From c9de4d9f9fa336b4bf6b6b68b18f7c536734d735 Mon Sep 17 00:00:00 2001 From: Edwin Brady Date: Wed, 3 Mar 2021 14:36:33 +0000 Subject: [PATCH] Remove more trailing whitespace --- tests/idris2/interface024/EH.idr | 46 ++++++++++++++++---------------- 1 file changed, 23 insertions(+), 23 deletions(-) diff --git a/tests/idris2/interface024/EH.idr b/tests/idris2/interface024/EH.idr index edbb3ba92..348ad9948 100644 --- a/tests/idris2/interface024/EH.idr +++ b/tests/idris2/interface024/EH.idr @@ -12,20 +12,20 @@ interface Additive a where interface Additive2 a where constructor MkAdditive2 (:+:) : a -> a -> a - O2 : a - + O2 : a + interface Multiplicative a where constructor MkMultiplicative (.*.) : a -> a -> a I : a -record MonoidOver U where +record MonoidOver U where constructor WithStruct Unit : U Mult : U -> U -> U lftUnit : (x : U) -> Unit `Mult` x = x rgtUnit : (x : U) -> x `Mult` Unit = x - assoc : (x,y,z : U) + assoc : (x,y,z : U) -> x `Mult` (y `Mult` z) = (x `Mult` y) `Mult` z record Monoid where @@ -34,12 +34,12 @@ record Monoid where Struct : MonoidOver U AdditiveStruct : (m : MonoidOver a) -> Additive a -AdditiveStruct m = MkAdditive (Mult $ m) +AdditiveStruct m = MkAdditive (Mult $ m) (Unit $ m) AdditiveStruct2 : (m : MonoidOver a) -> Additive2 a -AdditiveStruct2 m = MkAdditive2 (Mult $ m) +AdditiveStruct2 m = MkAdditive2 (Mult $ m) (Unit $ m) -AdditiveStructs : (ma : MonoidOver a) -> (mb : MonoidOver b) +AdditiveStructs : (ma : MonoidOver a) -> (mb : MonoidOver b) -> (Additive a, Additive2 b) AdditiveStructs ma mb = (AdditiveStruct ma, AdditiveStruct2 mb) @@ -49,46 +49,46 @@ getAdditive m = AdditiveStruct (Struct m) MultiplicativeStruct : (m : Monoid) -> Multiplicative (U m) MultiplicativeStruct m = MkMultiplicative (Mult $ Struct m) (Unit $ Struct m) ------------------------------------------------------ +----------------------------------------------------- Commutative : MonoidOver a -> Type Commutative m = (x,y : a) -> let _ = AdditiveStruct m in x .+. y = y .+. x - + Commute : (Additive a, Additive2 a) => Type Commute = - (x11,x12,x21,x22 : a) -> + (x11,x12,x21,x22 : a) -> ((x11 :+: x12) .+. (x21 :+: x22)) = ((x11 .+. x21) :+: (x12 .+. x22)) -product : (ma, mb : Monoid) -> Monoid -product ma mb = - let +product : (ma, mb : Monoid) -> Monoid +product ma mb = + let %hint aStruct : Additive (U ma) aStruct = getAdditive ma %hint bStruct : Additive (U mb) bStruct = getAdditive mb - + in MkMonoid (U ma, U mb) $ WithStruct (O, O) (\(x1,y1), (x2, y2) => (x1 .+. x2, y1 .+. y2)) - (\(x,y) => rewrite lftUnit (Struct ma) x in + (\(x,y) => rewrite lftUnit (Struct ma) x in rewrite lftUnit (Struct mb) y in Refl) (\(x,y) => rewrite rgtUnit (Struct ma) x in rewrite rgtUnit (Struct mb) y in Refl) - (\(x1,y1),(x2,y2),(x3,y3) => + (\(x1,y1),(x2,y2),(x3,y3) => rewrite assoc (Struct ma) x1 x2 x3 in rewrite assoc (Struct mb) y1 y2 y3 in Refl) -EckmannHilton : forall a . (ma,mb : MonoidOver a) +EckmannHilton : forall a . (ma,mb : MonoidOver a) -> let ops = AdditiveStructs ma mb in Commute @{ops} -> (Commutative ma, (x,y : a) -> x .+. y = x :+: y) -EckmannHilton ma mb prf = +EckmannHilton ma mb prf = let %hint first : Additive a first = AdditiveStruct ma %hint second : Additive2 a @@ -97,7 +97,7 @@ EckmannHilton ma mb prf = SameUnits = Calc $ |~ O ~~ O .+. O ...(sym $ lftUnit ma O) - ~~ (O :+: O2) .+. (O2 :+: O) ...(sym $ cong2 (.+.) + ~~ (O :+: O2) .+. (O2 :+: O) ...(sym $ cong2 (.+.) (rgtUnit mb O) (lftUnit mb O)) ~~ (O .+. O2) :+: (O2 .+. O) ...(prf O O2 O2 O) @@ -105,7 +105,7 @@ EckmannHilton ma mb prf = (lftUnit ma O2) (rgtUnit ma O2)) ~~ O2 ...(lftUnit mb O2) - + SameMults : (x,y : a) -> (x .+. y) === (x :+: y) SameMults x y = Calc $ |~ x .+. y @@ -113,13 +113,13 @@ EckmannHilton ma mb prf = (rgtUnit mb x) (lftUnit mb y)) ~~ (x .+. O2) :+: (O2 .+. y) ...(prf x O2 O2 y) - ~~ (x .+. O ) :+: (O .+. y) ...(cong (\u => + ~~ (x .+. O ) :+: (O .+. y) ...(cong (\u => (x .+. u) :+: (u .+. y)) (sym SameUnits)) ~~ x :+: y ...(cong2 (:+:) (rgtUnit ma x) (lftUnit ma y)) - + Commutativity : Commutative ma Commutativity x y = Calc $ |~ x .+. y @@ -127,7 +127,7 @@ EckmannHilton ma mb prf = (lftUnit mb x) (rgtUnit mb y)) ~~ (O2 .+. y) :+: (x .+. O2) ...(prf O2 x y O2) - ~~ (O .+. y) :+: (x .+. O ) ...(cong (\u => + ~~ (O .+. y) :+: (x .+. O ) ...(cong (\u => (u .+. y) :+: (x .+. u)) (sym SameUnits)) ~~ y :+: x ...(cong2 (:+:)