quox/lib/Quox/Syntax/Term/Base.idr

110 lines
3 KiB
Idris

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