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linear.ss
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linear.ss
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(module linear mzscheme
(require (lib "plt-match.ss")
(lib "list.ss")
(lib "etc.ss")
(lib "pretty.ss"))
(define-struct atom () (make-inspector))
(define-struct (atom:var atom) (mult id) (make-inspector))
(define-struct (atom:int atom) (int) (make-inspector))
(define-struct simple-expr () (make-inspector))
(define-struct (simple-expr:+ simple-expr) (args) (make-inspector))
(define-struct (simple-expr:- simple-expr) (arg1 arg2) (make-inspector))
(define parse-simple-expr
(match-lambda
[`(+ ,a1 ,a2)
(make-simple-expr:+
(list
(parse-simple-expr a1)
(parse-simple-expr a2)))]
[`(- ,a1 ,a2)
(make-simple-expr:-
(parse-simple-expr a1)
(parse-simple-expr a2))]
[`(* ,(? number? n) ,(? symbol? v))
(make-atom:var n v)]
[(? number? n)
(make-atom:int n)]
[(? symbol? v)
(make-atom:var 1 v)]))
(define simple-expr->sexp
(match-lambda
[(struct simple-expr:+ (lst))
`(+ ,@(map simple-expr->sexp lst))]
[(struct simple-expr:- (a1 a2))
`(- ,(simple-expr->sexp a1) ,(simple-expr->sexp a2))]
[(struct atom:var (n i))
(if (eq? 1 n)
i
`(* ,n ,i))]
[(struct atom:int (n))
n]))
(define simplify-simple-expr
(match-lambda
[(struct simple-expr:+ (lst))
(make-simple-expr:+
(foldl (lambda (t a)
(if (simple-expr:+? t)
(append (simple-expr:+-args (simplify-simple-expr t)) a)
(list* t a)))
empty
lst))]
[(struct simple-expr:- (a1 a2))
(make-simple-expr:- a1 a2)]
[(struct atom:var (n i))
(make-atom:var n i)]
[(struct atom:int (n))
(make-atom:int n)]))
(define-struct simple-eq () (make-inspector))
(define-struct (simple-eq:eq simple-eq) (left right) (make-inspector))
(define-struct (simple-eq:ne simple-eq) (left right) (make-inspector))
(define-struct (simple-eq:lt simple-eq) (left right) (make-inspector))
(define-struct (simple-eq:gt simple-eq) (left right) (make-inspector))
(define-struct (simple-eq:lte simple-eq) (left right) (make-inspector))
(define-struct (simple-eq:gte simple-eq) (left right) (make-inspector))
(define-struct ele () (make-inspector))
(define-struct (ele:and ele) (left right) (make-inspector))
(define-struct (ele:or ele) (left right) (make-inspector))
(define-struct (ele:not ele) (term) (make-inspector))
(define-struct standard-eq () (make-inspector))
(define-struct (standard-eq:lte standard-eq) (left right) (make-inspector))
(define-struct (standard-eq:gte standard-eq) (left right) (make-inspector))
(define-struct le () (make-inspector))
(define-struct (le:and le) (parts) (make-inspector))
(define simplify-le
(match-lambda
[(struct le:and (lst))
(make-le:and
(foldl (lambda (t a)
(if (le:and? t)
(append (le:and-parts t) a)
(list* t a)))
empty
(map simplify-le lst)))]
[(struct standard-eq:lte (l r))
(make-standard-eq:lte (simplify-simple-expr l) (simplify-simple-expr r))]
[(struct standard-eq:gte (l r))
(make-standard-eq:gte (simplify-simple-expr l) (simplify-simple-expr r))]))
(define le->sexp
(match-lambda
[(struct le:and (lst))
`(and ,@(map le->sexp lst))]
[(struct standard-eq:lte (l r))
`(<= ,(simple-expr->sexp l) ,(simple-expr->sexp r))]
[(struct standard-eq:gte (l r))
