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A library for writing infix mathematical notation in Common Lisp.


This library was originally written by Mark Kantrowitz in 1993 with updates the following few years. The code in this repository was derived from the original library provided by the CMU AI Repository. For posterity, a copy of this original file—otherwise unused by this library—can be found in attic/

With minimal changes to the core functionality, the library was modernized by Robert Smith to be in-line with contemporary Common Lisp usage.

Example Use

This package uses named-readtables to manage the readtables. If you've loaded CMU-INFIX successfully, then you'll have this package loaded as well.

To use CMU-INFIX, simply use the readtable named cmu-infix:syntax:

(named-readtables:in-readtable cmu-infix:syntax)

Once you have this, you can use the #I syntax for infix syntax. Here are some examples.

Example: Pythagorean Theorem

(defun hypot (a b)
  "Compute the length of the hypotenuse of a right triangle
   with sides A and B."
  #I( sqrt(a^^2 + b^^2) ))

Example: Power-of-Two Check

(defun power-of-two-p (n)
  "Check if N is a power of 2."
  #I( n != 0 and (n & (n - 1)) == 0 ))

Example: Euclidean Algorithm

(defun euclid (a b)
  "Compute the GCD of A and B using Euclid's algorithm."
  (let (temp)
    (loop :until #I( b == 0 ) :do
      #I( temp := b,
          b := a % b,
          a := temp

Example: Matrix Multiplication

(defun matmul (A B)
  "Compute C = A * B for matrices A and B."
  (let* ((m (array-dimension A 0))
         (n (array-dimension A 1))
         (q (array-dimension B 1))
         (C (make-array (list m q) :initial-element 0)))
    (loop :for i :below m :do
      (loop :for k :below q :do
        (loop :for j :below n :do
          #I( C[i, k] += A[i, j] * B[j, k] ))))

;; Example:
(let ((A (make-array '(2 2) :initial-contents '((0 1) (1 0))))
      (B (make-array '(2 1) :initial-contents '((2) (3)))))
  #I( matmul(A, B) ))

A full description of the supported operators is in the package documentation for CMU-INFIX:

(format t "~A" (documentation (find-package :cmu-infix) t))

Modernization Updates

The library has been updated in the following ways:

  • The package of this library has been renamed CMU-INFIX so as to not conflict with existing Quicklisp libraries.

  • A system of the same name has been made so it is loadable by ASDF.

  • The tests have been lifted and put into a separate system called CMU-INFIX-TESTS. You can run them by doing

    (asdf:test-system :cmu-infix)
  • The library was modified to use NAMED-READTABLES to not eagerly pollute your readtable.

  • Some out-of-date comments have been deleted.


After receiving permission from Mark Kantrowitz, Rigetti Computing has taken stewardship of the library. Questions and issues should be filed on GitHub here, and pull requests are welcome. The licensing terms are described in LICENSE.txt.


Updated of the CMU AI repository, originally written by Mark Kantrowitz








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