;; Copyright 1994, Brown University, Providence, RI
;; file: intro.lisp

;; Part 1
;; Description: - first lecture on symbolic programming 
;;              - `pure lisp' with functions and no assignment
;;              - substitution model of function invocation

(in-package 'user)

;; **************************************************************************
;;                          Symbolic Programming
;; **************************************************************************

;; Symbols: +, -, 1, 2 etc. 

;; Symbolic expressions: (+ 1 2), (+ (* 3 4) 2)

;; Symbolic programs are programs that manipulate symbolic expressions.

;; Symbolic manipulation: you do it all the time;
;;                        now you'll write programs to do it.

;; Example
;; Logical rules can be represented as symbolic expressions of 
;; the form, `antecedent' implies `consequent'.
;; The following rule states that the relation of `being inside 
;; something is transitive,
;; `x is inside y and y is inside z' implies `x is inside z'.
;; In lisp notation, we would represent this rule as
;;                  (implies (and (inside x y)
;;                                (inside y z))
;;                           (inside x z))

(setq rule `(implies (and (inside x y)       ;; You will learn about SETQ, 
                          (inside y z))      ;; FIRST, and SECOND in the 
                     (inside x z)))          ;; second lecture on Lisp?

;; Manipulating symbolic expressions

(first rule)           ;; This tells us that the expression is a rule.
                       ;; (FIRST RULE) -> IMPLIES

(second rule)          ;; This gives us the antecedent of the rule.
                       ;; (SECOND RULE) -> (AND (INSIDE X Y) (INSIDE Y Z))

(third rule)           ;; This gives us the consequent of the rule.
                       ;; (THIRD RULE) -> (INSIDE X Z)

(first (second rule))  ;; This tells us that the antecedent is a conjunction.
                       ;; (FIRST (SECOND RULE)) -> AND

(second (second rule)) ;; This gives us the first conjunct of the antecedent.
                       ;; (SECOND (SECOND RULE)) -> (INSIDE X Y)

;; **************************************************************************
;;                           Lisp and Common Lisp
;; **************************************************************************

;; What are you looking for in a programming language?
;;  - primitive data types: strings, numbers, arrays
;;  - operators: +, -, +, /, etc.
;;  - flow of control: if, or, and, while, for
;;  - input/output: file handling, loading, compiling programs

;; Lisp has all of this and more.
;;  - developed by John McCarthy at MIT 
;;  - second oldest programming language still in use (FORTRAN is oldest)
;;  - specifically designed for symbolic programming

;; We use a dialect of Lisp called Common Lisp.
;;  - Common Lisp is the standard dialect

;; We use a subset of Common Lisp.
;;  - the subset is specific to our purposes but still quite general
;;  - the description in the text is completely self-contained

;; **************************************************************************
;;                       Basic Data Types and Syntax
;; **************************************************************************

;; Numbers: 1, 2, 2.72, 3.14, 2/3 (integers, floating point, rationals)

;; Strings: "abc", "FOO", "this is also a string"

;; Characters:
;;  - characters:               a,b,...,z,A,B,...,Z,0,1,2,...,9,_,-,+,*
;;  - alpha characters:         a,b,...,z,A,B,...,Z
;;  - numeric characters:       0,1,2,...,9

;; Symbols - sequence of characters including one or more alpha characters
;;         - its actually more complicated than this but this will suffice

;; Examples 
;; foo, my-foo, your_foo, 1foo, foo2, FOO, FOO2

;; Lisp programs and data are represented by expressions.

;; Expressions - (inductive definition)
;;  - any instance of a primitive data type: numbers, strings, symbols
;;  - a list of zero or more expressions

;; List 
;;  - open paren ``('' 
;;  - zero or more Lisp objects separated by white space
;;  - close paren ``)''

;; Examples 
;; 1, "foo", BAR                   (primitive data types)
;; (), (1), (1 "foo" BAR)          (flat list structures) 
;; (1 (1 "foo" BAR) biz 3.14)      (nested list structure)

;; Comment character `;'
;; Lisp `ignores' anything to the right of a comment character. 

;; Lisp is case insensitive with regard to symbols.
;;  FOO, Foo, foo, fOO designate the same symbol, but
;;  "FOO", "Foo", "foo", "fOO" designate different strings.

;; **************************************************************************
;;                   Interacting with the Lisp Interpreter
;; **************************************************************************

;; Instead of 
;;  1. Write program 
;;  2. Compile program 
;;  3. Execute program
;;  you can simply type expressions to the Lisp `interpreter.'

