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binders-uniqueness.agda
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binders-uniqueness.agda
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open import List
open import Nat
open import Prelude
open import binders-disjointness
open import core
open import freshness
open import patterns-core
-- various judgements stating that all binders
-- or hole binders in a term are unique à la
-- Barendregt's convention
module binders-uniqueness where
mutual
data binders-unique-p : pattrn → Set where
BUPUnit : binders-unique-p unit
BUPNum : ∀{n} →
binders-unique-p (N n)
BUPVar : ∀{x} →
binders-unique-p (X x)
BUPInl : ∀{p} →
binders-unique-p p →
binders-unique-p (inl p)
BUPInr : ∀{p} →
binders-unique-p p →
binders-unique-p (inr p)
BUPPair : ∀{p1 p2} →
binders-unique-p p1 →
binders-unique-p p2 →
binders-disjoint-p p1 p2 →
binders-unique-p ⟨ p1 , p2 ⟩
BUPWild : binders-unique-p wild
BUPEHole : ∀{w} →
binders-unique-p ⦇-⦈[ w ]
BUPHole : ∀{p w τ} →
binders-unique-p p →
binders-unique-p ⦇⌜ p ⌟⦈[ w , τ ]
data binders-unique-r : rule → Set where
BURule : ∀{p e} →
binders-unique-p p →
binders-unique e →
binders-disjoint-p p e →
binders-unique-r (p => e)
data binders-unique-rs : rules → Set where
BUNoRules : binders-unique-rs nil
BURules : ∀{r rs} →
binders-unique-r r →
binders-unique-rs rs →
binders-disjoint-r r rs →
binders-unique-rs (r / rs)
data binders-unique-zrs : zrules → Set where
BUZRules : ∀{rs-pre r rs-post} →
binders-unique-rs rs-pre →
binders-unique-rs (r / rs-post) →
binders-disjoint-rs rs-pre (r / rs-post) →
binders-unique-zrs (rs-pre / r / rs-post)
data binders-unique-σ : subst-env → Set where
BUσId : ∀{Γ} →
binders-unique-σ (Id Γ)
BUσSubst : ∀{d y σ} →
binders-unique d →
binders-unique-σ σ →
binders-disjoint-σ σ d →
binders-unique-σ (Subst d y σ)
data binders-unique : ihexp → Set where
BUUnit : binders-unique unit
BUNum : ∀{n} →
binders-unique (N n)
BUVar : ∀{x} →
binders-unique (X x)
BULam : ∀{x τ e} →
binders-unique e →
unbound-in-e x e →
binders-unique (·λ x ·[ τ ] e)
BUEHole : ∀{u σ} →
binders-unique-σ σ →
binders-unique ⦇-⦈⟨ u , σ ⟩
BUHole : ∀{e u σ} →
binders-unique-σ σ →
binders-unique e →
binders-disjoint-σ σ e →
binders-unique ⦇⌜ e ⌟⦈⟨ u , σ ⟩
BUAp : ∀{e1 e2} →
binders-unique e1 →
binders-unique e2 →
binders-disjoint e1 e2 →
binders-unique (e1 ∘ e2)
BUInl : ∀{e τ} →
binders-unique e →
binders-unique (inl τ e)
BUInr : ∀{e τ} →
binders-unique e →
binders-unique (inr τ e)
BUMatch : ∀{e τ rs} →
binders-unique e →
binders-unique-zrs rs →
binders-disjoint-zrs rs e →
binders-unique (match e ·: τ of rs)
BUPair : ∀{e1 e2} →
binders-unique e1 →
binders-unique e2 →
binders-disjoint e1 e2 →
binders-unique ⟨ e1 , e2 ⟩
BUFst : ∀{e} →
binders-unique e →
binders-unique (fst e)
