Edit detail for LispInFriCAS revision 2 of 2

It is possible to enter Lisp expressions directly into FriCAS (including function definitions) using the )lisp command, but this is rather awkward for long Lisp programs.

(1) -> )lisp (defun foo1 (x y) (+ x y))

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      available. See the )set userlevel command for more information.

)lisp (foo1 2 3)

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      available. See the )set userlevel command for more information.

One can put longer programs in files and use )read file.lisp to compile and run them.

On the FriCAS wiki we can enter Lisp code in the same way that we enter FriCAS code. For example:

  \begin{lisp}
  (defun FOO2 (x y)
    (+ x y))
  \end{lisp}

The text between the \begin{lisp} ... \end{lisp} is saved in a temporary file (e.g. tempfile.lisp). It is then compiled and loaded into Lisp via the command:

  )lisp (load (compile-file "tempfile.lisp"))

;;; Just a silly example
(defun FOO2 (x y)
  (+ x y))

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      available. See the )set userlevel command for more information.

Click +lisp to check the Lisp output for errors.

We can call the function from FriCAS like this:

FOO2(3,4)$Lisp

   FOO2 is not a lisp function and so cannot be used with $Lisp.

Or we can call the function from Lisp like this:

(format t "(FOO2 1 2) = ~a~%" (FOO2 1 2) )

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      available. See the )set userlevel command for more information.

Notice that the Value = T is the result of the (load ...) function call, not the value of the FOO2 function.

In the case of an error:

(defunny FOO3 (x y)
  (+ x y))

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      available. See the )set userlevel command for more information.

+lisp shows the error message.

This is a lisp expression that generates some output.

(format t "hello, world")

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      available. See the )set userlevel command for more information.

Lisp Tutorial 1

http://www.cs.sfu.ca/CC/310/pwfong/Lisp/1/tutorial1.html

Common LISP reads in an expression, evaluates it, and then prints out the result. For example, if you want to compute the value of (2 * cos(0) * (4 + 6)), you type in:

)lisp (* 2 (cos 0) (+ 4 6))

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      available. See the )set userlevel command for more information.

Here is a more complex recursive function.

(defun fibonacci (N)
  "Compute the N'th Fibonacci number."
  (if (or (zerop N) (= N 1))
      1
    (+ (fibonacci (- N 1)) (fibonacci (- N 2)))))

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      available. See the )set userlevel command for more information.

We can trace its execution.

)lisp (trace fibonacci)

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      available. See the )set userlevel command for more information.

)lisp (fibonacci 5)

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      available. See the )set userlevel command for more information.

Lisp specification:

http://www.lispworks.com/documentation/HyperSpec/Front/

Lisp Links & Notes (advanced)

http://www.cs.ucla.edu/classes/winter04/cs161/l1/lispLinks.html

by Michael G. Dyer http://www.cs.ucla.edu/classes/winter04/cs161/l1

lambda, closures, apply, funcall, and mapcar

One thing to note here is that the word "thunk" is often used as a synonym for "closure".

A closure is defined as a double whose two elements are a pointer to code and a pointer to an environment. In the adder example below, the reason we need the "environment pointer" is that we need a way to remember what n was bound to at the time that (adder 3) was created.

This particular "adder" example comes from the CL Cookbook

(defun adder (n)
   (function (lambda (x) (+ x n)))
)

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      available. See the )set userlevel command for more information.

)lisp (adder 3)

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      available. See the )set userlevel command for more information.

)lisp (apply (adder 3) '(4))

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      available. See the )set userlevel command for more information.

)lisp (funcall (adder 3) 4)

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      available. See the )set userlevel command for more information.

)lisp (mapcar (adder 3) '(1 2 3 4))

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      available. See the )set userlevel command for more information.

There are two slightly different ways of using mapcar. One is by passing it a lambda block, which is created by simply prepending the #' in front of the function name. The other is to pass it a closure:

(defun increment (i)
   (+ i 1)
)

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      available. See the )set userlevel command for more information.

)lisp #'increment

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      available. See the )set userlevel command for more information.

)lisp (mapcar #'increment '(1 2 3))

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      available. See the )set userlevel command for more information.

)lisp #'(lambda (x) (increment x))

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      available. See the )set userlevel command for more information.

)lisp (mapcar #'(lambda (x) (increment x)) '(1 2 3))

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      available. See the )set userlevel command for more information.

compose

Let's take a look at a "higher-order" function, which means that it takes functions as arguments. The compose function is the same as in mathematics. f(g(x)) = compose(f,g)(x)

(defun increment (i)
  (+ i 1)
)

(defun square (z)
  (* z z)
)

(defun compose (f g)
   #'(lambda (x) (funcall f (funcall g x)))
)

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      available. See the )set userlevel command for more information.

)lisp (funcall (compose #'increment #'square) 3)

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      available. See the )set userlevel command for more information.

curry and uncurry

(defun printthree (arg1 arg2 arg3)
  (format *query-io* "arg1 = ~A, arg2 = ~A, arg3 = ~A~%" arg1 arg2 arg3)
)

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      available. See the )set userlevel command for more information.

)lisp (printthree 3 4 4)

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      available. See the )set userlevel command for more information.

(defun curry (function &rest args)
  (function (lambda (&rest more-args)
   (apply function (append args more-args)))))

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      available. See the )set userlevel command for more information.

)lisp (curry #'printthree 'a)

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      available. See the )set userlevel command for more information.

)lisp (apply (curry #'printthree 'a) '(b c))

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      available. See the )set userlevel command for more information.

)lisp (curry #'printthree 'a 'b)

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      available. See the )set userlevel command for more information.

)lisp (apply (curry #'printthree 'a 'b) '(c))

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      available. See the )set userlevel command for more information.

(defun uncurry (f)
   #'(lambda (x y)  (funcall (funcall f x) y))
)

(defun uncurry (f)
   #'(lambda (x y)  (funcall (funcall f x) y))
)

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      available. See the )set userlevel command for more information.

)lisp (uncurry (curry #'+ 1))

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      available. See the )set userlevel command for more information.