seacomb 0.3.2

A formally verified seccomp compiler.
Documentation 
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//! Supporting witnesses and proofs for chain evaluation and compilation.

use vstd::prelude::*;
use crate::spec::cbpf::*;
use crate::spec::policy::*;

verus! {

impl Policy {
    /// The witness in the nonempty branch of `Policy::eval_chain`.
    pub(super) open spec fn chain_wins(policies: Seq<Policy>, ev: Event, act: Action, i: int) -> bool {
        &&& 0 <= i < policies.len()
        &&& policies[i].eval(ev, act)
        &&& forall |j: int, other: Action| 0 <= j < policies.len()
            && #[trigger] policies[j].eval(ev, other) ==> {
                ||| other.precedence() < act.precedence()
                ||| other.precedence() == act.precedence() && j <= i
            }
    }

    pub(super) proof fn lemma_chain_eval_witness(policies: Seq<Policy>, ev: Event, act: Action)
        requires policies.len() != 0, Self::eval_chain(policies, ev, act)
        ensures exists |i: int| #[trigger] Self::chain_wins(policies, ev, act, i)
    {
        hide(Policy::eval);
        let i = choose |i: int| {
            &&& 0 <= i < policies.len()
            &&& #[trigger] policies[i].eval(ev, act)
            &&& forall |j: int, other: Action| 0 <= j < policies.len()
                && #[trigger] policies[j].eval(ev, other) ==> {
                    ||| other.precedence() < act.precedence()
                    ||| other.precedence() == act.precedence() && j <= i
                }
        };
        assert(Self::chain_wins(policies, ev, act, i));
    }

    /// Pointwise compilation guarantee using each policy's action witness.
    pub(super) proof fn lemma_eval_chain_compiled_at(
        policies: Seq<Policy>, filters: Seq<Program>, actions: Seq<Action>,
        ev: Event, data: &[u8], act: Action,
    )
        requires
            policies.len() == filters.len(),
            actions.len() == policies.len(),
            forall |i: int| 0 <= i < policies.len() ==> #[trigger] policies[i].wf(),
            forall |i: int| 0 <= i < filters.len() ==> #[trigger] filters[i].wf(),
            forall |i: int| 0 <= i < filters.len() ==> {
                &&& policies[i].eval(ev, #[trigger] actions[i])
                &&& filters[i].eval(data) == Outcome::Return(actions[i].to_ret())
            },
        ensures Self::eval_chain(policies, ev, act)
            <==> Program::eval_chain(filters, data, act.to_ret()),
    {
        hide(Policy::eval);
        hide(Program::eval);
        Action::lemma_to_ret_injective(act, Action::Allow);
        assert(Action::RET_ALLOW & Action::RET_ACTION == Action::RET_ALLOW) by (bit_vector);
        let ret = act.to_ret();
        if policies.len() != 0 {
            if Self::eval_chain(policies, ev, act) {
                Self::lemma_chain_eval_witness(policies, ev, act);
                let i = choose |i: int| #[trigger] Self::chain_wins(policies, ev, act, i);
                policies[i].lemma_eval_unique(ev, act, actions[i]);
                assert(filters[i].eval(data) == Outcome::Return(ret));
                if act == Action::Allow {
                    assert forall |j: int| 0 <= j < filters.len() implies {
                        &&& #[trigger] filters[j].eval(data) matches Outcome::Return(other)
                        &&& other & Action::RET_ACTION == Action::RET_ALLOW
                    } by {
                        assert(policies[j].eval(ev, actions[j]));
                        assert(actions[j].precedence() <= act.precedence());
                        assert(actions[j] == Action::Allow);
                    }
                } else {
                    Action::lemma_ret_precedence(act, Action::Allow);
                    assert forall |j: int| 0 <= j < filters.len() implies {
                        &&& #[trigger] filters[j].eval(data) matches Outcome::Return(other)
                        &&& {
                            let priority = (ret & Action::RET_ACTION) as i32;
                            let other_priority = (other & Action::RET_ACTION) as i32;
                            priority < other_priority || (priority == other_priority && j <= i)
                        }
                    } by {
                        assert(policies[j].eval(ev, actions[j]));
                        Action::lemma_ret_precedence(act, actions[j]);
                    }
                    assert(Program::chain_wins(filters, data, ret, i));
                }
                assert(Program::eval_chain(filters, data, ret));
            }
            if Program::eval_chain(filters, data, ret) {
                if ret == Action::RET_ALLOW {
                    assert(act == Action::Allow);
                    let i = policies.len() - 1;
                    Action::lemma_ret_precedence(actions[i], Action::Allow);
                    assert(actions[i] == Action::Allow);
                    assert(policies[i].eval(ev, act));
                    assert forall |j: int, other: Action| 0 <= j < policies.len()
                        && #[trigger] policies[j].eval(ev, other) implies {
                            ||| other.precedence() < act.precedence()
                            ||| other.precedence() == act.precedence() && j <= i
                        } by {
                        Action::lemma_ret_precedence(actions[j], Action::Allow);
                        assert(actions[j] == Action::Allow);
                        policies[j].lemma_eval_unique(ev, other, actions[j]);
                    }
                    assert(Self::chain_wins(policies, ev, act, i));
                } else {
                    Program::lemma_chain_eval_witness(filters, data, ret);
                    let i = choose |i: int| #[trigger] Program::chain_wins(filters, data, ret, i);
                    Action::lemma_to_ret_injective(act, actions[i]);
                    assert(policies[i].eval(ev, act));
                    assert forall |j: int, other: Action| 0 <= j < policies.len()
                        && #[trigger] policies[j].eval(ev, other) implies {
                            ||| other.precedence() < act.precedence()
                            ||| other.precedence() == act.precedence() && j <= i
                        } by {
                        policies[j].lemma_eval_unique(ev, other, actions[j]);
                        Action::lemma_ret_precedence(act, other);
                    }
                    assert(Self::chain_wins(policies, ev, act, i));
                }
                assert(Self::eval_chain(policies, ev, act));
            }
        }
    }
}

