;;;; This software is part of the SBCL system. See the README file for
;;;; more information.
;;;;
;;;; This software is derived from the CMU CL system, which was
;;;; written at Carnegie Mellon University and released into the
;;;; public domain. The software is in the public domain and is
;;;; provided with absolutely no warranty. See the COPYING and CREDITS
;;;; files for more information.

(in-package "SB!KERNEL")

(!begin-collecting-cold-init-forms)

;;;; representations of types

;;; A HAIRY-TYPE represents anything too weird to be described
;;; reasonably or to be useful, such as NOT, SATISFIES, unknown types,
;;; and unreasonably complicated types involving AND. We just remember
;;; the original type spec.
(defstruct (hairy-type (:include ctype
                                 (class-info (type-class-or-lose 'hairy))
                                 (enumerable t)
                                 (might-contain-other-types-p t))
                       (:copier nil)
                       #!+cmu (:pure nil))
  ;; the Common Lisp type-specifier of the type we represent
  (specifier nil :type t))

(!define-type-class hairy)

;;; An UNKNOWN-TYPE is a type not known to the type system (not yet
;;; defined). We make this distinction since we don't want to complain
;;; about types that are hairy but defined.
(defstruct (unknown-type (:include hairy-type)
                         (:copier nil)))

(defun maybe-reparse-specifier (type)
  (when (unknown-type-p type)
    (let* ((spec (unknown-type-specifier type))
           (name (if (consp spec)
                     (car spec)
                     spec)))
      (when (info :type :kind name)
        (let ((new-type (specifier-type spec)))
          (unless (unknown-type-p new-type)
            new-type))))))

;;; Evil macro.
(defmacro maybe-reparse-specifier! (type)
  (assert (symbolp type))
  (with-unique-names (new-type)
    `(let ((,new-type (maybe-reparse-specifier ,type)))
       (when ,new-type
         (setf ,type ,new-type)
         t))))

(defstruct (negation-type (:include ctype
                                    (class-info (type-class-or-lose 'negation))
                                    ;; FIXME: is this right?  It's
                                    ;; what they had before, anyway
                                    (enumerable t)
                                    (might-contain-other-types-p t))
                          (:copier nil)
                          #!+cmu (:pure nil))
  (type (missing-arg) :type ctype))

(!define-type-class negation)

;;; ARGS-TYPE objects are used both to represent VALUES types and
;;; to represent FUNCTION types.
(defstruct (args-type (:include ctype)
                      (:constructor nil)
                      (:copier nil))
  ;; Lists of the type for each required and optional argument.
  (required nil :type list)
  (optional nil :type list)
  ;; The type for the rest arg. NIL if there is no &REST arg.
  (rest nil :type (or ctype null))
  ;; true if &KEY arguments are specified
  (keyp nil :type boolean)
  ;; list of KEY-INFO structures describing the &KEY arguments
  (keywords nil :type list)
  ;; true if other &KEY arguments are allowed
  (allowp nil :type boolean))

(defun canonicalize-args-type-args (required optional rest &optional keyp)
  (when (eq rest *empty-type*)
    ;; or vice-versa?
    (setq rest nil))
  (loop with last-not-rest = nil
        for i from 0
        for opt in optional
        do (cond ((eq opt *empty-type*)
                  (return (values required (subseq optional i) rest)))
                 ((and (not keyp) (neq opt rest))
                  (setq last-not-rest i)))
        finally (return (values required
                                (cond (keyp
                                       optional)
                                      (last-not-rest
                                       (subseq optional 0 (1+ last-not-rest))))
                                rest))))

(defun parse-args-types (lambda-list-like-thing)
  (multiple-value-bind
        (required optional restp rest keyp keys allowp auxp aux
                  morep more-context more-count llk-p)
      (parse-lambda-list-like-thing lambda-list-like-thing :silent t)
    (declare (ignore aux morep more-context more-count))
    (when auxp
      (error "&AUX in a FUNCTION or VALUES type: ~S." lambda-list-like-thing))
    (let ((required (mapcar #'single-value-specifier-type required))
          (optional (mapcar #'single-value-specifier-type optional))
          (rest (when restp (single-value-specifier-type rest)))
          (keywords
           (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-like-thing))
                 (key-info
                  (make-key-info
                   :name kwd
                   :type (single-value-specifier-type (second key))))))
             (key-info))))
      (multiple-value-bind (required optional rest)
          (canonicalize-args-type-args required optional rest keyp)
        (values required optional rest keyp keywords allowp llk-p)))))

