Struct Positive 

pub struct Positive(/* private fields */);

Positive numbers, i.e. numbers that are strictly greater than 0.

Implementations

impl Positive

pub fn to_int(self) -> Int

logic

ensures

result > 0

pub fn new(n: Int) -> Self

logic

requires

n > 0

ensures

result.to_int() == n

pub fn ext_eq(self, other: Self) -> bool

logic(open)

let _ = Subset::<PositiveInner>::inner_inj;
self.to_int() == other.to_int()

ensures

#[trigger(self == other)] result == (self == other)

Trait Implementations

impl AddLogic for Positive

fn add_logic(self, other: Self) -> Self

logic

ensures

result@ == self@ + other@

type Output = Positive

impl Clone for Positive

fn clone(&self) -> Self

ghost

ensures

result == *self

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for Positive

impl MulLogic for Positive

fn mul_logic(self, other: Self) -> Self

logic

ensures

result@ == self@ * other@

type Output = Positive

impl OrdLogic for Positive

fn lt_log_total(self, other: Self)

logic(law)

ensures

self < other || self == other || other < self

fn cmp_log(self, other: Self) -> Ordering

The comparison operation.

impl PartialOrdLogic for Positive

fn lt_log(self, other: Self) -> bool

logic(open)

self.to_int() < other.to_int()

fn le_log(self, other: Self) -> bool

logic(open)

self.to_int() <= other.to_int()

fn irreflexive(self)

logic

ensures

!(self < self)

fn transitive(x: Self, y: Self, z: Self)

logic

requires

x < y

requires

y < z

ensures

x < z

fn le_lt_log(self, other: Self)

logic(law)

ensures

(self <= other) == (self < other || self == other)

fn gt_log(self, other: Self) -> bool

The logical > operation.

fn ge_log(self, other: Self) -> bool

The logical >= operation.

fn partial_cmp_log(self, other: Self) -> Option<Ordering>

logic(open, sealed)

impl Plain for Positive

fn into_ghost(s: Snapshot<Self>) -> Ghost<Self>

ghost

ensures

*result == *s

impl RA for Positive

fn op(self, other: Self) -> Option<Self>

logic(open)

Some(self + other)

fn incl(self, other: Self) -> bool

logic(open)

let _ = Self::ext_eq;
let r = self < other;
proof_assert!(r ==> self.op(Self::new(other@ - self@)) == Some(other));
r

ensures

result == (exists<factor> self.op(factor) == Some(other))

fn commutative(a: Self, b: Self)

logic(law)

ensures

a.op(b) == b.op(a)

fn associative(a: Self, b: Self, c: Self)

logic

ensures

a.op(b).and_then_logic(|ab: Self| ab.op(c)) == b.op(c).and_then_logic(|bc| a.op(bc))

fn core(self) -> Option<Self>

logic(open)

None

fn core_idemp(self)

logic

requires

self.core() != None

ensures

let c = self.core().unwrap_logic();
c.op(c) == Some(c)

ensures

self.core().unwrap_logic().op(self) == Some(self)

fn core_is_maximal_idemp(self, i: Self)

logic

requires

i.op(i) == Some(i)

requires

i.op(self) == Some(self)

ensures

match self.core() {
    Some(c) => i.incl(c),
    None => false,
}

fn cancelable(self) -> bool

logic(open)

let _ = Self::ext_eq;
true

ensures

result == (forall<x, y> self.op(x) != None ==>
    self.op(x) == self.op(y) ==> x == y)

fn eq(self, other: Self) -> bool

logic(open, inline)

fn incl_op(self, other: Self, comb: Self)

logic(law)

fn incl_eq(self, other: Self) -> bool

logic(open, sealed)

fn incl_eq_op(a: Self, b: Self, x: Self) -> bool

logic(open, sealed)

fn factor(self, factor: Self) -> Self

Factorizing elements of the RA

fn update(self, x: Self) -> bool

Ensures that we can go from self to x without making composition with the frame invalid.

fn update_nondet(self, s: Set<Self>) -> bool

This is used in Resource::update_nondet.

fn associative_none(a: Self, b: Self, c: Self, bc: Self)

Specialized version of Self::associative, in the case where a.op(b) == None.

fn associative_some(a: Self, b: Self, c: Self, ab: Self, bc: Self)

Specialized version of Self::associative, in the case where a.op(b) and b.op(c) are both valid.

fn incl_transitive(a: Self, b: Self, c: Self)

RA::incl is transitive.

impl View for Positive

fn view(self) -> Int

logic(open)

self.to_int()

type ViewTy = Int