;; EVAL compiles, and executes symbolic expressions interpreted as programs.

;; The READ-EVAL-PRINT loop reads, EVALs, and prints the result of  
;; executing symbolic expressions.

;; Instances of simple data types EVALuate to themselves. 

"string"

3.14

t 

nil

;; sym ;; This expression would cause an error if typed to the interpreter.
       ;; Interpreter errors look like 
       ;; > sym  
       ;; Error: The symbol SYM has no global value

;; EVAL expression 
;;  - expression is a string
;;    return the expression
;;  - expression is a number
;;    return the expression
;;  - expression is a symbol 
;;    look up the value of the expression

;; You will learn how symbols get values in the second Lisp lecture.

;; **************************************************************************
;;                  Invoking Functions (Procedures) in Lisp
;; **************************************************************************

;; Function names are symbols, +, -, *, sort, merge, concatenate

;; Lisp uses prefix notation (function argument_1 ... argument_n)

(+ 1 2)   ;; + is the function, 1 and 2 are the arguments

(+ 1 2 3) ;; + takes any number of arguments

;; What happens when EVAL encounters a list?
;; Lists (with the exception of special forms) are assumed 
;; to signal the invocation of a function.

;; APPLY handles function invocation

;; EVAL expression 
;;  - expression is a string
;;    return the expression
;;  - expression is a number
;;    return the expression
;;  - expression is a symbol 
;;    look up the value of the expression
;;  - expression is of the form (function_name expression_1 ... expression_n)
;;    APPLY function_name to expression_1 ... expression_n 

;; APPLY function_name to expression_1 ... expression_n
;;  - EVAL expression_1 -> result_1
;;    ...
;;    EVAL expression_n -> result_n
;;  - function_name better have a definition; look it up!
;;    the definition for function_name should look something like
;;    function_name formal_parameter_1 ... formal_parameter_n
;;      expression involving formal_parameter_1 ... formal_parameter_n
;;  - substitute result_i for formal_parameter_i in the expression
;;  - EVAL the resulting expression

;; Example
;; function name WEIRD 
;; formal parameters X1 X2 X3 
;; definition X2
;; > (WEIRD 1 "one" 1.0)
;; EVAL (WEIRD 1 "one" 1.0)
;; APPLY WEIRD to 1 "one" 1.0
;; EVAL 1 -> 1
;; EVAL "one" -> "one"
;; EVAL 1.0 -> 1.0
;; substitute 1 for X1
;; substitute "one" for X2
;; substitute 1.0 for X3
;; EVAL "one"

;; > (WEIRD "1st arg 1st call"  
;;          (weird "1st arg 2nd call"  
;;                 "2nd arg 2nd call"  
;;                 (weird "1st arg 3rd call"  
;;                        "2nd arg 3rd call"  
;;                        "3rd arg 3rd call"))
;;          "3rd arg 1st call")
;; "2nd arg 2nd call"

(+ (* (+ 1 2) 3) (/ 12 2))

(+ (* (+ 1     ;; Indenting helps to make nested 
         2)    ;; function invocation clearer.
      3)       
   (/ 12       ;; What is the order of evaluation 
      2))      ;; in this nested list expression?

;;              (+ (* (+ 1 2) 3) (/ 12 2)) [9]
;;                 /              \
;;           (* (+ 1 2) 3) [5]     (/ 12 2) [8]
;;              /       \             /   \
;;        (+ 1 2) [3]    3 [4]     12 [6]  2 [7]
;;           /  \
;;       1 [1]  2 [2]


;; **************************************************************************
;;                  Defining Functions (Procedures) in Lisp
;; **************************************************************************

;; (defun function_name list_of_formal_parameters function_definition)
;; The function_name is a symbol.
;; The formal_parameters are symbols.
;; The function_definition is one or more expressions.  

;; Examples
;; (defun weird (x y z) y)
;;        ^     ^       ^
;;        |     |       |
;;        function name |
;;              |       |
;;              list of three formal parameters
;;                      |
;;                      function definition consisting of one expression
;;
;; (defun square (x) (* x x))
;;
;; (defun hypotenuse (a b)
;;   (sqrt (square a)
;;         (square b)))

;; How would these functions appear in a text file?