`(>= ,(simple-expr->sexp l) ,(simple-expr->sexp r))]))
(define parse-ele
(match-lambda
[`(not ,term)
(make-ele:not (parse-ele term))]
[`(and ,left ,right)
(make-ele:and (parse-ele left)
(parse-ele right))]
[`(or ,left ,right)
(make-ele:or (parse-ele left)
(parse-ele right))]
[`(= ,left ,right)
(make-simple-eq:eq (parse-simple-expr left)
(parse-simple-expr right))]
[`(!= ,left ,right)
(make-simple-eq:ne (parse-simple-expr left)
(parse-simple-expr right))]
[`(< ,left ,right)
(make-simple-eq:lt (parse-simple-expr left)
(parse-simple-expr right))]
[`(> ,left ,right)
(make-simple-eq:gt (parse-simple-expr left)
(parse-simple-expr right))]
[`(=< ,left ,right)
(make-simple-eq:lte (parse-simple-expr left)
(parse-simple-expr right))]
[`(>= ,left ,right)
(make-simple-eq:gte (parse-simple-expr left)
(parse-simple-expr right))]))
(define (ele->le term on off)
(define (add-M t)
(foldl (lambda (v a)
(make-simple-expr:+ (list a (make-atom:var 'M v))))
(foldl (lambda (v a)
(make-simple-expr:+
(list
a
(make-simple-expr:-
(make-atom:int 'M)
(make-atom:var 'M v)))))
t
off)
on))
(match term
[(struct ele:and (l r))
(make-le:and
(list
(ele->le l on off)
(ele->le r on off)))]
[(struct ele:or (l r))
(let ([new (gensym 'b)])
(make-le:and
(list
(ele->le l (list* new on) off)
(ele->le r on (list* new off)))))]
[(struct ele:not ((struct ele:and (l r))))
(ele->le
(make-ele:or (make-ele:not l) (make-ele:not r))
on off)]
[(struct ele:not ((struct ele:or (l r))))
(ele->le
(make-ele:and (make-ele:not l) (make-ele:not r))
on off)]
[(struct ele:not ((struct ele:not (t))))
(ele->le t on off)]
[(struct ele:not ((struct simple-eq:eq (l r))))
(ele->le (make-simple-eq:ne l r) on off)]
[(struct ele:not ((struct simple-eq:ne (l r))))
(ele->le (make-simple-eq:eq l r) on off)]
[(struct ele:not ((struct simple-eq:lt (l r))))
(ele->le (make-simple-eq:gte l r) on off)]
[(struct ele:not ((struct simple-eq:gt (l r))))
(ele->le (make-simple-eq:lte l r) on off)]
[(struct ele:not ((struct simple-eq:lte (l r))))
(ele->le (make-simple-eq:gt l r) on off)]
[(struct ele:not ((struct simple-eq:gte (l r))))
(ele->le (make-simple-eq:lt l r) on off)]
[(struct simple-eq:eq (l r))
(make-le:and
(list
(ele->le (make-simple-eq:lte l r) on off)
(ele->le (make-simple-eq:gte l r) on off)))]
[(struct simple-eq:ne (l r))
(ele->le
(make-ele:or (make-simple-eq:lt l r)
(make-simple-eq:gt l r))
on off)]
[(struct simple-eq:lt (l r))
(ele->le
(make-simple-eq:lte l (make-simple-expr:- r (make-atom:int 1)))
on off)]
[(struct simple-eq:gt (l r))
(ele->le
(make-simple-eq:gte l (make-simple-expr:+ (list r (make-atom:int 1))))
on off)]
[(struct simple-eq:lte (l r))
(make-standard-eq:lte l (add-M r))]
[(struct simple-eq:gte (l r))
(make-standard-eq:gte (add-M l) r)]))
(define (convert sexp)
(le->sexp (simplify-le (ele->le (parse-ele sexp) empty empty))))
(define (test)
(let ([term
`(and (or (or (or (= x1 (+ s 1))
(= x2 (+ s 1)))
(or (= x3 (+ s 1))
(= x4 (+ s 1))))
(or (or (= x5 (+ s 1))
(= x6 (+ s 1)))
(or (= x7 (+ s 1))
(= x8 (+ s 1)))))
(or (or (or (= x1 (- s 1))
(= x2 (- s 1)))
(or (= x3 (- s 1))
(= x4 (- s 1))))
(or (or (= x5 (- s 1))
(= x6 (- s 1)))
(or (= x7 (- s 1))
(= x8 (- s 1))))))])
(pretty-print
(convert term)))))