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import { addition, multiplication } from './index';
import { Add, Multiply, Succ } from './nat';
import { ApplyRewrite, ChainRewrites, Flip, Eq, VerifyEquation, Equation, assert, Evaluate } from './util';
export type specChainRewrites = [
assert<Eq<
ChainRewrites<
[
addition.Commutativity<'0', 'B'>,
addition.Identity<'B'>,
],
Add<Add<'0', 'B'>, 'C'>
>,
Add<'B', 'C'>
>>,
assert<Eq<
ChainRewrites<
[
addition.Commutativity<'0', 'B'>,
addition.Identity<'B'>,
Flip<addition.Identity<Add<'B', 'C'>>>,
addition.Commutativity<Add<'B', 'C'>, '0'>,
],
Add<Add<'0', 'B'>, 'C'>
>,
Add<'0', Add<'B', 'C'>>
>>,
]
export namespace spec_addition {
export type specIdentity = [
assert<Eq<
ApplyRewrite<Add<'A', Add<'B', '0'>>, addition.Identity<'B'>>,
Add<'A', 'B'>
>>,
assert<Eq<
ApplyRewrite<Add<Add<'A', 'B'>, '0'>, addition.Identity<Add<'A', 'B'>>>,
Add<'A', 'B'>
>>,
assert<Eq<
ApplyRewrite<Add<'A', 'B'>, Flip<addition.Identity<Add<'A', 'B'>>>>,
Add<Add<'A', 'B'>, '0'>
>>,
assert<Eq<
ApplyRewrite<Add<'A', Add<'B', Add<'C', '0'>>>, addition.Identity<'C'>>,
Add<'A', Add<'B', 'C'>>
>>,
]
export type specCommutativity = [
assert<Eq<
ApplyRewrite<Add<'A', 'B'>, addition.Commutativity<'A', 'B'>>,
Add<'B', 'A'>
>>,
assert<Eq<
ApplyRewrite<Add<Add<'A', 'B'>, 'C'>, addition.Commutativity<'A', 'B'>>,
Add<Add<'B', 'A'>, 'C'>
>>,
assert<Eq<
ApplyRewrite<Add<'A', Add<'B', 'C'>>, addition.Commutativity<'B', 'C'>>,
Add<'A', Add<'C', 'B'>>
>>,
]
}
export namespace multiplication_spec {
export type specCommutativity = [
assert<Eq<
ApplyRewrite<Multiply<Multiply<'A', 'B'>, 'C'>, multiplication.Commutativity<'A', 'B'>>,
Multiply<Multiply<'B', 'A'>, 'C'>
>>,
]
export type specDistributivity = [
assert<Eq<
Evaluate<multiplication.Distributivity<'A', 'B', 'C'>>,
Add<Multiply<'A', 'C'>, Multiply<'B', 'C'>>
>>,
]
export type specAssociativity = [
assert<Eq<
Evaluate<multiplication.Associativity<'A', 'B', 'C'>>,
Multiply<'A', Multiply<'B', 'C'>>
>>,
]
}
|
