diff --git a/read.scm b/read.scm
index 1007c00..fb60fdf 100644
--- a/read.scm
+++ b/read.scm
@@ -54,6 +54,16 @@
     (lambda ()
       (read-char port))))
 
+(define string->read-function
+  (lambda (str)
+    (let ((i -1)
+          (length (string-length str)))
+      (lambda ()
+        (set! i (+ i 1))
+        (if (>= i length)
+            #f
+            (string-ref str i))))))
+
 ;;; READ:
 ;;; 
 ;;; Stream readers contain mutable state. This is the case-folding mode
@@ -67,9 +77,13 @@
 ;;; (FOLD-CASE?): Returns a boolean if case folding is enabled.
 ;;; (FOLD-CASE! BOOL): Sets the case folding to BOOL.
 (define port->read
-  (lambda (read-function filename)
-    (let ((line-number 1)
-          (offset 0)
+  (lambda (read-function filename . location)
+    (let ((line-number (if (null? location)
+                           1
+                           (car location)))
+          (offset (if (null? location)
+                      0
+                      (cadr location)))
           (pushback-buffer '())
           (datum-labels '())
           (fold-case? #f))
@@ -141,6 +155,11 @@
                     (else (error 'read->port 'invalid (cons op args)))))))
         port))))
 
+(define ident->read
+  (lambda (location ident)
+    (apply port->read (string->read-function (ident 'value))
+           location)))
+
 ;;; ;;;;;;;;;;;;;;
 ;;; Character maps
 ;;; ;;;;;;;;;;;;;;
@@ -180,6 +199,7 @@
 ;;; An "action" is a procedure that takes four arguments:
 ;;; 
 ;;; TABLE: The current table.
+
 ;;; CHAR: The character that was matched against the CHARMAP in TABLE.
 ;;; ACC: An arbitrary "accumulator" value that is different depending
 ;;; on the readtable in question.
@@ -210,18 +230,16 @@
 
 ;;; Return a new readtable where CHAR is bound to ACTION.
 (define readtable:update
-  (lambda (table char action)
-    (readtable:new (%readtable:default-action table)
-                   (car (charmap:insert
-                         (%readtable:charmap table) char action)))))
-
-;;; Update TABLE to act on all characters in LST with ACTION.
-(define readtable:update-list
-  (lambda (table lst action)
-    (fold (lambda (char table)
-            (readtable:update table char action))
-          table
-          lst)))
+  (lambda (table chars action)
+    (let ((chars (if (pair? chars)
+                     chars
+                     (list chars))))
+      (fold (lambda (char table)
+              (readtable:new (%readtable:default-action table)
+                             (car (charmap:insert
+                                   (%readtable:charmap table) char action))))
+            table
+            chars))))
 
 ;;; Construct new readtable with no characters in its map and
 ;;; DEFAULT-ACTION as the default action.
@@ -392,7 +410,7 @@
                     (readtable:empty/default (readtable:error
                                               'read-improper-cdr
                                               "improper list has 1 cdr"))
-                    (list readtable:update-list
+                    (list readtable:update
                           readtable:ASCII-whitespace
                           readtable:skip)
                     (list readtable:update %eol
@@ -458,6 +476,236 @@
         (error 'expect-port-list 'no-list-found)
         (readtable:read-proper-list table port))))
 
