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[ performance ] More stack safety in the Prelude (#2704)

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Stefan Höck 2022-10-26 08:54:53 +00:00 committed by GitHub
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7 changed files with 341 additions and 59 deletions
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54
libs/base/Data/List.idr
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@ -445,6 +445,10 @@ public export
replaceOn : Eq a => (e : a) -> (b : a) -> (l : List a) -> List a
replaceOn e = replaceWhen (== e)
replicateTR : List a -> Nat -> a -> List a
replicateTR as Z _ = as
replicateTR as (S n) x = replicateTR (x :: as) n x
||| Construct a list with `n` copies of `x`.
|||
||| @ n how many copies
@ -454,6 +458,10 @@ replicate : (n : Nat) -> (x : a) -> List a
replicate Z _ = []
replicate (S n) x = x :: replicate n x
-- Data.List.replicateTRIsReplicate proves these are equivalent.
%transform "tailRecReplicate" List.replicate = List.replicateTR Nil
||| Compute the intersect of two lists by user-supplied equality predicate.
export
intersectBy : (a -> a -> Bool) -> List a -> List a -> List a
@ -1066,3 +1074,49 @@ export
mapAppend : (f : a -> b) -> (xs, ys : List a) -> map f (xs ++ ys) = map f xs ++ map f ys
mapAppend f [] ys = Refl
mapAppend f (x::xs) ys = rewrite mapAppend f xs ys in Refl
0 mapTRIsMap : (f : a -> b) -> (as : List a) -> mapTR f as === map f as
mapTRIsMap f = lemma Lin
where lemma : (sb : SnocList b)
-> (as : List a)
-> mapAppend sb f as === (sb <>> map f as)
lemma sb [] = Refl
lemma sb (x :: xs) = lemma (sb :< f x) xs
0 mapMaybeTRIsMapMaybe : (f : a -> Maybe b)
-> (as : List a)
-> mapMaybeTR f as === mapMaybe f as
mapMaybeTRIsMapMaybe f = lemma Lin
where lemma : (sb : SnocList b)
-> (as : List a)
-> mapMaybeAppend sb f as === (sb <>> mapMaybe f as)
lemma sb [] = Refl
lemma sb (x :: xs) with (f x)
lemma sb (x :: xs) | Nothing = lemma sb xs
lemma sb (x :: xs) | Just v = lemma (sb :< v) xs
0 filterTRIsFilter : (f : a -> Bool)
-> (as : List a)
-> filterTR f as === filter f as
filterTRIsFilter f = lemma Lin
where lemma : (sa : SnocList a)
-> (as : List a)
-> filterAppend sa f as === (sa <>> filter f as)
lemma sa [] = Refl
lemma sa (x :: xs) with (f x)
lemma sa (x :: xs) | False = lemma sa xs
lemma sa (x :: xs) | True = lemma (sa :< x) xs
0 replicateTRIsReplicate : (n : Nat) -> (x : a) -> replicateTR [] n x === replicate n x
replicateTRIsReplicate n x = trans (lemma [] n) (appendNilRightNeutral _)
where lemma1 : (as : List a) -> (m : Nat) -> (x :: replicate m x) ++ as === replicate m x ++ (x :: as)
lemma1 as 0 = Refl
lemma1 as (S k) = cong (x ::) (lemma1 as k)
lemma : (as : List a) -> (m : Nat) -> replicateTR as m x === replicate m x ++ as
lemma as 0 = Refl
lemma as (S k) =
let prf := lemma (x :: as) k
in trans prf (sym $ lemma1 as k)

