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| //! Since existence proofs don't support analysis, | ||
| //! we test egg without analysis here. | ||
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| use egg::{rewrite as rw, *}; | ||
| use ordered_float::NotNan; | ||
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| pub type EGraph = egg::EGraph<Math, ()>; | ||
| pub type Rewrite = egg::Rewrite<Math, ()>; | ||
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| pub type Constant = NotNan<f64>; | ||
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| define_language! { | ||
| pub enum Math { | ||
| "d" = Diff([Id; 2]), | ||
| "i" = Integral([Id; 2]), | ||
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| "+" = Add([Id; 2]), | ||
| "-" = Sub([Id; 2]), | ||
| "*" = Mul([Id; 2]), | ||
| "/" = Div([Id; 2]), | ||
| "pow" = Pow([Id; 2]), | ||
| "ln" = Ln(Id), | ||
| "sqrt" = Sqrt(Id), | ||
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| "sin" = Sin(Id), | ||
| "cos" = Cos(Id), | ||
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| Constant(Constant), | ||
| Symbol(Symbol), | ||
| } | ||
| } | ||
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| // You could use egg::AstSize, but this is useful for debugging, since | ||
| // it will really try to get rid of the Diff operator | ||
| pub struct MathCostFn; | ||
| impl egg::CostFunction<Math> for MathCostFn { | ||
| type Cost = usize; | ||
| fn cost<C>(&mut self, enode: &Math, mut costs: C) -> Self::Cost | ||
| where | ||
| C: FnMut(Id) -> Self::Cost, | ||
| { | ||
| let op_cost = match enode { | ||
| Math::Diff(..) => 100, | ||
| Math::Integral(..) => 100, | ||
| _ => 1, | ||
| }; | ||
| enode.fold(op_cost, |sum, i| sum + costs(i)) | ||
| } | ||
| } | ||
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| #[rustfmt::skip] | ||
| pub fn rules() -> Vec<Rewrite> { vec![ | ||
| rw!("add-1-1"; "(+ 1 1)" => "2"), | ||
| rw!("add-0-r"; "(+ ?a 0)" => "?a"), | ||
| rw!("add-0-l"; "(+ 0 ?a)" => "?a"), | ||
| rw!("add-2-2"; "(+ 2 2)" => "4"), | ||
| rw!("add-3-1"; "(+ 3 1)" => "4"), | ||
| rw!("sub-0-r"; "(- ?a 0)" => "?a"), | ||
| rw!("sub-0-1"; "(- 0 1)" => "-1"), | ||
| rw!("sub-1-0"; "(- 1 0)" => "1"), | ||
| rw!("sub-1-1"; "(- 1 1)" => "0"), | ||
| rw!("add-2-neg1"; "(+ 2 -1)" => "1"), | ||
| rw!("comm-add"; "(+ ?a ?b)" => "(+ ?b ?a)"), | ||
| rw!("comm-mul"; "(* ?a ?b)" => "(* ?b ?a)"), | ||
| rw!("assoc-add"; "(+ ?a (+ ?b ?c))" => "(+ (+ ?a ?b) ?c)"), | ||
| rw!("assoc-mul"; "(* ?a (* ?b ?c))" => "(* (* ?a ?b) ?c)"), | ||
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| rw!("sub-canon"; "(- ?a ?b)" => "(+ ?a (* -1 ?b))"), | ||
| rw!("div-canon"; "(/ ?a ?b)" => "(* ?a (pow ?b -1))"), | ||
| // rw!("canon-sub"; "(+ ?a (* -1 ?b))" => "(- ?a ?b)"), | ||
| // rw!("canon-div"; "(* ?a (pow ?b -1))" => "(/ ?a ?b)" if is_not_zero("?b")), | ||
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| rw!("zero-add"; "(+ ?a 0)" => "?a"), | ||
| rw!("zero-mul"; "(* ?a 0)" => "0"), | ||
| rw!("one-mul"; "(* ?a 1)" => "?a"), | ||
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| rw!("add-zero"; "?a" => "(+ ?a 0)"), | ||
| rw!("mul-one"; "?a" => "(* ?a 1)"), | ||
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| rw!("cancel-sub"; "(- ?a ?a)" => "0"), | ||
| rw!("cancel-div"; "(/ ?a ?a)" => "1"), | ||
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| rw!("distribute"; "(* ?a (+ ?b ?c))" => "(+ (* ?a ?b) (* ?a ?c))"), | ||
| rw!("factor" ; "(+ (* ?a ?b) (* ?a ?c))" => "(* ?a (+ ?b ?c))"), | ||
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| rw!("pow-mul"; "(* (pow ?a ?b) (pow ?a ?c))" => "(pow ?a (+ ?b ?c))"), | ||
| rw!("pow0"; "(pow ?x 0)" => "1"), | ||
| rw!("pow1"; "(pow ?x 1)" => "?x"), | ||
| rw!("pow2"; "(pow ?x 2)" => "(* ?x ?x)"), | ||
| rw!("pow-recip"; "(pow ?x -1)" => "(/ 1 ?x)"), | ||
| rw!("recip-mul-div"; "(* ?x (/ 1 ?x))" => "1"), | ||
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| rw!("d-variable"; "(d ?x ?x)" => "1"), | ||
| rw!("d-constant"; "(d ?x ?c)" => "0"), | ||
