{-# LANGUAGE CPP          #-}
{-# LANGUAGE ViewPatterns #-}

{-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-}

{-
(c) The University of Glasgow 2006
(c) The GRASP/AQUA Project, Glasgow University, 1992-1998
-}

-- | A language to express the evaluation context of an expression as a
-- 'Demand' and track how an expression evaluates free variables and arguments
-- in turn as a 'DmdType'.
--
-- Lays out the abstract domain for "GHC.Core.Opt.DmdAnal".
module GHC.Types.Demand (
    -- * Demands
    Card(..), Demand(..), SubDemand(Prod), mkProd, viewProd,
    -- ** Algebra
    absDmd, topDmd, botDmd, seqDmd, topSubDmd,
    -- *** Least upper bound
    lubCard, lubDmd, lubSubDmd,
    -- *** Plus
    plusCard, plusDmd, plusSubDmd,
    -- *** Multiply
    multCard, multDmd, multSubDmd,
    -- ** Predicates on @Card@inalities and @Demand@s
    isAbs, isUsedOnce, isStrict,
    isAbsDmd, isUsedOnceDmd, isStrUsedDmd, isStrictDmd,
    isTopDmd, isSeqDmd, isWeakDmd,
    -- ** Special demands
    evalDmd,
    -- *** Demands used in PrimOp signatures
    lazyApply1Dmd, lazyApply2Dmd, strictOnceApply1Dmd, strictManyApply1Dmd,
    -- ** Other @Demand@ operations
    oneifyCard, oneifyDmd, strictifyDmd, strictifyDictDmd, mkWorkerDemand,
    peelCallDmd, peelManyCalls, mkCalledOnceDmd, mkCalledOnceDmds,
    addCaseBndrDmd,
    -- ** Extracting one-shot information
    argOneShots, argsOneShots, saturatedByOneShots,

    -- * Demand environments
    DmdEnv, emptyDmdEnv,
    keepAliveDmdEnv, reuseEnv,

    -- * Divergence
    Divergence(..), topDiv, botDiv, exnDiv, lubDivergence, isDeadEndDiv,

    -- * Demand types
    DmdType(..), dmdTypeDepth,
    -- ** Algebra
    nopDmdType, botDmdType,
    lubDmdType, plusDmdType, multDmdType,
    -- *** PlusDmdArg
    PlusDmdArg, mkPlusDmdArg, toPlusDmdArg,
    -- ** Other operations
    peelFV, findIdDemand, addDemand, splitDmdTy, deferAfterPreciseException,
    keepAliveDmdType,

    -- * Demand signatures
    StrictSig(..), mkStrictSigForArity, mkClosedStrictSig,
    splitStrictSig, strictSigDmdEnv, hasDemandEnvSig,
    nopSig, botSig, isTopSig, isDeadEndSig, appIsDeadEnd,
    -- ** Handling arity adjustments
    prependArgsStrictSig, etaConvertStrictSig,

    -- * Demand transformers from demand signatures
    DmdTransformer, dmdTransformSig, dmdTransformDataConSig, dmdTransformDictSelSig,

    -- * Trim to a type shape
    TypeShape(..), trimToType,

    -- * @seq@ing stuff
    seqDemand, seqDemandList, seqDmdType, seqStrictSig,

    -- * Zapping usage information
    zapUsageDemand, zapDmdEnvSig, zapUsedOnceDemand, zapUsedOnceSig
  ) where

#include "HsVersions.h"

import GHC.Prelude

import GHC.Types.Var ( Var, Id )
import GHC.Types.Var.Env
import GHC.Types.Var.Set
import GHC.Types.Unique.FM
import GHC.Types.Basic
import GHC.Data.Maybe   ( orElse )

import GHC.Core.Type    ( Type )
import GHC.Core.TyCon   ( isNewTyCon, isClassTyCon )
import GHC.Core.DataCon ( splitDataProductType_maybe )
import GHC.Core.Multiplicity    ( scaledThing )

import GHC.Utils.Binary
import GHC.Utils.Misc
import GHC.Utils.Outputable
import GHC.Utils.Panic

{-
************************************************************************
*                                                                      *
           Card: Combining Strictness and Usage
*                                                                      *
************************************************************************
-}

{- Note [Evaluation cardinalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The demand analyser uses an /evaluation cardinality/ of type Card,
to specify how many times a term is evaluated.  A cardinality C_lu
represents an /interval/ [l..u], meaning
    C_lu means evaluated /at least/ 'l' times and
                         /at most/  'u' times

* The lower bound corresponds to /strictness/
  Hence 'l' is either 0 (lazy)
                   or 1 (strict)

* The upper bound corresponds to /usage/
  Hence 'u' is either 0 (not used at all),
                   or 1 (used at most once)
                   or n (no information)

Intervals describe sets, so the underlying lattice is the powerset lattice.

Usually l<=u, but we also have C_10, the interval [1,0], the empty interval,
denoting the empty set.   This is the bottom element of the lattice.

See Note [Demand notation] for the notation we use for each of the constructors.
-}


-- | Describes an interval of /evaluation cardinalities/.
-- See Note [Evaluation cardinalities]
data Card
  = C_00 -- ^ {0}     Absent.
  | C_01 -- ^ {0,1}   Used at most once.
  | C_0N -- ^ {0,1,n} Every possible cardinality; the top element.
  | C_11 -- ^ {1}     Strict and used once.
  | C_1N -- ^ {1,n}   Strict and used (possibly) many times.
  | C_10 -- ^ {}      The empty interval; the bottom element of the lattice.
  deriving Card -> Card -> Bool
(Card -> Card -> Bool) -> (Card -> Card -> Bool) -> Eq Card
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Card -> Card -> Bool
$c/= :: Card -> Card -> Bool
== :: Card -> Card -> Bool
$c== :: Card -> Card -> Bool
Eq

_botCard, topCard :: Card
_botCard :: Card
_botCard = Card
C_10
topCard :: Card
topCard = Card
C_0N

-- | True <=> lower bound is 1.
isStrict :: Card -> Bool
isStrict :: Card -> Bool
isStrict Card
C_10 = Bool
True
isStrict Card
C_11 = Bool
True
isStrict Card
C_1N = Bool
True
isStrict Card
_    = Bool
False

-- | True <=> upper bound is 0.
isAbs :: Card -> Bool
isAbs :: Card -> Bool
isAbs Card
C_00 = Bool
True
isAbs Card
C_10 = Bool
True -- Bottom cardinality is also absent
isAbs Card
_    = Bool
False

-- | True <=> upper bound is 1.
isUsedOnce :: Card -> Bool
isUsedOnce :: Card -> Bool
isUsedOnce Card
C_0N = Bool
False
isUsedOnce Card
C_1N = Bool
False
isUsedOnce Card
_    = Bool
True

-- | Intersect with [0,1].
oneifyCard :: Card -> Card
oneifyCard :: Card -> Card
oneifyCard Card
C_0N = Card
C_01
oneifyCard Card
C_1N = Card
C_11
oneifyCard Card
c    = Card
c

-- | Denotes '∪' on 'Card'.
lubCard :: Card -> Card -> Card
-- Handle C_10 (bot)
lubCard :: Card -> Card -> Card
lubCard Card
C_10 Card
n    = Card
n    -- bot
lubCard Card
n    Card
C_10 = Card
n    -- bot
-- Handle C_0N (top)
lubCard Card
C_0N Card
_    = Card
C_0N -- top
lubCard Card
_    Card
C_0N = Card
C_0N -- top
-- Handle C_11
lubCard Card
C_00 Card
C_11 = Card
C_01 -- {0} ∪ {1} = {0,1}
lubCard Card
C_11 Card
C_00 = Card
C_01 -- {0} ∪ {1} = {0,1}
lubCard Card
C_11 Card
n    = Card
n    -- {1} is a subset of all other intervals
lubCard Card
n    Card
C_11 = Card
n    -- {1} is a subset of all other intervals
-- Handle C_1N
lubCard Card
C_1N Card
C_1N = Card
C_1N -- reflexivity
lubCard Card
_    Card
C_1N = Card
C_0N -- {0} ∪ {1,n} = top
lubCard Card
C_1N Card
_    = Card
C_0N -- {0} ∪ {1,n} = top
-- Handle C_01
lubCard Card
C_01 Card
_    = Card
C_01 -- {0} ∪ {0,1} = {0,1}
lubCard Card
_    Card
C_01 = Card
C_01 -- {0} ∪ {0,1} = {0,1}
-- Handle C_00
lubCard Card
C_00 Card
C_00 = Card
C_00 -- reflexivity

-- | Denotes '+' on 'Card'.
plusCard :: Card -> Card -> Card
-- Handle C_00
plusCard :: Card -> Card -> Card
plusCard Card
C_00 Card
n    = Card
n    -- {0}+n = n
plusCard Card
n    Card
C_00 = Card
n    -- {0}+n = n
-- Handle C_10
plusCard Card
C_10 Card
C_01 = Card
C_11 -- These follow by applying + to lower and upper
plusCard Card
C_10 Card
C_0N = Card
C_1N -- bounds individually
plusCard Card
C_10 Card
n    = Card
n
plusCard Card
C_01 Card
C_10 = Card
C_11
plusCard Card
C_0N Card
C_10 = Card
C_1N
plusCard Card
n    Card
C_10 = Card
n
-- Handle the rest (C_01, C_0N, C_11, C_1N)
plusCard Card
C_01 Card
C_01 = Card
C_0N -- The upper bound is at least 1, so upper bound of
plusCard Card
C_01 Card
C_0N = Card
C_0N -- the result must be 1+1 ~= N.
plusCard Card
C_0N Card
C_01 = Card
C_0N -- But for the lower bound we have 4 cases where
plusCard Card
C_0N Card
C_0N = Card
C_0N -- 0+0 ~= 0 (as opposed to 1), so we match on these.
plusCard Card
_    Card
_    = Card
C_1N -- Otherwise we return {1,n}

-- | Denotes '*' on 'Card'.
multCard :: Card -> Card -> Card
-- Handle C_11 (neutral element)
multCard :: Card -> Card -> Card
multCard Card
C_11 Card
c    = Card
c
multCard Card
c    Card
C_11 = Card
c
-- Handle C_00 (annihilating element)
multCard Card
C_00 Card
_    = Card
C_00
multCard Card
_    Card
C_00 = Card
C_00
-- Handle C_10
multCard Card
C_10 Card
c    = if Card -> Bool
isStrict Card
c then Card
C_10 else Card
C_00
multCard Card
c    Card
C_10 = if Card -> Bool
isStrict Card
c then Card
C_10 else Card
C_00
-- Handle reflexive C_1N, C_01
multCard Card
C_1N Card
C_1N = Card
C_1N
multCard Card
C_01 Card
C_01 = Card
C_01
-- Handle C_0N and the rest (C_01, C_1N):
multCard Card
_    Card
_    = Card
C_0N

{-
************************************************************************
*                                                                      *
           Demand: Evaluation contexts
*                                                                      *
************************************************************************
-}

-- | A demand describes a /scaled evaluation context/, e.g. how many times
-- and how deep the denoted thing is evaluated.
--
-- The "how many" component is represented by a 'Card'inality.
-- The "how deep" component is represented by a 'SubDemand'.
-- Examples (using Note [Demand notation]):
--
--   * 'seq' puts demand @1A@ on its first argument: It evaluates the argument
--     strictly (@1@), but not any deeper (@A@).
--   * 'fst' puts demand @1P(1L,A)@ on its argument: It evaluates the argument
--     pair strictly and the first component strictly, but no nested info
--     beyond that (@L@). Its second argument is not used at all.
--   * '$' puts demand @1C1(L)@ on its first argument: It calls (@C@) the
--     argument function with one argument, exactly once (@1@). No info
--     on how the result of that call is evaluated (@L@).
--   * 'maybe' puts demand @MCM(L)@ on its second argument: It evaluates
--     the argument function at most once ((M)aybe) and calls it once when
--     it is evaluated.
--   * @fst p + fst p@ puts demand @SP(SL,A)@ on @p@: It's @1P(1L,A)@
--     multiplied by two, so we get @S@ (used at least once, possibly multiple
--     times).
--
-- This data type is quite similar to @'Scaled' 'SubDemand'@, but it's scaled
-- by 'Card', which is an /interval/ on 'Multiplicity', the upper bound of
-- which could be used to infer uniqueness types.
data Demand
  = !Card :* !SubDemand
  deriving Demand -> Demand -> Bool
(Demand -> Demand -> Bool)
-> (Demand -> Demand -> Bool) -> Eq Demand
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Demand -> Demand -> Bool
$c/= :: Demand -> Demand -> Bool
== :: Demand -> Demand -> Bool
$c== :: Demand -> Demand -> Bool
Eq