(defstruct (values-type
            (:include args-type
                      (class-info (type-class-or-lose 'values)))
            (:constructor %make-values-type)
            (:predicate %values-type-p)
            (:copier nil)))

(declaim (inline value-type-p))
(defun values-type-p (x)
  (or (eq x *wild-type*)
      (%values-type-p x)))

(defun-cached (make-values-type-cached
               :hash-bits 8
               :hash-function
               (lambda (req opt rest allowp)
                 (logand (logxor
                          (type-list-cache-hash req)
                          (type-list-cache-hash opt)
                          (if rest
                              (type-hash-value rest)
                              42)
                          ;; Results (logand #xFF (sxhash t/nil))
                          ;; hardcoded to avoid relying on the xc host.
                          (if allowp
                              194
                              11))
                         #xFF)))
    ((required equal-but-no-car-recursion)
     (optional equal-but-no-car-recursion)
     (rest eq)
     (allowp eq))
  (%make-values-type :required required
                     :optional optional
                     :rest rest
                     :allowp allowp))

(defun make-values-type (&key required optional rest allowp)
  (multiple-value-bind (required optional rest)
      (canonicalize-args-type-args required optional rest)
    (cond ((and (null required)
                (null optional)
                (eq rest *universal-type*))
           *wild-type*)
          ((memq *empty-type* required)
           *empty-type*)
          (t (make-values-type-cached required optional
                                      rest allowp)))))

(!define-type-class values)

;;; (SPECIFIER-TYPE 'FUNCTION) and its subtypes
(defstruct (fun-type (:include args-type
                               (class-info (type-class-or-lose 'function)))
                     (:constructor
                      make-fun-type (&key required optional rest
                                          keyp keywords allowp
                                          wild-args
                                          returns
                                     &aux (rest (if (eq rest *empty-type*)
                                                    nil
                                                    rest)))))
  ;; true if the arguments are unrestrictive, i.e. *
  (wild-args nil :type boolean)
  ;; type describing the return values. This is a values type
  ;; when multiple values were specified for the return.
  (returns (missing-arg) :type ctype))

;;; The CONSTANT-TYPE structure represents a use of the CONSTANT-ARG
;;; "type specifier", which is only meaningful in function argument
;;; type specifiers used within the compiler. (It represents something
;;; that the compiler knows to be a constant.)
(defstruct (constant-type
            (:include ctype
                      (class-info (type-class-or-lose 'constant)))
            (:copier nil))
  ;; The type which the argument must be a constant instance of for this type
  ;; specifier to win.
  (type (missing-arg) :type ctype))

;;; The NAMED-TYPE is used to represent *, T and NIL, the standard
;;; special cases, as well as other special cases needed to
;;; interpolate between regions of the type hierarchy, such as
;;; INSTANCE (which corresponds to all those classes with slots which
;;; are not funcallable), FUNCALLABLE-INSTANCE (those classes with
;;; slots which are funcallable) and EXTENDED-SEQUUENCE (non-LIST
;;; non-VECTOR classes which are also sequences).  These special cases
;;; are the ones that aren't really discussed by Baker in his
;;; "Decision Procedure for SUBTYPEP" paper.
(defstruct (named-type (:include ctype
                                 (class-info (type-class-or-lose 'named)))
                       (:copier nil))
  (name nil :type symbol))

;;; a list of all the float "formats" (i.e. internal representations;
;;; nothing to do with #'FORMAT), in order of decreasing precision
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter *float-formats*
    '(long-float double-float single-float short-float)))

;;; The type of a float format.
(deftype float-format () `(member ,@*float-formats*))