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| rw!("d-add"; "(d ?x (+ ?a ?b))" => "(+ (d ?x ?a) (d ?x ?b))"), | ||
| rw!("d-mul"; "(d ?x (* ?a ?b))" => "(+ (* ?a (d ?x ?b)) (* ?b (d ?x ?a)))"), | ||
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| rw!("d-sin"; "(d ?x (sin ?x))" => "(cos ?x)"), | ||
| rw!("d-cos"; "(d ?x (cos ?x))" => "(* -1 (sin ?x))"), | ||
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| rw!("d-ln"; "(d ?x (ln ?x))" => "(/ 1 ?x)"), | ||
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| rw!("d-power"; | ||
| "(d ?x (pow ?f ?g))" => | ||
| "(* (pow ?f ?g) | ||
| (+ (* (d ?x ?f) | ||
| (/ ?g ?f)) | ||
| (* (d ?x ?g) | ||
| (ln ?f))))" | ||
| ), | ||
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| rw!("i-one"; "(i 1 ?x)" => "?x"), | ||
| rw!("i-power-const"; "(i (pow ?x ?c) ?x)" => | ||
| "(/ (pow ?x (+ ?c 1)) (+ ?c 1))"), | ||
| rw!("i-cos"; "(i (cos ?x) ?x)" => "(sin ?x)"), | ||
| rw!("i-sin"; "(i (sin ?x) ?x)" => "(* -1 (cos ?x))"), | ||
| rw!("i-sum"; "(i (+ ?f ?g) ?x)" => "(+ (i ?f ?x) (i ?g ?x))"), | ||
| rw!("i-dif"; "(i (- ?f ?g) ?x)" => "(- (i ?f ?x) (i ?g ?x))"), | ||
| rw!("i-parts"; "(i (* ?a ?b) ?x)" => | ||
| "(- (* ?a (i ?b ?x)) (i (* (d ?x ?a) (i ?b ?x)) ?x))"), | ||
| ]} | ||
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| egg::test_fn! { | ||
| existence_associate_adds, [ | ||
| rw!("comm-add"; "(+ ?a ?b)" => "(+ ?b ?a)"), | ||
| rw!("assoc-add"; "(+ ?a (+ ?b ?c))" => "(+ (+ ?a ?b) ?c)"), | ||
| ], | ||
| runner = Runner::default() | ||
| .with_iter_limit(7) | ||
| .with_scheduler(SimpleScheduler), | ||
| "(+ 1 (+ 2 (+ 3 (+ 4 (+ 5 (+ 6 7))))))" | ||
| => | ||
| "(+ 7 (+ 6 (+ 5 (+ 4 (+ 3 (+ 2 1))))))" | ||
| @check |r: Runner<Math, ()>| assert_eq!(r.egraph.number_of_classes(), 127), | ||
| @existence true | ||
| } | ||
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| egg::test_fn! { | ||
| #[should_panic(expected = "Could not prove goal 0")] | ||
| existence_fail, rules(), | ||
| "(+ x y)" => "(/ x y)", | ||
| @existence true | ||
| } | ||
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| egg::test_fn! {existence_simplify_add, rules(), "(+ x (+ x (+ x x)))" => "(* 4 x)", @existence true } | ||
| egg::test_fn! {existence_powers, rules(), "(* (pow 2 x) (pow 2 y))" => "(pow 2 (+ x y))", @existence true} | ||
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| egg::test_fn! { | ||
| existence_simplify_const, rules(), | ||
| "(+ 1 (- a (* (- 2 1) a)))" => "1", | ||
| @existence true | ||
| } | ||
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| egg::test_fn! { | ||
| existence_simplify_factor, rules(), | ||
| "(* (+ x 3) (+ x 1))" | ||
| => | ||
| "(+ (+ (* x x) (* 4 x)) 3)" | ||
| @existence true | ||
| } | ||
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| egg::test_fn! {existence_diff_same, rules(), "(d x x)" => "1", @existence true} | ||
| egg::test_fn! {existence_diff_different, rules(), "(d x y)" => "0", @existence true} | ||
| egg::test_fn! {existence_diff_simple2, rules(), "(d x (+ 1 (* y x)))" => "y", @existence true} | ||
| egg::test_fn! {existence_diff_ln, rules(), "(d x (ln x))" => "(/ 1 x)", @existence true} | ||
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| egg::test_fn! { | ||
| existence_diff_power_simple, rules(), | ||
| "(d x (pow x 3))" => "(* 3 (pow x 2))", | ||
| @existence true | ||
| } | ||
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| egg::test_fn! { | ||
| existence_integ_one, rules(), "(i 1 x)" => "x", | ||
| @existence true | ||
| } | ||
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| egg::test_fn! { | ||
| existence_integ_sin, rules(), "(i (cos x) x)" => "(sin x)", @existence true | ||
| } | ||
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| egg::test_fn! { | ||
| existence_integ_x, rules(), "(i (pow x 1) x)" => "(/ (pow x 2) 2)", @existence true | ||
| } | ||
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| egg::test_fn! { | ||
| existence_integ_part1, rules(), "(i (* x (cos x)) x)" => "(+ (* x (sin x)) (cos x))", @existence true | ||
| } |