93
libs/base/Data/SnocList.idr
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@ -62,9 +62,26 @@ Show a => Show (SnocList a) where
show' acc (xs :< x) = show' (show x :: acc) xs
public export
mapImpl : (a -> b) -> SnocList a -> SnocList b
mapImpl f Lin = Lin
mapImpl f (sx :< x) = (mapImpl f sx) :< (f x)
-- Utility for implementing `mapTR`
mapTR' : List b -> (a -> b) -> SnocList a -> SnocList b
mapTR' xs f (sx :< x) = mapTR' (f x :: xs) f sx
mapTR' xs f Lin = Lin <>< xs
-- Tail recursive version of `map`. This is automatically used
-- at runtime due to a `transform` rule.
mapTR : (a -> b) -> SnocList a -> SnocList b
mapTR = mapTR' []
-- mapTRIsMap proves these are equivalent.
%transform "tailRecMapSnocList" SnocList.mapImpl = SnocList.mapTR
public export %inline
Functor SnocList where
map f Lin = Lin
map f (sx :< x) = (map f sx) :< (f x)
map = mapImpl
public export
Semigroup (SnocList a) where
@ -357,3 +374,75 @@ mapMaybeCast f (x::xs) = do
mapMaybeStepLemma with (f x)
_ | Nothing = rewrite appendLinLeftNeutral $ [<] <>< mapMaybe f xs in Refl
_ | (Just y) = rewrite fishAsSnocAppend [<y] (mapMaybe f xs) in Refl
0 mapTRIsMap : (f : a -> b) -> (sa : SnocList a) -> mapTR f sa === map f sa
mapTRIsMap f = lemma []
where lemma : (bs : List b)
-> (sa : SnocList a)
-> mapTR' bs f sa === (map f sa <>< bs)
lemma bs Lin = Refl
lemma bs (sx :< x) = lemma (f x :: bs) sx
0 mapMaybeTRIsMapMaybe : (f : a -> Maybe b)
-> (sa : SnocList a)
-> mapMaybeTR f sa === mapMaybe f sa
mapMaybeTRIsMapMaybe f = lemma []
where lemma : (bs : List b)
-> (sa : SnocList a)
-> mapMaybeAppend bs f sa === (mapMaybe f sa <>< bs)
lemma bs Lin = Refl
lemma bs (sx :< x) with (f x)
lemma bs (sx :< x) | Nothing = lemma bs sx
lemma bs (sx :< x) | Just v = lemma (v :: bs) sx
0 filterTRIsFilter : (f : a -> Bool)
-> (sa : SnocList a)
-> filterTR f sa === filter f sa
filterTRIsFilter f = lemma []
where lemma : (as : List a)
-> (sa : SnocList a)
-> filterAppend as f sa === (filter f sa <>< as)
lemma as Lin = Refl
lemma as (sx :< x) with (f x)
lemma as (sx :< x) | False = lemma as sx
lemma as (sx :< x) | True = lemma (x :: as) sx
-- SnocList `reverse` applied to `reverseOnto` is equivalent to swapping the
-- arguments of `reverseOnto`.
reverseReverseOnto : (l, r : SnocList a) ->
reverse (reverseOnto l r) = reverseOnto r l
reverseReverseOnto _ Lin = Refl
reverseReverseOnto l (sx :< x) = reverseReverseOnto (l :< x) sx
||| SnocList `reverse` applied twice yields the identity function.
export
reverseInvolutive : (sx : SnocList a) -> reverse (reverse sx) = sx
reverseInvolutive = reverseReverseOnto Lin
-- Appending `x` to `l` and then reversing the result onto `r` is the same as
-- using (::) with `x` and the result of reversing `l` onto `r`.
snocReverse : (x : a) -> (l, r : SnocList a) ->
reverseOnto r l :< x = reverseOnto r (reverseOnto [<x] (reverse l))
snocReverse _ Lin _ = Refl
snocReverse x (sy :< y) r
= rewrite snocReverse x sy (r :< y) in
rewrite cong (reverseOnto r . reverse) $ snocReverse x sy [<y] in
rewrite reverseInvolutive (reverseOnto [<x] (reverse sy) :< y) in
Refl
-- Proof that it is safe to lift a (::) out of the first `tailRecAppend`
-- argument.
snocTailRecAppend : (x : a) -> (l, r : SnocList a) ->
tailRecAppend l (r :< x) = (tailRecAppend l r) :< x
snocTailRecAppend x l r =
rewrite snocReverse x (reverse r) l in
rewrite reverseInvolutive r in
Refl
-- Proof that `(++)` and `tailRecAppend` do the same thing, so the %transform
-- directive is safe.
tailRecAppendIsAppend : (sx, sy : SnocList a) -> tailRecAppend sx sy = sx ++ sy
tailRecAppendIsAppend sx Lin = Refl
tailRecAppendIsAppend sx (sy :< y) =
trans (snocTailRecAppend y sx sy) (cong (:< y) $ tailRecAppendIsAppend sx sy)

