The cmu-infix Reference Manual

Table of Contents

The cmu-infix Reference Manual

This is the cmu-infix Reference Manual, generated automatically by Declt version 3.0 "Montgomery Scott" on Mon Apr 19 15:41:41 2021 GMT+0.

1 Introduction

CMU-INFIX

A library for writing infix mathematical notation in Common Lisp.

Origin

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 infix.cl 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/infix.cl.

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
        ))
    a))

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] ))))
    C))

;; 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.

Contributing

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](LICENSE.t

2 Systems

The main system appears first, followed by any subsystem dependency.

2.1 cmu-infix

Maintainer

Robert Smith <robert@rigetti.com>

Author

Mark Kantrowitz

License

Custom (See LICENSE.txt)

Description

Mathematical infix notation for Common Lisp.

Dependency

named-readtables

Source

cmu-infix.asd (file)

Components

• package.lisp (file)
• cmu-infix.lisp (file)

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

3.1 Lisp

3.1.1 cmu-infix.asd

Location

/home/quickref/quicklisp/dists/quicklisp/software/cmu-infix-20180228-git/cmu-infix.asd

Systems

cmu-infix (system)

3.1.2 cmu-infix/package.lisp

Parent

cmu-infix (system)

Location

package.lisp

Packages

cmu-infix

3.1.3 cmu-infix/cmu-infix.lisp

Dependency

package.lisp (file)

Parent

cmu-infix (system)

Location

cmu-infix.lisp

Exported Definitions

string->prefix (function)

Internal Definitions

• *infix-readtable* (special variable)
• *normal-readtable* (special variable)
• *operator-ordering* (special variable)
• *peeked-token* (special variable)
• *right-associative-operators* (special variable)
• *token-infix-operator-table* (special variable)
• *token-operators* (special variable)
• *token-prefix-operator-table* (special variable)
• apply-token-infix-operator (function)
• apply-token-prefix-operator (function)
• define-character-tokenization (macro)
• define-token-operator (macro)
• fancy-number-format-p (function)
• gather-superiors (function)
• get-first-token (function)
• get-next-token (function)
• get-token-infix-operator (function)
• get-token-prefix-operator (function)
• infix-error (macro)
• infix-read-delimited-list (function)
• infix-reader (function)
• operator-lessp (function)
• operator-right-associative-p (function)
• peek-token (function)
• post-process-expression (function)
• read-infix (function)
• read-regular (function)
• read-token (function)
• same-operator-p (function)
• same-token-p (function)
• token-operator-p (function)
• valid-numberp (function)

4 Packages

Packages are listed by definition order.

4.1 cmu-infix

Package holding the readtable designator for mathematical infix notation.

The following two tables enumerate the supported operators along with their precedence.

Operators:

NOTE: == is equality, = is assignment (C-style).

\ quoting character: x\-y –> x-y
! lisp escape !(foo bar) –> (foo bar)
; comment
x = y assignment (setf x y)
x += y increment (incf x y)
x -= y decrement (decf x y)
x *= y multiply and store (setf x (* x y)) x /= y divide and store (setf x (/ x y)) x|y bitwise logical inclusive or (logior x y) x^y bitwise logical exclusive or (logxor x y) x&y bitwise logical and (logand x y) x<<y left shift (ash x y)
x>>y right shift (ash x (- y)) ~x ones complement (unary) (lognot x)
x and y conjunction (and x y)
x && y conjunction (and x y)
x or y disjunction (or x y)
x || y disjunction (or x y)
not x negation (not x)
x^^y exponentiation (expt x y)
x,y sequence (progn x y) (x,y) sequence (progn x y) also parenthesis (x+y)/z –> (/ (+ x y) z) f(x,y) functions (f x y)
a[i,j] array reference (aref a i j) x+y x*y arithmetic (+ x y) (* x y) x-y x/y arithmetic (- x y) (/ x y) -y value negation (- y)
x % y remainder (mod x y)
x<y x>y inequalities (< x y) (> x y) x <= y x >= y inequalities (<= x y) (>= x y) x == y equality (= x y)
x != y equality (not (= x y)) if p then q conditional (when p q)
if p then q else r conditional (if p q r)

Precedence:

The following precedence conventions are obeyed by the infix operators: [ ( !
^^
~
* / %
+ -
<< >>
< == > <= != >=
&
^
|
not
and
or
= += -= *= /=
,
if
then else
] )

Note that logical negation has lower precedence than numeric comparison so that "not a<b" becomes (not (< a b)), which is different from the C precedence conventions. You can change the precedence conventions by modifying the value of the variable *operator-ordering*.

