egglog 3.0.0

egglog is a language that combines the benefits of equality saturation and datalog. It can be used for analysis, optimization, and synthesis of programs. It is the successor to the popular rust library egg.
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; Converted from the egg demo at
; https://github.com/egraphs-good/egg/blob/fb6167957beb5dd7c784121459e08ebd1ccb1a00/tests/math.rs

(datatype Math
    (Diff Math Math :cost 100)
    (Integral Math Math :cost 100)

    (Add Math Math)
    (Sub Math Math)
    (Mul Math Math)
    (Div Math Math)
    (Pow Math Math)
    (Ln Math)
    (Sqrt Math)

    (Sin Math)
    (Cos Math)

    (Const f64)
    (Var String))

; Need to table for all math expressions since egglog does not allow unbound variables
(relation MathU (Math))
(rule ((= e (Diff x y))) ((MathU e)))
(rule ((= e (Integral x y))) ((MathU e)))
(rule ((= e (Add x y))) ((MathU e)))
(rule ((= e (Sub x y))) ((MathU e)))
(rule ((= e (Mul x y))) ((MathU e)))
(rule ((= e (Div x y))) ((MathU e)))
(rule ((= e (Pow x y))) ((MathU e)))
(rule ((= e (Ln x))) ((MathU e)))
(rule ((= e (Sqrt x))) ((MathU e)))
(rule ((= e (Sin x))) ((MathU e)))
(rule ((= e (Cos x))) ((MathU e)))
(rule ((= e (Const x))) ((MathU e)))
(rule ((= e (Var x))) ((MathU e)))

; same as constant fold in egg, but instead of an analysis we just
; merge with constant nodes.
; The behavior should be the same since it will union as well in egg.
(rewrite (Add (Const a) (Const b)) (Const (+ a b)))
(rewrite (Sub (Const a) (Const b)) (Const (- a b)))
(rewrite (Mul (Const a) (Const b)) (Const (* a b)))
(rewrite (Div (Const a) (Const b)) (Const (/ a b)) :when ((!= b 0.0)))


;; implement pruning with subsuming, so that it still saturates after pruning instead of thrashing
(ruleset prune)
(rule ((= (Const _) (Diff x y))) ((subsume (Diff x y))) :ruleset prune)
(rule ((= (Const _) (Integral x y))) ((subsume (Integral x y))) :ruleset prune)
(rule ((= (Const _) (Add x y))) ((subsume (Add x y))) :ruleset prune)
(rule ((= (Const _) (Sub x y))) ((subsume (Sub x y))) :ruleset prune)
(rule ((= (Const _) (Mul x y))) ((subsume (Mul x y))) :ruleset prune)
(rule ((= (Const _) (Div x y))) ((subsume (Div x y))) :ruleset prune)
(rule ((= (Const _) (Pow x y))) ((subsume (Pow x y))) :ruleset prune)
(rule ((= (Const _) (Ln x))) ((subsume (Ln x))) :ruleset prune)
(rule ((= (Const _) (Sqrt x))) ((subsume (Sqrt x))) :ruleset prune)
(rule ((= (Const _) (Sin x))) ((subsume (Sin x))) :ruleset prune)
(rule ((= (Const _) (Cos x))) ((subsume (Cos x))) :ruleset prune)

(relation is-not-zero (Math))
; Is not zero is set as anything besides the constant 0.0
(rule ((MathU x)
       (!= x (Const 0.0)))
      ((is-not-zero x)))

; If something is unioned to be the constant, then remove the is-not-zero
(rule ((is-not-zero x) (= x (Const 0.0)))
      ((delete (is-not-zero x))))

(relation is-const-or-distinct-var-demand (Math String))
(relation is-const-or-distinct-var (Math String))
(rule ((is-const-or-distinct-var-demand (Var w) v)
       (!= v w))
      ((is-const-or-distinct-var (Var w) v)))
(rule ((is-const-or-distinct-var-demand (Const c) v))
      ((is-const-or-distinct-var (Const c) v)))

(rewrite (Add a b) (Add b a))
(rewrite (Mul a b) (Mul b a))
(rewrite (Add a (Add b c)) (Add (Add a b) c))
(rewrite (Mul a (Mul b c)) (Mul (Mul a b) c))

(rewrite (Sub a b) (Add a (Mul (Const -1.0) b)))
(rewrite (Div a b) (Mul a (Pow b (Const -1.0))) :when ((is-not-zero b)))

(rewrite (Add a (Const 0.0)) a)
(rewrite (Mul a (Const 0.0)) (Const 0.0))
(rewrite (Mul a (Const 1.0)) a)

(rule ((MathU a)) ((union a (Add a (Const 0.0)))))
(rule ((MathU a)) ((union a (Mul a (Const 1.0)))))

(rewrite (Sub a a) (Const 0.0))
(rewrite (Div a a) (Const 1.0) :when ((is-not-zero a)))

(rewrite (Mul a (Add b c)) (Add (Mul a b) (Mul a c)))
(rewrite (Add (Mul a b) (Mul a c)) (Mul a (Add b c)))

