517 lines
23 KiB
Racket
517 lines
23 KiB
Racket
#lang planet dyoo/whalesong/base
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(let ()
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;; (define (caar l)
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;; (car (car l)))
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;; (define (map f l)
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;; (if (null? l)
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;; null
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;; (cons (f (car l))
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;; (map f (cdr l)))))
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;; (define (for-each f l)
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;; (if (null? l)
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;; null
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;; (begin (f (car l))
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;; (for-each f (cdr l)))))
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;; (define (memq x l)
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;; (if (null? l)
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;; #f
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;; (if (eq? x (car l))
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;; l
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;; (memq x (cdr l)))))
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;; (define (assq x l)
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;; (if (null? l)
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;; #f
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;; (if (eq? x (caar l))
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;; (car l)
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;; (assq x (cdr l)))))
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;; (define (length l)
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;; (if (null? l)
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;; 0
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;; (add1 (length (cdr l)))))
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;; (define (append l1 l2)
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;; (if (nullb? l1)
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;; l2
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;; (cons (car l1) (append (cdr l1) l2))))
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(define vector-copy
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(lambda (v)
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(let ((length (vector-length v)))
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(let ((result (make-vector length)))
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((letrec ((loop
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(lambda (n) (vector-set! result n (vector-ref v n)) (if (= n length) v (loop (+ n '1))))))
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loop)
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'0)))))
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(define sort
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(lambda (obj pred)
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(letrec ((loop (lambda (l) (if (if (pair? l) (pair? (cdr l)) '#f) (split l '() '()) l)))
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(split
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(lambda (l one two)
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(if (pair? l) (split (cdr l) two (cons (car l) one)) (merge (loop one) (loop two)))))
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(merge
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(lambda (one two)
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(if (null? one)
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(begin two)
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(if (pred (car two) (car one))
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(begin (cons (car two) (merge (cdr two) one)))
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(begin (cons (car one) (merge (cdr one) two))))))))
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(if (let ((or-part (pair? obj))) (if or-part or-part (null? obj)))
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(begin (loop obj))
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(if (vector? obj)
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(begin (sort! (vector-copy obj) pred))
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(begin (error '"sort: argument should be a list or vector" obj)))))))
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(define sort!
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(lambda (v pred)
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(letrec ((sort-internal!
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(lambda (vec temp low high)
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(if (< low high)
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(let ((middle (quotient (+ low high) '2)))
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(let ((next (+ middle '1)))
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(sort-internal! temp vec low middle)
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(sort-internal! temp vec next high)
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((letrec ((loop
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(lambda (p p1 p2)
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(if (not (> p high))
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(if (> p1 middle)
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(begin
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(vector-set! vec p (vector-ref temp p2))
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(loop (+ p '1) p1 (+ p2 '1)))
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(if (let ((or-part (> p2 high)))
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(if or-part
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or-part
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(pred (vector-ref temp p1) (vector-ref temp p2))))
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(begin
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(vector-set! vec p (vector-ref temp p1))
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(loop (+ p '1) (+ p1 '1) p2))
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(begin
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(vector-set! vec p (vector-ref temp p2))
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(loop (+ p '1) p1 (+ p2 '1)))))
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(void)))))
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loop)
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low
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low
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next)))
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(void)))))
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(if (not (vector? v)) (error '"sort!: argument not a vector" v) (void))
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(sort-internal! v (vector-copy v) '0 (- (vector-length v) '1))
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v)))
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(define adjoin (lambda (element set) (if (memq element set) set (cons element set))))
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(define eliminate
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(lambda (element set)
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(if (null? set)
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(begin set)