;;; A NUMERIC-TYPE represents any numeric type, including things
;;; such as FIXNUM.
(defstruct (numeric-type (:include ctype
                                   (class-info (type-class-or-lose 'number)))
                         (:constructor %make-numeric-type)
                         (:copier nil))
  ;; the kind of numeric type we have, or NIL if not specified (just
  ;; NUMBER or COMPLEX)
  ;;
  ;; KLUDGE: A slot named CLASS for a non-CLASS value is bad.
  ;; Especially when a CLASS value *is* stored in another slot (called
  ;; CLASS-INFO:-). Perhaps this should be called CLASS-NAME? Also
  ;; weird that comment above says "Numeric-Type is used to represent
  ;; all numeric types" but this slot doesn't allow COMPLEX as an
  ;; option.. how does this fall into "not specified" NIL case above?
  ;; Perhaps someday we can switch to CLOS and make NUMERIC-TYPE
  ;; be an abstract base class and INTEGER-TYPE, RATIONAL-TYPE, and
  ;; whatnot be concrete subclasses..
  (class nil :type (member integer rational float nil) :read-only t)
  ;; "format" for a float type (i.e. type specifier for a CPU
  ;; representation of floating point, e.g. 'SINGLE-FLOAT -- nothing
  ;; to do with #'FORMAT), or NIL if not specified or not a float.
  ;; Formats which don't exist in a given implementation don't appear
  ;; here.
  (format nil :type (or float-format null) :read-only t)
  ;; Is this a complex numeric type?  Null if unknown (only in NUMBER).
  ;;
  ;; FIXME: I'm bewildered by FOO-P names for things not intended to
  ;; interpreted as truth values. Perhaps rename this COMPLEXNESS?
  (complexp :real :type (member :real :complex nil) :read-only t)
  ;; The upper and lower bounds on the value, or NIL if there is no
  ;; bound. If a list of a number, the bound is exclusive. Integer
  ;; types never have exclusive bounds, i.e. they may have them on
  ;; input, but they're canonicalized to inclusive bounds before we
  ;; store them here.
  (low nil :type (or number cons null) :read-only t)
  (high nil :type (or number cons null) :read-only t))

;;; Impose canonicalization rules for NUMERIC-TYPE. Note that in some
;;; cases, despite the name, we return *EMPTY-TYPE* instead of a
;;; NUMERIC-TYPE.
(defun make-numeric-type (&key class format (complexp :real) low high
                               enumerable)
  ;; if interval is empty
  (if (and low
           high
           (if (or (consp low) (consp high)) ; if either bound is exclusive
               (>= (type-bound-number low) (type-bound-number high))
               (> low high)))
      *empty-type*
      (multiple-value-bind (canonical-low canonical-high)
          (case class
            (integer
             ;; INTEGER types always have their LOW and HIGH bounds
             ;; represented as inclusive, not exclusive values.
             (values (if (consp low)
                         (1+ (type-bound-number low))
                         low)
                     (if (consp high)
                         (1- (type-bound-number high))
                         high)))
            (t
             ;; no canonicalization necessary
             (values low high)))
        (when (and (eq class 'rational)
                   (integerp canonical-low)
                   (integerp canonical-high)
                   (= canonical-low canonical-high))
          (setf class 'integer))
        (%make-numeric-type :class class
                            :format format
                            :complexp complexp
                            :low canonical-low
                            :high canonical-high
                            :enumerable enumerable))))

(defun modified-numeric-type (base
                              &key
                              (class      (numeric-type-class      base))
                              (format     (numeric-type-format     base))
                              (complexp   (numeric-type-complexp   base))
                              (low        (numeric-type-low        base))
                              (high       (numeric-type-high       base))
                              (enumerable (numeric-type-enumerable base)))
  (make-numeric-type :class class
                     :format format
                     :complexp complexp
                     :low low
                     :high high
                     :enumerable enumerable))

