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CprS376 Class 21

Logic Programming

Class 20 - Section 4.4



Contents

Stream ADT

;; streamADT-SICP.ss

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;   streams for the SICP QUERY SYSTEM
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; the SICP stream ADT is based on five definitions:

;     stream-car
;     stream-cdr
;     cons-stream
;     the-empty-stream
;     stream-null?

;; we assume that the underlying Scheme implementation supports force and delay

(define compose
  (lambda (f g)
    (lambda (x)
      (f (g x)))))

(define stream-car 
  (compose car force))

(define stream-cdr 
  (compose cdr force))

(extend-syntax (cons-stream)
               ((cons-stream expr stream) 
                (delay (cons expr stream))))

(define the-end-of-stream-tag "end of stream")

(define the-empty-stream
  (cons-stream the-end-of-stream-tag the-empty-stream))

(define stream-null?
  (let ((end-of-stream?
          (lambda (x)
            (eq? x the-end-of-stream-tag))))
    (compose end-of-stream? stream-car)))


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; coercions
;;     based on three utilities from Friedman, Wand, and Haynes, 
;;     "Scheme and the Art of Programming," Chapter 15, pages 484-485
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;


;; list->stream

(define list->stream
  (lambda (ls)
    (if (null? ls)
      the-empty-stream
      (cons-stream (car ls)
                   (list->stream (cdr ls))))))

;; stream->list

(define stream->list
  (lambda (strm n)
    (if (or (stream-null? strm) (zero? n))
        '()
        (cons (stream-car strm)
              (stream->list (stream-cdr strm) (sub1 n))))))

;; finite-stream->list

(define finite-stream->list
  (lambda (finite-stream)
    (stream->list finite-stream -1)))

;; compatibility

(define true #t)
(define false #f)


SICP Query System

;; ch4-query.ss

;;;;QUERY SYSTEM FROM SECTION 4.4.4 OF
;;;; STRUCTURE AND INTERPRETATION OF COMPUTER PROGRAMS

;;;;Matches code in ch4.scm
;;;;Includes:
;;;;  -- supporting code from 4.1, chapter 3, and instructor's manual
;;;;  -- data base from Section 4.4.1 -- see microshaft-data-base below

;;;;This file can be loaded into Scheme as a whole.
;;;;In order to run the query system, the Scheme must support streams.

;;;;NB. PUT's are commented out and no top-level table is set up.
;;;;Instead use initialize-data-base (from manual), supplied in this file.


;;;SECTION 4.4.4.1
;;;The Driver Loop and Instantiation

(define input-prompt ";;; Query input:")
(define output-prompt ";;; Query results:")

(define (query-driver-loop)
  (prompt-for-input input-prompt)
  (let ((q (query-syntax-process (read))))
    (cond ((assertion-to-be-added? q)
           (add-rule-or-assertion! (add-assertion-body q))
           (newline)
           (display "Assertion added to data base.")
           (query-driver-loop))
          (else
           (newline)
           (display output-prompt)
           ;; [extra newline at end] (announce-output output-prompt)
           (display-stream
             (stream-map
               (lambda (frame)
                 (instantiate q
                              frame
                              (lambda (v f)
                                (contract-question-mark v))))
               (qeval q (singleton-stream '()))))
           (query-driver-loop)))))

;; <cp: a more friendly driver loop>

(define (query-driver-loop)
  (prompt-for-input input-prompt)
  (let ((q (query-syntax-process (read))))
    (cond ((equal? q 'bye) 'chao)
          ((assertion-to-be-added? q)
           (add-rule-or-assertion! (add-assertion-body q))
           (newline)
           (display "Assertion added to data base.")
           (query-driver-loop))
          (else
           (newline)
           (display output-prompt)
           ;; [extra newline at end] (announce-output output-prompt)
           (display-stream
             (stream-map
               (lambda (frame)
                 (instantiate q
                              frame
                              (lambda (v f)
                                (contract-question-mark v))))
               (qeval q (singleton-stream '()))))
           (query-driver-loop)))))