-- | A sub-demand describes an /evaluation context/, e.g. how deep the
-- denoted thing is evaluated. See 'Demand' for examples.
--
-- The nested 'SubDemand' @d@ of a 'Call' @Cn(d)@ is /relative/ to a single such call.
-- E.g. The expression @f 1 2 + f 3 4@ puts call demand @SCS(C1(L))@ on @f@:
-- @f@ is called exactly twice (@S@), each time exactly once (@1@) with an
-- additional argument.
--
-- The nested 'Demand's @dn@ of a 'Prod' @P(d1,d2,...)@ apply /absolutely/:
-- If @dn@ is a used once demand (cf. 'isUsedOnce'), then that means that
-- the denoted sub-expression is used once in the entire evaluation context
-- described by the surrounding 'Demand'. E.g., @LP(ML)@ means that the
-- field of the denoted expression is used at most once, although the
-- entire expression might be used many times.
--
-- See Note [Call demands are relative]
-- and Note [Demand notation].
data SubDemand
  = Poly !Card
  -- ^ Polymorphic demand, the denoted thing is evaluated arbitrarily deep,
  -- with the specified cardinality at every level.
  -- Expands to 'Call' via 'viewCall' and to 'Prod' via 'viewProd'.
  --
  -- @Poly n@ is semantically equivalent to @Prod [n :* Poly n, ...]@ or
  -- @Call n (Poly n)@. 'mkCall' and 'mkProd' do these rewrites.
  --
  -- In Note [Demand notation]: @L === P(L,L,...)@ and @L === CL(L)@,
  --                            @1 === P(1,1,...)@ and @1 === C1(1)@, and so on.
  --
  -- We only really use 'Poly' with 'C_10' (B), 'C_00' (A), 'C_0N' (L) and
  -- sometimes 'C_1N' (S), but it's simpler to treat it uniformly than to
  -- have a special constructor for each of the three cases.
  | Call !Card !SubDemand
  -- ^ @Call n sd@ describes the evaluation context of @n@ function
  -- applications, where every individual result is evaluated according to @sd@.
  -- @sd@ is /relative/ to a single call, cf. Note [Call demands are relative].
  -- Used only for values of function type. Use the smart constructor 'mkCall'
  -- whenever possible!
  | Prod ![Demand]
  -- ^ @Prod ds@ describes the evaluation context of a case scrutinisation
  -- on an expression of product type, where the product components are
  -- evaluated according to @ds@.
  deriving SubDemand -> SubDemand -> Bool
(SubDemand -> SubDemand -> Bool)
-> (SubDemand -> SubDemand -> Bool) -> Eq SubDemand
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: SubDemand -> SubDemand -> Bool
$c/= :: SubDemand -> SubDemand -> Bool
== :: SubDemand -> SubDemand -> Bool
$c== :: SubDemand -> SubDemand -> Bool
Eq

poly00, poly01, poly0N, poly11, poly1N, poly10 :: SubDemand
topSubDmd, botSubDmd, seqSubDmd :: SubDemand
poly00 :: SubDemand
poly00 = Card -> SubDemand
Poly Card
C_00
poly01 :: SubDemand
poly01 = Card -> SubDemand
Poly Card
C_01
poly0N :: SubDemand
poly0N = Card -> SubDemand
Poly Card
C_0N
poly11 :: SubDemand
poly11 = Card -> SubDemand
Poly Card
C_11
poly1N :: SubDemand
poly1N = Card -> SubDemand
Poly Card
C_1N
poly10 :: SubDemand
poly10 = Card -> SubDemand
Poly Card
C_10
topSubDmd :: SubDemand
topSubDmd = SubDemand
poly0N
botSubDmd :: SubDemand
botSubDmd = SubDemand
poly10
seqSubDmd :: SubDemand
seqSubDmd = SubDemand
poly00

polyDmd :: Card -> Demand
polyDmd :: Card -> Demand
polyDmd Card
C_00 = Card
C_00 Card -> SubDemand -> Demand
:* SubDemand
poly00
polyDmd Card
C_01 = Card
C_01 Card -> SubDemand -> Demand
:* SubDemand
poly01
polyDmd Card
C_0N = Card
C_0N Card -> SubDemand -> Demand
:* SubDemand
poly0N
polyDmd Card
C_11 = Card
C_11 Card -> SubDemand -> Demand
:* SubDemand
poly11
polyDmd Card
C_1N = Card
C_1N Card -> SubDemand -> Demand
:* SubDemand
poly1N
polyDmd Card
C_10 = Card
C_10 Card -> SubDemand -> Demand
:* SubDemand
poly10

-- | A smart constructor for 'Prod', applying rewrite rules along the semantic
-- equality @Prod [polyDmd n, ...] === polyDmd n@, simplifying to 'Poly'
-- 'SubDemand's when possible. Note that this degrades boxity information! E.g. a
-- polymorphic demand will never unbox.
mkProd :: [Demand] -> SubDemand
mkProd :: [Demand] -> SubDemand
mkProd [] = SubDemand
seqSubDmd
mkProd ds :: [Demand]
ds@(Card
n:*SubDemand
sd : [Demand]
_)
  | Card -> Bool
want_to_simplify Card
n, (Demand -> Bool) -> [Demand] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Demand -> Demand -> Bool
forall a. Eq a => a -> a -> Bool
== Card -> Demand
polyDmd Card
n) [Demand]
ds = SubDemand
sd
  | Bool
otherwise                                 = [Demand] -> SubDemand
Prod [Demand]
ds
  where
    -- We only want to simplify absent and bottom demands and unbox the others.
    -- See also Note [L should win] and Note [Don't optimise LP(L,L,...) to L].
    want_to_simplify :: Card -> Bool
want_to_simplify Card
C_00 = Bool
True
    want_to_simplify Card
C_10 = Bool
True
    want_to_simplify Card
_    = Bool
False

-- | @viewProd n sd@ interprets @sd@ as a 'Prod' of arity @n@, expanding 'Poly'
-- demands as necessary.
viewProd :: Arity -> SubDemand -> Maybe [Demand]
-- It's quite important that this function is optimised well;
-- it is used by lubSubDmd and plusSubDmd. Note the strict
-- application to 'polyDmd':
viewProd :: Int -> SubDemand -> Maybe [Demand]
viewProd Int
n (Prod [Demand]
ds)   | [Demand]
ds [Demand] -> Int -> Bool
forall a. [a] -> Int -> Bool
`lengthIs` Int
n = [Demand] -> Maybe [Demand]
forall a. a -> Maybe a
Just [Demand]
ds
-- Note the strict application to replicate: This makes sure we don't allocate
-- a thunk for it, inlines it and lets case-of-case fire at call sites.
viewProd Int
n (Poly Card
card)                   = [Demand] -> Maybe [Demand]
forall a. a -> Maybe a
Just (Int -> Demand -> [Demand]
forall a. Int -> a -> [a]
replicate Int
n (Demand -> [Demand]) -> Demand -> [Demand]
forall a b. (a -> b) -> a -> b
$! Card -> Demand
polyDmd Card
card)
viewProd Int
_ SubDemand
_                             = Maybe [Demand]
forall a. Maybe a
Nothing
{-# INLINE viewProd #-} -- we want to fuse away the replicate and the allocation
                        -- for Arity. Otherwise, #18304 bites us.

-- | A smart constructor for 'Call', applying rewrite rules along the semantic
-- equality @Call n (Poly n) === Poly n@, simplifying to 'Poly' 'SubDemand's
-- when possible.
mkCall :: Card -> SubDemand -> SubDemand
mkCall :: Card -> SubDemand -> SubDemand
mkCall Card
n cd :: SubDemand
cd@(Poly Card
m) | Card
n Card -> Card -> Bool
forall a. Eq a => a -> a -> Bool
== Card
m = SubDemand
cd
mkCall Card
n SubDemand
cd                   = Card -> SubDemand -> SubDemand
Call Card
n SubDemand
cd

-- | @viewCall sd@ interprets @sd@ as a 'Call', expanding 'Poly' demands as
-- necessary.
viewCall :: SubDemand -> Maybe (Card, SubDemand)
viewCall :: SubDemand -> Maybe (Card, SubDemand)
viewCall (Call Card
n SubDemand
sd)    = (Card, SubDemand) -> Maybe (Card, SubDemand)
forall a. a -> Maybe a
Just (Card
n, SubDemand
sd)
viewCall sd :: SubDemand
sd@(Poly Card
card) = (Card, SubDemand) -> Maybe (Card, SubDemand)
forall a. a -> Maybe a
Just (Card
card, SubDemand
sd)
viewCall SubDemand
_              = Maybe (Card, SubDemand)
forall a. Maybe a
Nothing

topDmd, absDmd, botDmd, seqDmd :: Demand
topDmd :: Demand
topDmd = Card -> Demand
polyDmd Card
C_0N
absDmd :: Demand
absDmd = Card -> Demand
polyDmd Card
C_00
botDmd :: Demand
botDmd = Card -> Demand
polyDmd Card
C_10
seqDmd :: Demand
seqDmd = Card
C_11 Card -> SubDemand -> Demand
:* SubDemand
seqSubDmd

-- | Denotes '∪' on 'SubDemand'.
lubSubDmd :: SubDemand -> SubDemand -> SubDemand
-- Handle Prod
lubSubDmd :: SubDemand -> SubDemand -> SubDemand
lubSubDmd (Prod [Demand]
ds1) (Int -> SubDemand -> Maybe [Demand]
viewProd ([Demand] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [Demand]
ds1) -> Just [Demand]
ds2) =
  [Demand] -> SubDemand
Prod ([Demand] -> SubDemand) -> [Demand] -> SubDemand
forall a b. (a -> b) -> a -> b
$ (Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Demand -> Demand -> Demand
lubDmd [Demand]
ds2 [Demand]
ds1 -- try to fuse with ds2
-- Handle Call
lubSubDmd (Call Card
n1 SubDemand
d1) (SubDemand -> Maybe (Card, SubDemand)
viewCall -> Just (Card
n2, SubDemand
d2))
  -- See Note [Call demands are relative]
  | Card -> Bool
isAbs Card
n1  = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
lubCard Card
n1 Card
n2) (SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
botSubDmd SubDemand
d2)
  | Card -> Bool
isAbs Card
n2  = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
lubCard Card
n1 Card
n2) (SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
d1 SubDemand
botSubDmd)
  | Bool
otherwise = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
lubCard Card
n1 Card
n2) (SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
d1        SubDemand
d2)
-- Handle Poly
lubSubDmd (Poly Card
n1)  (Poly Card
n2) = Card -> SubDemand
Poly (Card -> Card -> Card
lubCard Card
n1 Card
n2)
-- Make use of reflexivity (so we'll match the Prod or Call cases again).
lubSubDmd sd1 :: SubDemand
sd1@Poly{} SubDemand
sd2       = SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
sd2 SubDemand
sd1
-- Otherwise (Call `lub` Prod) return Top
lubSubDmd SubDemand
_          SubDemand
_         = SubDemand
topSubDmd

-- | Denotes '∪' on 'Demand'.
lubDmd :: Demand -> Demand -> Demand
lubDmd :: Demand -> Demand -> Demand
lubDmd (Card
n1 :* SubDemand
sd1) (Card
n2 :* SubDemand
sd2) = Card -> Card -> Card
lubCard Card
n1 Card
n2 Card -> SubDemand -> Demand
:* SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
sd1 SubDemand
sd2