(defstruct (character-set-type
            (:include ctype
                      (class-info (type-class-or-lose 'character-set)))
            (:constructor %make-character-set-type)
            (:copier nil))
  (pairs (missing-arg) :type list :read-only t))
(defun make-character-set-type (&key pairs)
  ; (aver (equal (mapcar #'car pairs)
  ;              (sort (mapcar #'car pairs) #'<)))
  ;; aver that the cars of the list elements are sorted into increasing order
  (aver (or (null pairs)
            (do ((p pairs (cdr p)))
                ((null (cdr p)) t)
              (when (> (caar p) (caadr p)) (return nil)))))
  (let ((pairs (let (result)
                (do ((pairs pairs (cdr pairs)))
                    ((null pairs) (nreverse result))
                  (destructuring-bind (low . high) (car pairs)
                    (loop for (low1 . high1) in (cdr pairs)
                          if (<= low1 (1+ high))
                          do (progn (setf high (max high high1))
                                    (setf pairs (cdr pairs)))
                          else do (return nil))
                    (cond
                      ((>= low sb!xc:char-code-limit))
                      ((< high 0))
                      (t (push (cons (max 0 low)
                                     (min high (1- sb!xc:char-code-limit)))
                               result))))))))
    (if (null pairs)
       *empty-type*
       (%make-character-set-type :pairs pairs))))

;;; An ARRAY-TYPE is used to represent any array type, including
;;; things such as SIMPLE-BASE-STRING.
(defstruct (array-type (:include ctype
                                 (class-info (type-class-or-lose 'array)))
                       (:constructor %make-array-type)
                       (:copier nil))
  ;; the dimensions of the array, or * if unspecified. If a dimension
  ;; is unspecified, it is *.
  (dimensions '* :type (or list (member *)))
  ;; Is this not a simple array type? (:MAYBE means that we don't know.)
  (complexp :maybe :type (member t nil :maybe))
  ;; the element type as originally specified
  (element-type (missing-arg) :type ctype)
  ;; the element type as it is specialized in this implementation
  (specialized-element-type *wild-type* :type ctype))
(define-cached-synonym make-array-type)

;;; A MEMBER-TYPE represent a use of the MEMBER type specifier. We
;;; bother with this at this level because MEMBER types are fairly
;;; important and union and intersection are well defined.
(defstruct (member-type (:include ctype
                                  (class-info (type-class-or-lose 'member))
                                  (enumerable t))
                        (:copier nil)
                        (:constructor %make-member-type (xset fp-zeroes))
                        #-sb-xc-host (:pure nil))
  (xset (missing-arg) :type xset)
  (fp-zeroes (missing-arg) :type list))
(defun make-member-type (&key xset fp-zeroes members)
  (unless xset
    (aver (not fp-zeroes))
    (setf xset (alloc-xset))
    (dolist (elt members)
      (if (fp-zero-p elt)
          (pushnew elt fp-zeroes)
          (add-to-xset elt xset))))
  ;; if we have a pair of zeros (e.g. 0.0d0 and -0.0d0), then we can
  ;; canonicalize to (DOUBLE-FLOAT 0.0d0 0.0d0), because numeric
  ;; ranges are compared by arithmetic operators (while MEMBERship is
  ;; compared by EQL).  -- CSR, 2003-04-23
  (let ((unpaired nil)
        (union-types nil))
    (do ((tail (cdr fp-zeroes) (cdr tail))
         (zero (car fp-zeroes) (car tail)))
        ((not zero))
      (macrolet ((frob (c)
                   `(let ((neg (neg-fp-zero zero)))
                      (if (member neg tail)
                          (push (ctype-of ,c) union-types)
                          (push zero unpaired)))))
        (etypecase zero
          (single-float (frob 0.0f0))
          (double-float (frob 0.0d0))
          #!+long-float
          (long-float (frob 0.0l0)))))
    ;; The actual member-type contains the XSET (with no FP zeroes),
    ;; and a list of unpaired zeroes.
    (let ((member-type (unless (and (xset-empty-p xset) (not unpaired))
                         (%make-member-type xset unpaired))))
      (cond (union-types
             (make-union-type t (if member-type
                                    (cons member-type union-types)
                                    union-types)))
            (member-type
             member-type)
            (t
             *empty-type*)))))

(defun member-type-size (type)
  (+ (length (member-type-fp-zeroes type))
     (xset-count (member-type-xset type))))

(defun member-type-member-p (x type)
  (if (fp-zero-p x)
      (and (member x (member-type-fp-zeroes type)) t)
      (xset-member-p x (member-type-xset type))))

