110 lines
3 KiB
Idris
110 lines
3 KiB
Idris
module Quox.Syntax.Term.Base
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import public Quox.Syntax.Var
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import public Quox.Syntax.Shift
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import public Quox.Syntax.Subst
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import public Quox.Syntax.Universe
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import public Quox.Syntax.Qty
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import public Quox.Syntax.Dim
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import public Quox.Name
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-- import public Quox.OPE
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import Quox.Pretty
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import public Data.DPair
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import Data.List
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import Data.Maybe
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import Data.Nat
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import public Data.So
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import Data.String
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import Data.Vect
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%default total
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infixl 8 :#
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infixl 9 :@
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mutual
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public export
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TSubst : Nat -> Nat -> Nat -> Type
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TSubst d = Subst (\n => Elim d n)
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||| first argument `d` is dimension scope size, second `n` is term scope size
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public export
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data Term : (d, n : Nat) -> Type where
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||| type of types
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TYPE : (l : Universe) -> Term d n
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||| function type
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Pi : (qty : Qty) -> (x : Name) ->
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(arg : Term d n) -> (res : ScopeTerm d n) -> Term d n
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||| function term
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Lam : (x : Name) -> (body : ScopeTerm d n) -> Term d n
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||| elimination
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E : (e : Elim d n) -> Term d n
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||| term closure/suspended substitution
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CloT : (tm : Term d from) -> (th : Lazy (TSubst d from to)) -> Term d to
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||| dimension closure/suspended substitution
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DCloT : (tm : Term dfrom n) -> (th : Lazy (DSubst dfrom dto)) -> Term dto n
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||| first argument `d` is dimension scope size, second `n` is term scope size
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public export
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data Elim : (d, n : Nat) -> Type where
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||| free variable
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F : (x : Name) -> Elim d n
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||| bound variable
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B : (i : Var n) -> Elim d n
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||| term application
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(:@) : (fun : Elim d n) -> (arg : Term d n) -> Elim d n
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||| type-annotated term
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(:#) : (tm, ty : Term d n) -> Elim d n
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||| term closure/suspended substitution
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CloE : (el : Elim d from) -> (th : Lazy (TSubst d from to)) -> Elim d to
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||| dimension closure/suspended substitution
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DCloE : (el : Elim dfrom n) -> (th : Lazy (DSubst dfrom dto)) -> Elim dto n
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||| a scope with one more bound variable
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public export
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data ScopeTerm : (d, n : Nat) -> Type where
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||| variable is used
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TUsed : (body : Term d (S n)) -> ScopeTerm d n
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||| variable is unused
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TUnused : (body : Term d n) -> ScopeTerm d n
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||| a scope with one more bound dimension variable
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public export
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data DScopeTerm : (d, n : Nat) -> Type where
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||| variable is used
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DUsed : (body : Term (S d) n) -> DScopeTerm d n
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||| variable is unused
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DUnused : (body : Term d n) -> DScopeTerm d n
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%name Term s, t, r
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%name Elim e, f
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%name ScopeTerm body
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%name DScopeTerm body
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public export %inline
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Arr : (qty : Qty) -> (arg, res : Term d n) -> Term d n
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Arr {qty, arg, res} = Pi {qty, x = "_", arg, res = TUnused res}
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||| same as `F` but as a term
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public export %inline
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FT : Name -> Term d n
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FT = E . F
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||| abbreviation for a bound variable like `BV 4` instead of
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||| `B (VS (VS (VS (VS VZ))))`
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public export %inline
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BV : (i : Nat) -> (0 _ : LT i n) => Elim d n
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BV i = B $ V i
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||| same as `BV` but as a term
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public export %inline
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BVT : (i : Nat) -> (0 _ : LT i n) => Term d n
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BVT i = E $ BV i
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