Source

package.lisp (file)

Use List

• editor-hints.named-readtables
• common-lisp

Exported Definitions

string->prefix (function)

Internal Definitions

• *infix-readtable* (special variable)
• *normal-readtable* (special variable)
• *operator-ordering* (special variable)
• *peeked-token* (special variable)
• *right-associative-operators* (special variable)
• *token-infix-operator-table* (special variable)
• *token-operators* (special variable)
• *token-prefix-operator-table* (special variable)
• apply-token-infix-operator (function)
• apply-token-prefix-operator (function)
• define-character-tokenization (macro)
• define-token-operator (macro)
• fancy-number-format-p (function)
• gather-superiors (function)
• get-first-token (function)
• get-next-token (function)
• get-token-infix-operator (function)
• get-token-prefix-operator (function)
• infix-error (macro)
• infix-read-delimited-list (function)
• infix-reader (function)
• operator-lessp (function)
• operator-right-associative-p (function)
• peek-token (function)
• post-process-expression (function)
• read-infix (function)
• read-regular (function)
• read-token (function)
• same-operator-p (function)
• same-token-p (function)
• token-operator-p (function)
• valid-numberp (function)

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

5.1 Exported definitions

5.1.1 Functions

Function: string->prefix STRING

Convert a string to a prefix s-expression using the infix reader. If the argument is not a string, just return it as is.

Package

cmu-infix

Source

cmu-infix.lisp (file)

5.2 Internal definitions

5.2.1 Special variables

Special Variable: *infix-readtable*

Package

cmu-infix

Source

cmu-infix.lisp (file)

Special Variable: *normal-readtable*

Package

cmu-infix

Source

cmu-infix.lisp (file)

Special Variable: *operator-ordering*

Ordered list of operators of equal precedence.

Package

cmu-infix

Source

cmu-infix.lisp (file)

Special Variable: *peeked-token*

Package

cmu-infix

Source

cmu-infix.lisp (file)

Special Variable: *right-associative-operators*

Package

cmu-infix

Source

cmu-infix.lisp (file)

Special Variable: *token-infix-operator-table*

Package

cmu-infix

Source

cmu-infix.lisp (file)

Special Variable: *token-operators*

Package

cmu-infix

Source

cmu-infix.lisp (file)

Special Variable: *token-prefix-operator-table*

Package

cmu-infix

Source

cmu-infix.lisp (file)

5.2.2 Macros

Macro: define-character-tokenization CHAR FUNCTION

Package

cmu-infix

Source

cmu-infix.lisp (file)

Macro: define-token-operator OPERATOR-NAME &key PREFIX INFIX

Package

cmu-infix

Source

cmu-infix.lisp (file)

Macro: infix-error FORMAT-STRING &rest ARGS

Package

cmu-infix

Source

cmu-infix.lisp (file)

5.2.3 Functions

Function: apply-token-infix-operator TOKEN LEFT STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: apply-token-prefix-operator TOKEN STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: fancy-number-format-p LEFT OPERATOR STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: gather-superiors PREVIOUS-OPERATOR STREAM

Gathers an expression whose operators all exceed the precedence of the operator to the left.

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: get-first-token STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: get-next-token STREAM LEFT

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: get-token-infix-operator TOKEN

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: get-token-prefix-operator TOKEN

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: infix-read-delimited-list END-TOKEN DELIMITER-TOKEN STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: infix-reader STREAM SUBCHAR ARG

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: operator-lessp OP1 OP2

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: operator-right-associative-p OPERATOR

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: peek-token STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: post-process-expression EXPRESSION

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: read-infix STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: read-regular STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: read-token STREAM

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: same-operator-p X Y

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: same-token-p X Y

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: token-operator-p TOKEN

Package

cmu-infix

Source

cmu-infix.lisp (file)

Function: valid-numberp STRING

Package

cmu-infix

Source

cmu-infix.lisp (file)

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types