(rewrite (Mul (Pow a b) (Pow a c)) (Pow a (Add b c)))
(rewrite (Pow x (Const 0.0)) (Const 1.0) :when ((is-not-zero x)))
(rewrite (Pow x (Const 1.0)) x)
(rewrite (Pow x (Const 2.0)) (Mul x x))
(rewrite (Pow x (Const -1.0)) (Div (Const 1.0) x) :when ((is-not-zero x)))
(rewrite (Mul x (Div (Const 1.0) x)) (Const 1.0) :when ((is-not-zero x)))

(rewrite (Diff (Var x) (Var x)) (Const 1.0))
(rule ((Diff (Var x) c))
      ((is-const-or-distinct-var-demand c x)))
(rewrite (Diff (Var x) c) (Const 0.0) :when ((is-const-or-distinct-var c x)))

(rewrite (Diff x (Add a b)) (Add (Diff x a) (Diff x b)))
(rewrite (Diff x (Mul a b)) (Add (Mul a (Diff x b)) (Mul b (Diff x a))))

(rewrite (Diff x (Sin x)) (Cos x))
(rewrite (Diff x (Cos x)) (Mul (Const -1.0) (Sin x)))

(rewrite (Diff x (Ln x)) (Div (Const 1.0) x) :when ((is-not-zero x)))

(rewrite (Diff x (Pow f g))
         (Mul (Pow f g)
              (Add (Mul (Diff x f) (Div g f))
                   (Mul (Diff x g) (Ln f))))
         :when ((is-not-zero f)
                (is-not-zero g)))

(rewrite (Integral (Const 1.0) x) x)
(rewrite (Integral (Pow x (Const c)) x)
         (Div (Pow x (Add (Const c) (Const 1.0))) (Add (Const c) (Const 1.0))))
(rewrite (Integral (Cos x) x) (Sin x))
(rewrite (Integral (Sin x) x) (Mul (Const -1.0) (Cos x)))
(rewrite (Integral (Add f g) x) (Add (Integral f x) (Integral g x)))
(rewrite (Integral (Sub f g) x) (Sub (Integral f x) (Integral g x)))
(rewrite (Integral (Mul a b) x)
         (Sub (Mul a (Integral b x))
              (Integral (Mul (Diff x a) (Integral b x)) x)))

; math_associate_adds
(push)
  (ruleset add-ac)
  (rewrite (Add a b) (Add b a) :ruleset add-ac)
  (rewrite (Add a (Add b c)) (Add (Add a b) c) :ruleset add-ac)
  ; Add one through seven
  (let $res
    (Add (Const 1.0)
         (Add (Const 2.0)
              (Add (Const 3.0)
                   (Add (Const 4.0)
                        (Add (Const 5.0)
                             (Add (Const 6.0)
                                  (Const 7.0))))))))
  (run add-ac 7)
  (check (= $res
    (Add (Const 7.0)
         (Add (Const 6.0)
              (Add (Const 5.0)
                   (Add (Const 4.0)
                        (Add (Const 3.0)
                             (Add (Const 2.0)
                                  (Const 1.0)))))))))
(pop)

; math_fail
(push)
(let $res (Add (Var "x") (Var "y")))
(run-schedule (saturate (seq (run) (run prune))))
(fail (check (= $res (Div (Var "x") (Var "y")))))
(pop)

; math_simplify_add
(push)
(let $x (Var "x"))
(let $res (Add (Add (Add $x $x) $x) $x))
(run-schedule (saturate (seq (run :until (= $res (Mul (Const 4.0) $x))) (run prune))))
(check (= $res (Mul (Const 4.0) $x)))
(pop)

; math_powers
(push)
(let $res (Mul (Pow (Const 2.0) (Var "x")) (Pow (Const 2.0) (Var "y"))))
(run-schedule (saturate (seq
     (run :until (= $res (Pow (Const 2.0) (Add (Var "x") (Var "y")))))
     (run prune))))
(check (= $res (Pow (Const 2.0) (Add (Var "x") (Var "y")))))
(pop)

; math_simplify_const
(push)
(let $res (Add (Const 1.0)
               (Sub (Var "a")
                    (Mul (Sub (Const 2.0)
                              (Const 1.0))
                         (Var "a")))))
(run-schedule (saturate (seq (run :until (= $res (Const 1.0))) (run prune))))
(check (= $res (Const 1.0)))
(pop)

; math_simplify_root
(push)
(let $res (Div (Const 1.0)
              (Sub (Div (Add (Const 1.0) (Sqrt (Var "five")))
                        (Const 2.0))
                  (Div (Sub (Const 1.0) (Sqrt (Var "five")))
                        (Const 2.0)))))
(run-schedule (saturate (seq
  (run :until (= $res (Div (Const 1.0) (Sqrt (Var "five")))) )
  (run prune))))
(check (= $res (Div (Const 1.0) (Sqrt (Var "five")))))
(pop)