-- | Denotes '+' on 'SubDemand'.
plusSubDmd :: SubDemand -> SubDemand -> SubDemand
-- Handle Prod
plusSubDmd :: SubDemand -> SubDemand -> SubDemand
plusSubDmd (Prod [Demand]
ds1) (Int -> SubDemand -> Maybe [Demand]
viewProd ([Demand] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [Demand]
ds1) -> Just [Demand]
ds2) =
  [Demand] -> SubDemand
Prod ([Demand] -> SubDemand) -> [Demand] -> SubDemand
forall a b. (a -> b) -> a -> b
$ (Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Demand -> Demand -> Demand
plusDmd [Demand]
ds2 [Demand]
ds1 -- try to fuse with ds2
-- Handle Call
plusSubDmd (Call Card
n1 SubDemand
d1) (SubDemand -> Maybe (Card, SubDemand)
viewCall -> Just (Card
n2, SubDemand
d2))
  -- See Note [Call demands are relative]
  | Card -> Bool
isAbs Card
n1  = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
plusCard Card
n1 Card
n2) (SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
botSubDmd SubDemand
d2)
  | Card -> Bool
isAbs Card
n2  = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
plusCard Card
n1 Card
n2) (SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
d1 SubDemand
botSubDmd)
  | Bool
otherwise = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
plusCard Card
n1 Card
n2) (SubDemand -> SubDemand -> SubDemand
lubSubDmd SubDemand
d1        SubDemand
d2)
-- Handle Poly
plusSubDmd (Poly Card
n1)  (Poly Card
n2) = Card -> SubDemand
Poly (Card -> Card -> Card
plusCard Card
n1 Card
n2)
-- Make use of reflexivity (so we'll match the Prod or Call cases again).
plusSubDmd sd1 :: SubDemand
sd1@Poly{} SubDemand
sd2       = SubDemand -> SubDemand -> SubDemand
plusSubDmd SubDemand
sd2 SubDemand
sd1
-- Otherwise (Call `lub` Prod) return Top
plusSubDmd SubDemand
_          SubDemand
_         = SubDemand
topSubDmd

-- | Denotes '+' on 'Demand'.
plusDmd :: Demand -> Demand -> Demand
plusDmd :: Demand -> Demand -> Demand
plusDmd (Card
n1 :* SubDemand
sd1) (Card
n2 :* SubDemand
sd2) = Card -> Card -> Card
plusCard Card
n1 Card
n2 Card -> SubDemand -> Demand
:* SubDemand -> SubDemand -> SubDemand
plusSubDmd SubDemand
sd1 SubDemand
sd2

-- | The trivial cases of the @mult*@ functions.
-- If @multTrivial n abs a = ma@, we have the following outcomes
-- depending on @n@:
--
--   * 'C_11' => multiply by one, @ma = Just a@
--   * 'C_00', 'C_10' (e.g. @'isAbs' n@) => return the absent thing,
--      @ma = Just abs@
--   * Otherwise ('C_01', 'C_*N') it's not a trivial case, @ma = Nothing@.
multTrivial :: Card -> a -> a -> Maybe a
multTrivial :: forall a. Card -> a -> a -> Maybe a
multTrivial Card
C_11 a
_   a
a           = a -> Maybe a
forall a. a -> Maybe a
Just a
a
multTrivial Card
n    a
abs a
_ | Card -> Bool
isAbs Card
n = a -> Maybe a
forall a. a -> Maybe a
Just a
abs
multTrivial Card
_    a
_   a
_           = Maybe a
forall a. Maybe a
Nothing

multSubDmd :: Card -> SubDemand -> SubDemand
multSubDmd :: Card -> SubDemand -> SubDemand
multSubDmd Card
n SubDemand
sd
  | Just SubDemand
sd' <- Card -> SubDemand -> SubDemand -> Maybe SubDemand
forall a. Card -> a -> a -> Maybe a
multTrivial Card
n SubDemand
seqSubDmd SubDemand
sd = SubDemand
sd'
multSubDmd Card
n (Poly Card
n')    = Card -> SubDemand
Poly (Card -> Card -> Card
multCard Card
n Card
n')
multSubDmd Card
n (Call Card
n' SubDemand
sd) = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
multCard Card
n Card
n') SubDemand
sd -- See Note [Call demands are relative]
multSubDmd Card
n (Prod [Demand]
ds)    = [Demand] -> SubDemand
Prod ((Demand -> Demand) -> [Demand] -> [Demand]
forall a b. (a -> b) -> [a] -> [b]
map (Card -> Demand -> Demand
multDmd Card
n) [Demand]
ds)

multDmd :: Card -> Demand -> Demand
multDmd :: Card -> Demand -> Demand
multDmd Card
n    Demand
dmd
  | Just Demand
dmd' <- Card -> Demand -> Demand -> Maybe Demand
forall a. Card -> a -> a -> Maybe a
multTrivial Card
n Demand
absDmd Demand
dmd = Demand
dmd'
multDmd Card
n (Card
m :* SubDemand
dmd) = Card -> Card -> Card
multCard Card
n Card
m Card -> SubDemand -> Demand
:* Card -> SubDemand -> SubDemand
multSubDmd Card
n SubDemand
dmd

-- | Used to suppress pretty-printing of an uninformative demand
isTopDmd :: Demand -> Bool
isTopDmd :: Demand -> Bool
isTopDmd Demand
dmd = Demand
dmd Demand -> Demand -> Bool
forall a. Eq a => a -> a -> Bool
== Demand
topDmd

isAbsDmd :: Demand -> Bool
isAbsDmd :: Demand -> Bool
isAbsDmd (Card
n :* SubDemand
_) = Card -> Bool
isAbs Card
n

-- | Contrast with isStrictUsedDmd. See Note [Strict demands]
isStrictDmd :: Demand -> Bool
isStrictDmd :: Demand -> Bool
isStrictDmd (Card
n :* SubDemand
_) = Card -> Bool
isStrict Card
n

-- | Not absent and used strictly. See Note [Strict demands]
isStrUsedDmd :: Demand -> Bool
isStrUsedDmd :: Demand -> Bool
isStrUsedDmd (Card
n :* SubDemand
_) = Card -> Bool
isStrict Card
n Bool -> Bool -> Bool
&& Bool -> Bool
not (Card -> Bool
isAbs Card
n)

isSeqDmd :: Demand -> Bool
isSeqDmd :: Demand -> Bool
isSeqDmd (Card
C_11 :* SubDemand
sd) = SubDemand
sd SubDemand -> SubDemand -> Bool
forall a. Eq a => a -> a -> Bool
== SubDemand
seqSubDmd
isSeqDmd (Card
C_1N :* SubDemand
sd) = SubDemand
sd SubDemand -> SubDemand -> Bool
forall a. Eq a => a -> a -> Bool
== SubDemand
seqSubDmd -- I wonder if we need this case.
isSeqDmd Demand
_            = Bool
False

-- | Is the value used at most once?
isUsedOnceDmd :: Demand -> Bool
isUsedOnceDmd :: Demand -> Bool
isUsedOnceDmd (Card
n :* SubDemand
_) = Card -> Bool
isUsedOnce Card
n

-- | We try to avoid tracking weak free variable demands in strictness
-- signatures for analysis performance reasons.
-- See Note [Lazy and unleashable free variables] in "GHC.Core.Opt.DmdAnal".
isWeakDmd :: Demand -> Bool
isWeakDmd :: Demand -> Bool
isWeakDmd dmd :: Demand
dmd@(Card
n :* SubDemand
_) = Bool -> Bool
not (Card -> Bool
isStrict Card
n) Bool -> Bool -> Bool
&& Demand -> Bool
is_plus_idem_dmd Demand
dmd
  where
    -- @is_plus_idem_* thing@ checks whether @thing `plus` thing = thing@,
    -- e.g. if @thing@ is idempotent wrt. to @plus@.
    is_plus_idem_card :: Card -> Bool
is_plus_idem_card Card
c = Card -> Card -> Card
plusCard Card
c Card
c Card -> Card -> Bool
forall a. Eq a => a -> a -> Bool
== Card
c
    -- is_plus_idem_dmd dmd = plusDmd dmd dmd == dmd
    is_plus_idem_dmd :: Demand -> Bool
is_plus_idem_dmd (Card
n :* SubDemand
sd) = Card -> Bool
is_plus_idem_card Card
n Bool -> Bool -> Bool
&& SubDemand -> Bool
is_plus_idem_sub_dmd SubDemand
sd
    -- is_plus_idem_sub_dmd sd = plusSubDmd sd sd == sd
    is_plus_idem_sub_dmd :: SubDemand -> Bool
is_plus_idem_sub_dmd (Poly Card
n)   = Card -> Bool
is_plus_idem_card Card
n
    is_plus_idem_sub_dmd (Prod [Demand]
ds)  = (Demand -> Bool) -> [Demand] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all Demand -> Bool
is_plus_idem_dmd [Demand]
ds
    is_plus_idem_sub_dmd (Call Card
n SubDemand
_) = Card -> Bool
is_plus_idem_card Card
n -- See Note [Call demands are relative]

evalDmd :: Demand
evalDmd :: Demand
evalDmd = Card
C_1N Card -> SubDemand -> Demand
:* SubDemand
topSubDmd

-- | First argument of 'GHC.Exts.maskAsyncExceptions#': @1C1(L)@.
-- Called exactly once.
strictOnceApply1Dmd :: Demand
strictOnceApply1Dmd :: Demand
strictOnceApply1Dmd = Card
C_11 Card -> SubDemand -> Demand
:* Card -> SubDemand -> SubDemand
mkCall Card
C_11 SubDemand
topSubDmd

-- | First argument of 'GHC.Exts.atomically#': @SCS(L)@.
-- Called at least once, possibly many times.
strictManyApply1Dmd :: Demand
strictManyApply1Dmd :: Demand
strictManyApply1Dmd = Card
C_1N Card -> SubDemand -> Demand
:* Card -> SubDemand -> SubDemand
mkCall Card
C_1N SubDemand
topSubDmd

-- | First argument of catch#: @MCM(L)@.
-- Evaluates its arg lazily, but then applies it exactly once to one argument.
lazyApply1Dmd :: Demand
lazyApply1Dmd :: Demand
lazyApply1Dmd = Card
C_01 Card -> SubDemand -> Demand
:* Card -> SubDemand -> SubDemand
mkCall Card
C_01 SubDemand
topSubDmd

-- | Second argument of catch#: @MCM(C1(L))@.
-- Calls its arg lazily, but then applies it exactly once to an additional argument.
lazyApply2Dmd :: Demand
lazyApply2Dmd :: Demand
lazyApply2Dmd = Card
C_01 Card -> SubDemand -> Demand
:* Card -> SubDemand -> SubDemand
mkCall Card
C_01 (Card -> SubDemand -> SubDemand
mkCall Card
C_11 SubDemand
topSubDmd)

-- | Make a 'Demand' evaluated at-most-once.
oneifyDmd :: Demand -> Demand
oneifyDmd :: Demand -> Demand
oneifyDmd (Card
n :* SubDemand
sd) = Card -> Card
oneifyCard Card
n Card -> SubDemand -> Demand
:* SubDemand
sd

-- | Make a 'Demand' evaluated at-least-once (e.g. strict).
strictifyDmd :: Demand -> Demand
strictifyDmd :: Demand -> Demand
strictifyDmd (Card
n :* SubDemand
sd) = Card -> Card -> Card
plusCard Card
C_10 Card
n Card -> SubDemand -> Demand
:* SubDemand
sd

-- | If the argument is a used non-newtype dictionary, give it strict demand.
-- Also split the product type & demand and recur in order to similarly
-- strictify the argument's contained used non-newtype superclass dictionaries.
-- We use the demand as our recursive measure to guarantee termination.
strictifyDictDmd :: Type -> Demand -> Demand
strictifyDictDmd :: Type -> Demand -> Demand
strictifyDictDmd Type
ty (Card
n :* Prod [Demand]
ds)
  | Bool -> Bool
not (Card -> Bool
isAbs Card
n)
  , Just [Type]
field_tys <- Type -> Maybe [Type]
as_non_newtype_dict Type
ty
  = Card
C_1N Card -> SubDemand -> Demand
:* -- main idea: ensure it's strict
      if (Demand -> Bool) -> [Demand] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Bool -> Bool
not (Bool -> Bool) -> (Demand -> Bool) -> Demand -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Demand -> Bool
isAbsDmd) [Demand]
ds
        then SubDemand
topSubDmd -- abstract to strict w/ arbitrary component use,
                         -- since this smells like reboxing; results in CBV
                         -- boxed
                         --
                         -- TODO revisit this if we ever do boxity analysis
        else [Demand] -> SubDemand
Prod ((Type -> Demand -> Demand) -> [Type] -> [Demand] -> [Demand]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Type -> Demand -> Demand
strictifyDictDmd [Type]
field_tys [Demand]
ds)
  where
    -- | Return a TyCon and a list of field types if the given
    -- type is a non-newtype dictionary type
    as_non_newtype_dict :: Type -> Maybe [Type]
as_non_newtype_dict Type
ty
      | Just (TyCon
tycon, [Type]
_arg_tys, DataCon
_data_con, (Scaled Type -> Type) -> [Scaled Type] -> [Type]
forall a b. (a -> b) -> [a] -> [b]
map Scaled Type -> Type
forall a. Scaled a -> a
scaledThing -> [Type]
inst_con_arg_tys)
          <- Type -> Maybe (TyCon, [Type], DataCon, [Scaled Type])
splitDataProductType_maybe Type
ty
      , Bool -> Bool
not (TyCon -> Bool
isNewTyCon TyCon
tycon)
      , TyCon -> Bool
isClassTyCon TyCon
tycon
      = [Type] -> Maybe [Type]
forall a. a -> Maybe a
Just [Type]
inst_con_arg_tys
      | Bool
otherwise
      = Maybe [Type]
forall a. Maybe a
Nothing
strictifyDictDmd Type
_  Demand
dmd = Demand
dmd

