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test.rkt
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test.rkt
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#lang racket
(require "./egraph.rkt")
(define E (init-egraph))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; (datatype expr ;;
;; (Num int) ;;
;; (Var int) ;;
;; (Neg expr) ;;
(add-symbol! E 'neg 1)
;; (Abs expr) ;;
(add-symbol! E 'abs 1)
;; (Add expr expr) ;;
(add-symbol! E 'add 2)
;; (Sub expr expr) ;;
(add-symbol! E 'sub 2)
;; (Mul expr expr) ;;
(add-symbol! E 'mul 2)
;; (Div expr expr)) ;;
(add-symbol! E 'div 2)
;; # evaluation rules ;;
;; (eq ;;
;; (Neg (Num ?i)) ;;
;; (Num [~ ?i])) ;;
(rw-rule ((neg (num i) @ a)) =>
((num ,(- i) @ a)))
;; (eq ;;
;; (Abs (Num ?i)) ;;
;; (Num [abs ?i])) ;;
(rw-rule ((abs (num i) @ a)) =>
((num ,(abs i) @ a)))
;; (eq ;;
;; (Add (Num ?i1) (Num ?i2)) ;;
;; (Num [+ ?i1 ?i2])) ;;
(rw-rule ((add (num i1) (num i2) @ a)) =>
((num ,(+ i1 i2) @ a)))
;; (eq ;;
;; (Sub (Num ?i1) (Num ?i2)) ;;
;; (Num [- ?i1 ?i2])) ;;
(rw-rule ((sub (num i1) (num i2) @ a)) =>
((num ,(- i1 i2) @ a)))
;; (eq ;;
;; (Mul (Num ?i1) (Num ?i2)) ;;
;; (Num [* ?i1 ?i2])) ;;
(rw-rule ((mul (num i1) (num i2) @ a)) =>
((num ,(* i1 i2) @ a)))
;; (rule ( ;;
;; (eq ?a (Div (Num ?i1) (Num ?i2))) ;;
;; (<> ?i2 0) # guard Div eval ;;
;; )( ;;
;; (eq ?a (Num [/ ?i1 ?i2]))) ;;
;; )) ;;
(rw-rule ((div (num i1) (num i2) @ a)
,(not (equal? i2 0))) =>
((num ,(- i1 i2) @ a)))
;; # syntactic rewrites ;;
;; (eq ;;
;; (Neg (Neg ?x)) ;;
;; ?x) ;;
(rw-rule ((neg (neg x) @ a)) =>
((neg (neg x) @ x)))
;; (eq ;;
;; (Abs (Abs ?x)) ;;
;; (Abs ?x)) ;;
(rw-rule ((abs (abs x) @ a)) =>
((abs x @ a)))
;; (eq ;;
;; (Abs (Neg ?x)) ;;
;; (Abs ?x)) ;;
(rw-rule ((abs (neg x) @ a)) =>
((abs x @ a)))
;; (eq ;;
;; (Add ?x (Num 0)) ;;
;; ?x) ;;
;; (eq ;;
;; (Add ?x ?y) ;;
;; (Add ?y ?x)) ;;
;; (eq ;;
;; (Add (Add ?x ?y) ?z) ;;
;; (Add ?x (Add ?y ?z))) ;;
;; (eq ;;
;; (Sub ?x (Num 0)) ;;
;; ?x) ;;
;; (eq ;;
;; (Sub ?x ?x) ;;
;; (Num 0)) ;;
;; (eq ;;
;; (Sub ?x ?y) ;;
;; (Add ?x (Neg ?y))) ;;
;; (eq ;;
;; (Mul ?x (Num 0)) ;;
;; (Num 0)) ;;
;; (eq ;;
;; (Mul ?x (Num 1)) ;;
;; ?x) ;;
;; (eq ;;
;; (Mul ?x ?y) ;;
;; (Mul ?y ?x)) ;;
;; (eq ;;
;; (Mul (Mul ?x ?y) ?z) ;;
;; (Mul ?x (Mul ?y ?z))) ;;
;; (eq ;;
;; (Mul ?x (Add ?y ?z)) ;;
;; (Add (Mul ?x ?y) (Mul ?x ?z))) ;;
;; (eq ;;
;; (Div ?x (Num 1)) ;;
;; ?x) ;;
;; ;;
;; ;;
;; (symmetric-relation not_eq ;;
;; (type (Expr Expr))) ;;
(add-symbol E 'not-eq 2)
(add-symbol E 'PANIC 1)
;; # following rule implicit b/c symrel ;;
;; # (rule ( ;;
;; # (not_eq ?a ?b) ;;
;; # )( ;;
;; # (not_eq ?b ?a) ;;
;; # )) ;;
(rw-rule ((not-eq a b)) =>
((not-eq b a)))
;; # check expected invariant ;;
;; (rule ( ;;
;; (not_eq ?a ?a) ;;
;; )( ;;
;; (PANIC ?a) ;;
;; )) ;;
(rw-rule ((not-eq a a)) =>
((PANIC a)))
;; # "Int+" is "extended integers", i.e., Z U {-inf, inf} ;;