218
libs/prelude/Prelude/Types.idr
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@ -392,6 +392,119 @@ Ord a => Ord (List a) where
EQ => compare xs ys
c => c
namespace SnocList
infixl 7 <><
infixr 6 <>>
||| 'fish': Action of lists on snoc-lists
public export
(<><) : SnocList a -> List a -> SnocList a
sx <>< [] = sx
sx <>< (x :: xs) = sx :< x <>< xs
||| 'chips': Action of snoc-lists on lists
public export
(<>>) : SnocList a -> List a -> List a
Lin <>> xs = xs
(sx :< x) <>> xs = sx <>> x :: xs
public export
(++) : (sx, sy : SnocList a) -> SnocList a
(++) sx Lin = sx
(++) sx (sy :< y) = (sx ++ sy) :< y
public export
length : SnocList a -> Nat
length Lin = Z
length (sx :< x) = S $ length sx
||| Filters a snoc-list according to a simple classifying function
public export
filter : (a -> Bool) -> SnocList a -> SnocList a
filter f [<] = [<]
filter f (xs:<x) = let rest = filter f xs in if f x then rest :< x else rest
||| Apply a partial function to the elements of a list, keeping the ones at which
||| it is defined.
public export
mapMaybe : (a -> Maybe b) -> SnocList a -> SnocList b
mapMaybe f [<] = [<]
mapMaybe f (sx :< x) = case f x of
Nothing => mapMaybe f sx
Just j => mapMaybe f sx :< j
||| Reverse the second snoclist, prepending its elements to the first.
public export
reverseOnto : SnocList a -> SnocList a -> SnocList a
reverseOnto acc Lin = acc
reverseOnto acc (sx :< x) = reverseOnto (acc :< x) sx
||| Reverses the given list.
public export
reverse : SnocList a -> SnocList a
reverse = reverseOnto Lin
||| Tail-recursive append. Uses of (++) are automatically transformed to
||| this. The only reason this is exported is that the proof of equivalence
||| lives in a different module.
public export
tailRecAppend : (sx, sy : SnocList a) -> SnocList a
tailRecAppend sx sy = reverseOnto sx (reverse sy)
-- Always use tailRecAppend at runtime. Data.SnocList.tailRecAppendIsAppend
-- proves these are equivalent.
%transform "tailRecAppendSnocList" SnocList.(++) = SnocList.tailRecAppend
||| Returns the first argument plus the length of the second.
public export
lengthPlus : Nat -> SnocList a -> Nat
lengthPlus n Lin = n
lengthPlus n (sx :< _) = lengthPlus (S n) sx
||| `length` implementation that uses tail recursion. Exported so
||| lengthTRIsLength can see it.
public export
lengthTR : SnocList a -> Nat
lengthTR = lengthPlus Z
-- Data.List.lengthTRIsLength proves these are equivalent.
%transform "tailRecLengthSnocList" SnocList.length = SnocList.lengthTR
||| Utility for implementing `mapMaybeTR`
public export
mapMaybeAppend : List b -> (a -> Maybe b) -> SnocList a -> SnocList b
mapMaybeAppend xs f (sx :< x) = case f x of
Just v => mapMaybeAppend (v :: xs) f sx
Nothing => mapMaybeAppend xs f sx
mapMaybeAppend xs f Lin = Lin <>< xs
||| Tail recursive version of `mapMaybe`. This is automatically used
||| at runtime due to a `transform` rule.
public export %inline
mapMaybeTR : (a -> Maybe b) -> SnocList a -> SnocList b
mapMaybeTR = mapMaybeAppend []
-- Data.List.mapMaybeTRIsMapMaybe proves these are equivalent.
%transform "tailRecMapMaybeSnocList" SnocList.mapMaybe = SnocList.mapMaybeTR
||| Utility for implementing `filterTR`
public export
filterAppend : List a -> (a -> Bool) -> SnocList a -> SnocList a
filterAppend xs f (sx :< x) = case f x of
True => filterAppend (x :: xs) f sx
False => filterAppend xs f sx
filterAppend xs f Lin = Lin <>< xs
||| Tail recursive version of `filter`. This is automatically used
||| at runtime due to a `transform` rule.
public export %inline
filterTR : (a -> Bool) -> SnocList a -> SnocList a
filterTR = filterAppend []
-- Data.List.listTRIsList proves these are equivalent.
%transform "tailRecFilterSnocList" SnocList.filter = SnocList.filterTR
namespace List