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(if (eq? element (car set)) (begin (cdr set)) (begin (cons (car set) (eliminate element (cdr set))))))))
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(define intersect
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(lambda (list1 list2)
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((letrec ((loop
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(lambda (l)
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(if (null? l)
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(begin '())
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(if (memq (car l) list2) (begin (cons (car l) (loop (cdr l)))) (begin (loop (cdr l))))))))
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loop)
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list1)))
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(define union (lambda (list1 list2) (if (null? list1) list2 (union (cdr list1) (adjoin (car list1) list2)))))
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(define make-internal-node vector)
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(define internal-node-name (lambda (node) (vector-ref node '0)))
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(define internal-node-green-edges (lambda (node) (vector-ref node '1)))
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(define internal-node-red-edges (lambda (node) (vector-ref node '2)))
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(define internal-node-blue-edges (lambda (node) (vector-ref node '3)))
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(define set-internal-node-name! (lambda (node name) (vector-set! node '0 name)))
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(define set-internal-node-green-edges! (lambda (node edges) (vector-set! node '1 edges)))
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(define set-internal-node-red-edges! (lambda (node edges) (vector-set! node '2 edges)))
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(define set-internal-node-blue-edges! (lambda (node edges) (vector-set! node '3 edges)))
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(define make-node
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(lambda (name blue-edges)
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(let ((name (if (symbol? name) (symbol->string name) name))
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(blue-edges (if (null? blue-edges) 'NOT-A-NODE-YET (car blue-edges))))
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(make-internal-node name '() '() blue-edges))))
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(define copy-node (lambda (node) (make-internal-node (name node) '() '() (blue-edges node))))
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(define name internal-node-name)
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(define make-edge-getter
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(lambda (selector)
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(lambda (node)
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(if (let ((or-part (none-node? node))) (if or-part or-part (any-node? node)))
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(error '"Can't get edges from the ANY or NONE nodes")
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(selector node)))))
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(define red-edges (make-edge-getter internal-node-red-edges))
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(define green-edges (make-edge-getter internal-node-green-edges))
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(define blue-edges (make-edge-getter internal-node-blue-edges))
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(define make-edge-setter
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(lambda (mutator!)
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(lambda (node value)
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(if (any-node? node)
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(begin (error '"Can't set edges from the ANY node"))
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(if (none-node? node) (begin 'OK) (begin (mutator! node value)))))))
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(define set-red-edges! (make-edge-setter set-internal-node-red-edges!))
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(define set-green-edges! (make-edge-setter set-internal-node-green-edges!))
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(define set-blue-edges! (make-edge-setter set-internal-node-blue-edges!))
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(define make-blue-edge vector)
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(define blue-edge-operation (lambda (edge) (vector-ref edge '0)))
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(define blue-edge-arg-node (lambda (edge) (vector-ref edge '1)))
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(define blue-edge-res-node (lambda (edge) (vector-ref edge '2)))
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(define set-blue-edge-operation! (lambda (edge value) (vector-set! edge '0 value)))
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(define set-blue-edge-arg-node! (lambda (edge value) (vector-set! edge '1 value)))
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(define set-blue-edge-res-node! (lambda (edge value) (vector-set! edge '2 value)))
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(define operation blue-edge-operation)
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(define arg-node blue-edge-arg-node)
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(define res-node blue-edge-res-node)
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(define set-arg-node! set-blue-edge-arg-node!)
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(define set-res-node! set-blue-edge-res-node!)
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(define lookup-op
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(lambda (op node)
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((letrec ((loop
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(lambda (edges)
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(if (null? edges)
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(begin '())
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(if (eq? op (operation (car edges))) (begin (car edges)) (begin (loop (cdr edges))))))))
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loop)
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(blue-edges node))))
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(define has-op? (lambda (op node) (not (null? (lookup-op op node)))))
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(define make-internal-graph vector)
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(define internal-graph-nodes (lambda (graph) (vector-ref graph '0)))
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(define internal-graph-already-met (lambda (graph) (vector-ref graph '1)))
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(define internal-graph-already-joined (lambda (graph) (vector-ref graph '2)))
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(define set-internal-graph-nodes! (lambda (graph nodes) (vector-set! graph '0 nodes)))
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(define make-graph (lambda (nodes) (make-internal-graph nodes (make-empty-table) (make-empty-table))))
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(define graph-nodes internal-graph-nodes)
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(define already-met internal-graph-already-met)
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(define already-joined internal-graph-already-joined)
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(define add-graph-nodes!