(define (instantiate exp frame unbound-var-handler)
  (define (copy exp)
    (cond ((var? exp)
           (let ((binding (binding-in-frame exp frame)))
             (if binding
                 (copy (binding-value binding))
                 (unbound-var-handler exp frame))))
          ((pair? exp)
           (cons (copy (car exp)) (copy (cdr exp))))
          (else exp)))
  (copy exp))


;;;SECTION 4.4.4.2
;;;The Evaluator

(define (qeval query frame-stream)
  (let ((qproc (get (type query) 'qeval)))
    (if qproc
        (qproc (contents query) frame-stream)
        (simple-query query frame-stream))))

;;;Simple queries

(define (simple-query query-pattern frame-stream)
  (stream-flatmap
   (lambda (frame)
     (stream-append-delayed
      (find-assertions query-pattern frame)
      (delay (apply-rules query-pattern frame))))
   frame-stream))

;;;Compound queries

(define (conjoin conjuncts frame-stream)
  (if (empty-conjunction? conjuncts)
      frame-stream
      (conjoin (rest-conjuncts conjuncts)
               (qeval (first-conjunct conjuncts)
                      frame-stream))))

;;(put 'and 'qeval conjoin)


(define (disjoin disjuncts frame-stream)
  (if (empty-disjunction? disjuncts)
      the-empty-stream
      (interleave-delayed
       (qeval (first-disjunct disjuncts) frame-stream)
       (delay (disjoin (rest-disjuncts disjuncts)
                       frame-stream)))))

;;(put 'or 'qeval disjoin)

;;;Filters

(define (negate operands frame-stream)
  (stream-flatmap
   (lambda (frame)
     (if (stream-null? (qeval (negated-query operands)
                              (singleton-stream frame)))
         (singleton-stream frame)
         the-empty-stream))
   frame-stream))

;;(put 'not 'qeval negate)

(define (lisp-value call frame-stream)
  (stream-flatmap
   (lambda (frame)
     (if (execute
          (instantiate
           call
           frame
           (lambda (v f)
             (error "Unknown pat var -- LISP-VALUE" v))))
         (singleton-stream frame)
         the-empty-stream))
   frame-stream))

;;(put 'lisp-value 'qeval lisp-value)

; (define (execute exp)
;   (apply (eval (predicate exp) user-initial-environment)
;          (args exp)))

;; <cp: eliminate user-initial-environment>

(define (execute exp)
  (apply (eval (predicate exp))
         (args exp)))

(define (always-true ignore frame-stream) frame-stream)

;;(put 'always-true 'qeval always-true)

;;;SECTION 4.4.4.3
;;;Finding Assertions by Pattern Matching

(define (find-assertions pattern frame)
  (stream-flatmap (lambda (datum)
                    (check-an-assertion datum pattern frame))
                  (fetch-assertions pattern frame)))

(define (check-an-assertion assertion query-pat query-frame)
  (let ((match-result
         (pattern-match query-pat assertion query-frame)))
    (if (eq? match-result 'failed)
        the-empty-stream
        (singleton-stream match-result))))

(define (pattern-match pat dat frame)
  (cond ((eq? frame 'failed) 'failed)
        ((equal? pat dat) frame)
        ((var? pat) (extend-if-consistent pat dat frame))
        ((and (pair? pat) (pair? dat))
         (pattern-match (cdr pat)
                        (cdr dat)
                        (pattern-match (car pat)
                                       (car dat)
                                       frame)))
        (else 'failed)))

(define (extend-if-consistent var dat frame)
  (let ((binding (binding-in-frame var frame)))
    (if binding
        (pattern-match (binding-value binding) dat frame)
        (extend var dat frame))))

;;;SECTION 4.4.4.4
;;;Rules and Unification

(define (apply-rules pattern frame)
  (stream-flatmap (lambda (rule)
                    (apply-a-rule rule pattern frame))
                  (fetch-rules pattern frame)))

