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BPM: pattern matching for Common Lisp


BPM is a simple pattern matching library for Common Lisp.

STOP -- BPM is depricated in favor of BPM2, BPM's ideological successor. BPM2 is quasi-vapourware slowly developing here


Download the latest gzipped tarball:

or get the latest version from the Git repository:

git clone git://



A Bird's Eye View of BPM

MATCH is like `CASE' except it uses pattern matching instead of keys and it executes success forms within the lexical scope of the matched pattern.

DEF! and DEF allow you to write lisp functions in pattern matching style.

BPM-LAMBDA is a pattern matching lambda.

-> and --> are self-evaluating constants provided as syntactic spice to help make pattern matching forms more readable.

CREATE-BPM-COMPILER is the low-level reification of everything BPM has to offer. It can safely be ignored if your not implementing your own domain specific syntactic abstractions or logic system on top of BPM.

Pattern Matching

BPM uses "S-Expression Patterns" to match sexps. S-Expression Patterns are sexps that may or may not contain logic variables.

The following sexps are s-expression patterns:

(a . b)

They do not have any logic variables and they match the sexps:

(a . b)


By default, CREATE-BPM-COMPILER recognises any symbol starting with _ (the underscore) as a logic variable. In the pattern

(foo . _bar)

_BAR is a logic variable. This pattern matches:

(foo 1)
(foo 1 2)
(foo 1 2 4)
(foo . anything)

In fact it matches any list with foo as its first element. Within the respective scope of these matches, _BAR would be bound to

(1 2)
(1 2 3)

The variable _ (just the underscore) is the "wildcard". It is a special variable that can match anything and never remembers what it's bound to. So the pattern

(_ _ _)

matches any list of the length 3, and _ isn't bound to anything within the scope of this match.

BPM also matches/destructure simple vectors, so

#(_1 _1 _2 _2)

matches a simple vector of length 4 whose first two elements are the same and last two elements are the same.

Caveat: It is not immediately assumed that _1 != _2. So this pattern matches

#(a a a a)


#(b b b b)

as well as

#(a a b b)

Note: you can use a WHERE or WHERE-NOT clauses within DEF!/DEF or MATCH forms to give your matches arbitrary constraints such as (not (eql _1 _2)).


CREATE-BPM-COMPULER uses EQL as the default equality test. This can be overwritten by rebinding *LOGIC-VAR-EQUALITY-TEST* during bpm-compile-time.

Changing the Syntax



  • MATCH (form &amp clauses)

macro Match is like CASE except it uses S-Expression Patterns instead of keys and success forms re executed within the lexical scope of their respective matches.

cl-user> (match '(1 2)
	       ((_h . _t) -> (format nil "list with a head of ~A and a tail of ~A" _h _t))
        (_x -> (format nil "~A is an atom" _x)))
"list with a head of 1 and a tail of (2)"

cl-user> (match 3
      ((_h . _t) -> (format nil "list with a head of ~A and a tail of ~A" _h _t))
      (_x -> (format nil "~A is an atom" _x)))
"3 is an atom"

MATCH clauses can optionally take an arbitrary number of WHERE and WHERE-NOT clauses.

  • DEF! (name pattern &body body) DEF (name pattern &body body)

macro DEF! is like DEFUN except it takes an S-Expression Pattern instead of a lambda list. The created function takes one argument: if that argument matches PATTERN, then the function executes BODY within the lexical scope of the match. Otherwise it simply returns NIL.

cl-user> (def! foo (_x . _y)
           -> (cons _y _x))

cl-user> (foo '(1 . 2))
(2 . 1)

cl-user> (foo 1)

DEF adds additional pattern matching clauses to functions define with DEF!. A DEF! can be thought of as the first clause to a MATCH form where subsequent DEF forms are the subsequent MATCH clauses.

cl-user> (def foo _ -> 'not-a-cons)

cl-user> (foo '(1 2 3))
((2 3) . 1)

cl-user> (foo 1)

Both DEF! and DEF can optionally have an arbitrary number of WHERE and WHERE-NOT clauses in BODY.


symbols The symbols WHERE and WHERE-NOT act as special keywords when seen inside MATCH clauses or DEF!/DEF bodies.