;; HYPOTENUSE takes two arguments corresponding
;; to the length of the two legs of a right triangle and
;; returns the length of the hypotenuse of the triangle.
(defun hypotenuse (a b) 
  ;; SQRT is a built-in function that
  ;; computes the square root of a number.
  (sqrt (+ (square a)
           (square b))))

;; SQUARE computes the square of its single argument.
(defun square (x) 
  (* x x))

;; **************************************************************************
;;                   Boolean Functions and Predicates
;; **************************************************************************

;; In Lisp, NIL is boolean false and any expression that evaluates to 
;; anything other than NIL is interpreted as boolean true. 

nil

;; T is the default boolean true. T evaluates to itself. 
t

;; Boolean predicates return T or NIL.

(oddp 3)

(evenp 3)

(< 2 3)

(= 1 2)

;; Boolean functions return non-NIL or NIL.

;; An OR expression evaluates to non-NIL if at least one 
;; of its arguments must evaluate to non-NIL.
(or t nil)

;; Degenerate case of no arguments.
(or)

;; An AND expression evaluates to non-NIL if All of its 
;; arguments must evaluate to non-NIL.
(and t nil)

;; Degenerate case of no arguments.
(and)

;; A NOT expression evaluates to non-NIL if its only argument
;; evaluates to NIL. 
(not t)

;; Any expression can be interpreted as a boolean value.

(and 3.14 "this string is interpreted as boolean true")

;; **************************************************************************
;;                 Conditional Statements and Flow of Control
;; **************************************************************************

;; Any expression can be used as a test in a conditional statement.

;; Simple conditional statements
;;  (if test_expression consequent_expression alternative_expression)
;;
;; Formatted differently using automatic indentation.
;; (if test_expression 
;;     consequent_expression 
;;   alternative_expression)

(if t "consequent" "alternative")

(if nil "consequent" "alternative")

;; You do not need to include the alternative.

(if t "consequent")

;; The `default' alternative is NIL.

(if nil "consequent")

;; General CONDitional statement
;;  (cond conditional_clause_1 ... conditional_clause_n)
;;  Conditional clause
;;  (test_expression expression_1 ... expression_m)

(cond ((and t nil) 1)
      ((or (not t)) 2)
      ((and) 3))

(cond (t nil))

(if t nil)

(defun classify (x)
  (cond ((= x 0) "zero")
        ((evenp x) "even")
        ((oddp x) "odd")))

(defun classify_again (x)
  (cond ((= x 0) "zero")
        ((evenp x) "even")
        (t "odd")))             ;; Good programming practice!

(classify_again 0)

(defun classify_once_more (x)
  (cond ((= x 0) "waste of time" "zero")
        ((evenp x) "who cares" "even")      ;; Why would we need more than
        (t (+ x x) "what a waste" "odd")))  ;; one expression in a clause?

(classify_once_more 2)

(defun classify_for_the_last_time (x)
  (cond ((= x 0) (princ "so far our lisp is pure") "zero")
        ((evenp x) (princ "side effects simplify coding") "even")
        (t (+ x x) (princ "side effects complicate understanding") "odd")))

(classify_for_the_last_time 3)


;; **************************************************************************
;;                           Recursive functions   
;; **************************************************************************

;; Recursion works by reducing problems to simpler problems
;; and then combining the results. 

(defun raise (x n)
  (if (= n 0)     ;; We can handle this case since x^0 is just 1.
      1           
    (* x          ;; Reduce the problem using x^n = x * x^(n-1).
       (raise x (- n 1)))))

;; Example 
;;                             Order                                Level
;;                             -----                                -----
;; call RAISE 3 2               RAISE is called for the first time   1
;;  call RAISE 3 1              RAISE is called for the second time  2
;;   call RAISE 3 0             RAISE is called for the third time   3
;;   return 1 from RAISE        value returned from the third call
;;  return 3 from RAISE         value returned from the second call
;; return 9 from RAISE          value returned from the first call

;; Example 
;; APPLY and EVAL work together recursively
;; 
;;                                  Order                               Level
;;                                  -----                               -----
;; call EVAL (+ (* 2 3) 4)           EVAL is called for the first time   1
;;  call APPLY + with (* 2 3) and 4  
;;   call EVAL (* 2 3)               EVAL is called for the second time  2
;;    call APPLY * with 2 and 3      
;;     call EVAL 2                   EVAL is called for the third time   3
;;     return 2 from EVAL            value returned by the third call 
;;     call EVAL 3                   EVAL is called for the fourth time  3
;;     return 3 from EVAL            value returned by the fourth call
;;    return 6 from APPLY            
;;   return 6 from EVAL              value returned by the second call
;;   call EVAL 4                     EVAL is called for the fifth time   2
;;   return 4 from EVAL              value returned by the fifth call
;;  return 10 from APPLY             
;; return 10 from EVAL               value returned by the first call


;; **************************************************************************
;;                      Evaluating Functions in Files
;; **************************************************************************

;; (load "one.lisp") or just 

;; (load "one") if the extension is ".lisp".