(define (apply-a-rule rule query-pattern query-frame)
  (let ((clean-rule (rename-variables-in rule)))
    (let ((unify-result
           (unify-match query-pattern
                        (conclusion clean-rule)
                        query-frame)))
      (if (eq? unify-result 'failed)
          the-empty-stream
          (qeval (rule-body clean-rule)
                 (singleton-stream unify-result))))))

(define (rename-variables-in rule)
  (let ((rule-application-id (new-rule-application-id)))
    (define (tree-walk exp)
      (cond ((var? exp)
             (make-new-variable exp rule-application-id))
            ((pair? exp)
             (cons (tree-walk (car exp))
                   (tree-walk (cdr exp))))
            (else exp)))
    (tree-walk rule)))

(define (unify-match p1 p2 frame)
  (cond ((eq? frame 'failed) 'failed)
        ((equal? p1 p2) frame)
        ((var? p1) (extend-if-possible p1 p2 frame))
        ((var? p2) (extend-if-possible p2 p1 frame)) ; {\em ; ***}
        ((and (pair? p1) (pair? p2))
         (unify-match (cdr p1)
                      (cdr p2)
                      (unify-match (car p1)
                                   (car p2)
                                   frame)))
        (else 'failed)))

(define (extend-if-possible var val frame)
  (let ((binding (binding-in-frame var frame)))
    (cond (binding
           (unify-match
            (binding-value binding) val frame))
          ((var? val)                     ; {\em ; ***}
           (let ((binding (binding-in-frame val frame)))
             (if binding
                 (unify-match
                  var (binding-value binding) frame)
                 (extend var val frame))))
          ((depends-on? val var frame)    ; {\em ; ***}
           'failed)
          (else (extend var val frame)))))

(define (depends-on? exp var frame)
  (define (tree-walk e)
    (cond ((var? e)
           (if (equal? var e)
               true
               (let ((b (binding-in-frame e frame)))
                 (if b
                     (tree-walk (binding-value b))
                     false))))
          ((pair? e)
           (or (tree-walk (car e))
               (tree-walk (cdr e))))
          (else false)))
  (tree-walk exp))

;;;SECTION 4.4.4.5
;;;Maintaining the Data Base

(define THE-ASSERTIONS the-empty-stream)

(define (fetch-assertions pattern frame)
  (if (use-index? pattern)
      (get-indexed-assertions pattern)
      (get-all-assertions)))

(define (get-all-assertions) THE-ASSERTIONS)

(define (get-indexed-assertions pattern)
  (get-stream (index-key-of pattern) 'assertion-stream))

(define (get-stream key1 key2)
  (let ((s (get key1 key2)))
    (if s s the-empty-stream)))

(define THE-RULES the-empty-stream)

(define (fetch-rules pattern frame)
  (if (use-index? pattern)
      (get-indexed-rules pattern)
      (get-all-rules)))

(define (get-all-rules) THE-RULES)

(define (get-indexed-rules pattern)
  (stream-append
   (get-stream (index-key-of pattern) 'rule-stream)
   (get-stream '? 'rule-stream)))

(define (add-rule-or-assertion! assertion)
  (if (rule? assertion)
      (add-rule! assertion)
      (add-assertion! assertion)))

(define (add-assertion! assertion)
  (store-assertion-in-index assertion)
  (let ((old-assertions THE-ASSERTIONS))
    (set! THE-ASSERTIONS
          (cons-stream assertion old-assertions))
    'ok))

(define (add-rule! rule)
  (store-rule-in-index rule)
  (let ((old-rules THE-RULES))
    (set! THE-RULES (cons-stream rule old-rules))
    'ok))

(define (store-assertion-in-index assertion)
  (if (indexable? assertion)
      (let ((key (index-key-of assertion)))
        (let ((current-assertion-stream
               (get-stream key 'assertion-stream)))
          (put key
               'assertion-stream
               (cons-stream assertion
                            current-assertion-stream))))))