BUSnd : ∀{e} →
binders-unique e →
binders-unique (snd e)
mutual
data hole-binders-unique-p : pattrn → Set where
HBUPUnit : hole-binders-unique-p unit
HBUPNum : ∀{n} →
hole-binders-unique-p (N n)
HBUPVar : ∀{x} →
hole-binders-unique-p (X x)
HBUPInl : ∀{p} →
hole-binders-unique-p p →
hole-binders-unique-p (inl p)
HBUPInr : ∀{p} →
hole-binders-unique-p p →
hole-binders-unique-p (inr p)
HBUPPair : ∀{p1 p2} →
hole-binders-unique-p p1 →
hole-binders-unique-p p2 →
hole-binders-disjoint-p p1 p2 →
hole-binders-unique-p ⟨ p1 , p2 ⟩
HBUPWild : hole-binders-unique-p wild
HBUPEHole : ∀{w} →
hole-binders-unique-p ⦇-⦈[ w ]
HBUPHole : ∀{p w τ} →
hole-binders-unique-p p →
hole-unbound-in-p w p →
hole-binders-unique-p ⦇⌜ p ⌟⦈[ w , τ ]
data hole-binders-unique-r : rule → Set where
HBURule : ∀{p e} →
hole-binders-unique-p p →
hole-binders-unique e →
hole-binders-disjoint-p p e →
hole-binders-unique-r (p => e)
data hole-binders-unique-rs : rules → Set where
HBUNoRules : hole-binders-unique-rs nil
HBURules : ∀{r rs} →
hole-binders-unique-r r →
hole-binders-unique-rs rs →
hole-binders-disjoint-r r rs →
hole-binders-unique-rs (r / rs)
data hole-binders-unique-zrs : zrules → Set where
HBUZRules : ∀{rs-pre r rs-post} →
hole-binders-unique-rs rs-pre →
hole-binders-unique-rs (r / rs-post) →
hole-binders-disjoint-rs rs-pre (r / rs-post) →
hole-binders-unique-zrs (rs-pre / r / rs-post)
data hole-binders-unique-σ : subst-env → Set where
HBUσId : ∀{Γ} →
hole-binders-unique-σ (Id Γ)
HBUσSubst : ∀{d y σ} →
hole-binders-unique d →
hole-binders-unique-σ σ →
hole-binders-disjoint-σ σ d →
hole-binders-unique-σ (Subst d y σ)
data hole-binders-unique : ihexp → Set where
HBUUnit : hole-binders-unique unit
HBUNum : ∀{n} →
hole-binders-unique (N n)
HBUVar : ∀{x} →
hole-binders-unique (X x)
HBULam : ∀{x τ e} →
hole-binders-unique e →
hole-binders-unique (·λ x ·[ τ ] e)
HBUEHole : ∀{u σ} →
hole-binders-unique-σ σ →
hole-binders-unique ⦇-⦈⟨ u , σ ⟩
HBUHole : ∀{e u σ} →
hole-binders-unique-σ σ →
hole-binders-unique e →
hole-binders-disjoint-σ σ e →
hole-binders-unique ⦇⌜ e ⌟⦈⟨ u , σ ⟩
HBUAp : ∀{e1 e2} →
hole-binders-unique e1 →
hole-binders-unique e2 →
hole-binders-disjoint e1 e2 →
hole-binders-unique (e1 ∘ e2)
HBUInl : ∀{e τ} →
hole-binders-unique e →
hole-binders-unique (inl τ e)
HBUInr : ∀{e τ} →
hole-binders-unique e →
hole-binders-unique (inr τ e)
HBUMatch : ∀{e τ rs} →
hole-binders-unique e →
hole-binders-unique-zrs rs →
hole-binders-disjoint-zrs rs e →
hole-binders-unique (match e ·: τ of rs)
HBUPair : ∀{e1 e2} →
hole-binders-unique e1 →
hole-binders-unique e2 →
hole-binders-disjoint e1 e2 →
hole-binders-unique ⟨ e1 , e2 ⟩
HBUFst : ∀{e} →
hole-binders-unique e →
hole-binders-unique (fst e)
HBUSnd : ∀{e} →
hole-binders-unique e →
hole-binders-unique (snd e)