Created
July 5, 2024 12:21
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Simple extrinsically typed signatures with two universes (one included in another)
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| ------------ SYNTAX ------------- | |
| Γ ::= ε | Γ (x : A) | |
| A, B, f, e ::= Sort | Sort₁ | x | f e | (x : A) → B | |
| ------------ JUDGEMENT FORMS ------------- | |
| Γ con | |
| Γ con | |
| ---------- | |
| Γ ⊦ A sig | |
| Γ ⊦ A sig | |
| --------- | |
| Γ ⊦ a : A | |
| ------------ INFERENCE RULES ------------- | |
| ε con | |
| Γ con | |
| Γ ⊦ A sig | |
| ------------- | |
| Γ (x : A) con | |
| Γ con | |
| ------------ | |
| Γ ⊦ Sort sig | |
| Γ con | |
| ------------ | |
| Γ ⊦ Sort₁ sig | |
| Γ con | |
| ---------------- | |
| Γ ⊦ Sort : Sort₁ | |
| Γ ⊦ A : Sort | |
| ------------- | |
| Γ ⊦ A : Sort₁ | |
| Γ ⊦ A : Sort₁ | |
| ------------- | |
| Γ ⊦ A sig | |
| Γ ⊦ A : Sort₁ | |
| Γ (x : A) ⊦ B sig | |
| ------------------- | |
| Γ ⊦ (x : A) → B sig | |
| Γ₀ (x : A) Γ₁ ⊦ x : A | |
| Γ ⊦ f : (x : A) → B | |
| Γ ⊦ e : A | |
| ------------------- | |
| Γ ⊦ f e : B[e/x] |
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