+;;; ;;;;;;;;;;;;;;;;;;;;;;;;;
+;;; Implementation of a Pratt parser. In a Pratt parser, all tokens are
+;;; "operators" with "precedence".
+;;; 
+;;; Since Pratt parsers are implemented in terms of procedures, they can
+;;; parse any grammar.
+;;; 
+;;; This file implements the algorithm found in:
+;;; 
+;;; van de Vanter, Michael L. "A Formalization and Correctness Proof of
+;;;   the CGOL Language System." (Master's Thesis). MIT Laboratory for
+;;;   Computer Science Technical Report MIT-LCS-TR-147 (Cambridge,
+;;;   Massachusetts). 1975.  https://hdl.handle.net/1721.1/149442.
+
+;;; (PRATT:OPERATOR PRECEDENCE PROCEDURE)
+;;; constructs a description of an operator.
+;;; 
+;;; PRECEDENCE is an exact number describing the precedence of the
+;;; operator, and for portability should only be an integer.
+;;; 
+;;; (The special EOF operator, which always exists, has negative
+;;; infinity precedence.)
+;;; 
+;;; PROCEDURE is of the form (PROCEDURE OPERATORS LEFT TOKEN READER).
+;;; OPERATORS is the operators map.
+;;; LEFT is a PRATT:TOKEN, which was to the left of the operator.
+;;; TOKEN is the token read from the reader wit the same type.
+;;; READER is a reader object.
+;;; 
+;;; PROCEDURE consumes tokens to obtain the
+;;; right hand side of its expression. PROCEDURE produces a PRATT:TOKEN.
+(define pratt:operator cons)
+(define pratt:precedence car)
+(define pratt:procedure cdr)
+
+(define pratt:search-token
+  (lambda (operators token)
+    (smap:search operators (symbol->string (token 'type)))))
+
+;;; Parse a stream from READER, where the precedence limit is specified as
+;;; BINDING-POWER. If BINDING-POWER is #F, then there is no precedence
+;;; limit. Operators are read from OPERATORS, which is a SMAP.
+(define pratt
+  (lambda (operators binding-power reader)
+    (letrec
+        ((loop
+          (lambda (left)
+            (let ((token (reader 'peek)))
+              (let ((operator (pratt:search-token operators token)))
+                (if (null? next-operator)
+                    (error 'pratt 'unknown-operator token
+                           operators binding-power reader))
+                (if (and binding-power
+                         (>= (pratt:precedence operator)
+                             binding-power))
+                    left
+                    (parse operator left (reader 'read) reader))))))
+         (parse
+          (lambda (operator left token reader)
+            (loop ((pratt:procedure operator)
+                   operators
+                   left
+                   token
+                   reader)))))
+      ;; Read the first token.
+      (let ((token (reader 'read)))
+        (let ((operator (pratt:search-token operators token)))
+          (if (null? operator)
+              (error 'pratt 'unknown-operator token
+                     operators binding-power reader))
+          (parse operator #f token reader))))))
+
+;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;; Math reader.
+;;; 
+;;; Scheme numbers are a kludge. A proper LISP would either represent
+;;; numbers as
+;;; 
+;;;    (+ 4 (*i 6)) or (@ (. 12 34) 2) or (e 12 3) etc.
+;;; 
+;;; or just bite the bullet and include a full infix expression parser.
+;;; 
+;;; This is a full infix expression parser. It will parse expressions
+;;; such as SIN(X) or X * 5I/6. Identifiers and functions are any Scheme
+;;; object.
+;;; 
+;;; The math reader can be invoked using #MATH(expr). EXPR is an infix
+;;; mathematical expression. #PREFIX(expr) reads EXPR in the normal
+;;; reader. All other hash identifiers are unsupported in #MATH.
+
+;;; The basic number reader. The basic syntax is
+;;; 
+;;; PREFIXES* SIGN? (RADIX+ ("." RADIX+)? | "." RADIX+) ("e" RADIX+)? "i"?
+;;; Prefixes are handled by the "#" reader.
+
+;;; Incremental builder for a number, driven by the lexer.
+;;; TODO: how will this be turned into a number, in the end?
+(define read:number-builder
+  (lambda (radix-table)
+    (let ((main '())
+          (decimal '())
+          (exp-char #f)
+          (exp-digits '())
+          (imaginary? #f)
+          (current-part 'main)
+          (exactness #f))
+      (let ((append-part
+             (lambda (char)
+               (cond
+                 ((eq? current-part 'main)
+                  (set! main (cons char main)))
+                 ((eq? current-part 'decimal)
+                  (set! decimal (cons char decimal)))
+                 ((eq? current-part 'exp)
+                  (set! exp-digits (cons char exp-digits)))))))
+        (lambda (op . args)
+          (cond
+            ((eq? op 'finalize)
+             (if (not exactness)
+                 (set! exactness 'exact))
+             (list 'number-builder
+                   main exactness decimal exp-char exp-digits imaginary?))
+            ((eq? op 'exactness!) (set! exactness (car args)))
+            ((eq? op 'radix-table!) (set! radix-table (car args)))
+            ((eq? op 'set-imaginary!)
+             (set! imaginary? #t))
+            ((eq? op 'set-decimal!)
+             (if (not exactness)
+                 (set! exactness 'inexact))
+             ;; 
+             (if (not (eq? current-part 'main))
+                 (error 'number-builder "cannot set to decimal" current-part)
+                 (set! current-part 'decimal)))
+            ((eq? op 'set-exponential!)
+             (if (not exactness)
+                 (set! exactness 'inexact))
+             ;; 
+             (if (eq? current-part 'exp)
+                 (error 'number-builder "cannot set to exponential"))
+             (set! current-part 'exp)
+             (set! exp-char (car args)))
+            ;; 
+            ((eq? op 'radix-table) radix-table)
+            (else (append-part op))))))))
+
+(define readtable:return-number
+  (lambda (_ char acc port)
+    (port 'push char)
+    (acc 'finalize)))
+
+;;; Main lexer for number table.
+(define readtable:number-main-table
+  (readtable:process
+   (readtable:empty/default readtable:return-number)
+   (list readtable:update #\.
+         (lambda (table char number-builder port)
+           (number-builder 'set-decimal!)
+           (readtable:next table
+                           number-builder
+                           port)))
+   (list readtable:update (list #\e #\s #\f #\d #\l)
+         (lambda (table char number-builder port)
+           (number-builder 'set-exponential! char)
+           (readtable:next table
+                           number-builder
+                           port)))
+   (list readtable:update #\_ readtable:skip)
+   (list readtable:update #\i
+         (lambda (table char number-builder port)
+           (number-builder 'set-imaginary!)
+           (number-builder 'finalize)))))
+
+;;; Generate a lexer given a list of numbers in the radix.
+(define readtable:for-radix
+  (lambda (radix-list)
+    (readtable:process
+     readtable:number-main-table
+     (list readtable:update radix-list
+           (lambda (table char number-builder port)
+             (number-builder char)
+             (readtable:next table number-builder port))))))
+
+(define readtable:for-bin
+  (readtable:for-radix '(#\0 #\1)))
+(define readtable:for-oct
+  (readtable:for-radix '(#\0 #\1 #\2 #\3 #\4 #\5 #\6 #\7)))
+(define readtable:for-dec
+  (readtable:for-radix '(#\0 #\1 #\2 #\3 #\4 #\5 #\6 #\7 #\8 #\9)))
+(define readtable:for-hex
+  (readtable:for-radix '(#\0 #\1 #\2 #\3 #\4 #\5 #\6 #\7 #\8 #\9
+                             #\a #\b #\c #\d #\e #\f)))
+
+;;; Read the sign at the start of a number.
+(define readtable:read-sign
+  (readtable:process
+   (readtable:empty/default
+    (lambda (_ char number-builder port)
+      (readtable:act (number-builder 'radix-table)
+                     char
+                     number-builder
+                     port)))
+   (list readtable:update (list #\+ #\-)
+         (lambda (_ char number-builder port)
+           (number-builder 'sign! char)
+           (readtable:next (number-builder 'radix-table)
+                           number-builder
+                           port)))
+   (list readtable:update #\_ readtable:skip)))
+
+(define readtable:read-prefix-char
+  (let ((act (lambda args
+               (lambda (_ char number-builder port)
+                 (apply number-builder args)
+                 (readtable:next readtable:read-number-prefix
+                                 number-builder
+                                 port)))))
+    (readtable:process
+     (readtable:empty/default (readtable:error "invalid prefix"))
+     (list readtable:update #\i (act 'exactness! 'inexact))
+     (list readtable:update #\e (act 'exactness! 'exact))
+     (list readtable:update #\b (act 'radix-table! readtable:for-bin))
+     (list readtable:update #\o (act 'radix-table! readtable:for-oct))
+     (list readtable:update #\d (act 'radix-table! readtable:for-dec))
+     (list readtable:update #\x (act 'radix-table! readtable:for-hex)))))
+
+(define readtable:read-number-prefix
+  (readtable:process
+   (readtable:empty/default (readtable:jump readtable:read-sign))
+   (list readtable:update #\# (readtable:jump/next readtable:read-prefix-char))))
+
 ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 ;;; Reader for stuff that start with "#"
 ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@@ -559,7 +807,7 @@
   (readtable:process
    (readtable:empty/default (readtable:error 'datum-label-next
                                              "invalid datum label/ref"))
-   (list readtable:update-list readtable:digits readtable:push-char)
+   (list readtable:update readtable:digits readtable:push-char)
    (list readtable:update #\=
          (lambda (_ __ acc port)
            (acc 'finalize->ident)
@@ -631,10 +879,12 @@
     (let ((ident (readtable:read-ident #f char #f port)))
       (let ((container (smap:search read:hash-messages
                                     (ident 'value))))
-        ;; TODO: check if the hash message starts a number.
         (if (null? container)
-            (error 'read-hash-messages 'unknown-constant
-                   (ident 'value))
+            (let ((number-port (ident->read (port 'location) ident)))
+              (number-port 'fold-case! #t)
+              (readtable:next readtable:read-prefix-char
+                              (read:number-builder readtable:for-dec)
+                              number-port))
             ((map:val container) acc port))))))
 