;; Part 2
;; Description: second lecture on symbolic programming
;;              environments, lambda, and functions as arguments


;; **************************************************************************
;;                   Some Comments Regarding Recursion
;; **************************************************************************

;; 1. We use recursive function definitions frequently.
;; 2. We expect you to become facile understanding recursive definitions.
;; 3. We realize that this will require some practice for those of you 
;;    who are not familiar with recursion. 
;; 4. You'll have to get most of this practice outside of class time.
;; 5. Homeworks and help sessions are designed to provide some practice 
;;    using recursion, but you'll also have to practice on your own. 
;; 6. The lecture on list processing will include more recursion.

;; **************************************************************************
;;                      Symbols can be assigned Values
;; **************************************************************************

;; The global environment is just a big table that EVAL uses to 
;; look up or change the value of symbols. 

;; There are other environments beside the global environment.

;; SETQ changes values of symbols in environments. 

;; Changing the value of a symbol is one example of a side effect.

;; Assign the symbol FOO the value 1 in the global environment

(setq foo 1)

(setq bar 2)

(setq baz (+ foo bar))

;; **************************************************************************
;;   Symbols assigned values in the global environment are global variables
;; **************************************************************************

(setq sym 3)

(defun double (x) (+ x x))

(double sym)

;; We use the terms `variable' and `symbol' interchangeably.

;; Global variables can be referenced inside function definitions.

(setq factor 3)

(defun scale (x) (* x factor))

(scale sym)

;; From a structured programming perspective, global variables are discouraged.

;; **************************************************************************
;;                    Function Invocation Revisited
;; **************************************************************************

;; New environments are created during function invocation.
;; ghostview /u/tld/papers/books/intro/symbolic/figures/local.ps &

(defun local (x)
  (setq x (+ x 1))
  (* x x))

;; In the following example, the symbol X is assigned 2 in the
;; global environment prior to invoking LOCAL on (+ X 1).  

(setq x 2)

;; In APPLYing LOCAL to (+ X 1), the single argument expression (+ X 1)
;; EVALuates to 3.  Before EVALuating the definition of LOCAL, APPLY
;; creates a new environment that points to the global environment.  In
;; this new environment, the formal parameter X is assigned the value 3
;; of the argument expression. In looking up the value of a symbol while
;; EVALuating the definition of LOCAL, EVAL looks first in the new
;; environment and, if it can't find the symbol listed there, then it
;; looks in the global environment. 

(local (+ x 1))

;; In general, function invocation builds a sequence of environments 
;; that EVAL searches through.

;; Reconsider the roles of EVAL and APPLY. 

;; EVAL expression in ENV
;;  - expression is a string
;;    return the expression
;;  - expression is a number
;;    return the expression
;;  - expression is a symbol 
;;    look up the value of expression in ENV
;;  - expression is a special form
;;    do something special!
;;  - expression has form (function_name arg_expression_1 ... arg_expression_n)
;;    APPLY function_name to arg_expression_1 ... arg_expression_n in ENV

;; Note that now that we have side effects, order of evaluation is 
;; important. Now it makes sense for COND clauses to have more than
;; one expression besides the test and for function definitions to 
;; consist of more than one expression. 

(setq x 1) (setq x (+ x x)) (setq x (* x x)) ;; x -> 4

(setq x 1) (setq x (* x x)) (setq x (+ x x)) ;; x -> 2

;; APPLY function_name to arg_expression_1 ... arg_expression_n in ENV
;;  - evaluate the arguments in left to right order 
;;    - EVAL arg_expression_1 in ENV -> arg_result_1 
;;      ...
;;    - EVAL arg_expression_n in ENV -> arg_result_n 
;;  - look up the definition of function_name:
;;    function_name formal_parameter_1 ... formal_parameter_n
;;      definition = def_expression_1 ... def_expression_m
;;  - create a new environment ENV' in which for each i
;;    formal_parameter_i is assigned the value arg_result_i
;;  - evaluate the expressions in the definition in left to right order
;;    - EVAL def_expression_1 in ENV' -> def_result_1
;;      ...
;;    - EVAL def_expression_m in ENV' -> def_result_m
;;    - return def_result_m

;; Question: How is ENV' constructed? In the book, environments are
;; described as sequences (linked lists) of tables where each table
;; assigns symbols to values. Each function is associated with (maintains
;; a pointer to) the environment that was in place at the time the
;; function was defined. In many cases, this is just the global
;; environment, but there are exceptions as you will soon see.
;; ENV' is constructed by creating a new table in which the symbols
;; corresponding to formal parameters are assigned the values of the
;; arguments. This table then points to the environment associated with
;; the function.