(defun mapcar-member-type-members (function type)
  (declare (function function))
  (collect ((results))
    (map-xset (lambda (x)
                (results (funcall function x)))
              (member-type-xset type))
    (dolist (zero (member-type-fp-zeroes type))
      (results (funcall function zero)))
    (results)))

(defun mapc-member-type-members (function type)
  (declare (function function))
  (map-xset function (member-type-xset type))
  (dolist (zero (member-type-fp-zeroes type))
    (funcall function zero)))

(defun member-type-members (type)
  (append (member-type-fp-zeroes type)
          (xset-members (member-type-xset type))))

;;; A COMPOUND-TYPE is a type defined out of a set of types, the
;;; common parent of UNION-TYPE and INTERSECTION-TYPE.
(defstruct (compound-type (:include ctype
                                    (might-contain-other-types-p t))
                          (:constructor nil)
                          (:copier nil))
  (types nil :type list :read-only t))

;;; A UNION-TYPE represents a use of the OR type specifier which we
;;; couldn't canonicalize to something simpler. Canonical form:
;;;   1. All possible pairwise simplifications (using the UNION2 type
;;;      methods) have been performed. Thus e.g. there is never more
;;;      than one MEMBER-TYPE component. FIXME: As of sbcl-0.6.11.13,
;;;      this hadn't been fully implemented yet.
;;;   2. There are never any UNION-TYPE components.
(defstruct (union-type (:include compound-type
                                 (class-info (type-class-or-lose 'union)))
                       (:constructor %make-union-type (enumerable types))
                       (:copier nil)))
(define-cached-synonym make-union-type)

;;; An INTERSECTION-TYPE represents a use of the AND type specifier
;;; which we couldn't canonicalize to something simpler. Canonical form:
;;;   1. All possible pairwise simplifications (using the INTERSECTION2
;;;      type methods) have been performed. Thus e.g. there is never more
;;;      than one MEMBER-TYPE component.
;;;   2. There are never any INTERSECTION-TYPE components: we've
;;;      flattened everything into a single INTERSECTION-TYPE object.
;;;   3. There are never any UNION-TYPE components. Either we should
;;;      use the distributive rule to rearrange things so that
;;;      unions contain intersections and not vice versa, or we
;;;      should just punt to using a HAIRY-TYPE.
(defstruct (intersection-type (:include compound-type
                                        (class-info (type-class-or-lose
                                                     'intersection)))
                              (:constructor %make-intersection-type
                                            (enumerable types))
                              (:copier nil)))

;;; Return TYPE converted to canonical form for a situation where the
;;; "type" '* (which SBCL still represents as a type even though ANSI
;;; CL defines it as a related but different kind of placeholder) is
;;; equivalent to type T.
(defun type-*-to-t (type)
  (if (type= type *wild-type*)
      *universal-type*
      type))

;;; A CONS-TYPE is used to represent a CONS type.
(defstruct (cons-type (:include ctype (class-info (type-class-or-lose 'cons)))
                      (:constructor
                       %make-cons-type (car-type
                                        cdr-type))
                      (:copier nil))
  ;; the CAR and CDR element types (to support ANSI (CONS FOO BAR) types)
  ;;
  ;; FIXME: Most or all other type structure slots could also be :READ-ONLY.
  (car-type (missing-arg) :type ctype :read-only t)
  (cdr-type (missing-arg) :type ctype :read-only t))
(defun make-cons-type (car-type cdr-type)
  (aver (not (or (eq car-type *wild-type*)
                 (eq cdr-type *wild-type*))))
  (if (or (eq car-type *empty-type*)
          (eq cdr-type *empty-type*))
      *empty-type*
      (%make-cons-type car-type cdr-type)))

(defun cons-type-length-info (type)
  (declare (type cons-type type))
  (do ((min 1 (1+ min))
       (cdr (cons-type-cdr-type type) (cons-type-cdr-type cdr)))
      ((not (cons-type-p cdr))
       (cond
         ((csubtypep cdr (specifier-type 'null))
          (values min t))
         ((csubtypep *universal-type* cdr)
          (values min nil))
         ((type/= (type-intersection (specifier-type 'cons) cdr) *empty-type*)
          (values min nil))
         ((type/= (type-intersection (specifier-type 'null) cdr) *empty-type*)
          (values min t))
         (t (values min :maybe))))
    ()))