;   math_simplify_factor, rules(),
(push)
(let $x (Var "x"))
(let $res (Mul (Add $x (Const 3.0)) (Add $x (Const 1.0))))
(run-schedule (saturate (seq
  (run :until (= $res (Add (Add (Mul $x $x) (Mul (Const 4.0) $x)) (Const 3.0))))
  (run prune))))
(check (= $res (Add (Add (Mul $x $x) (Mul (Const 4.0) $x)) (Const 3.0))))
(pop)

; math_diff_same
(push)
(let $res (Diff (Var "x") (Var "x")))
(run-schedule (saturate (seq (run :until (= $res (Const 1.0))) (run prune))))
(check (= $res (Const 1.0)))
(pop)

; math_diff_different
(push)
(let $res (Diff (Var "x") (Var "y")))
(run-schedule (saturate (seq (run :until (= $res (Const 0.0))) (run prune))))
(check (= $res (Const 0.0)))
(pop)

; math_diff_simple1
(push)
(let $res (Diff (Var "x") (Add (Const 1.0) (Mul (Const 2.0) (Var "x")))))
(run-schedule (saturate (seq (run :until (= $res (Const 2.0))) (run prune))))
(check (= $res (Const 2.0)))
(pop)

; math_diff_simple2
(push)
(let $res (Diff (Var "x") (Add (Const 1.0) (Mul (Var "y") (Var "x")))))
(run-schedule (saturate (seq (run :until (= $res (Var "y"))) (run prune))))
(check (= $res (Var "y")))
(pop)

; math_diff_ln
(push)
(let $res (Diff (Var "x") (Ln (Var "x"))))
(run-schedule (saturate (seq (run :until (= $res (Div (Const 1.0) (Var "x")))) (run prune))))
(check (= $res (Div (Const 1.0) (Var "x"))))
(pop)

; diff_power_simple
(push)
(let $res (Diff (Var "x") (Pow (Var "x") (Const 3.0))))
(run-schedule (saturate (seq
  (run :until (= $res (Mul (Const 3.0) (Pow (Var "x") (Const 2.0))))))
  (run prune)))
(check (= $res (Mul (Const 3.0) (Pow (Var "x") (Const 2.0)))))
(pop)

; diff_power_harder
(push)
(let $res (Diff (Var "x") (Sub (Pow (Var "x") (Const 3.0))
                              (Mul (Const 7.0) (Pow (Var "x") (Const 2.0))))))
; need to add this manually, same as in egg
(Mul (Var "x") (Sub (Mul (Const 3.0) (Var "x")) (Const 14.0)))
(run-schedule (repeat 60 (seq
  (run :until (= $res (Mul (Var "x") (Sub (Mul (Const 3.0) (Var "x"))
                                 (Const 14.0)))))
  (run prune))))
(check (= $res (Mul (Var "x") (Sub (Mul (Const 3.0) (Var "x"))
                                 (Const 14.0)))))
(pop)

; integ_one
(push)
(let $res (Integral (Const 1.0) (Var "x")))
(run-schedule (saturate (seq (run :until (= $res (Var "x"))) (run prune))))
(check (= $res (Var "x")))
(pop)

; integ_sin
(push)
(let $res (Integral (Cos (Var "x")) (Var "x")))
(run-schedule (saturate (seq (run :until (= $res (Sin (Var "x")))) (run prune))))
(check (= $res (Sin (Var "x"))))
(pop)

; integ_x
(push)
(let $res (Integral (Pow (Var "x") (Const 1.0)) (Var "x")))
(run-schedule (saturate (seq
  (run :until (= $res (Div (Pow (Var "x") (Const 2.0)) (Const 2.0))))
  (run prune))))
(check (= $res (Div (Pow (Var "x") (Const 2.0)) (Const 2.0))))
(pop)

; integ_part1
(push)
(let $res (Integral (Mul (Var "x") (Cos (Var "x"))) (Var "x")))
(run-schedule (saturate (seq
  (run :until (= $res (Add (Mul (Var "x") (Sin (Var "x")))
                          (Cos (Var "x")))))
  (run prune))))
(check (= $res (Add (Mul (Var "x") (Sin (Var "x")))
                   (Cos (Var "x")))))
(pop)

; integ_part2
(push)
(let $res (Integral (Mul (Cos (Var "x")) (Var "x")) (Var "x")))
(run-schedule (saturate (seq
  (run :until (= $res (Add (Mul (Var "x") (Sin (Var "x")))
                          (Cos (Var "x")))))
  (run prune))))
(check (= $res (Add (Mul (Var "x") (Sin (Var "x")))
                   (Cos (Var "x")))))
(pop)

; integ_part3
(push)
(let $res (Integral (Ln (Var "x")) (Var "x")))
(run-schedule (saturate (seq
  (run :until (= $res (Sub (Mul (Var "x") (Ln (Var "x"))) (Var "x"))))
  (run prune))))
(check (= $res (Sub (Mul (Var "x") (Ln (Var "x"))) (Var "x"))))
(pop)

; assoc_mul_saturates
(push)
(Mul (Var "x") (Const 1.0))
(run-schedule (saturate (seq (run) (run prune))))
(pop)