Generalize Prelude proof helpers

idris-lang · Jul 5, 2023 · af3c5fd · af3c5fd
1 parent ecf4765
commit af3c5fd
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Showing 15 changed files with 95 additions and 95 deletions.
diff --git a/libs/base/Control/Function.idr b/libs/base/Control/Function.idr
@@ -53,7 +53,7 @@ public export
 public export
 [BiinjFromComp] {f : a -> b -> c} -> {g : c -> d} ->
   Biinjective (g .: f) => Biinjective f where
-    biinjective = biinjective {f = (g .: f)} . cong g
+    biinjective prf = biinjective {f = (g .: f)} $ cong g prf
 
 public export
 [FlipBiinjective] {f : a -> b -> c} ->

diff --git a/libs/base/Data/Fin/Order.idr b/libs/base/Data/Fin/Order.idr
@@ -43,7 +43,7 @@ using (k : Nat)
     connex {x = FZ} _ =  Left $ FromNatPrf LTEZero
     connex {y = FZ} _ = Right $ FromNatPrf LTEZero
     connex {x = FS k} {y = FS j} prf =
-      case connex {rel = FinLTE} $ prf . (cong FS) of
+      case connex {rel = FinLTE} $ \c => prf $ cong FS c of
         Left  (FromNatPrf p) => Left  $ FromNatPrf $ LTESucc p
         Right (FromNatPrf p) => Right $ FromNatPrf $ LTESucc p
 

diff --git a/libs/base/Data/Nat.idr b/libs/base/Data/Nat.idr
@@ -123,7 +123,7 @@ Connex Nat LTE where
   connex {x = Z} _ = Left LTEZero
   connex {y = Z} _ = Right LTEZero
   connex {x = S _} {y = S _} prf =
-    case connex $ prf . (cong S) of
+    case connex $ \xy => prf $ cong S xy of
       Left jk => Left $ LTESucc jk
       Right kj => Right $ LTESucc kj
 

diff --git a/libs/base/Data/Vect.idr b/libs/base/Data/Vect.idr
@@ -259,7 +259,7 @@ replaceAtDiffIndexPreserves : (xs : Vect n a) -> (i, j : Fin n) -> Not (i = j) -
 replaceAtDiffIndexPreserves (_::_) FZ     FZ     co _ = absurd $ co Refl
 replaceAtDiffIndexPreserves (_::_) FZ     (FS _) _  _ = Refl
 replaceAtDiffIndexPreserves (_::_) (FS _) FZ     _  _ = Refl
-replaceAtDiffIndexPreserves (_::_) (FS z) (FS w) co y = replaceAtDiffIndexPreserves _ z w (co . cong FS) y
+replaceAtDiffIndexPreserves (_::_) (FS z) (FS w) co y = replaceAtDiffIndexPreserves _ z w (\zw => co $ cong FS zw) y
 
 --------------------------------------------------------------------------------
 -- Transformations

diff --git a/libs/base/Decidable/Equality/Core.idr b/libs/base/Decidable/Equality/Core.idr
@@ -45,7 +45,7 @@ decEqCong $ No contra = No $ \c => contra $ inj f c
 public export
 decEqInj : (0 _ : Injective f) => Dec (f x = f y) -> Dec (x = y)
 decEqInj $ Yes prf   = Yes $ inj f prf
-decEqInj $ No contra = No $ contra . cong f
+decEqInj $ No contra = No $ \c => contra $ cong f c
 
 public export
 decEqCong2 : (0 _ : Biinjective f) => Dec (x = y) -> Lazy (Dec (v = w)) -> Dec (f x v = f y w)

diff --git a/libs/papers/Data/Container.idr b/libs/papers/Data/Container.idr
@@ -288,12 +288,12 @@ namespace Derivative
   toPair v = case fromSum {c = Pair (Derivative c) d} {d = Pair c (Derivative d)} v of
     Left p => let (MkExtension (shp1 ** p1) chld1, MkExtension shp2 chld2) = fromPair {c = Derivative c} p in
               MkExtension ((shp1, shp2) ** Left p1) $ \ (p' ** neq) => case p' of
-                  Left p1' => chld1 (p1' ** (neq . cong Left))
+                  Left p1' => chld1 (p1' ** (\prf => neq $ cong Left prf))
                   Right p2' => chld2 p2'
     Right p => let (MkExtension shp1 chld1, MkExtension (shp2 ** p2) chld2) = fromPair {c} {d = Derivative d} p in
                MkExtension ((shp1, shp2) ** Right p2) $ \ (p' ** neq) => case p' of
                   Left p1' => chld1 p1'
-                  Right p2' => chld2 (p2' ** (neq . cong Right))
+                  Right p2' => chld2 (p2' ** (\prf => neq $ cong Right prf))
 