-- | Wraps the 'SubDemand' with a one-shot call demand: @d@ -> @C1(d)@.
mkCalledOnceDmd :: SubDemand -> SubDemand
mkCalledOnceDmd :: SubDemand -> SubDemand
mkCalledOnceDmd SubDemand
sd = Card -> SubDemand -> SubDemand
mkCall Card
C_11 SubDemand
sd

-- | @mkCalledOnceDmds n d@ returns @C1(C1...(C1 d))@ where there are @n@ @C1@'s.
mkCalledOnceDmds :: Arity -> SubDemand -> SubDemand
mkCalledOnceDmds :: Int -> SubDemand -> SubDemand
mkCalledOnceDmds Int
arity SubDemand
sd = (SubDemand -> SubDemand) -> SubDemand -> [SubDemand]
forall a. (a -> a) -> a -> [a]
iterate SubDemand -> SubDemand
mkCalledOnceDmd SubDemand
sd [SubDemand] -> Int -> SubDemand
forall a. [a] -> Int -> a
!! Int
arity

-- | Peels one call level from the sub-demand, and also returns how many
-- times we entered the lambda body.
peelCallDmd :: SubDemand -> (Card, SubDemand)
peelCallDmd :: SubDemand -> (Card, SubDemand)
peelCallDmd SubDemand
sd = SubDemand -> Maybe (Card, SubDemand)
viewCall SubDemand
sd Maybe (Card, SubDemand) -> (Card, SubDemand) -> (Card, SubDemand)
forall a. Maybe a -> a -> a
`orElse` (Card
topCard, SubDemand
topSubDmd)

-- Peels multiple nestings of 'Call' sub-demands and also returns
-- whether it was unsaturated in the form of a 'Card'inality, denoting
-- how many times the lambda body was entered.
-- See Note [Demands from unsaturated function calls].
peelManyCalls :: Int -> SubDemand -> Card
peelManyCalls :: Int -> SubDemand -> Card
peelManyCalls Int
0 SubDemand
_                          = Card
C_11
-- See Note [Call demands are relative]
peelManyCalls Int
n (SubDemand -> Maybe (Card, SubDemand)
viewCall -> Just (Card
m, SubDemand
sd)) = Card
m Card -> Card -> Card
`multCard` Int -> SubDemand -> Card
peelManyCalls (Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1) SubDemand
sd
peelManyCalls Int
_ SubDemand
_                          = Card
C_0N

-- See Note [Demand on the worker] in GHC.Core.Opt.WorkWrap
mkWorkerDemand :: Int -> Demand
mkWorkerDemand :: Int -> Demand
mkWorkerDemand Int
n = Card
C_01 Card -> SubDemand -> Demand
:* Int -> SubDemand
forall {t}. (Eq t, Num t) => t -> SubDemand
go Int
n
  where go :: t -> SubDemand
go t
0 = SubDemand
topSubDmd
        go t
n = Card -> SubDemand -> SubDemand
Call Card
C_01 (SubDemand -> SubDemand) -> SubDemand -> SubDemand
forall a b. (a -> b) -> a -> b
$ t -> SubDemand
go (t
nt -> t -> t
forall a. Num a => a -> a -> a
-t
1)

addCaseBndrDmd :: SubDemand -- On the case binder
               -> [Demand]  -- On the components of the constructor
               -> [Demand]  -- Final demands for the components of the constructor
addCaseBndrDmd :: SubDemand -> [Demand] -> [Demand]
addCaseBndrDmd (Poly Card
n) [Demand]
alt_dmds
  | Card -> Bool
isAbs Card
n   = [Demand]
alt_dmds
-- See Note [Demand on case-alternative binders]
addCaseBndrDmd SubDemand
sd       [Demand]
alt_dmds = (Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Demand -> Demand -> Demand
plusDmd [Demand]
ds [Demand]
alt_dmds -- fuse ds!
  where
    Just [Demand]
ds = Int -> SubDemand -> Maybe [Demand]
viewProd ([Demand] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [Demand]
alt_dmds) SubDemand
sd -- Guaranteed not to be a call

argsOneShots :: StrictSig -> Arity -> [[OneShotInfo]]
-- ^ See Note [Computing one-shot info]
argsOneShots :: StrictSig -> Int -> [[OneShotInfo]]
argsOneShots (StrictSig (DmdType DmdEnv
_ [Demand]
arg_ds Divergence
_)) Int
n_val_args
  | Bool
unsaturated_call = []
  | Bool
otherwise = [Demand] -> [[OneShotInfo]]
go [Demand]
arg_ds
  where
    unsaturated_call :: Bool
unsaturated_call = [Demand]
arg_ds [Demand] -> Int -> Bool
forall a. [a] -> Int -> Bool
`lengthExceeds` Int
n_val_args

    go :: [Demand] -> [[OneShotInfo]]
go []               = []
    go (Demand
arg_d : [Demand]
arg_ds) = Demand -> [OneShotInfo]
argOneShots Demand
arg_d [OneShotInfo] -> [[OneShotInfo]] -> [[OneShotInfo]]
forall {a}. [a] -> [[a]] -> [[a]]
`cons` [Demand] -> [[OneShotInfo]]
go [Demand]
arg_ds

    -- Avoid list tail like [ [], [], [] ]
    cons :: [a] -> [[a]] -> [[a]]
cons [] [] = []
    cons [a]
a  [[a]]
as = [a]
a[a] -> [[a]] -> [[a]]
forall a. a -> [a] -> [a]
:[[a]]
as

argOneShots :: Demand          -- ^ depending on saturation
            -> [OneShotInfo]
-- ^ See Note [Computing one-shot info]
argOneShots :: Demand -> [OneShotInfo]
argOneShots (Card
_ :* SubDemand
sd) = SubDemand -> [OneShotInfo]
go SubDemand
sd -- See Note [Call demands are relative]
  where
    go :: SubDemand -> [OneShotInfo]
go (Call Card
n SubDemand
sd)
      | Card -> Bool
isUsedOnce Card
n = OneShotInfo
OneShotLam    OneShotInfo -> [OneShotInfo] -> [OneShotInfo]
forall a. a -> [a] -> [a]
: SubDemand -> [OneShotInfo]
go SubDemand
sd
      | Bool
otherwise    = OneShotInfo
NoOneShotInfo OneShotInfo -> [OneShotInfo] -> [OneShotInfo]
forall a. a -> [a] -> [a]
: SubDemand -> [OneShotInfo]
go SubDemand
sd
    go SubDemand
_    = []

-- |
-- @saturatedByOneShots n CM(CM(...)) = True@
--   <=>
-- There are at least n nested CM(..) calls.
-- See Note [Demand on the worker] in GHC.Core.Opt.WorkWrap
saturatedByOneShots :: Int -> Demand -> Bool
saturatedByOneShots :: Int -> Demand -> Bool
saturatedByOneShots Int
n (Card
_ :* SubDemand
sd) = Card -> Bool
isUsedOnce (Int -> SubDemand -> Card
peelManyCalls Int
n SubDemand
sd)

{- Note [Strict demands]
~~~~~~~~~~~~~~~~~~~~~~~~
'isStrUsedDmd' returns true only of demands that are
   both strict
   and  used

In particular, it is False for <B> (i.e. strict and not used,
cardinality C_10), which can and does arise in, say (#7319)
   f x = raise# <some exception>
Then 'x' is not used, so f gets strictness <B> -> .
Now the w/w generates
   fx = let x <B> = absentError "unused"
        in raise <some exception>
At this point we really don't want to convert to
   fx = case absentError "unused" of x -> raise <some exception>
Since the program is going to diverge, this swaps one error for another,
but it's really a bad idea to *ever* evaluate an absent argument.
In #7319 we get
   T7319.exe: Oops!  Entered absent arg w_s1Hd{v} [lid] [base:GHC.Base.String{tc 36u}]

Note [Call demands are relative]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The expression @if b then 0 else f 1 2 + f 3 4@ uses @f@ according to the demand
@LCL(C1(P(L)))@, meaning

  "f is called multiple times or not at all (CL), but each time it
   is called, it's called with *exactly one* (C1) more argument.
   Whenever it is called with two arguments, we have no info on how often
   the field of the product result is used (L)."

So the 'SubDemand' nested in a 'Call' demand is relative to exactly one call.
And that extends to the information we have how its results are used in each
call site. Consider (#18903)

  h :: Int -> Int
  h m =
    let g :: Int -> (Int,Int)
        g 1 = (m, 0)
        g n = (2 * n, 2 `div` n)
        {-# NOINLINE g #-}
    in case m of
      1 -> 0
      2 -> snd (g m)
      _ -> uncurry (+) (g m)

We want to give @g@ the demand @MCM(P(MP(L),1P(L)))@, so we see that in each call
site of @g@, we are strict in the second component of the returned pair.

This relative cardinality leads to an otherwise unexpected call to 'lubSubDmd'
in 'plusSubDmd', but if you do the math it's just the right thing.

There's one more subtlety: Since the nested demand is relative to exactly one
call, in the case where we have *at most zero calls* (e.g. CA(...)), the premise
is hurt and we can assume that the nested demand is 'botSubDmd'. That ensures
that @g@ above actually gets the @1P(L)@ demand on its second pair component,
rather than the lazy @MP(L)@ if we 'lub'bed with an absent demand.

Demand on case-alternative binders]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The demand on a binder in a case alternative comes
  (a) From the demand on the binder itself
  (b) From the demand on the case binder
Forgetting (b) led directly to #10148.

Example. Source code:
  f x@(p,_) = if p then foo x else True

  foo (p,True) = True
  foo (p,q)    = foo (q,p)

After strictness analysis:
  f = \ (x_an1 [Dmd=1P(1L,ML)] :: (Bool, Bool)) ->
      case x_an1
      of wild_X7 [Dmd=MP(ML,ML)]
      { (p_an2 [Dmd=1L], ds_dnz [Dmd=A]) ->
      case p_an2 of _ {
        False -> GHC.Types.True;
        True -> foo wild_X7 }

It's true that ds_dnz is *itself* absent, but the use of wild_X7 means
that it is very much alive and demanded.  See #10148 for how the
consequences play out.

This is needed even for non-product types, in case the case-binder
is used but the components of the case alternative are not.

Note [Don't optimise LP(L,L,...) to L]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
These two SubDemands:
   LP(L,L) (@Prod [topDmd, topDmd]@)   and   L (@topSubDmd@)
are semantically equivalent, but we do not turn the former into
the latter, for a regrettable-subtle reason.  Consider
  f p1@(x,y) = (y,x)
  g h p2@(_,_) = h p
We want to unbox @p1@ of @f@, but not @p2@ of @g@, because @g@ only uses
@p2@ boxed and we'd have to rebox. So we give @p1@ demand LP(L,L) and @p2@
demand @L@ to inform 'GHC.Core.Opt.WorkWrap.Utils.wantToUnbox', which will
say "unbox" for @p1@ and "don't unbox" for @p2@.

So the solution is: don't aggressively collapse @Prod [topDmd, topDmd]@ to
@topSubDmd@; instead leave it as-is. In effect we are using the UseDmd to do a
little bit of boxity analysis.  Not very nice.

Note [L should win]
~~~~~~~~~~~~~~~~~~~
Both in 'lubSubDmd' and 'plusSubDmd' we want @L `plusSubDmd` LP(..))@ to be @L@.
Why?  Because U carries the implication the whole thing is used, box and all,
so we don't want to w/w it, cf. Note [Don't optimise LP(L,L,...) to L].
If we use it both boxed and unboxed, then we are definitely using the box,
and so we are quite likely to pay a reboxing cost. So we make U win here.
TODO: Investigate why since 2013, we don't.