;; Note that the book has a typo on page 50 in which it states that APPLY
;; creates a new environment from the `initial environment.'  This is
;; just plain wrong. APPLY creates a new environment from the environment
;; associated with the function being applied.

;; Environments created during recursive function invocation.
;; ghostview /u/tld/papers/books/intro/symbolic/figures/raise.ps &

(defun raise (x n)
  (if (= n 0) 
      1           
    (* x (raise x (- n 1)))))

(raise 3 2)

;; **************************************************************************
;;                              Local Variables 
;; **************************************************************************

;; As noted above, you can change the value of symbols in environments

;; In the following function definition, the formal parameters X and Y 
;; are treated as variables whose values are determined locally with
;; respect to the function in which the formal parameters are introduced. 

(defun sqrt-sum-squares (x y)
  (setq x (* x x))
  (setq y (* y y))
  (sqrt (+ x y)))

;; You can also introduce additional local variables using LET.
;; LET is a special form meaning it handled specially by EVAL.

;; (let ((var_1 var_expression_1) ... (var_n expression_n))
;;    body_expression_1 ... body_expression_m)

(let ((x (+ 1 2)))
  (sqrt x))

;; (let (var_1 ... var_n)
;;     body_expression_1 ... body_expression_m)

(let (x)
  (setq x (+ 1 2))
  (sqrt x))

(defun sqrt-sum-squares-let (x y)
  (let ((p (* x x)) (q (* y y)))
    (sqrt (+ p q))))

;; LET statements are not strictly necessary but they can 
;; dramatically improve the readability of code. 

;; Environments created using nested LET statements. 
;; ghostview /u/tld/papers/books/intro/symbolic/figures/lexical.ps &

(let ((x 1))
  (let ((x 2))
    (let ((x 3))
      (princ x))
    (princ x))
  (princ x))

;; Note that the scope of local variables is determined lexically
;; by the text and specifically by the nesting of expressions.

;; **************************************************************************
;;                       Functions with Local State            
;; **************************************************************************

;; Environments persist over time. 

;; State information (local memory) for a specific function or 
;; set of functions. 
(let ((sum 0))
  (defun give (x)
    (setq sum (- sum x)))
  (defun take (x)
    (setq sum (+ sum x)))
  (defun report ()
    sum))

(take 5)

(take 10)

(report)

(give 7)

(report)

;; **************************************************************************
;;                           Functions as Arguments
;; **************************************************************************

;; FUNCTION tells EVAL to interpret its single argument as a function. 
;; FUNCTION does not evaluate its single argument.

(setq foo (function oddp))

;; FUNCALL takes a FUNCTION and zero or more arguments for that function
;; and applies the function to the arguments.

(funcall foo 1)

(funcall (function +) 1 2)

;; There is a convenient abbreviation for FUNCTION.

(funcall #'+ 1 2)

;; What is FUNCALL good for? Generic functions add flexibility.

(defun generic-function (x y test)
  (if (funcall test x y)
      "do something positive"
    "do something negative"))

(generic-function 1 2 #'<)

;; There are lots of generic functions built into Common Lisp.

(sort '(1 3 2 5 4) #'<)  ;; Ignore the '(1 3 2 5 4) for the time being.

(sort '(1 3 2 5 4) #'>)

;; **************************************************************************
;;                  Lambda Functions (or what's in a name?>
;; **************************************************************************

;; LAMBDA specifies a function without giving it a name.

(setq foo #'(lambda (x) (* x x)))

(funcall foo 3)

(funcall #'(lambda (x y) (+ x y)) 2 3)

;; LAMBDA functions are convenient for specifying 
;; arguments to GENERIC functions. 

(sort '(1 3 2 5 4) 
      #'(lambda (x y) (< (mod x 3) (mod y 3))))

;; Lambda functions can have local memory just like named functions.

