59 lines
1.5 KiB
Lean4
59 lines
1.5 KiB
Lean4
import BidirTT.Level
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namespace BidirTT
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abbrev Name := String
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inductive Raw where
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| var : Name → Raw
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| lam : Name → Raw → Raw
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| app : Raw → Raw → Raw
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| pi : Name → Raw → Raw → Raw
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| sig : Name → Raw → Raw → Raw
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| pair : Raw → Raw → Raw
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| fst : Raw → Raw
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| snd : Raw → Raw
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| nat : Raw
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| zero : Raw
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| succ : Raw → Raw
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| natElim : Name → Raw → Raw → Name → Name → Raw → Raw → Raw
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| unit : Raw
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| triv : Raw
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| unitElim : Name → Raw → Raw → Raw → Raw
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| empty : Raw
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| emptyElim : Name → Raw → Raw → Raw
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| id : Raw → Raw → Raw → Raw
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| refl : Raw
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| idElim : Name → Name → Raw → Raw → Raw → Raw → Raw
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| univ : Level → Raw
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| letE : Name → Raw → Raw → Raw → Raw
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| ann : Raw → Raw → Raw
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deriving Repr, Inhabited, BEq, DecidableEq
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inductive Tm where
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| var : Nat → Tm
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| lam : Tm → Tm
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| app : Tm → Tm → Tm
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| pi : Tm → Tm → Tm
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| sig : Tm → Tm → Tm
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| pair : Tm → Tm → Tm
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| fst : Tm → Tm
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| snd : Tm → Tm
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| nat : Tm
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| zero : Tm
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| succ : Tm → Tm
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| natElim : Tm → Tm → Tm → Tm → Tm
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| unit : Tm
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| triv : Tm
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| unitElim : Tm → Tm → Tm → Tm
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| empty : Tm
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| emptyElim : Tm → Tm → Tm
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| id : Tm → Tm → Tm → Tm
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| refl : Tm
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| idElim : Tm → Tm → Tm → Tm → Tm
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| univ : Level → Tm
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| letE : Tm → Tm → Tm → Tm
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deriving Repr, Inhabited, BEq, DecidableEq
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end BidirTT
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