (type-intersection accumulator union))))))))
+

 (!def-type-translator and (&whole whole &rest type-specifiers)
   (apply #'type-intersection
         (mapcar #'specifier-type
 (!def-type-translator and (&whole whole &rest type-specifiers)
   (apply #'type-intersection
         (mapcar #'specifier-type

@@ -2225,7 +2578,7 @@
     ((type= type (specifier-type 'float)) 'float)
     ((type= type (specifier-type 'real)) 'real)
     ((type= type (specifier-type 'sequence)) 'sequence)
     ((type= type (specifier-type 'float)) 'float)
     ((type= type (specifier-type 'real)) 'real)
     ((type= type (specifier-type 'sequence)) 'sequence)

-    ((type= type (specifier-type 'string-stream)) 'string-stream)
+    ((type= type (specifier-type 'bignum)) 'bignum)

     (t `(or ,@(mapcar #'type-specifier (union-type-types type))))))
 
 ;;; Two union types are equal if they are each subtypes of each
     (t `(or ,@(mapcar #'type-specifier (union-type-types type))))))
 
 ;;; Two union types are equal if they are each subtypes of each

@@ -2253,7 +2606,8 @@
 
 (!define-type-method (union :complex-=) (type1 type2)
   (declare (ignore type1))
 
 (!define-type-method (union :complex-=) (type1 type2)
   (declare (ignore type1))

-  (if (some #'hairy-type-p (union-type-types type2))
+  (if (some #'type-might-contain-other-types-p 
+           (union-type-types type2))

       (values nil nil)
       (values nil t)))
 
       (values nil nil)
       (values nil t)))
 

@@ -2365,12 +2719,8 @@
         (let ((accumulator *empty-type*))
           (dolist (t2 (union-type-types type2) accumulator)
             (setf accumulator
         (let ((accumulator *empty-type*))
           (dolist (t2 (union-type-types type2) accumulator)
             (setf accumulator

-                  (type-union2 accumulator
-                               (type-intersection type1 t2)))
-            ;; When our result isn't simple any more (because
-            ;; TYPE-UNION2 was unable to give us a simple result)
-            (unless accumulator
-              (return nil)))))))
+                  (type-union accumulator
+                              (type-intersection type1 t2))))))))

 
 (!def-type-translator or (&rest type-specifiers)
   (apply #'type-union
 
 (!def-type-translator or (&rest type-specifiers)
   (apply #'type-union

@@ -2382,8 +2732,9 @@
 (!define-type-class cons)
 
 (!def-type-translator cons (&optional (car-type-spec '*) (cdr-type-spec '*))
 (!define-type-class cons)
 
 (!def-type-translator cons (&optional (car-type-spec '*) (cdr-type-spec '*))

-  (make-cons-type (specifier-type car-type-spec)
-                 (specifier-type cdr-type-spec)))
+  (let ((car-type (single-value-specifier-type car-type-spec))
+       (cdr-type (single-value-specifier-type cdr-type-spec)))
+    (make-cons-type car-type cdr-type)))

  
 (!define-type-method (cons :unparse) (type)
   (let ((car-eltype (type-specifier (cons-type-car-type type)))
  
 (!define-type-method (cons :unparse) (type)
   (let ((car-eltype (type-specifier (cons-type-car-type type)))

@@ -2416,13 +2767,35 @@
        (car-type2 (cons-type-car-type type2))
        (cdr-type1 (cons-type-cdr-type type1))
        (cdr-type2 (cons-type-cdr-type type2)))
        (car-type2 (cons-type-car-type type2))
        (cdr-type1 (cons-type-cdr-type type1))
        (cdr-type2 (cons-type-cdr-type type2)))