(defun spawn (x)
  #'(lambda (request)
      (cond ((= 1 request) (setq x (+ x 1)))
            ((= 2 request) (setq x (- x 1)))
            (t x))))

(setq spawn1 (spawn 10)
      spawn2 (spawn 0))

(funcall spawn1 1)

(funcall spawn1 1)

(funcall spawn2 2)

(funcall spawn2 2)

(funcall spawn1 0)

(funcall spawn2 0)


;; Part 3
;; Description: third lecture on symbolic programming
;;              lists, list processing, and data abstraction, 


;; Review of environments.
;; view env.doc using FrameMaker

;; **************************************************************************
;;               Referring to Symbols Instead of their Values
;; **************************************************************************

;; QUOTE causes EVAL to suspend evaluation.

(quote foo)

;; Quote works for arbitrary expressions not just symbols.

(quote (foo bar))

;; There is a convenient abbreviation for QUOTE.

'foo

'(foo bar)

;; **************************************************************************
;;                Building Lists and Referring to List Elements
;; **************************************************************************

;; Build a list with LIST.

(setq sym (list 1 2 3 4))

;; Refer to its components with FIRST, SECOND, REST, etc.

(first sym)

(second sym)

(rest sym)

;; LIST, FIRST, REST, etc provide a convenient abstraction for pointers.
;; In fact, you don't have to know much at all about pointers to do
;; list manipulation in Lisp. 

;; Put together a list with pieces of other lists.

(setq new (list 7 sym))

;; What if you want a list that looks just like SYM but has 7 for its 
;; first element and you want to use the REST of SYM? 

;; Use CONS.

(cons 7 (rest sym))

;; If you want a list L such that (FIRST L) = X and (REST L) = Y
;; then (CONS X Y) does the trick.

(cons 7 ())

;; Here is a simple (but not particularly useful) recursive function.

(defun sanitize-list (x)
  (if (null x) 
      x
    (cons 'element 
	  (sanitize-list (rest x)))))

(sanitize-list '(1 2 3))

;; (CONS 1 2) is perfectly legal, but it isn't a list. 
;; For the time being assume that we only use CONS to construct lists.

;; What about nested lists?

;; Nested lists correspond to trees.

;;               (1 (2 3 (4)) (5 6 7))         Each nonterminal node in 
;;               /      |         \            the tree is a list.
;;              /       |          \           
;;             /        |           \          
;;            /         |            \         The children of a node
;;           1      (2 3 (4))      (5 6 7)     corresponding to a list are
;;                  /  |   \       /  |  \     the elements of the list.
;;                 /   |    \     /   |   \
;;                2    3    (4)  5    6    7
;;                            \
;;                             4

;; How would you SANITIZE a tree?

(defun sanitize-tree (x)
  (cond ((null x) x)                           ;; No more children.
	((not (listp x)) 'element)             ;; Terminal node.
	(t (cons (sanitize-tree (first x))     ;; Break the problem down 
		 (sanitize-tree (rest x))))))  ;; into two subproblems.

(sanitize-tree '(1 2 (3 4) ((3))))

;; EQUAL determines structural equality.

(equal (list 1 2) (cons 1 (cons 2 nil)))

;; Is there another kind of equality?

;; Given (SETQ X (LIST 1 2)) and (SETQ Y (LIST 1 2))
;; what is the difference between X and Y?

;; What's the different between (list 1 2) and `(1 2) ?

;; It could be that you don't need to know!

;; **************************************************************************
;;                          List Structures in Memory
;; **************************************************************************

;; CONS creates dotted pairs also called cons cells.
;; ghostview /u/tld/papers/books/intro/symbolic/figures/cons.ps &

(setq pair (cons 1 2))

;; CONSP checks for dotted pairs.

(consp pair)

;; CAR and CDR are the archaic names for FIRST and REST

(car pair)

(cdr pair)

;; EQ checks to see if two pointers (memory locations) are equivalent.

(eq (list 1 2) (list 1 2))

(setq point pair)

(eq point pair)

;; Integers point to unique locations in memory.
(eq 1 1)

(setq one 1)

(eq 1 one)

;; Floating numbers are not uniquely represented.
(eq 1.0 1.0)

;; **************************************************************************
;;           Destructive Modification of List Structures in Memory 
;; **************************************************************************

;; SETF allows us to modify structures in memory.
;; The first argument to SETF must reference a location in memory.

;; Change the first element of the pair from 1 to 3.
(setf (first pair) 3)

;; Create a nested list structure.
(setq nest (list 1 2 (list 3 4) 5))

;; Change the first element of the embedded list from 3 to 7.
(setf (first (third nest)) 7)

;; Why would we want to destructively modify memory?

;; To maintain consistency in data structures that share memory.