;;; A SIMD-PACK-TYPE is used to represent a SIMD-PACK type.
#!+sb-simd-pack
(defstruct (simd-pack-type
            (:include ctype (class-info (type-class-or-lose 'simd-pack)))
            (:constructor %make-simd-pack-type (element-type))
            (:copier nil))
  (element-type (missing-arg)
   :type (cons #||(member #.*simd-pack-element-types*) ||#)
   :read-only t))

#!+sb-simd-pack
(defun make-simd-pack-type (element-type)
  (aver (neq element-type *wild-type*))
  (if (eq element-type *empty-type*)
      *empty-type*
      (%make-simd-pack-type
       (dolist (pack-type *simd-pack-element-types*
                          (error "~S element type must be a subtype of ~
                                     ~{~S~#[~;, or ~:;, ~]~}."
                                 'simd-pack *simd-pack-element-types*))
         (when (csubtypep element-type (specifier-type pack-type))
           (return (list pack-type)))))))


;;;; type utilities

;;; Return the type structure corresponding to a type specifier. We
;;; pick off structure types as a special case.
;;;
;;; Note: VALUES-SPECIFIER-TYPE-CACHE-CLEAR must be called whenever a
;;; type is defined (or redefined).
(defun-cached (values-specifier-type
               :hash-function (lambda (x)
                                (logand (sxhash x) #x3FF))
               :hash-bits 10
               :init-wrapper !cold-init-forms)
              ((orig equal-but-no-car-recursion))
  (let ((u (uncross orig)))
    (or (info :type :builtin u)
        (let ((spec (typexpand u)))
          (cond
           ((and (not (eq spec u))
                 (info :type :builtin spec)))
           ((and (consp spec) (symbolp (car spec))
                 (info :type :builtin (car spec))
                 (let ((expander (info :type :expander (car spec))))
                   (and expander (values-specifier-type (funcall expander spec))))))
           ((eq (info :type :kind spec) :instance)
            (find-classoid spec))
           ((typep spec 'classoid)
            (if (typep spec 'built-in-classoid)
                (or (built-in-classoid-translation spec) spec)
                spec))
           (t
            (when (and (atom spec)
                       (member spec '(and or not member eql satisfies values)))
              (error "The symbol ~S is not valid as a type specifier." spec))
            (let ((fun (info :type :translator (if (consp spec) (car spec) spec))))
              (cond (fun
                     (funcall fun (if (atom spec) (list spec) spec)))
                    ((or (and (consp spec) (symbolp (car spec))
                              (not (info :type :builtin (car spec))))
                         (and (symbolp spec) (not (info :type :builtin spec))))
                     (when (and *type-system-initialized*
                                (not (eq (info :type :kind spec)
                                         :forthcoming-defclass-type)))
                       (signal 'parse-unknown-type :specifier spec))
                     ;; (The RETURN-FROM here inhibits caching; this
                     ;; does not only make sense from a compiler
                     ;; diagnostics point of view but is also
                     ;; indispensable for proper workingness of
                     ;; VALID-TYPE-SPECIFIER-P.)
                     (return-from values-specifier-type
                       (make-unknown-type :specifier spec)))
                    (t
                     (error "bad thing to be a type specifier: ~S"
                            spec))))))))))

;;; This is like VALUES-SPECIFIER-TYPE, except that we guarantee to
;;; never return a VALUES type.
(defun specifier-type (x)
  (let ((res (values-specifier-type x)))
    (when (or (values-type-p res)
              ;; bootstrap magic :-(
              (and (named-type-p res)
                   (eq (named-type-name res) '*)))
      (error "VALUES type illegal in this context:~%  ~S" x))
    res))

(defun single-value-specifier-type (x)
  (if (eq x '*)
      *universal-type*
      (specifier-type x)))