impl Program {
    /// The witness in the non-ALLOW branch of `Program::eval_chain`.
    pub(super) open spec fn chain_wins(filters: Seq<Program>, data: &[u8], ret: u32, i: int) -> bool {
        &&& 0 <= i < filters.len()
        &&& filters[i].eval(data) == Outcome::Return(ret)
        &&& ((ret & Action::RET_ACTION) as i32) < (Action::RET_ALLOW as i32)
        &&& forall |j: int| 0 <= j < filters.len() ==> {
            &&& #[trigger] filters[j].eval(data) matches Outcome::Return(other)
            &&& {
                let priority = (ret & Action::RET_ACTION) as i32;
                let other_priority = (other & Action::RET_ACTION) as i32;
                priority < other_priority || (priority == other_priority && j <= i)
            }
        }
    }

    proof fn lemma_chain_eval_witness(filters: Seq<Program>, data: &[u8], ret: u32)
        requires Self::eval_chain(filters, data, ret), ret != Action::RET_ALLOW
        ensures exists |i: int| #[trigger] Self::chain_wins(filters, data, ret, i)
    {
        hide(Program::eval);
        let i = choose |i: int| {
            &&& 0 <= i < filters.len()
            &&& #[trigger] filters[i].eval(data) == Outcome::Return(ret)
            &&& ((ret & Action::RET_ACTION) as i32) < (Action::RET_ALLOW as i32)
            &&& forall |j: int| 0 <= j < filters.len() ==> {
                &&& #[trigger] filters[j].eval(data) matches Outcome::Return(other)
                &&& {
                    let priority = (ret & Action::RET_ACTION) as i32;
                    let other_priority = (other & Action::RET_ACTION) as i32;
                    priority < other_priority || (priority == other_priority && j <= i)
                }
            }
        };
        assert(Self::chain_wins(filters, data, ret, i));
    }
}

} // verus!