(setq mom '(person (name Lynn) (status employed)))

(setq dad '(person (name Fred) (status employed)))

(setq relation (list 'married mom dad))

(setf (second (third dad)) 'retired)

dad

relation
 
;; The difference between list and quote can be critical. 
(defun mem1 ()
  (let ((x (list 1 2))) x))

(defun mem2 ()
  (let ((x `(1 2))) x))

(setq xmem1 (mem1))

(setf (first xmem1) 3)

(setq xmem2 (mem2))

(setf (first xmem2) 3)

(mem1)

(mem2)

;; See text for how to simulate passing parameters by reference. 

;; **************************************************************************
;;            Predicates and Builtin Lisp Processing Functions    
;; **************************************************************************

(setq x (list 1 2 3))

(setq y (list 4 5))

;; LAST returns the last CONS cell in an expression. 

(last x)

(defun alt_last (x)
  (if (consp (rest x))
      (alt_last (rest x)) x))

(alt_last x)

;; APPEND two or more lists together. APPEND uses new CONS cells.
(append x y)

x

(defun alt_append (x y)
  (if (null x)
      y
    (cons (first x) 
	  (alt_append (rest x) y))))

(alt_append x y)
      
;; NCONC is like APPEND except that it modifies structures in memory.
;; NCONC does not use any new cons cells.
(nconc x y)

x

(defun alt_nconc (x y)
  (setf (rest (last x)) y) x)

(alt_nconc x y)

;; If X is an element of Y then MEMBER returns the list corresponding
;; to that sublist of Y starting with X, otherwise MEMBER returns NIL.

(member 1 '(2 3 1 4))

(defun alt_member (x y)
  (cond ((null y) nil)
	((eq x (first y)) y)
	(t (alt_member x (rest y)))))

(alt_member 1 '(2 3 1 4))

;; Check if X is EQ to Y or any subpart of Y.
(defun subexpressionp (x y)
  (cond ((eq x y) t)
	((not (consp y)) nil)
	((subexpressionp x (first y)) t)
	((subexpressionp x (rest y)) t)
	(t nil)))

(setq z (list 1 2 (list 3 4 (list 5)) 6))

(subexpressionp 5 z)

;; An alternate definition of SUBEXPRESSIONP.
(defun alt_subexpressionp (x y)
  (or (eq x y)
      (and (consp y)
	   (or (alt_subexpressionp x (first y))
	       (alt_subexpressionp x (rest y))))))

(alt_subexpressionp 4 z)

;; **************************************************************************
;;                      Functions with Optional Arguments
;; **************************************************************************

(member '(3 4) '((1 2) (3 4) (5 6)))

(member '(3 4) '((1 2) (3 4) (5 6)) :test #'equal)

(member '(3 4) '((1 2) (3 4) (5 6)) 
	:test #'(lambda (x y) 
		  (= (+ (first x) (second x)) 
		     (+ (first y) (second y)))))

(member '(3 4) '((1 2) (3 4) (5 6)) 
	:test #'(lambda (x y) 
		  (= (apply #'+ x) (apply #'+ y))))

;; **************************************************************************
;;                              Data Abstraction 
;; **************************************************************************

;; A data abstraction for input/output pairs.

;; Constructor for PAIRs.
(defun make-PAIR (input output) (list 'PAIR input output))

;; Type tester for pairs.
(defun is-PAIR (x) 
  (and (listp x) (eq 'PAIR (first x))))

;; Access for PAIRs.
(defun PAIR-input (pair) (second pair))
(defun PAIR-output (pair) (third pair))

;; Modifying PAIRs. 
(defun set-PAIR-input (pair new) (setf (second pair) new))
(defun set-PAIR-output (pair new) (setf (third pair) new))

;; Using the data abstraction.

(setq pairs (list (make-PAIR 3 8)
		  (make-PAIR 2 4)
		  (make-PAIR 3 1)
		  (make-PAIR 4 16)))

(defun monotonic_increasingp (pairs)
  (cond ((null pairs) t)
	((> (PAIR-input (first pairs))
	    (PAIR-output (first pairs))) nil)
	(t (monotonic_increasingp (rest pairs)))))

(monotonic_increasingp pairs)

(setq increasing (list (make-PAIR 1 2)
		       (make-PAIR 2 3)
		       (make-PAIR 3 4)
		       (make-PAIR 4 5)))

(monotonic_increasingp increasing)

(defun funapply (input fun)
  (cond ((null fun) nil)
	((= input (PAIR-input (first fun)))
	 (PAIR-output (first fun)))
	(t (funapply input (rest fun)))))

