198 lines
4.5 KiB
Idris
198 lines
4.5 KiB
Idris
module Quox.Syntax.Term.Split
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import Quox.Syntax.Term.Base
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import Quox.Syntax.Term.Subst
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import Quox.No
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import Data.Vect
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%default total
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public export %inline
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isLam : Term {} -> Bool
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isLam (Lam {}) = True
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isLam _ = False
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public export
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0 NotLam : Pred $ Term {}
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NotLam = No . isLam
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public export %inline
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isDLam : Term {} -> Bool
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isDLam (DLam {}) = True
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isDLam _ = False
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public export
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0 NotDLam : Pred $ Term {}
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NotDLam = No . isDLam
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public export %inline
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isPair : Term {} -> Bool
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isPair (Pair {}) = True
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isPair _ = False
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public export
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0 NotPair : Pred $ Term {}
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NotPair = No . isPair
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public export %inline
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isApp : Elim {} -> Bool
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isApp (_ :@ _) = True
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isApp _ = False
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public export
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0 NotApp : Pred $ Elim {}
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NotApp = No . isApp
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public export %inline
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isDApp : Elim {} -> Bool
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isDApp (_ :% _) = True
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isDApp _ = False
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public export
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0 NotDApp : Pred $ Elim {}
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NotDApp = No . isDApp
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infixl 9 :@@
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||| apply multiple arguments at once
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public export %inline
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(:@@) : Elim q d n -> List (Term q d n) -> Elim q d n
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f :@@ ss = foldl (:@) f ss
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public export
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record GetArgs q d n where
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constructor GotArgs
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fun : Elim q d n
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args : List (Term q d n)
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0 notApp : NotApp fun
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export
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getArgs' : Elim q d n -> List (Term q d n) -> GetArgs q d n
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getArgs' fun args = case nchoose $ isApp fun of
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Left y => let f :@ a = fun in getArgs' f (a :: args)
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Right n => GotArgs {fun, args, notApp = n}
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||| splits an application into its head and arguments. if it's not an
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||| application then the list is just empty
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export %inline
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getArgs : Elim q d n -> GetArgs q d n
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getArgs e = getArgs' e []
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infixl 9 :%%
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||| apply multiple dimension arguments at once
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public export %inline
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(:%%) : Elim q d n -> List (Dim d) -> Elim q d n
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f :%% ss = foldl (:%) f ss
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public export
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record GetDArgs q d n where
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constructor GotDArgs
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fun : Elim q d n
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args : List (Dim d)
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0 notDApp : NotDApp fun
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export
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getDArgs' : Elim q d n -> List (Dim d) -> GetDArgs q d n
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getDArgs' fun args = case nchoose $ isDApp fun of
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Left y => let f :% d = fun in getDArgs' f (d :: args)
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Right n => GotDArgs {fun, args, notDApp = n}
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||| splits a dimension application into its head and arguments. if it's not an
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||| d application then the list is just empty
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export %inline
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getDArgs : Elim q d n -> GetDArgs q d n
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getDArgs e = getDArgs' e []
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infixr 1 :\\
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public export
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absN : Vect m Name -> Term q d (m + n) -> Term q d n
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absN {m = 0} [] s = s
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absN {m = S m} (x :: xs) s = Lam x $ TUsed $ absN xs $
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rewrite sym $ plusSuccRightSucc m n in s
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public export %inline
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(:\\) : Vect m Name -> Term q d (m + n) -> Term q d n
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(:\\) = absN
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infixr 1 :\\%
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public export
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dabsN : Vect m Name -> Term q (m + d) n -> Term q d n
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dabsN {m = 0} [] s = s
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dabsN {m = S m} (x :: xs) s = DLam x $ DUsed $ dabsN xs $
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rewrite sym $ plusSuccRightSucc m d in s
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public export %inline
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(:\\%) : Vect m Name -> Term q (m + d) n -> Term q d n
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(:\\%) = dabsN
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public export
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record GetLams q d n where
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constructor GotLams
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{0 lams, rest : Nat}
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names : Vect lams Name
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body : Term q d rest
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0 eq : lams + n = rest
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0 notLam : NotLam body
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export
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getLams' : forall lams, rest.
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Vect lams Name -> Term q d rest -> (0 eq : lams + n = rest) ->
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GetLams q d n
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getLams' xs s Refl = case nchoose $ isLam s of
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Left y => let Lam x body = s in
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getLams' (x :: xs) (assert_smaller s body.term) Refl
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Right n => GotLams xs s Refl n
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export %inline
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getLams : Term q d n -> GetLams q d n
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getLams s = getLams' [] s Refl
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public export
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record GetDLams q d n where
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constructor GotDLams
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{0 lams, rest : Nat}
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names : Vect lams Name
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body : Term q rest n
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0 eq : lams + d = rest
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0 notDLam : NotDLam body
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export
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getDLams' : forall lams, rest.
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Vect lams Name -> Term q rest n -> (0 eq : lams + d = rest) ->
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GetDLams q d n
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getDLams' is s Refl = case nchoose $ isDLam s of
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Left y => let DLam i body = s in
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getDLams' (i :: is) (assert_smaller s body.term) Refl
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Right n => GotDLams is s Refl n
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export %inline
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getDLams : Term q d n -> GetDLams q d n
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getDLams s = getDLams' [] s Refl
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public export
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record GetPairs q d n where
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constructor GotPairs
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init : List $ Term q d n
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last : Term q d n
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notPair : NotPair last
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export
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getPairs : Term q d n -> GetPairs q d n
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getPairs t = case nchoose $ isPair t of
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Left y =>
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let Pair s t = t; GotPairs ts t np = getPairs t in
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GotPairs (s :: ts) t np
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Right n => GotPairs [] t n
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