WHERE and WHERE-NOT can be thought of as functions that take a single argument (TEST): when WHERE or WHERE-NOT forms appear immediatly after a sexp pattern, a match against that pattern is not considered successful unless all the WHERE arguments evaluate to non-NIL values and the WHERE-NOT arguments evaluate to NIL.

Note: WHERE and WHERE-NOT clauses are "short-circuiting" (like AND).

(match request
  (#(_user _a) (where (find-user _user))
           --> (do-user-actions _a))
  (_req       --> (error 'bad-request :request _req)))

(def! get-username #(_id _node)

  ;; validate node
  (where (node? _node))
  (where (node-exists? _node))

  ;; find username 
  (.get-username _id _node))

(def get-username #(_id _node)
  (error 'bad-node :node _node))

(def get-username _req
  (error 'bad-request :request _req))
  • BPM-LAMBDA (pattern &body body)

macro BPM-LAMBDA is just like LAMBDA except that it takes an S-Expression pattern as a first argument instead of a lambda list.

The resultant function takes on argument: if that argument matches PATTERN then the function executes BODY within the lexical scope of the match. Otherwise it simply returns NIL.

Caveat: BPM-LAMBDA does not understand WHERE or WHERE-NOT clauses.

  • CREATE-BPM-COMPILER (pattern &optional bound)

function CREATE-BPM-COMPILER takes an S-Expression Pattern and a list of already bound logic variables. It returns a function (FUNCTION1) and a new list of logiv variables.

This new function takes a piece of unevaluated lisp code and returns the source of a new unary function (FUNCTION2). If FUNCTION2's argument matches PATTERN, then FUNCTION2 executes the lisp code given to FUNCTION2 within the lexical scope of the match. Otherwise it simply returns NIL.

BPM-LAMBDA can be implemented as:

(defmacro bpm-lambda (pattern &body body)
  (funcall (create-bpm-compiler pattern) `(progn ,@body)))

CREATE-BPM-COMPILER's second return value is the accumulated list of logiv variables that will be bound within FUNCTION2's evaluation of the lisp form given as an argument to FUNCTION1. This list can be given as the argument to CREATE-BPM-COMPILER's optional BOUND argument in recursive calls to CREATE-BPM-COMPILER: in this way it is possible to create nested pattern matchers that are lexically aware of the pattern matching environment around them.

cl-user> (create-bpm-compiler '(1 _1 #(_1 _2) _2))
#<Closure (:internal create-bpm-compiler 1) @ #x10719da2>
(_2 _1)

cl-user> (funcall * '(progn (print _1) (print _2)))
(lambda (#:g6249)
  (declare (dynamic-extent #:g6249))
  (and (listp #:g6249)
       (eql (first #:g6249) '1)
       (let ((#:g6252 (rest #:g6249)))
         (declare (dynamic-extent #:g6252))
         (if (listp #:g6252)
             (let ((_1 (first #:g6252))
		   (#:g6255 (rest #:g6252)))
               (declare (dynamic-extent #:g6255))
               (if (listp #:g6255)
                   (let ((#:g6257 (first #:g6255)))
                     (declare (dynamic-extent #:g6257))
                     (and (simple-vector-p #:g6257)
                          (= (length #:g6257) 2)
                          (eql (svref #:g6257 0) _1)
                          (let ((_2 (svref #:g6257 1))
                                (#:g6261 (rest #:g6255)))
                            (declare (dynamic-extent #:g6261))
                            (and (listp #:g6261)
                                 (eql (first #:g6261) _2)
                                 (not (rest #:g6261))
                                 (progn (print _1)
					(print _2))))))))))))

cl-user> (funcall (coerce * 'function) '(1 one #(one two) two))

variable The character that indicates logic and wildcard variables. Initially set to #\_.


variable A unary predicate that returns if its argument is a logic variable. Initially set to a function that looks for symbols whose names start with *LOGIC-VAR-PREFIX-CHAR*


variable A unary predicate that returns T if its argument is a logic var wildcard. Initially set to a function that looks for symbols with the name *LOGIC-VAR-PREFIX-CHAR*


variable Initially set to T. Bind this to NIL if you want vectors to be seen as atomic objects in your S-Expression Patterns.


    variable Lambda form or name of function that tests whether or not S-Expressions match parts of an S-Expression pattern. Initially set to EQL.

  • -> / -->

constants Syntactic spice. These self-evaluating constants exist only to help make your code more visually intuitive.