Example is in the Buffer argument of GHC.IO.Handle.Internals.writeCharBuffer

Baseline: (A) Not making Used win (LP(..) wins)
Compare with: (B) making Used win for lub and both

            Min          -0.3%     -5.6%    -10.7%    -11.0%    -33.3%
            Max          +0.3%    +45.6%    +11.5%    +11.5%     +6.9%
 Geometric Mean          -0.0%     +0.5%     +0.3%     +0.2%     -0.8%

Baseline: (B) Making L win for both lub and both
Compare with: (C) making L win for plus, but LP(..) win for lub

            Min          -0.1%     -0.3%     -7.9%     -8.0%     -6.5%
            Max          +0.1%     +1.0%    +21.0%    +21.0%     +0.5%
 Geometric Mean          +0.0%     +0.0%     -0.0%     -0.1%     -0.1%

Note [Computing one-shot info]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider a call
    f (\pqr. e1) (\xyz. e2) e3
where f has usage signature
    <CM(CL(CM(L)))><CM(L)><L>
Then argsOneShots returns a [[OneShotInfo]] of
    [[OneShot,NoOneShotInfo,OneShot],  [OneShot]]
The occurrence analyser propagates this one-shot infor to the
binders \pqr and \xyz;
see Note [Use one-shot information] in "GHC.Core.Opt.OccurAnal".
-}

{- *********************************************************************
*                                                                      *
                 Divergence: Whether evaluation surely diverges
*                                                                      *
********************************************************************* -}

-- | 'Divergence' characterises whether something surely diverges.
-- Models a subset lattice of the following exhaustive set of divergence
-- results:
--
-- [n] nontermination (e.g. loops)
-- [i] throws imprecise exception
-- [p] throws precise exceTtion
-- [c] converges (reduces to WHNF).
--
-- The different lattice elements correspond to different subsets, indicated by
-- juxtaposition of indicators (e.g. __nc__ definitely doesn't throw an
-- exception, and may or may not reduce to WHNF).
--
-- @
--             Dunno (nipc)
--                  |
--            ExnOrDiv (nip)
--                  |
--            Diverges (ni)
-- @
--
-- As you can see, we don't distinguish __n__ and __i__.
-- See Note [Precise exceptions and strictness analysis] for why __p__ is so
-- special compared to __i__.
data Divergence
  = Diverges -- ^ Definitely throws an imprecise exception or diverges.
  | ExnOrDiv -- ^ Definitely throws a *precise* exception, an imprecise
             --   exception or diverges. Never converges, hence 'isDeadEndDiv'!
             --   See scenario 1 in Note [Precise exceptions and strictness analysis].
  | Dunno    -- ^ Might diverge, throw any kind of exception or converge.
  deriving Divergence -> Divergence -> Bool
(Divergence -> Divergence -> Bool)
-> (Divergence -> Divergence -> Bool) -> Eq Divergence
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Divergence -> Divergence -> Bool
$c/= :: Divergence -> Divergence -> Bool
== :: Divergence -> Divergence -> Bool
$c== :: Divergence -> Divergence -> Bool
Eq

lubDivergence :: Divergence -> Divergence -> Divergence
lubDivergence :: Divergence -> Divergence -> Divergence
lubDivergence Divergence
Diverges Divergence
div      = Divergence
div
lubDivergence Divergence
div      Divergence
Diverges = Divergence
div
lubDivergence Divergence
ExnOrDiv Divergence
ExnOrDiv = Divergence
ExnOrDiv
lubDivergence Divergence
_        Divergence
_        = Divergence
Dunno
-- This needs to commute with defaultFvDmd, i.e.
-- defaultFvDmd (r1 `lubDivergence` r2) = defaultFvDmd r1 `lubDmd` defaultFvDmd r2
-- (See Note [Default demand on free variables and arguments] for why)

-- | See Note [Asymmetry of 'plus*'], which concludes that 'plusDivergence'
-- needs to be symmetric.
-- Strictly speaking, we should have @plusDivergence Dunno Diverges = ExnOrDiv@.
-- But that regresses in too many places (every infinite loop, basically) to be
-- worth it and is only relevant in higher-order scenarios
-- (e.g. Divergence of @f (throwIO blah)@).
-- So 'plusDivergence' currently is 'glbDivergence', really.
plusDivergence :: Divergence -> Divergence -> Divergence
plusDivergence :: Divergence -> Divergence -> Divergence
plusDivergence Divergence
Dunno    Divergence
Dunno    = Divergence
Dunno
plusDivergence Divergence
Diverges Divergence
_        = Divergence
Diverges
plusDivergence Divergence
_        Divergence
Diverges = Divergence
Diverges
plusDivergence Divergence
_        Divergence
_        = Divergence
ExnOrDiv

-- | In a non-strict scenario, we might not force the Divergence, in which case
-- we might converge, hence Dunno.
multDivergence :: Card -> Divergence -> Divergence
multDivergence :: Card -> Divergence -> Divergence
multDivergence Card
n Divergence
_ | Bool -> Bool
not (Card -> Bool
isStrict Card
n) = Divergence
Dunno
multDivergence Card
_ Divergence
d                    = Divergence
d

topDiv, exnDiv, botDiv :: Divergence
topDiv :: Divergence
topDiv = Divergence
Dunno
exnDiv :: Divergence
exnDiv = Divergence
ExnOrDiv
botDiv :: Divergence
botDiv = Divergence
Diverges

-- | True if the 'Divergence' indicates that evaluation will not return.
-- See Note [Dead ends].
isDeadEndDiv :: Divergence -> Bool
isDeadEndDiv :: Divergence -> Bool
isDeadEndDiv Divergence
Diverges = Bool
True
isDeadEndDiv Divergence
ExnOrDiv = Bool
True
isDeadEndDiv Divergence
Dunno    = Bool
False

-- See Notes [Default demand on free variables and arguments]
-- and Scenario 1 in [Precise exceptions and strictness analysis]
defaultFvDmd :: Divergence -> Demand
defaultFvDmd :: Divergence -> Demand
defaultFvDmd Divergence
Dunno    = Demand
absDmd
defaultFvDmd Divergence
ExnOrDiv = Demand
absDmd -- This is the whole point of ExnOrDiv!
defaultFvDmd Divergence
Diverges = Demand
botDmd -- Diverges

defaultArgDmd :: Divergence -> Demand
-- TopRes and BotRes are polymorphic, so that
--      BotRes === (Bot -> BotRes) === ...
--      TopRes === (Top -> TopRes) === ...
-- This function makes that concrete
-- Also see Note [Default demand on free variables and arguments]
defaultArgDmd :: Divergence -> Demand
defaultArgDmd Divergence
Dunno    = Demand
topDmd
-- NB: not botDmd! We don't want to mask the precise exception by forcing the
-- argument. But it is still absent.
defaultArgDmd Divergence
ExnOrDiv = Demand
absDmd
defaultArgDmd Divergence
Diverges = Demand
botDmd

{- Note [Precise vs imprecise exceptions]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
An exception is considered to be /precise/ when it is thrown by the 'raiseIO#'
primop. It follows that all other primops (such as 'raise#' or
division-by-zero) throw /imprecise/ exceptions. Note that the actual type of
the exception thrown doesn't have any impact!

GHC undertakes some effort not to apply an optimisation that would mask a
/precise/ exception with some other source of nontermination, such as genuine
divergence or an imprecise exception, so that the user can reliably
intercept the precise exception with a catch handler before and after
optimisations.

See also the wiki page on precise exceptions:
https://gitlab.haskell.org/ghc/ghc/wikis/exceptions/precise-exceptions
Section 5 of "Tackling the awkward squad" talks about semantic concerns.
Imprecise exceptions are actually more interesting than precise ones (which are
fairly standard) from the perspective of semantics. See the paper "A Semantics
for Imprecise Exceptions" for more details.