-    (cond ((type= car-type1 car-type2)
-          (make-cons-type car-type1
-                          (type-union cdr-type1 cdr-type2)))
-         ((type= cdr-type1 cdr-type2)
-          (make-cons-type (type-union cdr-type1 cdr-type2)
-                          cdr-type1)))))
-
+    ;; UGH.  -- CSR, 2003-02-24
+    (macrolet ((frob-car (car1 car2 cdr1 cdr2)
+                `(type-union
+                  (make-cons-type ,car1 (type-union ,cdr1 ,cdr2))
+                  (make-cons-type
+                   (type-intersection ,car2
+                    (specifier-type
+                     `(not ,(type-specifier ,car1))))
+                   ,cdr2))))
+      (cond ((type= car-type1 car-type2)
+            (make-cons-type car-type1
+                            (type-union cdr-type1 cdr-type2)))
+           ((type= cdr-type1 cdr-type2)
+            (make-cons-type (type-union car-type1 car-type2)
+                            cdr-type1))
+           ((csubtypep car-type1 car-type2)
+            (frob-car car-type1 car-type2 cdr-type1 cdr-type2))
+           ((csubtypep car-type2 car-type1)
+            (frob-car car-type2 car-type1 cdr-type2 cdr-type1))
+           ;; Don't put these in -- consider the effect of taking the
+           ;; union of (CONS (INTEGER 0 2) (INTEGER 5 7)) and
+           ;; (CONS (INTEGER 0 3) (INTEGER 5 6)).
+           #+nil
+           ((csubtypep cdr-type1 cdr-type2)
+            (frob-cdr car-type1 car-type2 cdr-type1 cdr-type2))
+           #+nil
+           ((csubtypep cdr-type2 cdr-type1)
+            (frob-cdr car-type2 car-type1 cdr-type2 cdr-type1))))))
+           

 (!define-type-method (cons :simple-intersection2) (type1 type2)
   (declare (type cons-type type1 type2))
   (let (car-int2
 (!define-type-method (cons :simple-intersection2) (type1 type2)
   (declare (type cons-type type1 type2))
   (let (car-int2

@@ -2485,14 +2858,19 @@
                                       (dimensions '*))
   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)
                                       (dimensions '*))
   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)

-                   :element-type (specifier-type element-type))))
+                    :complexp :maybe
+                   :element-type (if (eq element-type '*)
+                                      *wild-type*
+                                      (specifier-type element-type)))))

 
 (!def-type-translator simple-array (&optional (element-type '*)
                                              (dimensions '*))
   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)
 
 (!def-type-translator simple-array (&optional (element-type '*)
                                              (dimensions '*))
   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)

-                   :element-type (specifier-type element-type)
-                   :complexp nil)))
+                    :complexp nil
+                   :element-type (if (eq element-type '*)
+                                      *wild-type*
+                                      (specifier-type element-type)))))

 \f
 ;;;; utilities shared between cross-compiler and target system
 
 \f
 ;;;; utilities shared between cross-compiler and target system
 

@@ -2501,8 +2879,8 @@
 (defun defined-ftype-matches-declared-ftype-p (defined-ftype declared-ftype)
   (declare (type ctype defined-ftype declared-ftype))
   (flet ((is-built-in-class-function-p (ctype)
 (defun defined-ftype-matches-declared-ftype-p (defined-ftype declared-ftype)
   (declare (type ctype defined-ftype declared-ftype))
   (flet ((is-built-in-class-function-p (ctype)

-          (and (built-in-class-p ctype)
-               (eq (built-in-class-%name ctype) 'function))))
+          (and (built-in-classoid-p ctype)
+               (eq (built-in-classoid-name ctype) 'function))))

     (cond (;; DECLARED-FTYPE could certainly be #<BUILT-IN-CLASS FUNCTION>;
           ;; that's what happens when we (DECLAIM (FTYPE FUNCTION FOO)).
           (is-built-in-class-function-p declared-ftype)
     (cond (;; DECLARED-FTYPE could certainly be #<BUILT-IN-CLASS FUNCTION>;
           ;; that's what happens when we (DECLAIM (FTYPE FUNCTION FOO)).
           (is-built-in-class-function-p declared-ftype)