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(lambda (graph nodes) (set-internal-graph-nodes! graph (cons nodes (graph-nodes graph)))))
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(define copy-graph
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(lambda (g)
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(letrec ((copy-list (lambda (l) (vector->list (list->vector l)))))
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(make-internal-graph (copy-list (graph-nodes g)) (already-met g) (already-joined g)))))
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(define clean-graph
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(lambda (g)
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(letrec ((clean-node
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(lambda (node)
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(if (not (let ((or-part (any-node? node))) (if or-part or-part (none-node? node))))
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(begin (set-green-edges! node '()) (set-red-edges! node '()))
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(void)))))
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(for-each clean-node (graph-nodes g))
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g)))
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(define canonicalize-graph
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(lambda (graph classes)
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(letrec ((fix
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(lambda (node)
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(letrec ((fix-set
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(lambda (object selector mutator)
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(mutator
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object
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(map
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(lambda (node) (find-canonical-representative node classes))
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(selector object))))))
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(if (not (let ((or-part (none-node? node))) (if or-part or-part (any-node? node))))
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(begin
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(fix-set node green-edges set-green-edges!)
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(fix-set node red-edges set-red-edges!)
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(for-each
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(lambda (blue-edge)
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(set-arg-node! blue-edge (find-canonical-representative (arg-node blue-edge) classes))
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(set-res-node! blue-edge (find-canonical-representative (res-node blue-edge) classes)))
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(blue-edges node)))
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(void))
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node)))
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(fix-table
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(lambda (table)
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(letrec ((canonical? (lambda (node) (eq? node (find-canonical-representative node classes))))
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(filter-and-fix
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(lambda (predicate-fn update-fn list)
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((letrec ((loop
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(lambda (list)
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(if (null? list)
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(begin '())
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(if (predicate-fn (car list))
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(begin (cons (update-fn (car list)) (loop (cdr list))))
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(begin (loop (cdr list))))))))
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loop)
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list)))
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(fix-line
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(lambda (line)
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(filter-and-fix
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(lambda (entry) (canonical? (car entry)))
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(lambda (entry)
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(cons (car entry) (find-canonical-representative (cdr entry) classes)))
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line))))
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(if (null? table)
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'()
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(cons
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(car table)
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(filter-and-fix
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(lambda (entry) (canonical? (car entry)))
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(lambda (entry) (cons (car entry) (fix-line (cdr entry))))
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(cdr table))))))))
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(make-internal-graph
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(map (lambda (class) (fix (car class))) classes)
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(fix-table (already-met graph))
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(fix-table (already-joined graph))))))
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(define none-node (make-node 'none '(#t)))
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(define none-node? (lambda (node) (eq? node none-node)))
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(define any-node (make-node 'any '(())))
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(define any-node? (lambda (node) (eq? node any-node)))
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(define green-edge?
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(lambda (from-node to-node)
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(if (any-node? from-node)
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(begin '#f)
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(if (none-node? from-node)
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(begin '#t)
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(if (memq to-node (green-edges from-node)) (begin '#t) (begin '#f))))))
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(define red-edge?
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(lambda (from-node to-node)
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(if (any-node? from-node)
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(begin '#f)
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(if (none-node? from-node)
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(begin '#t)
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(if (memq to-node (red-edges from-node)) (begin '#t) (begin '#f))))))
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(define sig
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(let ((none-comma-any (cons none-node any-node)))
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(lambda (op node)
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(let ((the-edge (lookup-op op node)))
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(if (not (null? the-edge)) (cons (arg-node the-edge) (res-node the-edge)) none-comma-any)))))
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(define arg (lambda (pair) (car pair)))
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(define res (lambda (pair) (cdr pair)))
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(define conforms?
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(lambda (t1 t2)
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(letrec ((nodes-with-red-edges-out '())
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(add-red-edge!
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(lambda (from-node to-node)
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(set-red-edges! from-node (adjoin to-node (red-edges from-node)))
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(set! nodes-with-red-edges-out (adjoin from-node nodes-with-red-edges-out))))
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(greenify-red-edges!