Note [Dead ends]
~~~~~~~~~~~~~~~~
We call an expression that either diverges or throws a precise or imprecise
exception a "dead end". We used to call such an expression just "bottoming",
but with the measures we take to preserve precise exception semantics
(see Note [Precise exceptions and strictness analysis]), that is no longer
accurate: 'exnDiv' is no longer the bottom of the Divergence lattice.

Yet externally to demand analysis, we mostly care about being able to drop dead
code etc., which is all due to the property that such an expression never
returns, hence we consider throwing a precise exception to be a dead end.
See also 'isDeadEndDiv'.

Note [Precise exceptions and strictness analysis]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We have to take care to preserve precise exception semantics in strictness
analysis (#17676). There are two scenarios that need careful treatment.

The fixes were discussed at
https://gitlab.haskell.org/ghc/ghc/wikis/fixing-precise-exceptions

Recall that raiseIO# raises a *precise* exception, in contrast to raise# which
raises an *imprecise* exception. See Note [Precise vs imprecise exceptions].

Scenario 1: Precise exceptions in case alternatives
---------------------------------------------------
Unlike raise# (which returns botDiv), we want raiseIO# to return exnDiv.
Here's why. Consider this example from #13380 (similarly #17676):
  f x y | x>0       = raiseIO# Exc
        | y>0       = return 1
        | otherwise = return 2
Is 'f' strict in 'y'? One might be tempted to say yes! But that plays fast and
loose with the precise exception; after optimisation, (f 42 (error "boom"))
turns from throwing the precise Exc to throwing the imprecise user error
"boom". So, the defaultFvDmd of raiseIO# should be lazy (topDmd), which can be
achieved by giving it divergence exnDiv.
See Note [Default demand on free variables and arguments].

Why don't we just give it topDiv instead of introducing exnDiv?
Because then the simplifier will fail to discard raiseIO#'s continuation in
  case raiseIO# x s of { (# s', r #) -> <BIG> }
which we'd like to optimise to
  case raiseIO# x s of {}
Hence we came up with exnDiv. The default FV demand of exnDiv is lazy (and
its default arg dmd is absent), but otherwise (in terms of 'isDeadEndDiv') it
behaves exactly as botDiv, so that dead code elimination works as expected.
This is tracked by T13380b.

Scenario 2: Precise exceptions in case scrutinees
-------------------------------------------------
Consider (more complete examples in #148, #1592, testcase strun003)

  case foo x s of { (# s', r #) -> y }

Is this strict in 'y'? Often not! If @foo x s@ might throw a precise exception
(ultimately via raiseIO#), then we must not force 'y', which may fail to
terminate or throw an imprecise exception, until we have performed @foo x s@.

So we have to 'deferAfterPreciseException' (which 'lub's with 'exnDmdType' to
model the exceptional control flow) when @foo x s@ may throw a precise
exception. Motivated by T13380{d,e,f}.
See Note [Which scrutinees may throw precise exceptions] in "GHC.Core.Opt.DmdAnal".

We have to be careful not to discard dead-end Divergence from case
alternatives, though (#18086):

  m = putStrLn "foo" >> error "bar"

'm' should still have 'exnDiv', which is why it is not sufficient to lub with
'nopDmdType' (which has 'topDiv') in 'deferAfterPreciseException'.

Historical Note: This used to be called the "IO hack". But that term is rather
a bad fit because
1. It's easily confused with the "State hack", which also affects IO.
2. Neither "IO" nor "hack" is a good description of what goes on here, which
   is deferring strictness results after possibly throwing a precise exception.
   The "hack" is probably not having to defer when we can prove that the
   expression may not throw a precise exception (increasing precision of the
   analysis), but that's just a favourable guess.

Note [Exceptions and strictness]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We used to smart about catching exceptions, but we aren't anymore.
See #14998 for the way it's resolved at the moment.

Here's a historic breakdown:

Apparently, exception handling prim-ops didn't use to have any special
strictness signatures, thus defaulting to nopSig, which assumes they use their
arguments lazily. Joachim was the first to realise that we could provide richer
information. Thus, in 0558911f91c (Dec 13), he added signatures to
primops.txt.pp indicating that functions like `catch#` and `catchRetry#` call
their argument, which is useful information for usage analysis. Still with a
'Lazy' strictness demand (i.e. 'lazyApply1Dmd'), though, and the world was fine.

In 7c0fff4 (July 15), Simon argued that giving `catch#` et al. a
'strictApply1Dmd' leads to substantial performance gains. That was at the cost
of correctness, as #10712 proved. So, back to 'lazyApply1Dmd' in
28638dfe79e (Dec 15).

Motivated to reproduce the gains of 7c0fff4 without the breakage of #10712,
Ben opened #11222. Simon made the demand analyser "understand catch" in
9915b656 (Jan 16) by adding a new 'catchArgDmd', which basically said to call
its argument strictly, but also swallow any thrown exceptions in
'multDivergence'. This was realized by extending the 'Str' constructor of
'ArgStr' with a 'ExnStr' field, indicating that it catches the exception, and
adding a 'ThrowsExn' constructor to the 'Divergence' lattice as an element
between 'Dunno' and 'Diverges'. Then along came #11555 and finally #13330,
so we had to revert to 'lazyApply1Dmd' again in 701256df88c (Mar 17).

This left the other variants like 'catchRetry#' having 'catchArgDmd', which is
where #14998 picked up. Item 1 was concerned with measuring the impact of also
making `catchRetry#` and `catchSTM#` have 'lazyApply1Dmd'. The result was that
there was none. We removed the last usages of 'catchArgDmd' in 00b8ecb7
(Apr 18). There was a lot of dead code resulting from that change, that we
removed in ef6b283 (Jan 19): We got rid of 'ThrowsExn' and 'ExnStr' again and
removed any code that was dealing with the peculiarities.

Where did the speed-ups vanish to? In #14998, item 3 established that
turning 'catch#' strict in its first argument didn't bring back any of the
alleged performance benefits. Item 2 of that ticket finally found out that it
was entirely due to 'catchException's new (since #11555) definition, which
was simply

    catchException !io handler = catch io handler

While 'catchException' is arguably the saner semantics for 'catch', it is an
internal helper function in "GHC.IO". Its use in
"GHC.IO.Handle.Internals.do_operation" made for the huge allocation differences:
Remove the bang and you find the regressions we originally wanted to avoid with
'catchArgDmd'. See also #exceptions_and_strictness# in "GHC.IO".

So history keeps telling us that the only possibly correct strictness annotation
for the first argument of 'catch#' is 'lazyApply1Dmd', because 'catch#' really
is not strict in its argument: Just try this in GHCi

  :set -XScopedTypeVariables
  import Control.Exception
  catch undefined (\(_ :: SomeException) -> putStrLn "you'll see this")

Any analysis that assumes otherwise will be broken in some way or another
(beyond `-fno-pendantic-bottoms`).

But then #13380 and #17676 suggest (in Mar 20) that we need to re-introduce a
subtly different variant of `ThrowsExn` (which we call `ExnOrDiv` now) that is
only used by `raiseIO#` in order to preserve precise exceptions by strictness
analysis, while not impacting the ability to eliminate dead code.
See Note [Precise exceptions and strictness analysis].

Note [Default demand on free variables and arguments]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free variables not mentioned in the environment of a 'DmdType'
are demanded according to the demand type's Divergence:
  * In a Diverges (botDiv) context, that demand is botDmd
    (strict and absent).
  * In all other contexts, the demand is absDmd (lazy and absent).
This is recorded in 'defaultFvDmd'.

Similarly, we can eta-expand demand types to get demands on excess arguments
not accounted for in the type, by consulting 'defaultArgDmd':
  * In a Diverges (botDiv) context, that demand is again botDmd.
  * In a ExnOrDiv (exnDiv) context, that demand is absDmd: We surely diverge
    before evaluating the excess argument, but don't want to eagerly evaluate
    it (cf. Note [Precise exceptions and strictness analysis]).
  * In a Dunno context (topDiv), the demand is topDmd, because
    it's perfectly possible to enter the additional lambda and evaluate it
    in unforeseen ways (so, not absent).

Note [Bottom CPR iff Dead-Ending Divergence]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Both CPR analysis and Demand analysis handle recursive functions by doing
fixed-point iteration. To find the *least* (e.g., most informative) fixed-point,
iteration starts with the bottom element of the semantic domain. Diverging
functions generally have the bottom element as their least fixed-point.

One might think that CPR analysis and Demand analysis then agree in when a
function gets a bottom denotation. E.g., whenever it has 'botCpr', it should
also have 'botDiv'. But that is not the case, because strictness analysis has to
be careful around precise exceptions, see Note [Precise vs imprecise exceptions].

So Demand analysis gives some diverging functions 'exnDiv' (which is *not* the
bottom element) when the CPR signature says 'botCpr', and that's OK. Here's an
example (from #18086) where that is the case:

ioTest :: IO ()
ioTest = do
  putStrLn "hi"
  undefined

However, one can loosely say that we give a function 'botCpr' whenever its
'Divergence' is 'exnDiv' or 'botDiv', i.e., dead-ending. But that's just
a consequence of fixed-point iteration, it's not important that they agree.

************************************************************************
*                                                                      *
           Demand environments and types
*                                                                      *
************************************************************************
-}

-- Subject to Note [Default demand on free variables and arguments]
type DmdEnv = VarEnv Demand

emptyDmdEnv :: VarEnv Demand
emptyDmdEnv :: DmdEnv
emptyDmdEnv = DmdEnv
forall a. VarEnv a
emptyVarEnv

multDmdEnv :: Card -> DmdEnv -> DmdEnv
multDmdEnv :: Card -> DmdEnv -> DmdEnv
multDmdEnv Card
n DmdEnv
env
  | Just DmdEnv
env' <- Card -> DmdEnv -> DmdEnv -> Maybe DmdEnv
forall a. Card -> a -> a -> Maybe a
multTrivial Card
n DmdEnv
emptyDmdEnv DmdEnv
env = DmdEnv
env'
  | Bool
otherwise                                  = (Demand -> Demand) -> DmdEnv -> DmdEnv
forall a b. (a -> b) -> VarEnv a -> VarEnv b
mapVarEnv (Card -> Demand -> Demand
multDmd Card
n) DmdEnv
env

reuseEnv :: DmdEnv -> DmdEnv
reuseEnv :: DmdEnv -> DmdEnv
reuseEnv = Card -> DmdEnv -> DmdEnv
multDmdEnv Card
C_1N

-- | @keepAliveDmdType dt vs@ makes sure that the Ids in @vs@ have
-- /some/ usage in the returned demand types -- they are not Absent.
-- See Note [Absence analysis for stable unfoldings and RULES]
--     in "GHC.Core.Opt.DmdAnal".
keepAliveDmdEnv :: DmdEnv -> IdSet -> DmdEnv
keepAliveDmdEnv :: DmdEnv -> IdSet -> DmdEnv
keepAliveDmdEnv DmdEnv
env IdSet
vs
  = (Var -> DmdEnv -> DmdEnv) -> DmdEnv -> IdSet -> DmdEnv
forall a. (Var -> a -> a) -> a -> IdSet -> a
nonDetStrictFoldVarSet Var -> DmdEnv -> DmdEnv
add DmdEnv
env IdSet
vs
  where
    add :: Id -> DmdEnv -> DmdEnv
    add :: Var -> DmdEnv -> DmdEnv
add Var
v DmdEnv
env = (Demand -> Demand -> Demand) -> DmdEnv -> Var -> Demand -> DmdEnv
forall a. (a -> a -> a) -> VarEnv a -> Var -> a -> VarEnv a
extendVarEnv_C Demand -> Demand -> Demand
add_dmd DmdEnv
env Var
v Demand
topDmd

    add_dmd :: Demand -> Demand -> Demand
    -- If the existing usage is Absent, make it used
    -- Otherwise leave it alone
    add_dmd :: Demand -> Demand -> Demand
add_dmd Demand
dmd Demand
_ | Demand -> Bool
isAbsDmd Demand
dmd = Demand
topDmd
                  | Bool
otherwise    = Demand
dmd

-- | Characterises how an expression
--    * Evaluates its free variables ('dt_env')
--    * Evaluates its arguments ('dt_args')
--    * Diverges on every code path or not ('dt_div')
data DmdType
  = DmdType
  { DmdType -> DmdEnv
dt_env  :: DmdEnv     -- ^ Demand on explicitly-mentioned free variables
  , DmdType -> [Demand]
dt_args :: [Demand]   -- ^ Demand on arguments
  , DmdType -> Divergence
dt_div  :: Divergence -- ^ Whether evaluation diverges.
                          -- See Note [Demand type Divergence]
  }

instance Eq DmdType where
  == :: DmdType -> DmdType -> Bool
(==) (DmdType DmdEnv
fv1 [Demand]
ds1 Divergence
div1)
       (DmdType DmdEnv
fv2 [Demand]
ds2 Divergence
div2) = DmdEnv -> [(Unique, Demand)]
forall key elt. UniqFM key elt -> [(Unique, elt)]
nonDetUFMToList DmdEnv
fv1 [(Unique, Demand)] -> [(Unique, Demand)] -> Bool
forall a. Eq a => a -> a -> Bool
== DmdEnv -> [(Unique, Demand)]
forall key elt. UniqFM key elt -> [(Unique, elt)]
nonDetUFMToList DmdEnv
fv2
         -- It's OK to use nonDetUFMToList here because we're testing for
         -- equality and even though the lists will be in some arbitrary
         -- Unique order, it is the same order for both
                              Bool -> Bool -> Bool
&& [Demand]
ds1 [Demand] -> [Demand] -> Bool
forall a. Eq a => a -> a -> Bool
== [Demand]
ds2 Bool -> Bool -> Bool
&& Divergence
div1 Divergence -> Divergence -> Bool
forall a. Eq a => a -> a -> Bool
== Divergence
div2

-- | Compute the least upper bound of two 'DmdType's elicited /by the same
-- incoming demand/!
lubDmdType :: DmdType -> DmdType -> DmdType
lubDmdType :: DmdType -> DmdType -> DmdType
lubDmdType DmdType
d1 DmdType
d2
  = DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
lub_fv [Demand]
lub_ds Divergence
lub_div
  where
    n :: Int
n = Int -> Int -> Int
forall a. Ord a => a -> a -> a
max (DmdType -> Int
dmdTypeDepth DmdType
d1) (DmdType -> Int
dmdTypeDepth DmdType
d2)
    (DmdType DmdEnv
fv1 [Demand]
ds1 Divergence
r1) = Int -> DmdType -> DmdType
etaExpandDmdType Int
n DmdType
d1
    (DmdType DmdEnv
fv2 [Demand]
ds2 Divergence
r2) = Int -> DmdType -> DmdType
etaExpandDmdType Int
n DmdType
d2

    lub_fv :: DmdEnv
lub_fv  = (Demand -> Demand -> Demand)
-> DmdEnv -> Demand -> DmdEnv -> Demand -> DmdEnv
forall a.
(a -> a -> a) -> VarEnv a -> a -> VarEnv a -> a -> VarEnv a
plusVarEnv_CD Demand -> Demand -> Demand
lubDmd DmdEnv
fv1 (Divergence -> Demand
defaultFvDmd Divergence
r1) DmdEnv
fv2 (Divergence -> Demand
defaultFvDmd Divergence
r2)
    lub_ds :: [Demand]
lub_ds  = String
-> (Demand -> Demand -> Demand) -> [Demand] -> [Demand] -> [Demand]
forall a b c. String -> (a -> b -> c) -> [a] -> [b] -> [c]
zipWithEqual String
"lubDmdType" Demand -> Demand -> Demand
lubDmd [Demand]
ds1 [Demand]
ds2
    lub_div :: Divergence
lub_div = Divergence -> Divergence -> Divergence
lubDivergence Divergence
r1 Divergence
r2

type PlusDmdArg = (DmdEnv, Divergence)

mkPlusDmdArg :: DmdEnv -> PlusDmdArg
mkPlusDmdArg :: DmdEnv -> PlusDmdArg
mkPlusDmdArg DmdEnv
env = (DmdEnv
env, Divergence
topDiv)

toPlusDmdArg :: DmdType -> PlusDmdArg
toPlusDmdArg :: DmdType -> PlusDmdArg
toPlusDmdArg (DmdType DmdEnv
fv [Demand]
_ Divergence
r) = (DmdEnv
fv, Divergence
r)

plusDmdType :: DmdType -> PlusDmdArg -> DmdType
plusDmdType :: DmdType -> PlusDmdArg -> DmdType
plusDmdType (DmdType DmdEnv
fv1 [Demand]
ds1 Divergence
r1) (DmdEnv
fv2, Divergence
t2)
    -- See Note [Asymmetry of 'plus*']
    -- 'plus' takes the argument/result info from its *first* arg,
    -- using its second arg just for its free-var info.
  = DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType ((Demand -> Demand -> Demand)
-> DmdEnv -> Demand -> DmdEnv -> Demand -> DmdEnv
forall a.
(a -> a -> a) -> VarEnv a -> a -> VarEnv a -> a -> VarEnv a
plusVarEnv_CD Demand -> Demand -> Demand
plusDmd DmdEnv
fv1 (Divergence -> Demand
defaultFvDmd Divergence
r1) DmdEnv
fv2 (Divergence -> Demand
defaultFvDmd Divergence
t2))
            [Demand]
ds1
            (Divergence
r1 Divergence -> Divergence -> Divergence
`plusDivergence` Divergence
t2)

botDmdType :: DmdType
botDmdType :: DmdType
botDmdType = DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
emptyDmdEnv [] Divergence
botDiv

-- | The demand type of doing nothing (lazy, absent, no Divergence
-- information). Note that it is ''not'' the top of the lattice (which would be
-- "may use everything"), so it is (no longer) called topDmdType.
nopDmdType :: DmdType
nopDmdType :: DmdType
nopDmdType = DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
emptyDmdEnv [] Divergence
topDiv

isTopDmdType :: DmdType -> Bool
isTopDmdType :: DmdType -> Bool
isTopDmdType (DmdType DmdEnv
env [Demand]
args Divergence
div)
  = Divergence
div Divergence -> Divergence -> Bool
forall a. Eq a => a -> a -> Bool
== Divergence
topDiv Bool -> Bool -> Bool
&& [Demand] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [Demand]
args Bool -> Bool -> Bool
&& DmdEnv -> Bool
forall a. VarEnv a -> Bool
isEmptyVarEnv DmdEnv
env

-- | The demand type of an unspecified expression that is guaranteed to
-- throw a (precise or imprecise) exception or diverge.
exnDmdType :: DmdType
exnDmdType :: DmdType
exnDmdType = DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
emptyDmdEnv [] Divergence
exnDiv

dmdTypeDepth :: DmdType -> Arity
dmdTypeDepth :: DmdType -> Int
dmdTypeDepth = [Demand] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length ([Demand] -> Int) -> (DmdType -> [Demand]) -> DmdType -> Int
forall b c a. (b -> c) -> (a -> b) -> a -> c
. DmdType -> [Demand]
dt_args

-- | This makes sure we can use the demand type with n arguments after eta
-- expansion, where n must not be lower than the demand types depth.
-- It appends the argument list with the correct 'defaultArgDmd'.
etaExpandDmdType :: Arity -> DmdType -> DmdType
etaExpandDmdType :: Int -> DmdType -> DmdType
etaExpandDmdType Int
n d :: DmdType
d@DmdType{dt_args :: DmdType -> [Demand]
dt_args = [Demand]
ds, dt_div :: DmdType -> Divergence
dt_div = Divergence
div}
  | Int
n Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
depth = DmdType
d
  | Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>  Int
depth = DmdType
d{dt_args :: [Demand]
dt_args = [Demand]
inc_ds}
  | Bool
otherwise  = String -> SDoc -> DmdType
forall a. HasCallStack => String -> SDoc -> a
pprPanic String
"etaExpandDmdType: arity decrease" (Int -> SDoc
forall a. Outputable a => a -> SDoc
ppr Int
n SDoc -> SDoc -> SDoc
$$ DmdType -> SDoc
forall a. Outputable a => a -> SDoc
ppr DmdType
d)
  where depth :: Int
depth = [Demand] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [Demand]
ds
        -- Arity increase:
        --  * Demands on FVs are still valid
        --  * Demands on args also valid, plus we can extend with defaultArgDmd
        --    as appropriate for the given Divergence
        --  * Divergence is still valid:
        --    - A dead end after 2 arguments stays a dead end after 3 arguments
        --    - The remaining case is Dunno, which is already topDiv
        inc_ds :: [Demand]
inc_ds = Int -> [Demand] -> [Demand]
forall a. Int -> [a] -> [a]
take Int
n ([Demand]
ds [Demand] -> [Demand] -> [Demand]
forall a. [a] -> [a] -> [a]
++ Demand -> [Demand]
forall a. a -> [a]
repeat (Divergence -> Demand
defaultArgDmd Divergence
div))

-- | A conservative approximation for a given 'DmdType' in case of an arity
-- decrease. Currently, it's just nopDmdType.
decreaseArityDmdType :: DmdType -> DmdType
decreaseArityDmdType :: DmdType -> DmdType
decreaseArityDmdType DmdType
_ = DmdType
nopDmdType

splitDmdTy :: DmdType -> (Demand, DmdType)
-- Split off one function argument
-- We already have a suitable demand on all
-- free vars, so no need to add more!
splitDmdTy :: DmdType -> (Demand, DmdType)
splitDmdTy ty :: DmdType
ty@DmdType{dt_args :: DmdType -> [Demand]
dt_args=Demand
dmd:[Demand]
args} = (Demand
dmd, DmdType
ty{dt_args :: [Demand]
dt_args=[Demand]
args})
splitDmdTy ty :: DmdType
ty@DmdType{dt_div :: DmdType -> Divergence
dt_div=Divergence
div}       = (Divergence -> Demand
defaultArgDmd Divergence
div, DmdType
ty)

multDmdType :: Card -> DmdType -> DmdType
multDmdType :: Card -> DmdType -> DmdType
multDmdType Card
n (DmdType DmdEnv
fv [Demand]
args Divergence
res_ty)
  = -- pprTrace "multDmdType" (ppr n $$ ppr fv $$ ppr (multDmdEnv n fv)) $
    DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType (Card -> DmdEnv -> DmdEnv
multDmdEnv Card
n DmdEnv
fv)
            ((Demand -> Demand) -> [Demand] -> [Demand]
forall a b. (a -> b) -> [a] -> [b]
map (Card -> Demand -> Demand
multDmd Card
n) [Demand]
args)
            (Card -> Divergence -> Divergence
multDivergence Card
n Divergence
res_ty)

peelFV :: DmdType -> Var -> (DmdType, Demand)
peelFV :: DmdType -> Var -> (DmdType, Demand)
peelFV (DmdType DmdEnv
fv [Demand]
ds Divergence
res) Var
id = -- pprTrace "rfv" (ppr id <+> ppr dmd $$ ppr fv)
                               (DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
fv' [Demand]
ds Divergence
res, Demand
dmd)
  where
  fv' :: DmdEnv
fv' = DmdEnv
fv DmdEnv -> Var -> DmdEnv
forall a. VarEnv a -> Var -> VarEnv a
`delVarEnv` Var
id
  -- See Note [Default demand on free variables and arguments]
  dmd :: Demand
dmd  = DmdEnv -> Var -> Maybe Demand
forall a. VarEnv a -> Var -> Maybe a
lookupVarEnv DmdEnv
fv Var
id Maybe Demand -> Demand -> Demand
forall a. Maybe a -> a -> a
`orElse` Divergence -> Demand
defaultFvDmd Divergence
res

addDemand :: Demand -> DmdType -> DmdType
addDemand :: Demand -> DmdType -> DmdType
addDemand Demand
dmd (DmdType DmdEnv
fv [Demand]
ds Divergence
res) = DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
fv (Demand
dmdDemand -> [Demand] -> [Demand]
forall a. a -> [a] -> [a]
:[Demand]
ds) Divergence
res

findIdDemand :: DmdType -> Var -> Demand
findIdDemand :: DmdType -> Var -> Demand
findIdDemand (DmdType DmdEnv
fv [Demand]
_ Divergence
res) Var
id
  = DmdEnv -> Var -> Maybe Demand
forall a. VarEnv a -> Var -> Maybe a
lookupVarEnv DmdEnv
fv Var
id Maybe Demand -> Demand -> Demand
forall a. Maybe a -> a -> a
`orElse` Divergence -> Demand
defaultFvDmd Divergence
res

-- | When e is evaluated after executing an IO action that may throw a precise
-- exception, we act as if there is an additional control flow path that is
-- taken if e throws a precise exception. The demand type of this control flow
-- path
--   * is lazy and absent ('topDmd') in all free variables and arguments
--   * has 'exnDiv' 'Divergence' result
-- So we can simply take a variant of 'nopDmdType', 'exnDmdType'.
-- Why not 'nopDmdType'? Because then the result of 'e' can never be 'exnDiv'!
-- That means failure to drop dead-ends, see #18086.
-- See Note [Precise exceptions and strictness analysis]
deferAfterPreciseException :: DmdType -> DmdType
deferAfterPreciseException :: DmdType -> DmdType
deferAfterPreciseException = DmdType -> DmdType -> DmdType
lubDmdType DmdType
exnDmdType

-- | See 'keepAliveDmdEnv'.
keepAliveDmdType :: DmdType -> VarSet -> DmdType
keepAliveDmdType :: DmdType -> IdSet -> DmdType
keepAliveDmdType (DmdType DmdEnv
fvs [Demand]
ds Divergence
res) IdSet
vars =
  DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType (DmdEnv
fvs DmdEnv -> IdSet -> DmdEnv
`keepAliveDmdEnv` IdSet
vars) [Demand]
ds Divergence
res

{-
Note [Demand type Divergence]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In contrast to StrictSigs, DmdTypes are elicited under a specific incoming demand.
This is described in detail in Note [Understanding DmdType and StrictSig].
Here, we'll focus on what that means for a DmdType's Divergence in a higher-order
scenario.

Consider
  err x y = x `seq` y `seq` error (show x)
this has a strictness signature of
  <1L><1L>b
meaning that we don't know what happens when we call err in weaker contexts than
C1(C1(L)), like @err `seq` ()@ (1A) and @err 1 `seq` ()@ (CS(A)). We
may not unleash the botDiv, hence assume topDiv. Of course, in
@err 1 2 `seq` ()@ the incoming demand CS(CS(A)) is strong enough and we see
that the expression diverges.

Now consider a function
  f g = g 1 2
with signature <C1(C1(L))>, and the expression
  f err `seq` ()
now f puts a strictness demand of C1(C1(L)) onto its argument, which is unleashed
on err via the App rule. In contrast to weaker head strictness, this demand is
strong enough to unleash err's signature and hence we see that the whole
expression diverges!

Note [Asymmetry of 'plus*']
~~~~~~~~~~~~~~~~~~~~~~~~~~~
'plus' for DmdTypes is *asymmetrical*, because there can only one
be one type contributing argument demands!  For example, given (e1 e2), we get
a DmdType dt1 for e1, use its arg demand to analyse e2 giving dt2, and then do
(dt1 `plusType` dt2). Similarly with
  case e of { p -> rhs }
we get dt_scrut from the scrutinee and dt_rhs from the RHS, and then
compute (dt_rhs `plusType` dt_scrut).

