70 lines
1.9 KiB
Plaintext
70 lines
1.9 KiB
Plaintext
load "misc.quox"
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load "either.quox"
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namespace maybe {
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def0 Tag : ★ = {nothing, just}
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def0 Payload : ω.Tag → ω.★ → ★ =
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λ tag A ⇒ caseω tag return ★ of { 'nothing ⇒ True; 'just ⇒ A }
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def0 Maybe : ω.★ → ★ =
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λ A ⇒ (t : Tag) × Payload t A
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def tag : 0.(A : ★) → ω.(Maybe A) → Tag =
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λ _ x ⇒ caseω x return Tag of { (tag, _) ⇒ tag }
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def Nothing : 0.(A : ★) → Maybe A =
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λ _ ⇒ ('nothing, 'true)
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def Just : 0.(A : ★) → 1.A → Maybe A =
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λ _ x ⇒ ('just, x)
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def0 IsJustTag : ω.Tag → ★ =
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λ t ⇒ caseω t return ★ of { 'just ⇒ True; 'nothing ⇒ False }
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def0 IsJust : 0.(A : ★) → ω.(Maybe A) → ★ =
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λ A x ⇒ IsJustTag (tag A x)
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def is-just? : 0.(A : ★) → ω.(x : Maybe A) → Dec (IsJust A x) =
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λ A x ⇒
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caseω tag A x return t ⇒ Dec (IsJustTag t) of {
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'just ⇒ Yes True 'true;
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'nothing ⇒ No False (λ x ⇒ x)
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}
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def0 nothing-unique :
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0.(A : ★) → ω.(x : True) → ('nothing, x) ≡ Nothing A : Maybe A =
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λ A x ⇒
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caseω x return x' ⇒ ('nothing, x') ≡ Nothing A : Maybe A of {
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'true ⇒ δ _ ⇒ ('nothing, 'true)
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}
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def elim :
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0.(A : ★) →
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0.(P : 0.(Maybe A) → ★) →
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ω.(P (Nothing A)) →
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ω.(ω.(x : A) → P (Just A x)) →
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1.(x : Maybe A) → P x =
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λ A P n j x ⇒
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caseω x return x' ⇒ P x' of {
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(tag, payload) ⇒
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(caseω tag
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return t ⇒
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0.(eq : tag ≡ t : Tag) → P (t, coe (i ⇒ Payload (eq @i) A) payload)
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of {
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'nothing ⇒
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λ eq ⇒
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caseω coe (i ⇒ Payload (eq @i) A) payload
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return p ⇒ P ('nothing, p)
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of { 'true ⇒ n };
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'just ⇒ λ eq ⇒ j (coe (i ⇒ Payload (eq @i) A) payload)
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}) (δ _ ⇒ tag)
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}
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}
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def0 Maybe = maybe.Maybe
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def0 Just = maybe.Just
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def0 Nothing = maybe.Nothing
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