   export
   fromPair : Extension (Derivative (Pair c d)) x ->
@@ -323,7 +323,7 @@ namespace Derivative
       right = toCompose
             $ MkExtension (shp1 ** p1)
             $ \ (p1' ** neqp1) => MkExtension (shp2 p1')
-                                 $ \ p2' => chld ((p1' ** p2') ** (neqp1 . cong fst))
+                                 $ \ p2' => chld ((p1' ** p2') ** (\prf => neqp1 $ cong fst prf))
 
   export
   toCompose : ((s : _) -> DecEq (Position c s)) -> ((s : _) -> DecEq (Position d s)) ->

diff --git a/libs/papers/Search/Auto.idr b/libs/papers/Search/Auto.idr
@@ -259,8 +259,8 @@ thinApart FZ FZ neq = absurd (neq Refl)
 thinApart FZ (FS y') neq = (y' ** Refl)
 thinApart (FS FZ) FZ neq = (FZ ** Refl)
 thinApart (FS (FS x)) FZ neq = (FZ ** Refl)
-thinApart (FS x@FZ) (FS y) neq = bimap FS (cong FS) (thinApart x y (neq . cong FS))
-thinApart (FS x@(FS{})) (FS y) neq = bimap FS (cong FS) (thinApart x y (neq . cong FS))
+thinApart (FS x@FZ) (FS y) neq = bimap FS (\prf => cong FS prf) (thinApart x y (\prf => neq $ cong FS prf))
+thinApart (FS x@(FS{})) (FS y) neq = bimap FS (\prf => cong FS prf) (thinApart x y (\prf => neq $ cong FS prf))
 
 public export
 data Thicken : (x, y : Fin n) -> Type where
@@ -462,7 +462,7 @@ apply r args = let (premises, rest) = splitAt r.arity args in
 
 mkVars : (m : Nat) -> (vars : SnocList Name ** length vars = m)
 mkVars Z = ([<] ** Refl)
-mkVars m@(S m') = bimap (:< UN (Basic $ "_invalidName" ++ show m)) (cong S) (mkVars m')
+mkVars m@(S m') = bimap (:< UN (Basic $ "_invalidName" ++ show m)) (\prf => cong S prf) (mkVars m')
 
 solveAcc : {m : _} -> Nat -> HintDB -> PartialProof m -> Space Proof
 solveAcc idx rules (MkPartialProof 0     goals k)

diff --git a/libs/prelude/Prelude/Basics.idr b/libs/prelude/Prelude/Basics.idr
@@ -99,18 +99,18 @@ public export
 
 ||| Equality is a congruence.
 public export
-cong : (0 f : t -> u) -> (p : a = b) -> f a = f b
+cong : (0 f : t -> u) -> (0 p : a = b) -> f a = f b
 cong f Refl = Refl
 
 ||| Two-holed congruence.
 export
 -- These are natural in equational reasoning.
-cong2 : (0 f : t1 -> t2 -> u) -> (p1 : a = b) -> (p2 : c = d) -> f a c = f b d
+cong2 : (0 f : t1 -> t2 -> u) -> (0 p1 : a = b) -> (0 p2 : c = d) -> f a c = f b d
 cong2 f Refl Refl = Refl
 
 ||| Irrelevant equalities can always be made relevant
 export
-irrelevantEq : (0 _ : a === b) -> a === b
+irrelevantEq : (0 _ : a ~=~ b) -> a ~=~ b
 irrelevantEq Refl = Refl
 
 --------------

diff --git a/src/Core/Case/CaseBuilder.idr b/src/Core/Case/CaseBuilder.idr
@@ -381,7 +381,7 @@ conTypeEq (CName x tag) (CName x' tag')
              Yes Refl => Just Refl
              No contra => Nothing
 conTypeEq CDelay CDelay = Just Refl
-conTypeEq (CConst x) (CConst y) = cong CConst <$> constantEq x y
+conTypeEq (CConst x) (CConst y) = (\xy => cong CConst xy) <$> constantEq x y
 conTypeEq _ _ = Nothing
 
 data Group : List Name -> -- variables in scope

diff --git a/src/Core/Name.idr b/src/Core/Name.idr
@@ -410,7 +410,7 @@ nameEq (NS xs x) (NS ys y) with (decEq xs ys)
     nameEq (NS ys x) (NS ys y) | (Yes Refl) | Nothing = Nothing
     nameEq (NS ys y) (NS ys y) | (Yes Refl) | (Just Refl) = Just Refl
   nameEq (NS xs x) (NS ys y) | (No contra) = Nothing
-nameEq (UN x) (UN y) = map (cong UN) (userNameEq x y)
+nameEq (UN x) (UN y) = map (\xy => cong UN xy) (userNameEq x y)
 nameEq (MN x t) (MN x' t') with (decEq x x')
   nameEq (MN x t) (MN x t') | (Yes Refl) with (decEq t t')
     nameEq (MN x t) (MN x t) | (Yes Refl) | (Yes Refl) = Just Refl