We
 1. combine the information on the free variables,
 2. take the demand on arguments from the first argument
 3. combine the termination results, as in plusDivergence.

Since we don't use argument demands of the second argument anyway, 'plus's
second argument is just a 'PlusDmdType'.

But note that the argument demand types are not guaranteed to be observed in
left to right order. For example, analysis of a case expression will pass the
demand type for the alts as the left argument and the type for the scrutinee as
the right argument. Also, it is not at all clear if there is such an order;
consider the LetUp case, where the RHS might be forced at any point while
evaluating the let body.
Therefore, it is crucial that 'plusDivergence' is symmetric!

Note [Demands from unsaturated function calls]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider a demand transformer d1 -> d2 -> r for f.
If a sufficiently detailed demand is fed into this transformer,
e.g <C1(C1(L))> arising from "f x1 x2" in a strict, use-once context,
then d1 and d2 is precisely the demand unleashed onto x1 and x2 (similar for
the free variable environment) and furthermore the result information r is the
one we want to use.

An anonymous lambda is also an unsaturated function all (needs one argument,
none given), so this applies to that case as well.

But the demand fed into f might be less than C1(C1(L)). Then we have to
'multDmdType' the announced demand type. Examples:
 * Not strict enough, e.g. C1(C1(L)):
   - We have to multiply all argument and free variable demands with C_01,
     zapping strictness.
   - We have to multiply divergence with C_01. If r says that f Diverges for sure,
     then this holds when the demand guarantees that two arguments are going to
     be passed. If the demand is lower, we may just as well converge.
     If we were tracking definite convergence, than that would still hold under
     a weaker demand than expected by the demand transformer.
 * Used more than once, e.g. CS(C1(L)):
   - Multiply with C_1N. Even if f puts a used-once demand on any of its argument
     or free variables, if we call f multiple times, we may evaluate this
     argument or free variable multiple times.

In dmdTransformSig, we call peelManyCalls to find out the 'Card'inality with
which we have to multiply and then call multDmdType with that.

