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order-relation.rkt
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order-relation.rkt
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#lang racket/base
;;;; This file has been changed from its original dharmatech/mpl version.
(require racket/match
"misc.rkt")
(provide term
const
order-relation)
;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define (term u)
(match u
[(? number?) #f]
[`(* ,(and u1 (? number?)) . ,u-rest)
`(* ,@u-rest)]
[`(* . ,u-elts) u]
[else `(* ,u)]))
;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define (const u)
(match u
[(? number?) #f]
[`(* ,(and u1 (? number?)) . ,u-rest)
u1]
[`(* . ,u-elts) 1]
[else 1]))
;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; TODO: <=> comparators
(define (O-3 u-elts v-elts)
(cond ((null? u-elts) #t)
((null? v-elts) #f)
(else
(let ((u (car u-elts))
(v (car v-elts)))
(if (not (equal? u v))
(order-relation u v)
(O-3 (cdr u-elts)
(cdr v-elts)))))))
(define (order-relation u v [already-exchanged? #f])
(define uop (operator-kind u))
(define vop (operator-kind v))
(cond ((and (number? u)
(number? v)) ;; O-1
(< u v))
((and (symbol? u)
(symbol? v)) ;; O-2
(symbol<? u v))
[(eq? 'let* uop)
(not (order-relation v (list-ref u 2)))]
((or (and (product? u)
(product? v))
(and (sum? u)
(sum? v))) ;; O-3
(O-3 (reverse (cdr u))
(reverse (cdr v))))
((and (power? u)
(power? v)) ;; O-4
(if (equal? (base u)
(base v))
(order-relation (exponent u)
(exponent v))
(order-relation (base u)
(base v))))
((and (factorial? u)
(factorial? v)) ;; O-5
(order-relation (list-ref u 1)
(list-ref v 1)))
((and (function? u)
(function? v)) ;; O-6
(if (equal? (car u)
(car v))
(O-3 (cdr u)
(cdr v))
(order-relation (car u)
(car v))))
((and (number? u)
(not (number? v))) ;; O-7
#t)
((and (product? u)
(or (power? v)
(sum? v)
(factorial? v)
(function? v)
(symbol? v))) ;; O-8
(order-relation u `(* ,v)))
((and (power? u)
(or (sum? v)
(factorial? v)
(function? v)
(symbol? v))) ;; O-9
(order-relation u `(^ ,v 1)))
((and (sum? u)
(or (factorial? v)
(function? v)
(symbol? v))) ;; O-10
(order-relation u `(+ ,v)))
((and (factorial? u)
(or (function? v)
(symbol? v))) ;; O-11
(if (equal? (list-ref u 1) v)
#f
(order-relation u `(! ,v)))) ; ???
((and (function? u)
(symbol? v)) ;; O-12
(if (equal? (car u) v)
#f
(order-relation (car u) v)))
[already-exchanged?
(error "Cannot find an order relation for " (list u v))]
(else ;; O-13
(not (order-relation v u #t)))))