;; (functions ;;
;; (lo ;;
;; (type (Expr) Int+) ;;
;; (merge (a b) ;;
;; (max (lo a) (lo b))) ;;
;; (lo (e) ;;
;; (case e ;;
;; ((Num ?i) ;;
;; ?i) ;;
;; ((Var _) ;;
;; -inf) ;;
;; ((Neg ?x) ;;
;; (~ (hi ?x))) ;;
;; ((Abs ?x) ;;
;; (if (<= 0 (lo ?x)) ;;
;; (lo ?x) ;;
;; (if (<= 0 (hi ?x)) ;;
;; 0 ;;
;; (~ (hi ?x))))) ;;
;; ((Add ?x ?y) ;;
;; (+ (lo ?x) (lo ?y))) ;;
;; ((Sub ?x ?y) ;;
;; (- (lo ?x) (hi ?y))) ;;
;; ((Mul ?x ?y) ;;
;; (min ;;
;; (* (lo ?x) (lo ?y)) ;;
;; (* (lo ?x) (hi ?y)) ;;
;; (* (hi ?x) (lo ?y)) ;;
;; (* (hi ?x) (hi ?y)))) ;;
;; ((Div ?x ?y) ;;
;; ...)))) ;;
;; (hi ;;
;; (type (Expr) Int+) ;;
;; (merge (a b) ;;
;; (min (hi a) (hi b))) ;;
;; (hi (e) ;;
;; (case e ;;
;; ((Num ?i) ;;
;; ?i) ;;
;; ((Var _) ;;
;; inf) ;;
;; ((Neg ?x) ;;
;; (~ (lo ?x))) ;;
;; ((Abs ?x) ;;
;; (max (Abs (lo ?x)) (Abs (hi ?x)))) ;;
;; ((Add ?x ?y) ;;
;; (+ (hi ?x) (hi ?y))) ;;
;; ((Sub ?x ?y) ;;
;; (- (hi ?x) (lo ?y))) ;;
;; ((Mul ?x ?y) ;;
;; (max ;;
;; (* (lo ?x) (lo ?y)) ;;
;; (* (lo ?x) (hi ?y)) ;;
;; (* (hi ?x) (lo ?y)) ;;
;; (* (hi ?x) (hi ?y)))) ;;
;; ((Div ?x ?y) ;;
;; ...))))) ;;
;; ;;
;; # check expected invariant ;;
;; (rule ( ;;
;; (< (hi ?a) (lo ?a)) ;;
;; )( ;;
;; (PANIC ?a) ;;
;; )) ;;
;; ;;
;; ;;
;; # if intervals do not overlap, expressions cannot be eq ;;
;; (rule ( ;;
;; (< (hi ?a) (lo ?b)) ;;
;; )( ;;
;; (not_eq ?a ?b) ;;
;; )) ;;
;; ;;
;; ;;
;; # conditional rules ;;
;; (rule ( ;;
;; (eq ?a (Div ?x ?x)) ;;
;; (not_eq ?x (Num 0)) ;;
;; )( ;;
;; (eq ?a (Num 1)) ;;
;; )) ;;
;; ;;
;; ;;
;; # injectivity rules ;;
;; (rule ( ;;
;; (eq (Add ?x ?y) (Add ?x ?z)) ;;
;; )( ;;
;; (eq ?y ?z) ;;
;; )) ;;
;; ;;
;; (rule ( ;;
;; # "merge only" ;;
;; (eq ?a (Add ?x ?y)) ;;
;; (eq ?b (Add ?x ?z)) ;;
;; (not_eq ?y ?z) ;;
;; )( ;;
;; (not_eq ?a ?b) ;;
;; )) ;;
;; ;;
;; (rule ( ;;
;; (eq (Mul ?x ?y) (Mul ?x ?z)) ;;
;; (not_eq ?x (Num 0)) ;;
;; )( ;;
;; (eq ?y ?z) ;;
;; )) ;;
;; ;;
;; (rule ( ;;
;; # "merge only" ;;
;; (eq ?a (Mul ?x ?y)) ;;
;; (eq ?b (Mul ?x ?z)) ;;
;; (not_eq ?y ?z) ;;
;; (not_eq ?x (Num 0)) ;;
;; )( ;;
;; (not_eq ?a ?b) ;;
;; )) ;;
;; ;;
;; ;;
;; # add something and run eqsat ;;
;; (define root (ADD ;;
;; # like quadratic, but not sqrt ;;
;; (Div (Add (Neg b) (Sub (Mul b b) (Mul 4 (Mul a c)))) ;;
;; (Mul 2 a)))) ;;
;; (run (iters 5)) ;;
;; ;;
;; ;;
;; # extract ;;
;; (function cost ;;
;; (type (Expr) Int) ;;
;; (merge (a b) ;;
;; (min (cost a) (cost b))) ;;
;; (cost (e) ;;
;; (case e ;;
;; ((Num _) 1) ;;
;; ((Var _) 2) ;;
;; ((Neg ?x) ;;
;; (+ 3 (cost ?x))) ;;
;; ((Abs ?x) ;;
;; (+ 4 (cost ?x))) ;;
;; ((Add ?x ?y) ;;
;; (+ 5 (cost ?x) (cost ?y))) ;;
;; ((Sub ?x ?y) ;;
;; (+ 6 (cost ?x) (cost ?y))) ;;
;; ((Mul ?x ?y) ;;
;; (+ 7 (cost ?x) (cost ?y))) ;;
;; ((Div ?x ?y) ;;
;; (+ 8 (cost ?x) (cost ?y)))))) ;;
;; ;;
;; (extract cost root) ;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;