diff --git a/src/Core/TT.idr b/src/Core/TT.idr
@@ -189,7 +189,7 @@ constantEq (Ch x) (Ch y) = case decEq x y of
                                 Yes Refl => Just Refl
                                 No contra => Nothing
 constantEq (Db x) (Db y) = Nothing -- no DecEq for Doubles!
-constantEq (PrT x) (PrT y) = cong PrT <$> primTypeEq x y
+constantEq (PrT x) (PrT y) = (\xy => cong PrT xy) <$> primTypeEq x y
 constantEq WorldVal WorldVal = Just Refl
 
 constantEq _ _ = Nothing

diff --git a/tests/base/deriving_traversable/expected b/tests/base/deriving_traversable/expected
@@ -65,7 +65,7 @@ LOG derive.traversable.clauses:1:
   traverseIVect : {0 m : _} -> {0 a, b : Type} -> {0 f : Type -> Type} -> Applicative f => (a -> f b) -> IVect {n = m} a -> f (IVect {n = m} b)
   traverseIVect f (MkIVect x2) = MkIVect <$> (traverse f x2)
 LOG derive.traversable.clauses:1: 
-  traverseEqMap : {0 key, eq : _} -> {0 a, b : Type} -> {0 f : Type -> Type} -> Applicative f => (a -> f b) -> EqMap key {{conArg:13922} = eq} a -> f (EqMap key {{conArg:13922} = eq} b)
+  traverseEqMap : {0 key, eq : _} -> {0 a, b : Type} -> {0 f : Type -> Type} -> Applicative f => (a -> f b) -> EqMap key {{conArg:13919} = eq} a -> f (EqMap key {{conArg:13919} = eq} b)
   traverseEqMap f (MkEqMap x3) = MkEqMap <$> (traverse (traverse f) x3)
 LOG derive.traversable.clauses:1: 
   traverseTree : {0 l : _} -> {0 a, b : Type} -> {0 f : Type -> Type} -> Applicative f => (a -> f b) -> Tree l a -> f (Tree l b)

diff --git a/tests/idris2/evaluator002/expected b/tests/idris2/evaluator002/expected
@@ -1,89 +1,89 @@
 1/2: Building Lib (Lib.idr)
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2558}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2559}
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-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2558}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2558}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2558}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2555}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2556}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2556}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2556}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2556}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2556}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2555}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2555}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2555}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2559}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2556}
+LOG eval.stuck.outofscope:5: Stuck function: {_:2561}
 LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2562}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2559}
-LOG eval.stuck.outofscope:5: Stuck function: {_:2564}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2565}
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-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2567}
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-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2566}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2570}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2570}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2570}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2570}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2570}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2567}
-LOG eval.stuck.outofscope:5: Stuck function: {_:2573}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{b:2574}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2562}
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+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2563}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2564}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2564}
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+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2564}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2563}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2563}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2563}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2567}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2567}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2567}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2567}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2567}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2564}
+LOG eval.stuck.outofscope:5: Stuck function: {_:2570}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{b:2571}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2572}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2572}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2572}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2575}
 LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2575}
 LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2575}
 LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2575}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2578}
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-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2578}
 LOG eval.stuck.outofscope:5: Stuck function: Prelude.Types.List.reverse
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2593}
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-LOG eval.stuck.outofscope:5: Stuck function: Lib.{b:2598}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2599}
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-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2601}
-LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2590}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2591}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2591}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2591}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2591}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2591}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2591}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{_:2591}
+LOG eval.stuck.outofscope:5: Stuck function: {_:2594}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{b:2595}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2596}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2596}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2596}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2598}
+LOG eval.stuck.outofscope:5: Stuck function: Lib.{a:2598}
 LOG eval.stuck.outofscope:5: Stuck function: Lib.accMapAux
 2/2: Building Main (Main.idr)
-LOG eval.stuck.outofscope:5: Stuck function: Main.{b:2603}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{b:2600}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{b:2600}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{b:2600}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2604}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2604}
-LOG eval.stuck.outofscope:5: Stuck function: Main.{b:2603}
-LOG eval.stuck.outofscope:5: Stuck function: Main.{b:2603}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2604}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2607}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2607}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2607}
-LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2604}
-LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2604}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2610}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2610}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2612}
 LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2610}
-LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2604}
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-LOG eval.stuck.outofscope:5: Stuck function: Main.{ty:2624}
-LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2604}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2610}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{ty:2621}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{ty:2621}
+LOG eval.stuck.outofscope:5: Stuck function: Main.{a:2601}
 LOG eval.stuck.outofscope:5: Stuck function: Lib.accMap
 Main> LOG eval.stuck:5: Stuck function: Lib.accMapAux
 LOG eval.stuck:5: Stuck function: Lib.accMapAux