||| Concatenate one list with another.
@ -445,7 +558,7 @@ namespace List
-- Always use tailRecAppend at runtime. Data.List.tailRecAppendIsAppend
-- proves these are equivalent.
%transform "tailRecAppend" (++) = tailRecAppend
%transform "tailRecAppend" List.(++) = List.tailRecAppend
||| Returns the first argument plus the length of the second.
public export
@ -460,12 +573,65 @@ namespace List
lengthTR = lengthPlus Z
-- Data.List.lengthTRIsLength proves these are equivalent.
%transform "tailRecLength" length = lengthTR
%transform "tailRecLength" List.length = List.lengthTR
public export
public export
mapImpl : (a -> b) -> List a -> List b
mapImpl f [] = []
mapImpl f (x :: xs) = f x :: mapImpl f xs
||| Utility for implementing `mapTR`
public export
mapAppend : SnocList b -> (a -> b) -> List a -> List b
mapAppend sx f (x :: xs) = mapAppend (sx :< f x) f xs
mapAppend sx f [] = sx <>> []
||| Tail recursive version of `map`. This is automatically used
||| at runtime due to a `transform` rule.
public export %inline
mapTR : (a -> b) -> List a -> List b
mapTR = mapAppend Lin
-- Data.List.mapTRIsMap proves these are equivalent.
%transform "tailRecMap" mapImpl = List.mapTR
||| Utility for implementing `mapMaybeTR`
public export
mapMaybeAppend : SnocList b -> (a -> Maybe b) -> List a -> List b
mapMaybeAppend sx f (x :: xs) = case f x of
Just v => mapMaybeAppend (sx :< v) f xs
Nothing => mapMaybeAppend sx f xs
mapMaybeAppend sx f [] = sx <>> []
||| Tail recursive version of `mapMaybe`. This is automatically used
||| at runtime due to a `transform` rule.
public export %inline
mapMaybeTR : (a -> Maybe b) -> List a -> List b
mapMaybeTR = mapMaybeAppend Lin
-- Data.List.mapMaybeTRIsMapMaybe proves these are equivalent.
%transform "tailRecMapMaybe" List.mapMaybe = List.mapMaybeTR
||| Utility for implementing `filterTR`
public export
filterAppend : SnocList a -> (a -> Bool) -> List a -> List a
filterAppend sx f (x :: xs) = case f x of
True => filterAppend (sx :< x) f xs
False => filterAppend sx f xs
filterAppend sx f [] = sx <>> []
||| Tail recursive version of `filter`. This is automatically used
||| at runtime due to a `transform` rule.
public export %inline
filterTR : (a -> Bool) -> List a -> List a
filterTR = filterAppend Lin
-- Data.List.listTRIsList proves these are equivalent.
%transform "tailRecFilter" List.filter = List.filterTR
public export %inline
Functor List where
map f [] = []
map f (x :: xs) = f x :: map f xs
map = mapImpl
public export
Semigroup (List a) where
@ -519,48 +685,6 @@ Traversable List where
traverse f [] = pure []
traverse f (x::xs) = [| f x :: traverse f xs |]
namespace SnocList
infixl 7 <><
infixr 6 <>>
||| 'fish': Action of lists on snoc-lists
public export
(<><) : SnocList a -> List a -> SnocList a
sx <>< [] = sx
sx <>< (x :: xs) = sx :< x <>< xs
||| 'chips': Action of snoc-lists on lists
public export
(<>>) : SnocList a -> List a -> List a
Lin <>> xs = xs
(sx :< x) <>> xs = sx <>> x :: xs
public export
(++) : (sx, sy : SnocList a) -> SnocList a
(++) sx Lin = sx
(++) sx (sy :< y) = (sx ++ sy) :< y
public export
length : SnocList a -> Nat
length Lin = Z
length (sx :< x) = S $ length sx
||| Filters a snoc-list according to a simple classifying function
public export
filter : (a -> Bool) -> SnocList a -> SnocList a
filter f [<] = [<]
filter f (xs:<x) = let rest = filter f xs in if f x then rest :< x else rest
||| Apply a partial function to the elements of a list, keeping the ones at which
||| it is defined.
public export
mapMaybe : (a -> Maybe b) -> SnocList a -> SnocList b
mapMaybe f [<] = [<]
mapMaybe f (sx :< x) = case f x of
Nothing => mapMaybe f sx
Just j => mapMaybe f sx :< j
public export
Eq a => Eq (SnocList a) where
(==) Lin Lin = True