(define (store-rule-in-index rule)
  (let ((pattern (conclusion rule)))
    (if (indexable? pattern)
        (let ((key (index-key-of pattern)))
          (let ((current-rule-stream
                 (get-stream key 'rule-stream)))
            (put key
                 'rule-stream
                 (cons-stream rule
                              current-rule-stream)))))))

(define (indexable? pat)
  (or (constant-symbol? (car pat))
      (var? (car pat))))

(define (index-key-of pat)
  (let ((key (car pat)))
    (if (var? key) '? key)))

(define (use-index? pat)
  (constant-symbol? (car pat)))

;;;SECTION 4.4.4.6
;;;Stream operations

(define (stream-append-delayed s1 delayed-s2)
  (if (stream-null? s1)
      (force delayed-s2)
      (cons-stream
       (stream-car s1)
       (stream-append-delayed (stream-cdr s1) delayed-s2))))

(define (interleave-delayed s1 delayed-s2)
  (if (stream-null? s1)
      (force delayed-s2)
      (cons-stream
       (stream-car s1)
       (interleave-delayed (force delayed-s2)
                           (delay (stream-cdr s1))))))

(define (stream-flatmap proc s)
  (flatten-stream (stream-map proc s)))

(define (flatten-stream stream)
  (if (stream-null? stream)
      the-empty-stream
      (interleave-delayed
       (stream-car stream)
       (delay (flatten-stream (stream-cdr stream))))))


(define (singleton-stream x)
  (cons-stream x the-empty-stream))


;;;SECTION 4.4.4.7
;;;Query syntax procedures

(define (type exp)
  (if (pair? exp)
      (car exp)
      (error "Unknown expression TYPE" exp)))

(define (contents exp)
  (if (pair? exp)
      (cdr exp)
      (error "Unknown expression CONTENTS" exp)))

(define (assertion-to-be-added? exp)
  (eq? (type exp) 'assert!))

(define (add-assertion-body exp)
  (car (contents exp)))

(define (empty-conjunction? exps) (null? exps))
(define (first-conjunct exps) (car exps))
(define (rest-conjuncts exps) (cdr exps))

(define (empty-disjunction? exps) (null? exps))
(define (first-disjunct exps) (car exps))
(define (rest-disjuncts exps) (cdr exps))

(define (negated-query exps) (car exps))

(define (predicate exps) (car exps))
(define (args exps) (cdr exps))


(define (rule? statement)
  (tagged-list? statement 'rule))

(define (conclusion rule) (cadr rule))

(define (rule-body rule)
  (if (null? (cddr rule))
      '(always-true)
      (caddr rule)))

(define (query-syntax-process exp)
  (map-over-symbols expand-question-mark exp))

(define (map-over-symbols proc exp)
  (cond ((pair? exp)
         (cons (map-over-symbols proc (car exp))
               (map-over-symbols proc (cdr exp))))
        ((symbol? exp) (proc exp))
        (else exp)))

(define (expand-question-mark symbol)
  (let ((chars (symbol->string symbol)))
    (if (string=? (substring chars 0 1) "?")
        (list '?
              (string->symbol
               (substring chars 1 (string-length chars))))
        symbol)))

(define (var? exp)
  (tagged-list? exp '?))

(define (constant-symbol? exp) (symbol? exp))

(define rule-counter 0)

(define (new-rule-application-id)
  (set! rule-counter (+ 1 rule-counter))
  rule-counter)

(define (make-new-variable var rule-application-id)
  (cons '? (cons rule-application-id (cdr var))))

(define (contract-question-mark variable)
  (string->symbol
   (string-append "?" 
     (if (number? (cadr variable))
         (string-append (symbol->string (caddr variable))
                        "-"
                        (number->string (cadr variable)))
         (symbol->string (cadr variable))))))


;;;SECTION 4.4.4.8
;;;Frames and bindings
(define (make-binding variable value)
  (cons variable value))

(define (binding-variable binding)
  (car binding))

(define (binding-value binding)
  (cdr binding))


(define (binding-in-frame variable frame)
  (assoc variable frame))

(define (extend variable value frame)
  (cons (make-binding variable value) frame))