(funapply 2 increasing)

(defun alt_funapply (input fun)
  (let ((pairs (member input fun 
		       :test #'(lambda (x y) (= x (PAIR-input y))))))
    (if pairs
	(PAIR-output (first pairs)))))

(alt_funapply 2 increasing)



;; Part 4
;; Description: fourth lecture on symbolic programming
;;              mapping functions, other forms of iteration

;; **************************************************************************
;;                          Mapping Functions
;; **************************************************************************

;; MAPCAR

(mapcar #'first '((1 2) (3 4) (5 6)))

(mapcar #'(lambda (x y) (list x y))
	'(0 2 4 6 8)
	'(1 3 5 7 9))

;; MAPCAN

(mapcan #'(lambda (x) (if (oddp x) (list x) nil))
	'(1 2 3 4 5 6 7 8 9))

;; EVERY

(every #'oddp '(1 3 5 7))

;; SOME

(some #'evenp '(1 2 3))

;; APPLY

(apply #'+ '(1 2 3))

(apply #'+ 
       (mapcar #'(lambda (x) 
		   (if (oddp x) x 0))
	       '(1 2 3 4 5 6 7)))

;; **************************************************************************
;;                   Alternative Forms of Iteration
;; **************************************************************************

;; DO for general iteration

;; The general form is 
;;   (do index_variable_specification 
;;       (end_test result_expression)
;;       body)
;; where index_variable_specification is a list specs of the form
;;   (step_variable initial_value step_value)

(do ((i 0 (+ i 1))
     (nums nil))
    ((= i 10) nums)
    (setq nums (cons (random 1.0) nums)))

;; We could have done everything in the variable specs.
;; Notice the body of the DO in this case is empty.
(do ((i 0 (+ i 1))
     (nums nil (cons (random 1.0) nums)))
    ((= i 10) nums))

;; DOLIST for iteration over lists

(dolist (x '(1 2 3 4))
	(princ x))

;; DOTIMES for iterating i = 1 to n

(dotimes (i 10)
	 (princ i))

;; Which form of iteration should you use?

;; Which ever one you want, but you should practice using the less 
;; familiar methods.  In particular, we expect you to be able to 
;; understand code written using recursion and mapping functions.  

;; **************************************************************************
;;                   Tracing and Stepping Functions
;; **************************************************************************

(defun raise (x n)
  (if (= n 0)
      1
    (* x (raise x (- n 1)))))

;; Tell Lisp to TRACE the function RAISE.

(trace raise)

;; (raise 3 2)

;; Tell Lisp to stop tracing the function RAISE.

(untrace raise)

;; (raise 3 1)

;; STEP a function 

;; Use :n to step through evaluation. :h lists  options.

;; (step (raise 3 2))

;; **************************************************************************
;;                          Association Lists
;; **************************************************************************

;; An association list associates pairs of expressions.
;; ((name Lynn) (age 29) (profession lawyer) (status employed))

;; ASSOC 

(assoc 'b '((a 1) (b 2) (c 3)))

(setq features '((name Lynn) 
		 (profession lawyer) 
		 (status employed)))

(assoc 'status features)

;; FIND is more general than ASSOC

(find 'b '(a b c))

(find 'b '((a 1) (b 2) (c 3))
      :test #'(lambda (x y) (eq x (car y))))

(setq mom '(person (name Lynn) (status employed)))

(setq dad '(person (name Fred) (status employed)))

(setq parents (list mom dad)) 

(find 'Fred parents
      :test #'(lambda (x y)
		(eq x (second (assoc 'name (rest y))))))

;; **************************************************************************
;;                 Writing your own READ-EVAL-PRINT Loop
;; **************************************************************************


(defun alt_read_eval_print () 
  (format t "~%my prompt > ")
  (format t "~%~A" (alt_eval (read)))
  (alt_read_eval_print))

(let ((history ()) (max 3))
  (defun alt_eval (expression)
    (if (and (listp expression)
	     (eq (first expression) 'h)
	     (integerp (second expression)))
	(if (and (>= (second expression) 0)
		 (< (second expression) max))
	    (eval (nth (second expression) history))
	  "No such history expression!")
      (progn (setq history (cons expression history))
	     (if (> (length history) max)
		 (setf (rest (nthcdr (- max 1) history)) nil))
	     (eval expression)))))

;; PROGN specifies a sequence of expressions as a block; PROGN
;; returns the value of the last expresion in the sequence.