Enum InferenceRule 

pub enum InferenceRule {
    Identity,
    WeakeningLeft,
    WeakeningRight,
    ContractionLeft {
        index: usize,
    },
    ContractionRight {
        index: usize,
    },
    Exchange,
    Cut {
        index: usize,
    },
    AndLeft {
        index: usize,
    },
    AndRight {
        index: usize,
    },
    OrLeft {
        index: usize,
    },
    OrRight {
        index: usize,
    },
    NotLeft {
        index: usize,
    },
    NotRight {
        index: usize,
    },
    ImplyLeft {
        index: usize,
    },
    ImplyRight {
        index: usize,
    },
    ExistsLeft {
        index: usize,
        witness: Term,
    },
    ExistsRight {
        index: usize,
        witness: Term,
    },
    ForAllLeft {
        index: usize,
        term: Term,
    },
    ForAllRight {
        index: usize,
        witness: Term,
    },
}

Inference rules in sequent calculus.

Variants

Identity

Identity axiom: A ⊢ A

WeakeningLeft

Weakening left: add formula to antecedents

WeakeningRight

Weakening right: add formula to consequents

ContractionLeft

Contraction left: remove duplicate from antecedents

Fields

index: usize

ContractionRight

Contraction right: remove duplicate from consequents

Fields

index: usize

Exchange

Exchange: reorder formulas (implicit, not tracked)

Cut

Cut rule: eliminate intermediate formula (index in antecedents/consequents)

Fields

index: usize

AndLeft

AND introduction (left): Γ, A, B ⊢ Δ from Γ, A ∧ B ⊢ Δ

Fields

index: usize

AndRight

AND introduction (right): Γ ⊢ Δ, A ∧ B from Γ ⊢ Δ, A and Γ ⊢ Δ, B

Fields

index: usize

OrLeft

OR introduction (left): Γ, A ∨ B ⊢ Δ from Γ, A ⊢ Δ and Γ, B ⊢ Δ

Fields

index: usize

OrRight

OR introduction (right): Γ ⊢ Δ, A, B from Γ ⊢ Δ, A ∨ B

Fields

index: usize

NotLeft

NOT introduction (left): Γ, ¬A ⊢ Δ from Γ ⊢ Δ, A

Fields

index: usize

NotRight

NOT introduction (right): Γ ⊢ Δ, ¬A from Γ, A ⊢ Δ

Fields

index: usize

ImplyLeft

IMPLY introduction (left): Γ, A → B ⊢ Δ from Γ ⊢ Δ, A and Γ, B ⊢ Δ

Fields

index: usize

ImplyRight

IMPLY introduction (right): Γ ⊢ Δ, A → B from Γ, A ⊢ Δ, B

Fields

index: usize

ExistsLeft

EXISTS introduction (left): Γ, ∃x.A ⊢ Δ from Γ, A[t/x] ⊢ Δ (t fresh)

Fields

index: usize

witness: Term

ExistsRight

EXISTS introduction (right): Γ ⊢ Δ, ∃x.A from Γ ⊢ Δ, A[t/x]

Fields

index: usize

witness: Term

ForAllLeft

FORALL introduction (left): Γ, ∀x.A ⊢ Δ from Γ, A[t/x] ⊢ Δ

Fields

index: usize

term: Term

ForAllRight

FORALL introduction (right): Γ ⊢ Δ, ∀x.A from Γ ⊢ Δ, A[t/x] (t fresh)

Fields

index: usize

witness: Term

Trait Implementations

impl Clone for InferenceRule

fn clone(&self) -> InferenceRule

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for InferenceRule

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for InferenceRule

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl PartialEq for InferenceRule

fn eq(&self, other: &InferenceRule) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Serialize for InferenceRule

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for InferenceRule