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(lambda (from-node)
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(set-green-edges! from-node (append (red-edges from-node) (green-edges from-node)))
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(set-red-edges! from-node '())))
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(delete-red-edges! (lambda (from-node) (set-red-edges! from-node '())))
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(does-conform
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(lambda (t1 t2)
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(if (let ((or-part (none-node? t1))) (if or-part or-part (any-node? t2)))
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(begin '#t)
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(if (let ((or-part (any-node? t1))) (if or-part or-part (none-node? t2)))
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(begin '#f)
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(if (green-edge? t1 t2)
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(begin '#t)
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(if (red-edge? t1 t2)
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(begin '#t)
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(begin
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(add-red-edge! t1 t2)
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((letrec ((loop
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(lambda (blues)
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(if (null? blues)
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'#t
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(let ((current-edge (car blues)))
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(let ((phi (operation current-edge)))
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(if (has-op? phi t1)
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(if (does-conform (res (sig phi t1)) (res (sig phi t2)))
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(if (does-conform (arg (sig phi t2)) (arg (sig phi t1)))
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(loop (cdr blues))
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'#f)
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'#f)
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'#f)))))))
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loop)
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(blue-edges t2))))))))))
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(let ((result (does-conform t1 t2)))
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(for-each (if result greenify-red-edges! delete-red-edges!) nodes-with-red-edges-out)
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result))))
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(define equivalent? (lambda (a b) (if (conforms? a b) (conforms? b a) '#f)))
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(define classify
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(lambda (nodes)
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((letrec ((node-loop
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(lambda (classes nodes)
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(if (null? nodes)
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(map
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(lambda (class)
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(sort
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class
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(lambda (node1 node2) (< (string-length (name node1)) (string-length (name node2))))))
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classes)
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(let ((this-node (car nodes)))
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(letrec ((add-node
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(lambda (classes)
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(if (null? classes)
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(begin (list (list this-node)))
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(if (equivalent? this-node (caar classes))
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(begin (cons (cons this-node (car classes)) (cdr classes)))
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(begin (cons (car classes) (add-node (cdr classes)))))))))
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(node-loop (add-node classes) (cdr nodes))))))))
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node-loop)
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'()
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nodes)))
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(define find-canonical-representative
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(lambda (element classification)
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((letrec ((loop
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(lambda (classes)
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(if (null? classes)
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(begin (error '"Can't classify" element))
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(if (memq element (car classes)) (begin (car (car classes))) (begin (loop (cdr classes))))))))
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loop)
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classification)))
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(define reduce
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(lambda (graph) (let ((classes (classify (graph-nodes graph)))) (canonicalize-graph graph classes))))
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(define make-empty-table (lambda () (list 'TABLE)))
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(define lookup
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(lambda (table x y)
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(let ((one (assq x (cdr table)))) (if one (let ((two (assq y (cdr one)))) (if two (cdr two) '#f)) '#f))))
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(define insert!
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(lambda (table x y value)
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(letrec ((make-singleton-table (lambda (x y) (list (cons x y)))))
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(let ((one (assq x (cdr table))))
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(if one
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(set-cdr! one (cons (cons y value) (cdr one)))
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(set-cdr! table (cons (cons x (make-singleton-table y value)) (cdr table))))))))
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(define blue-edge-operate
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(lambda (arg-fn res-fn graph op sig1 sig2)
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(make-blue-edge op (arg-fn graph (arg sig1) (arg sig2)) (res-fn graph (res sig1) (res sig2)))))
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(define meet
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(lambda (graph node1 node2)
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(if (eq? node1 node2)
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(begin node1)
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(if (let ((or-part (any-node? node1))) (if or-part or-part (any-node? node2)))
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(begin any-node)
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(if (none-node? node1)
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(begin node2)
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(if (none-node? node2)
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(begin node1)
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(let ((c17352 (lookup (already-met graph) node1 node2)))
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(if c17352
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c17352
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(if (conforms? node1 node2)
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(begin node2)
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(if (conforms? node2 node1)
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(begin node1)
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(begin
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(let ((result (make-node (string-append '"(" (name node1) '" ^ " (name node2) '")") '())))
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(add-graph-nodes! graph result)
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(insert! (already-met graph) node1 node2 result)
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(set-blue-edges!
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result
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(map
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(lambda (op) (blue-edge-operate join meet graph op (sig op node1) (sig op node2)))
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(intersect (map operation (blue-edges node1)) (map operation (blue-edges node2)))))
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result))))))))))))
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(define join
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(lambda (graph node1 node2)
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(if (eq? node1 node2)
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(begin node1)
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(if (any-node? node1)
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(begin node2)
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(if (any-node? node2)
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(begin node1)
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(if (let ((or-part (none-node? node1))) (if or-part or-part (none-node? node2)))
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(begin none-node)
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(let ((c17353 (lookup (already-joined graph) node1 node2)))
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(if c17353
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c17353
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(if (conforms? node1 node2)
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(begin node1)
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(if (conforms? node2 node1)
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(begin node2)
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(begin
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(let ((result (make-node (string-append '"(" (name node1) '" v " (name node2) '")") '())))
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(add-graph-nodes! graph result)
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(insert! (already-joined graph) node1 node2 result)
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(set-blue-edges!