;;;;From Section 4.1

(define (tagged-list? exp tag)
  (if (pair? exp)
      (eq? (car exp) tag)
      false))

(define (prompt-for-input string)
  (newline) (newline) (display string) (newline))


;;;;Stream support from Chapter 3

(define (stream-map proc s)
  (if (stream-null? s)
      the-empty-stream
      (cons-stream (proc (stream-car s))
                   (stream-map proc (stream-cdr s)))))

(define (stream-for-each proc s)
  (if (stream-null? s)
      'done
      (begin (proc (stream-car s))
             (stream-for-each proc (stream-cdr s)))))

(define (display-stream s)
  (stream-for-each display-line s))
(define (display-line x)
  (newline)
  (display x))

(define (stream-filter pred stream)
  (cond ((stream-null? stream) the-empty-stream)
        ((pred (stream-car stream))
         (cons-stream (stream-car stream)
                      (stream-filter pred
                                     (stream-cdr stream))))
        (else (stream-filter pred (stream-cdr stream)))))

(define (stream-append s1 s2)
  (if (stream-null? s1)
      s2
      (cons-stream (stream-car s1)
                   (stream-append (stream-cdr s1) s2))))

(define (interleave s1 s2)
  (if (stream-null? s1)
      s2
      (cons-stream (stream-car s1)
                   (interleave s2 (stream-cdr s1)))))

;;;;Table support from Chapter 3, Section 3.3.3 (local tables)

(define (make-table)
  (let ((local-table (list '*table*)))
    (define (lookup key-1 key-2)
      (let ((subtable (assoc key-1 (cdr local-table))))
        (if subtable
            (let ((record (assoc key-2 (cdr subtable))))
              (if record
                  (cdr record)
                  false))
            false)))
    (define (insert! key-1 key-2 value)
      (let ((subtable (assoc key-1 (cdr local-table))))
        (if subtable
            (let ((record (assoc key-2 (cdr subtable))))
              (if record
                  (set-cdr! record value)
                  (set-cdr! subtable
                            (cons (cons key-2 value)
                                  (cdr subtable)))))
            (set-cdr! local-table
                      (cons (list key-1
                                  (cons key-2 value))
                            (cdr local-table)))))
      'ok)    
    (define (dispatch m)
      (cond ((eq? m 'lookup-proc) lookup)
            ((eq? m 'insert-proc!) insert!)
            (else (error "Unknown operation -- TABLE" m))))
    dispatch))


;;;; From instructor's manual

(define get '())

(define put '())

(define (initialize-data-base rules-and-assertions)
  (define (deal-out r-and-a rules assertions)
    (cond ((null? r-and-a)
           (set! THE-ASSERTIONS (list->stream assertions))
           (set! THE-RULES (list->stream rules))
           'done)
          (else
           (let ((s (query-syntax-process (car r-and-a))))
             (cond ((rule? s)
                    (store-rule-in-index s)
                    (deal-out (cdr r-and-a)
                              (cons s rules)
                              assertions))
                   (else
                    (store-assertion-in-index s)
                    (deal-out (cdr r-and-a)
                              rules
                              (cons s assertions))))))))
  (let ((operation-table (make-table)))
    (set! get (operation-table 'lookup-proc))
    (set! put (operation-table 'insert-proc!)))
  (put 'and 'qeval conjoin)
  (put 'or 'qeval disjoin)
  (put 'not 'qeval negate)
  (put 'lisp-value 'qeval lisp-value)
  (put 'always-true 'qeval always-true)
  (deal-out rules-and-assertions '() '()))

;; Do following to reinit the data base from microshaft-data-base
;;  in Scheme (not in the query driver loop)
;; (initialize-data-base microshaft-data-base)

(define microshaft-data-base
  '(
;; from section 4.4.1
(address (Bitdiddle Ben) (Slumerville (Ridge Road) 10))
(job (Bitdiddle Ben) (computer wizard))
(salary (Bitdiddle Ben) 60000)

