164 lines
4.5 KiB
Idris
164 lines
4.5 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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public export
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0 TermLike : Type
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TermLike = Type -> Nat -> Nat -> Type
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public export
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0 TSubstLike : Type
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TSubstLike = Type -> Nat -> Nat -> Nat -> Type
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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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0 TSubst : TSubstLike
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TSubst q d = Subst $ Elim q d
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||| first argument `q` is quantity type;
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||| second argument `d` is dimension scope size;
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||| third `n` is term scope size
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public export
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data Term : TermLike where
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||| type of types
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TYPE : (l : Universe) -> Term q d n
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||| function type
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Pi : (qty : q) -> (x : Name) ->
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(arg : Term q d n) -> (res : ScopeTerm q d n) -> Term q d n
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||| function term
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Lam : (x : Name) -> (body : ScopeTerm q d n) -> Term q d n
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||| pair type
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Sig : (x : Name) -> (fst : Term q d n) -> (snd : ScopeTerm q d n) ->
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Term q d n
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||| pair value
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Pair : (fst, snd : Term q d n) -> Term q d n
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||| equality type
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Eq : (i : Name) -> (ty : DScopeTerm q d n) -> (l, r : Term q d n) ->
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Term q d n
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||| equality term
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DLam : (i : Name) -> (body : DScopeTerm q d n) -> Term q d n
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||| elimination
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E : (e : Elim q d n) -> Term q d n
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||| term closure/suspended substitution
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CloT : (tm : Term q d from) -> (th : Lazy (TSubst q d from to)) ->
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Term q d to
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||| dimension closure/suspended substitution
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DCloT : (tm : Term q dfrom n) -> (th : Lazy (DSubst dfrom dto)) ->
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Term q 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 : TermLike where
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||| free variable
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F : (x : Name) -> Elim q d n
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||| bound variable
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B : (i : Var n) -> Elim q d n
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||| term application
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(:@) : (fun : Elim q d n) -> (arg : Term q d n) -> Elim q d n
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||| pair destruction
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|||
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||| `CasePair 𝜋 𝑒 𝑟 𝐴 𝑥 𝑦 𝑡` is
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||| `𝐜𝐚𝐬𝐞 𝜋 · 𝑒 𝐫𝐞𝐭𝐮𝐫𝐧 𝑟 ⇒ 𝐴 𝐨𝐟 { (𝑥, 𝑦) ⇒ 𝑡 }`
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CasePair : (qty : q) -> (pair : Elim q d n) ->
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(r : Name) -> (ret : ScopeTerm q d n) ->
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(x, y : Name) -> (body : ScopeTermN 2 q d n) ->
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Elim q d n
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||| dim application
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(:%) : (fun : Elim q d n) -> (arg : Dim d) -> Elim q d n
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||| type-annotated term
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(:#) : (tm, ty : Term q d n) -> Elim q d n
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||| term closure/suspended substitution
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CloE : (el : Elim q d from) -> (th : Lazy (TSubst q d from to)) ->
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Elim q d to
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||| dimension closure/suspended substitution
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DCloE : (el : Elim q dfrom n) -> (th : Lazy (DSubst dfrom dto)) ->
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Elim q dto n
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||| a scope with some more bound term variables
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public export
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data ScopeTermN : Nat -> TermLike where
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||| at least some variables are used
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TUsed : (body : Term q d (s + n)) -> ScopeTermN s q d n
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||| all variables are unused
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TUnused : (body : Term q d n) -> ScopeTermN s q d n
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public export
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0 ScopeTerm : TermLike
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ScopeTerm = ScopeTermN 1
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||| a scope with some more bound dimension variable
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public export
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data DScopeTermN : Nat -> TermLike where
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||| at least some variables are used
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DUsed : (body : Term q (s + d) n) -> DScopeTermN s q d n
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||| all variables are unused
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DUnused : (body : Term q d n) -> DScopeTermN s q d n
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public export
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0 DScopeTerm : TermLike
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DScopeTerm = DScopeTermN 1
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%name Term s, t, r
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%name Elim e, f
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%name ScopeTermN body
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%name DScopeTermN body
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||| non dependent function type
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public export %inline
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Arr : (qty : q) -> (arg, res : Term q d n) -> Term q d n
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Arr {qty, arg, res} = Pi {qty, x = "_", arg, res = TUnused res}
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||| non dependent equality type
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public export %inline
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Eq0 : (ty, l, r : Term q d n) -> Term q d n
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Eq0 {ty, l, r} = Eq {i = "_", ty = DUnused ty, l, r}
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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 q 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 q 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 q d n
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BVT i = E $ BV i
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