 ;;; ;;;;;;;;;;;;;;;;;;;;;;
@@ -676,12 +926,12 @@
 (define readtable:hash
   (readtable:process
    (readtable:empty/default read:read-hash-messages)
-   (list readtable:update-list readtable:ASCII-whitespace
+   (list readtable:update readtable:ASCII-whitespace
          (readtable:error 'hash 'whitespace-after-hash))
    (list readtable:update #\| (readtable:jump/next readtable:block-comment))
    (list readtable:update #\; readtable:datum-comment)
    (list readtable:update #\\ readtable:character)
-   (list readtable:update-list readtable:digits ; Datum labels
+   (list readtable:update readtable:digits ; Datum labels
          (lambda (_ char toplevel port)
            (readtable:act readtable:datum-label-next
                           char
@@ -698,7 +948,7 @@
   (lambda ()
     (readtable:process
      (readtable:empty/default readtable:read-ident)
-     (list readtable:update-list readtable:ASCII-whitespace readtable:skip)
+     (list readtable:update readtable:ASCII-whitespace readtable:skip)
      (list readtable:update #f (readtable:return 'eof))
      (list readtable:update %bol readtable:read-list)
      (list readtable:update %eol (readtable:error 'top "unbalanced list"))
@@ -794,3 +1044,10 @@
 (read-all "#u8(x y z w)")
 (read-all "#\\newline")
 (read-all "#\\a")
+
+(read-all "#b11")
+(read-all "#XFF")
+(read-all "#i#x10")
+(read-all "#d1234.5678")
+(read-all "#e10.5")
+(read-all "#d10.24f12")