;;;; -*- Mode: Lisp; Syntax: Common-Lisp -*-
;;;; Code from Paradigms of AI Programming
;;;; Copyright (c) 1991 Peter Norvig

(translate-to-expression '(if z is 3 |,| what is twice z))
; Input: (If z is 3, what is twice z)
; Rule: ((if ?x |,| ?y)       (?x ?y))
; Binding: ((?x . (z is 3))  (?y . (what is twice z)))
;  Input: (z is 3)
;  Rule: ((?x is ?y)          (= ?x ?y))
;  Result: (= z 3)
;  Input: (what is twice z ?)
;  Rule: ((?x is ?y)          (= ?x ?y))
;  Binding: ((?x . what) (?y . (twice z)))
;    Input: (twice z)
;    Rule: ((twice ?x)         (* 2 ?x))
;    Result: (* 2 z)
;  Result: (= what (* 2 z))
; Result: ((= z 3) (= what (* 2 z)))

(trace isolate solve)
;;;; -> (isolate solve)

(solve-equations '((= (+ 3 4) (* (- 5 (+ 2 x)) 7))
                   (= (+ (* 3 x) y) 12)))
; The equations to be solved are:
;   (3 + 4) = ((5 - (2 + X)) * 7)
;   ((3 * X) + Y) = 12
; (1 ENTER SOLVE: ((= (+ 3 4) (* (- 5 (+ 2 X)) 7))
;                 (= (+ (* 3 X) Y) 12)) NIL)
;  (1 ENTER ISOLATE: (= (+ 3 4) (* (- 5 (+ 2 X)) 7)) X)
;    (2 ENTER ISOLATE: (= (* (- 5 (+ 2 X)) 7) (+ 3 4)) X)
;      (3 ENTER ISOLATE: (= (- 5 (+ 2 X)) (/ (+ 3 4) 7)) X)
;        (4 ENTER ISOLATE: (= (+ 2 X) (- 5 (/ (+ 3 4) 7))) X)
;          (5 ENTER ISOLATE: (= X (- (- 5 (/ (+ 3 4) 7)) 2)) X)
;          (5 EXIT ISOLATE: (= X (- (- 5 (/ (+ 3 4) 7)) 2)))
;        (4 EXIT ISOLATE: (= X (- (- 5 (/ (+ 3 4) 7)) 2)))
;      (3 EXIT ISOLATE: (= X (- (- 5 (/ (+ 3 4) 7)) 2)))
;    (2 EXIT ISOLATE: (= X (- (- 5 (/ (+ 3 4) 7)) 2)))
;  (1 EXIT ISOLATE: (= X (- (- 5 (/ (+ 3 4) 7)) 2)))
;  (2 ENTER SOLVE: ((= (+ (* 3 2) Y) 12)) ((= X 2)))
;    (1 ENTER ISOLATE: (= (+ (* 3 2) Y) 12) Y)
;      (2 ENTER ISOLATE: (= Y (- 12 (* 3 2))) Y)
;      (2 EXIT ISOLATE: (= Y (- 12 (* 3 2))))
;    (1 EXIT ISOLATE: (= Y (- 12 (* 3 2))))
;    (3 ENTER SOLVE: NIL ((= Y 6) (= X 2)))
;    (3 EXIT SOLVE: ((= Y 6) (= X 2)))
;  (2 EXIT SOLVE: ((= Y 6) (= X 2)))
; (1 EXIT SOLVE: ((= Y 6) (= X 2)))
; The solution is:
;   Y = 6
;   X = 2
; -> NIL

(student '(If the number of customers Tom gets is twice the square of
           20 % of the number of advertisements he runs |,| 
           and the number of advertisements is 45 |,|
           then what is the number of customers Tom gets ?))
; The equations to be solved are:
;   CUSTOMERS = (2 * (((20 / 100) * ADVERTISEMENTS) * 
;                     ((20 / 100) * ADVERTISEMENTS)))
;   ADVERTISEMENTS = 45
;   WHAT = CUSTOMERS
; 
; The solution is:
;   WHAT = 162
;   CUSTOMERS = 162
;   ADVERTISEMENTS = 45
; -> NIL

(student '(The daily cost of living for a group is the overhead cost plus 
           the running cost for each person times the number of people in 
           the group |.|  This cost for one group equals $ 100 |,|
           and the number of people in the group is 40 |.|
           If the overhead cost is 10 times the running cost |,|
           find the overhead and running cost for each person |.|))
; The equations to be solved are:
;   DAILY = (OVERHEAD + (RUNNING * PEOPLE))
;   COST = 100
;   PEOPLE = 40
;   OVERHEAD = (10 * RUNNING)
;   TO-FIND-1 = OVERHEAD
;   TO-FIND-2 = RUNNING
; 
; The solution is:
;   PEOPLE = 40
;   COST = 100
; -> NIL

(student '(Fran's age divided by Robin's height is one half Kelly's IQ |.|
           Kelly's IQ minus 80 is Robin's height |.|
           If Robin is 4 feet tall |,| how old is Fran ?))
; The equations to be solved are:
;   (FRAN / ROBIN) = (KELLY / 2)
;   (KELLY - 80) = ROBIN
;   ROBIN = 4
;   HOW = FRAN
; 
; The solution is:
;   HOW = 168
;   FRAN = 168
;   KELLY = 84
;   ROBIN = 4
; -> NIL

(student '(Fran's age divided by Robin's height is one half Kelly's IQ |.|
           Kelly's IQ minus 80 is Robin's height |.|
           If Robin is 0 feet tall |,| how old is Fran ?))
; The equations to be solved are:
;   (FRAN / ROBIN) = (KELLY / 2)
;   (KELLY - 80) = ROBIN
;   ROBIN = 0
;   HOW = FRAN
; 
; The solution is:
;   HOW = 0
;   FRAN = 0
;   KELLY = 80
;   ROBIN = 0
; -> NIL

(student '(Fran's age times Robin's height is one half Kelly's IQ |.|
	   Kelly's IQ minus 80 is Robin's height |.|
	   If Robin is 0 feet tall |,| how old is Fran ?))
; The equations to be solved are:
;   (FRAN * ROBIN) = (KELLY / 2)
;   (KELLY - 80) = ROBIN
;   ROBIN = 0
;   HOW = FRAN
; 
; >>Error: There was an attempt to divide a number by zero