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result
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(map
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(lambda (op) (blue-edge-operate meet join graph op (sig op node1) (sig op node2)))
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(union (map operation (blue-edges node1)) (map operation (blue-edges node2)))))
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|
result))))))))))))
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|
(define make-lattice
|
|
(lambda (g print?)
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|
(letrec ((step
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|
(lambda (g)
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|
(let ((copy (copy-graph g)))
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|
(let ((nodes (graph-nodes copy)))
|
|
(for-each
|
|
(lambda (first)
|
|
(for-each (lambda (second) (meet copy first second) (join copy first second)) nodes))
|
|
nodes)
|
|
copy))))
|
|
(loop
|
|
(lambda (g count)
|
|
(if print? (display count) (void))
|
|
(let ((lattice (step g)))
|
|
(if print? (begin (display '" -> ") (display (length (graph-nodes lattice)))) (void))
|
|
(let ((new-g (reduce lattice)))
|
|
(let ((new-count (length (graph-nodes new-g))))
|
|
(if (= new-count count)
|
|
(begin (if print? (newline) (void)) new-g)
|
|
(begin
|
|
(if print? (begin (display '" -> ") (display new-count) (newline)) (void))
|
|
(loop new-g new-count)))))))))
|
|
(let ((graph (make-graph (adjoin any-node (adjoin none-node (graph-nodes (clean-graph g)))))))
|
|
(loop graph (length (graph-nodes graph)))))))
|
|
(define a '())
|
|
(define b '())
|
|
(define c '())
|
|
(define d '())
|
|
(define reset
|
|
(lambda ()
|
|
(set! a (make-node 'a '()))
|
|
(set! b (make-node 'b '()))
|
|
(set-blue-edges! a (list (make-blue-edge 'phi any-node b)))
|
|
(set-blue-edges! b (list (make-blue-edge 'phi any-node a) (make-blue-edge 'theta any-node b)))
|
|
(set! c (make-node '"c" '()))
|
|
(set! d (make-node '"d" '()))
|
|
(set-blue-edges! c (list (make-blue-edge 'theta any-node b)))
|
|
(set-blue-edges! d (list (make-blue-edge 'phi any-node c) (make-blue-edge 'theta any-node d)))
|
|
'(made a b c d)))
|
|
(define test
|
|
(lambda () (reset) (map name (graph-nodes (make-lattice (make-graph (list a b c d any-node none-node)) '#t)))))
|
|
(define go
|
|
(lambda ()
|
|
(reset)
|
|
(let ((result
|
|
'("(((b v d) ^ a) v c)"
|
|
"(c ^ d)"
|
|
"(b v (a ^ d))"
|
|
"((a v d) ^ b)"
|
|
"(b v d)"
|
|
"(b ^ (a v c))"
|
|
"(a v (c ^ d))"
|
|
"((b v d) ^ a)"
|
|
"(c v (a v d))"
|
|
"(a v c)"
|
|
"(d v (b ^ (a v c)))"
|
|
"(d ^ (a v c))"
|
|
"((a ^ d) v c)"
|
|
"((a ^ b) v d)"
|
|
"(((a v d) ^ b) v (a ^ d))"
|
|
"(b ^ d)"
|
|
"(b v (a v d))"
|
|
"(a ^ c)"
|
|
"(b ^ (c v d))"
|
|
"(a ^ b)"
|
|
"(a v b)"
|
|
"((a ^ d) ^ b)"
|
|
"(a ^ d)"
|
|
"(a v d)"
|
|
"d"
|
|
"(c v d)"
|
|
"a"
|
|
"b"
|
|
"c"
|
|
"any"
|
|
"none")))
|
|
(if (equal? (test) result) (display '" ok.") (display '" um."))
|
|
(newline))))
|
|
|
|
|
|
(void ((letrec ((loop (lambda (n) (if (zero? n) 'done (begin (go) (loop (- n '1))))))) loop) 1))) |