2
src/Core/Env.idr
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@ -72,7 +72,7 @@ bindEnv loc (b :: env) tm
Explicit
(binderType b)) tm)
revOnto : (xs, vs : _) -> reverseOnto xs vs = reverse vs ++ xs
revOnto : (xs, vs : List a) -> reverseOnto xs vs = reverse vs ++ xs
revOnto xs [] = Refl
revOnto xs (v :: vs)
= rewrite revOnto (v :: xs) vs in

4
tests/ideMode/ideMode005/expectedJ
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@ -48,7 +48,7 @@
0000cf(:return (:ok " n : Nat
------------------------------
prf : [2, 1, 0] = ?a" ((7 3 ((:decor :type))) (49 1 ((:decor :data))) (52 1 ((:decor :data))) (55 1 ((:decor :data))) (58 1 ((:decor :keyword))))) 2)
0000f6(:return (:ok " xs : List Nat
0000fa(:return (:ok " xs : List Nat
------------------------------
prf2 : map S xs = ?lgjgk" ((8 4 ((:decor :type))) (13 3 ((:decor :type))) (55 3 ((:decor :function))) (59 1 ((:decor :data))) (61 2 ((:decor :bound))) (64 1 ((:decor :keyword))))) 3)
prf2 : mapImpl S xs = ?lgjgk" ((8 4 ((:decor :type))) (13 3 ((:decor :type))) (55 7 ((:decor :function))) (63 1 ((:decor :data))) (65 2 ((:decor :bound))) (68 1 ((:decor :keyword))))) 3)
Alas the file is done, aborting

7
tests/node/tailrec_libs/expected
View File

@ -1 +1,8 @@
50001
50000
50000
50000
50001
50000
50000
50000

22
tests/node/tailrec_libs/tailrec.idr
View File

@ -9,14 +9,22 @@ So far, only Prelude.List.++ is tested.
module Main
-- Until replicate is tail recursive, we roll our own for this test.
import Data.List
import Data.SnocList
replicateOnto : List a -> Nat -> a -> List a
replicateOnto acc Z x = acc
replicateOnto acc (S n) x = replicateOnto (x :: acc) n x
values : List Nat
values = replicate 50000 1
tailRecReplicate : Nat -> a -> List a
tailRecReplicate = replicateOnto []
seulav : SnocList Nat
seulav = Lin <>< values
main : IO ()
main = putStrLn $ show $ length $ tailRecReplicate 50000 () ++ [()]
main = do
printLn $ length $ values ++ [1]
printLn $ length $ map Just values
printLn $ length $ mapMaybe Just values
printLn $ length $ filter (const True) values
printLn $ length $ seulav ++ [<1]
printLn $ length $ map Just seulav
printLn $ length $ mapMaybe Just seulav
printLn $ length $ filter (const True) seulav