(defun typexpand-1 (type-specifier &optional env)
  #!+sb-doc
  "Takes and expands a type specifier once like MACROEXPAND-1.
Returns two values: the expansion, and a boolean that is true when
expansion happened."
  (declare (type type-specifier type-specifier))
  (declare (ignore env))
  (multiple-value-bind (expander lspec)
      (let ((spec type-specifier))
        (cond ((and (symbolp spec) (info :type :builtin spec))
               ;; We do not expand builtins even though it'd be
               ;; possible to do so sometimes (e.g. STRING) for two
               ;; reasons:
               ;;
               ;; a) From a user's point of view, CL types are opaque.
               ;;
               ;; b) so (EQUAL (TYPEXPAND 'STRING) (TYPEXPAND-ALL 'STRING))
               (values nil nil))
              ((symbolp spec)
               (values (info :type :expander spec) spec))
              ((and (consp spec) (symbolp (car spec)) (info :type :builtin (car spec)))
               ;; see above
               (values nil nil))
              ((and (consp spec) (symbolp (car spec)))
               (values (info :type :expander (car spec)) spec))
              (t nil)))
    (if expander
        (values (funcall expander (if (symbolp lspec)
                                      (list lspec)
                                      lspec))
                t)
        (values type-specifier nil))))

(defun typexpand (type-specifier &optional env)
  #!+sb-doc
  "Takes and expands a type specifier repeatedly like MACROEXPAND.
Returns two values: the expansion, and a boolean that is true when
expansion happened."
  (declare (type type-specifier type-specifier))
  (multiple-value-bind (expansion flag)
      (typexpand-1 type-specifier env)
    (if flag
        (values (typexpand expansion env) t)
        (values expansion flag))))

(defun typexpand-all (type-specifier &optional env)
  #!+sb-doc
  "Takes and expands a type specifier recursively like MACROEXPAND-ALL."
  (declare (type type-specifier type-specifier))
  (declare (ignore env))
  ;; I first thought this would not be a good implementation because
  ;; it signals an error on e.g. (CONS 1 2) until I realized that
  ;; walking and calling TYPEXPAND would also result in errors, and
  ;; it actually makes sense.
  ;;
  ;; There's still a small problem in that
  ;;   (TYPEXPAND-ALL '(CONS * FIXNUM)) => (CONS T FIXNUM)
  ;; whereas walking+typexpand would result in (CONS * FIXNUM).
  ;;
  ;; Similiarly, (TYPEXPAND-ALL '(FUNCTION (&REST T) *)) => FUNCTION.
  (type-specifier (values-specifier-type type-specifier)))

(defun defined-type-name-p (name &optional env)
  #!+sb-doc
  "Returns T if NAME is known to name a type specifier, otherwise NIL."
  (declare (symbol name))
  (declare (ignore env))
  (and (info :type :kind name) t))

(defun valid-type-specifier-p (type-specifier &optional env)
  #!+sb-doc
  "Returns T if TYPE-SPECIFIER is a valid type specifier, otherwise NIL.

There may be different metrics on what constitutes a \"valid type
specifier\" depending on context. If this function does not suit your
exact need, you may be able to craft a particular solution using a
combination of DEFINED-TYPE-NAME-P and the TYPEXPAND functions.

The definition of \"valid type specifier\" employed by this function
is based on the following mnemonic:

          \"Would TYPEP accept it as second argument?\"

Except that unlike TYPEP, this function fully supports compound
FUNCTION type specifiers, and the VALUES type specifier, too.

In particular, VALID-TYPE-SPECIFIER-P will return NIL if
TYPE-SPECIFIER is not a class, not a symbol that is known to name a
type specifier, and not a cons that represents a known compound type
specifier in a syntactically and recursively correct way.

Examples:

  (valid-type-specifier-p '(cons * *))     => T
  (valid-type-specifier-p '#:foo)          => NIL
  (valid-type-specifier-p '(cons * #:foo)) => NIL
  (valid-type-specifier-p '(cons 1 *)      => NIL

Experimental."
  (declare (ignore env))
  (handler-case (prog1 t (values-specifier-type type-specifier))
    (parse-unknown-type () nil)
    (error () nil)))

;;; Note that the type NAME has been (re)defined, updating the
;;; undefined warnings and VALUES-SPECIFIER-TYPE cache.
(defun %note-type-defined (name)
  (declare (symbol name))
  (note-name-defined name :type)
  (values-specifier-type-cache-clear)
  (values))


(!defun-from-collected-cold-init-forms !early-type-cold-init)