(address (Hacker Alyssa P) (Cambridge (Mass Ave) 78))
(job (Hacker Alyssa P) (computer programmer))
(salary (Hacker Alyssa P) 40000)
(supervisor (Hacker Alyssa P) (Bitdiddle Ben))

(address (Fect Cy D) (Cambridge (Ames Street) 3))
(job (Fect Cy D) (computer programmer))
(salary (Fect Cy D) 35000)
(supervisor (Fect Cy D) (Bitdiddle Ben))

(address (Tweakit Lem E) (Boston (Bay State Road) 22))
(job (Tweakit Lem E) (computer technician))
(salary (Tweakit Lem E) 25000)
(supervisor (Tweakit Lem E) (Bitdiddle Ben))

(address (Reasoner Louis) (Slumerville (Pine Tree Road) 80))
(job (Reasoner Louis) (computer programmer trainee))
(salary (Reasoner Louis) 30000)
(supervisor (Reasoner Louis) (Hacker Alyssa P))

(supervisor (Bitdiddle Ben) (Warbucks Oliver))

(address (Warbucks Oliver) (Swellesley (Top Heap Road)))
(job (Warbucks Oliver) (administration big wheel))
(salary (Warbucks Oliver) 150000)

(address (Scrooge Eben) (Weston (Shady Lane) 10))
(job (Scrooge Eben) (accounting chief accountant))
(salary (Scrooge Eben) 75000)
(supervisor (Scrooge Eben) (Warbucks Oliver))

(address (Cratchet Robert) (Allston (N Harvard Street) 16))
(job (Cratchet Robert) (accounting scrivener))
(salary (Cratchet Robert) 18000)
(supervisor (Cratchet Robert) (Scrooge Eben))

(address (Aull DeWitt) (Slumerville (Onion Square) 5))
(job (Aull DeWitt) (administration secretary))
(salary (Aull DeWitt) 25000)
(supervisor (Aull DeWitt) (Warbucks Oliver))

(can-do-job (computer wizard) (computer programmer))
(can-do-job (computer wizard) (computer technician))

(can-do-job (computer programmer)
            (computer programmer trainee))

(can-do-job (administration secretary)
            (administration big wheel))

(rule (lives-near ?person-1 ?person-2)
      (and (address ?person-1 (?town . ?rest-1))
           (address ?person-2 (?town . ?rest-2))
           (not (same ?person-1 ?person-2))))

(rule (same ?x ?x))

(rule (wheel ?person)
      (and (supervisor ?middle-manager ?person)
           (supervisor ?x ?middle-manager)))

(rule (outranked-by ?staff-person ?boss)
      (or (supervisor ?staff-person ?boss)
          (and (supervisor ?staff-person ?middle-manager)
               (outranked-by ?middle-manager ?boss))))
))


Query Transcript

;; ch4-query.transcript

;; =============================

;; load query source code

(load "streamADT-SICP.ss")
(load "ch4-query.ss")

;; =============================

(initialize-data-base microshaft-data-base)

(query-driver-loop)

(job ?x (computer programmer))

(address ?x ?y)

(supervisor ?x ?x)

(job ?x (computer ?type))

(job ?x (computer . ?type))

;;; Compound queries

(and (job ?person (computer programmer))
     (address ?person ?where))

(or (supervisor ?x (Bitdiddle Ben))
    (supervisor ?x (Hacker Alyssa P)))

(and (supervisor ?x (Bitdiddle Ben))
     (not (job ?x (computer programmer))))

(and (salary ?person ?amount)
     (lisp-value > ?amount 30000))

;;; more queries

(lives-near ?x (Bitdiddle Ben))

(and (job ?x (computer programmer))
     (lives-near ?x (Bitdiddle Ben)))

bye



SICP Source Code

Programming Exercises

In class today we will continue our work on the following exercises from chapter 4: 1, 4, 5, 6, 7, 8, 11, 13, 14, 15, 16, 20, 23, 24, 25, 27, 29, 31, 33, 34, 38, 39, 42, 43, 45, 50, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 69.