diff --git a/src/classes.lisp b/src/classes.lisp
index 0a2857d..c8c515d 100644
--- a/src/classes.lisp
+++ b/src/classes.lisp
@@ -121,7 +121,33 @@ representation of combinations.
    ;; IDentification NuMber
    (idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
    ;; ORiGiN
-   (orgn :type list :initarg :orgn :reader orgn)))
+   (orgn :type list :initarg :orgn :reader orgn))
+  (:documentation
+   "-----------------------------------------------------------------[class-doc]
+CHAIN-COMPLEX
+Slots: (cmps basis bsgn dffr grmd efhm idnm orgn)
+Intances of this class represent chain complexes. The class has 8 slots:
+
+1. CMPR, a comparison function or method for generators, which returns :LESS,
+   :EQUAL, or :GREATER.
+
+2. BASIS, a Lisp function, which returns the ordered basis of the free
+   Z-modules (C_p), or the keyword :LOCALLY-EFFECTIVE.
+
+3. BSGN, a Lisp object representing the base generator in dimension 0.
+
+4. DFFR, the differential morphism, an instance of the class MORPHISM.
+
+5. GRMD, ???
+
+6. EFHM, ???
+
+7. IDNM, an integer, a system generated identifier for this object.
+
+8. ORGN, a list containg a comment indicating the origin of the object. The
+   should be unique (per session), since it is used in the implementation for
+   caching purposes.
+------------------------------------------------------------------------------"))
 
 ;; STRT = STRaTegy
 (DEFTYPE STRT () '(member :gnrt :cmbn))
diff --git a/src/combinations.lisp b/src/combinations.lisp
index a47a8e4..85fcbda 100644
--- a/src/combinations.lisp
+++ b/src/combinations.lisp
@@ -41,13 +41,6 @@ is ignored.
   (declare
    (type cmprf cmpr)
    (list list1 list2))
-  "--------------------------------------------------------------[function-doc]
-MAPLEXICO
-Args: (cmpr list1 list2)
-Returns :EQUAL, :GREATER or :LESS, based on the comparison of lists LIST1 and
-LIST2 according to lexicographical order, where list elements are compared with
-CMPR.
-------------------------------------------------------------------------------"
   (the boolean
        (do ((mark1 list1 (cdr mark1))
 	    (mark2 list2 (cdr mark2)))
@@ -68,8 +61,9 @@ CMPR.
   "--------------------------------------------------------------[function-doc]
 S-CMPR
 Args: (symbol1 symbol2)
-String-compares (SYMBOL-NAME SYMBOL1) and (SYMBOL-NAME SYMBOL2), and returns
-:EQUAL, :GREATER or :LESS.
+Returns :LESS, :EQUAL, or :GREATER, according to the result of the Lisp string
+comparison function of the strings (SYMBOL-NAME SYMBOL1) and
+(SYMBOL-NAME SYMBOL2).
 ------------------------------------------------------------------------------"
   (the cmpr
        (if (#+aclpc acl:whole-string<
@@ -86,7 +80,8 @@ String-compares (SYMBOL-NAME SYMBOL1) and (SYMBOL-NAME SYMBOL2), and returns
   "--------------------------------------------------------------[function-doc]
 F-CMPR
 Args: (n1 n2)
-Compares integers N1 and N2, and returns :EQUAL, :GREATER or :LESS.
+Returns :LESS, :EQUAL, or :GREATER, according to the result of the canonical
+comparison of the integers N1 and N2.
 ------------------------------------------------------------------------------"
   (the cmpr
        (if (< n1 n2)
@@ -101,8 +96,8 @@ Compares integers N1 and N2, and returns :EQUAL, :GREATER or :LESS.
   "--------------------------------------------------------------[function-doc]
 L-CMPR
 Args: (list1 list2)
-Compares the generator lists LIST1 and LIST2 according to lexicographical order
-and returns :EQUAL, :GREATER or :LESS.
+Returns :LESS, :EQUAL, or :GREATER, according to the lexicographical ordering
+of the generator lists LIST1 and LIST2.
 ------------------------------------------------------------------------------"
   (unless list1
     (return-from l-cmpr (if list2 :less :equal)))
@@ -165,7 +160,7 @@ combination is an instance of the null combination of degree DEGR.
   "--------------------------------------------------------------[function-doc]
 CHECK-CMBN
 Args: (chcm cmbn)
-Checks if the combination CMBN is a valid combination of chain complex CHCM.
+Tests if the combination CMBN is a valid combination of chain complex CHCM.
 CHECK-CMBN raises an error if the generators of CMBN are out-of-order.
 ------------------------------------------------------------------------------"
   (the boolean