quox/src/Quox/Equal.idr

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2022-02-26 20:18:16 -05:00
module Quox.Equal
import public Quox.Syntax
import Quox.Error
%default total
public export
data Error =
Clash SomeTerm SomeTerm
| ClashU Universe Universe
| ClashQ Qty Qty
private %inline
clashT' : Term d n -> Term d n -> Error
clashT' = Clash `on` some2
private %inline
clashE' : Elim d n -> Elim d n -> Error
clashE' = clashT' `on` E
parameters {auto _ : MonadThrow Error m}
private %inline
clashT : Term d n -> Term d n -> m a
clashT = throw .: clashT'
private %inline
clashE : Elim d n -> Elim d n -> m a
clashE = clashT `on` E
private %inline
eq : Eq a => (a -> a -> Error) -> a -> a -> m ()
eq err a b = unless (a == b) $ throw $ err a b
mutual
private covering
equalTN' : DSubst d 0 -> (s, t : Term d n) ->
(0 _ : NotRedexT s) -> (0 _ : NotRedexT t) -> m ()
equalTN' _ (TYPE k) (TYPE l) _ _ =
eq ClashU k l
equalTN' _ s@(TYPE _) t _ _ = clashT s t
equalTN' th (Pi qtm1 qty1 _ arg1 res1) (Pi qtm2 qty2 _ arg2 res2) _ _ = do
eq ClashQ qtm1 qtm2
eq ClashQ qty1 qty2
equalTS th arg1 arg2
equalTS th res1 res2
equalTN' _ s@(Pi {}) t _ _ = clashT s t
-- [todo] eta
equalTN' th (Lam _ body1) (Lam _ body2) _ _ =
equalTS th body1 body2
equalTN' _ s@(Lam {}) t _ _ = clashT s t
equalTN' th (E e) (E f) ps pt = equalES th e f
equalTN' _ s@(E _) t _ _ = clashT s t
equalTN' _ (CloT {}) _ ps _ = void $ ps IsCloT
equalTN' _ (DCloT {}) _ ps _ = void $ ps IsDCloT
private covering
equalEN' : DSubst d 0 -> (e, f : Elim d n) ->
(0 _ : NotRedexE e) -> (0 _ : NotRedexE f) -> m ()
equalEN' _ (F x) (F y) _ _ = do
eq (clashE' `on` F {d = 0, n = 0}) x y
equalEN' _ e@(F _) f _ _ = clashE e f
equalEN' _ (B i) (B j) _ _ = do
eq (clashE' `on` B {d = 0}) i j
equalEN' _ e@(B _) f _ _ = clashE e f
equalEN' th (fun1 :@ arg1) (fun2 :@ arg2) _ _ = do
equalES th fun1 fun2
equalTS th arg1 arg2
equalEN' _ e@(_ :@ _) f _ _ = clashE e f
equalEN' th (tm1 :# ty1) (tm2 :# ty2) _ _ = do
equalTS th tm1 tm2
equalTS th ty1 ty2
equalEN' _ e@(_ :# _) f _ _ = clashE e f
equalEN' _ (CloE {}) _ pe _ = void $ pe IsCloE
equalEN' _ (DCloE {}) _ pe _ = void $ pe IsDCloE
private covering %inline
equalTN : DSubst d 0 -> NonRedexTerm d n -> NonRedexTerm d n -> m ()
equalTN th s t = equalTN' th s.fst t.fst s.snd t.snd
private covering %inline
equalEN : DSubst d 0 -> NonRedexElim d n -> NonRedexElim d n -> m ()
equalEN th e f = equalEN' th e.fst f.fst e.snd f.snd
export covering %inline
equalTS : DSubst d 0 -> Term d n -> Term d n -> m ()
equalTS th s t = equalTN th (whnfT s) (whnfT t)
export covering %inline
equalES : DSubst d 0 -> Elim d n -> Elim d n -> m ()
equalES th e f = equalEN th (whnfE e) (whnfE f)
export covering %inline
equalT : DimEq d -> Term d n -> Term d n -> m ()
equalT eqs s t =
let s' = whnfT s; t' = whnfT t in
for_ (splits eqs) $ \th => equalTN th s' t'
export covering %inline
equalE : DimEq d -> Elim d n -> Elim d n -> m ()
equalE eqs e f =
let e' = whnfE e; f' = whnfE f in
for_ (splits eqs) $ \th => equalEN th e' f'
export covering %inline
equalT0 : Term 0 n -> Term 0 n -> m ()
equalT0 = equalT zeroEq
export covering %inline
equalE0 : Elim 0 n -> Elim 0 n -> m ()
equalE0 = equalE zeroEq