Similarly, dmdTransformDictSelSig and dmdAnal, when analyzing a Lambda, use
peelCallDmd, which peels only one level, but also returns the demand put on the
body of the function.
-}


{-
************************************************************************
*                                                                      *
                     Demand signatures
*                                                                      *
************************************************************************

In a let-bound Id we record its demand signature.
In principle, this demand signature is a demand transformer, mapping
a demand on the Id into a DmdType, which gives
        a) the free vars of the Id's value
        b) the Id's arguments
        c) an indication of the result of applying
           the Id to its arguments

However, in fact we store in the Id an extremely emascuated demand
transfomer, namely

                a single DmdType
(Nevertheless we dignify StrictSig as a distinct type.)

This DmdType gives the demands unleashed by the Id when it is applied
to as many arguments as are given in by the arg demands in the DmdType.
Also see Note [Demand type Divergence] for the meaning of a Divergence in a
strictness signature.

If an Id is applied to less arguments than its arity, it means that
the demand on the function at a call site is weaker than the vanilla
call demand, used for signature inference. Therefore we place a top
demand on all arguments. Otherwise, the demand is specified by Id's
signature.

For example, the demand transformer described by the demand signature
        StrictSig (DmdType {x -> <1L>} <A><1P(L,L)>)
says that when the function is applied to two arguments, it
unleashes demand 1L on the free var x, A on the first arg,
and 1P(L,L) on the second.

If this same function is applied to one arg, all we can say is that it
uses x with 1L, and its arg with demand 1P(L,L).

Note [Understanding DmdType and StrictSig]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Demand types are sound approximations of an expression's semantics relative to
the incoming demand we put the expression under. Consider the following
expression:

    \x y -> x `seq` (y, 2*x)

Here is a table with demand types resulting from different incoming demands we
put that expression under. Note the monotonicity; a stronger incoming demand
yields a more precise demand type:

    incoming demand   |  demand type
    --------------------------------
    1A                  |  <L><L>{}
    C1(C1(L))           |  <1P(L)><L>{}
    C1(C1(1P(1P(L),A))) |  <1P(A)><A>{}

Note that in the first example, the depth of the demand type was *higher* than
the arity of the incoming call demand due to the anonymous lambda.
The converse is also possible and happens when we unleash demand signatures.
In @f x y@, the incoming call demand on f has arity 2. But if all we have is a
demand signature with depth 1 for @f@ (which we can safely unleash, see below),
the demand type of @f@ under a call demand of arity 2 has a *lower* depth of 1.

So: Demand types are elicited by putting an expression under an incoming (call)
demand, the arity of which can be lower or higher than the depth of the
resulting demand type.
In contrast, a demand signature summarises a function's semantics *without*
immediately specifying the incoming demand it was produced under. Despite StrSig
being a newtype wrapper around DmdType, it actually encodes two things:

  * The threshold (i.e., minimum arity) to unleash the signature
  * A demand type that is sound to unleash when the minimum arity requirement is
    met.

Here comes the subtle part: The threshold is encoded in the wrapped demand
type's depth! So in mkStrictSigForArity we make sure to trim the list of
argument demands to the given threshold arity. Call sites will make sure that
this corresponds to the arity of the call demand that elicited the wrapped
demand type. See also Note [What are demand signatures?].
-}

-- | The depth of the wrapped 'DmdType' encodes the arity at which it is safe
-- to unleash. Better construct this through 'mkStrictSigForArity'.
-- See Note [Understanding DmdType and StrictSig]
newtype StrictSig
  = StrictSig DmdType
  deriving StrictSig -> StrictSig -> Bool
(StrictSig -> StrictSig -> Bool)
-> (StrictSig -> StrictSig -> Bool) -> Eq StrictSig
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: StrictSig -> StrictSig -> Bool
$c/= :: StrictSig -> StrictSig -> Bool
== :: StrictSig -> StrictSig -> Bool
$c== :: StrictSig -> StrictSig -> Bool
Eq

-- | Turns a 'DmdType' computed for the particular 'Arity' into a 'StrictSig'
-- unleashable at that arity. See Note [Understanding DmdType and StrictSig]
mkStrictSigForArity :: Arity -> DmdType -> StrictSig
mkStrictSigForArity :: Int -> DmdType -> StrictSig
mkStrictSigForArity Int
arity dmd_ty :: DmdType
dmd_ty@(DmdType DmdEnv
fvs [Demand]
args Divergence
div)
  | Int
arity Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< DmdType -> Int
dmdTypeDepth DmdType
dmd_ty = DmdType -> StrictSig
StrictSig (DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
fvs (Int -> [Demand] -> [Demand]
forall a. Int -> [a] -> [a]
take Int
arity [Demand]
args) Divergence
div)
  | Bool
otherwise                   = DmdType -> StrictSig
StrictSig (Int -> DmdType -> DmdType
etaExpandDmdType Int
arity DmdType
dmd_ty)

mkClosedStrictSig :: [Demand] -> Divergence -> StrictSig
mkClosedStrictSig :: [Demand] -> Divergence -> StrictSig
mkClosedStrictSig [Demand]
ds Divergence
res = Int -> DmdType -> StrictSig
mkStrictSigForArity ([Demand] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [Demand]
ds) (DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
emptyDmdEnv [Demand]
ds Divergence
res)

splitStrictSig :: StrictSig -> ([Demand], Divergence)
splitStrictSig :: StrictSig -> ([Demand], Divergence)
splitStrictSig (StrictSig (DmdType DmdEnv
_ [Demand]
dmds Divergence
res)) = ([Demand]
dmds, Divergence
res)

strictSigDmdEnv :: StrictSig -> DmdEnv
strictSigDmdEnv :: StrictSig -> DmdEnv
strictSigDmdEnv (StrictSig (DmdType DmdEnv
env [Demand]
_ Divergence
_)) = DmdEnv
env

hasDemandEnvSig :: StrictSig -> Bool
hasDemandEnvSig :: StrictSig -> Bool
hasDemandEnvSig = Bool -> Bool
not (Bool -> Bool) -> (StrictSig -> Bool) -> StrictSig -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. DmdEnv -> Bool
forall a. VarEnv a -> Bool
isEmptyVarEnv (DmdEnv -> Bool) -> (StrictSig -> DmdEnv) -> StrictSig -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. StrictSig -> DmdEnv
strictSigDmdEnv

botSig :: StrictSig
botSig :: StrictSig
botSig = DmdType -> StrictSig
StrictSig DmdType
botDmdType

nopSig :: StrictSig
nopSig :: StrictSig
nopSig = DmdType -> StrictSig
StrictSig DmdType
nopDmdType

isTopSig :: StrictSig -> Bool
isTopSig :: StrictSig -> Bool
isTopSig (StrictSig DmdType
ty) = DmdType -> Bool
isTopDmdType DmdType
ty

-- | True if the signature diverges or throws an exception in a saturated call.
-- See Note [Dead ends].
isDeadEndSig :: StrictSig -> Bool
isDeadEndSig :: StrictSig -> Bool
isDeadEndSig (StrictSig (DmdType DmdEnv
_ [Demand]
_ Divergence
res)) = Divergence -> Bool
isDeadEndDiv Divergence
res

-- | Returns true if an application to n args would diverge or throw an
-- exception.
--
-- If a function having 'botDiv' is applied to a less number of arguments than
-- its syntactic arity, we cannot say for sure that it is going to diverge.
-- Hence this function conservatively returns False in that case.
-- See Note [Dead ends].
appIsDeadEnd :: StrictSig -> Int -> Bool
appIsDeadEnd :: StrictSig -> Int -> Bool
appIsDeadEnd (StrictSig (DmdType DmdEnv
_ [Demand]
ds Divergence
res)) Int
n
  = Divergence -> Bool
isDeadEndDiv Divergence
res Bool -> Bool -> Bool
&& Bool -> Bool
not ([Demand] -> Int -> Bool
forall a. [a] -> Int -> Bool
lengthExceeds [Demand]
ds Int
n)

prependArgsStrictSig :: Int -> StrictSig -> StrictSig
-- ^ Add extra ('topDmd') arguments to a strictness signature.
-- In contrast to 'etaConvertStrictSig', this /prepends/ additional argument
-- demands. This is used by FloatOut.
prependArgsStrictSig :: Int -> StrictSig -> StrictSig
prependArgsStrictSig Int
new_args sig :: StrictSig
sig@(StrictSig dmd_ty :: DmdType
dmd_ty@(DmdType DmdEnv
env [Demand]
dmds Divergence
res))
  | Int
new_args Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
0       = StrictSig
sig
  | DmdType -> Bool
isTopDmdType DmdType
dmd_ty = StrictSig
sig
  | Int
new_args Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0        = String -> SDoc -> StrictSig
forall a. HasCallStack => String -> SDoc -> a
pprPanic String
"prependArgsStrictSig: negative new_args"
                                   (Int -> SDoc
forall a. Outputable a => a -> SDoc
ppr Int
new_args SDoc -> SDoc -> SDoc
$$ StrictSig -> SDoc
forall a. Outputable a => a -> SDoc
ppr StrictSig
sig)
  | Bool
otherwise           = DmdType -> StrictSig
StrictSig (DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
env [Demand]
dmds' Divergence
res)
  where
    dmds' :: [Demand]
dmds' = Int -> Demand -> [Demand]
forall a. Int -> a -> [a]
replicate Int
new_args Demand
topDmd [Demand] -> [Demand] -> [Demand]
forall a. [a] -> [a] -> [a]
++ [Demand]
dmds

etaConvertStrictSig :: Arity -> StrictSig -> StrictSig
-- ^ We are expanding (\x y. e) to (\x y z. e z) or reducing from the latter to
-- the former (when the Simplifier identifies a new join points, for example).
-- In contrast to 'prependArgsStrictSig', this /appends/ extra arg demands if
-- necessary.
-- This works by looking at the 'DmdType' (which was produced under a call
-- demand for the old arity) and trying to transfer as many facts as we can to
-- the call demand of new arity.
-- An arity increase (resulting in a stronger incoming demand) can retain much
-- of the info, while an arity decrease (a weakening of the incoming demand)
-- must fall back to a conservative default.
etaConvertStrictSig :: Int -> StrictSig -> StrictSig
etaConvertStrictSig Int
arity (StrictSig DmdType
dmd_ty)
  | Int
arity Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< DmdType -> Int
dmdTypeDepth DmdType
dmd_ty = DmdType -> StrictSig
StrictSig (DmdType -> StrictSig) -> DmdType -> StrictSig
forall a b. (a -> b) -> a -> b
$ DmdType -> DmdType
decreaseArityDmdType DmdType
dmd_ty
  | Bool
otherwise                   = DmdType -> StrictSig
StrictSig (DmdType -> StrictSig) -> DmdType -> StrictSig
forall a b. (a -> b) -> a -> b
$ Int -> DmdType -> DmdType
etaExpandDmdType Int
arity DmdType
dmd_ty

{-
************************************************************************
*                                                                      *
                     Demand transformers
*                                                                      *
************************************************************************
-}

-- | A /demand transformer/ is a monotone function from an incoming evaluation
-- context ('SubDemand') to a 'DmdType', describing how the denoted thing
-- (i.e. expression, function) uses its arguments and free variables, and
-- whether it diverges.
--
-- See Note [Understanding DmdType and StrictSig]
-- and Note [What are demand signatures?].
type DmdTransformer = SubDemand -> DmdType

-- | Extrapolate a demand signature ('StrictSig') into a 'DmdTransformer'.
--
-- Given a function's 'StrictSig' and a 'SubDemand' for the evaluation context,
-- return how the function evaluates its free variables and arguments.
dmdTransformSig :: StrictSig -> DmdTransformer
dmdTransformSig :: StrictSig -> DmdTransformer
dmdTransformSig (StrictSig dmd_ty :: DmdType
dmd_ty@(DmdType DmdEnv
_ [Demand]
arg_ds Divergence
_)) SubDemand
sd
  = Card -> DmdType -> DmdType
multDmdType (Int -> SubDemand -> Card
peelManyCalls ([Demand] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [Demand]
arg_ds) SubDemand
sd) DmdType
dmd_ty
    -- see Note [Demands from unsaturated function calls]
    -- and Note [What are demand signatures?]

-- | A special 'DmdTransformer' for data constructors that feeds product
-- demands into the constructor arguments.
dmdTransformDataConSig :: Arity -> DmdTransformer
dmdTransformDataConSig :: Int -> DmdTransformer
dmdTransformDataConSig Int
arity SubDemand
sd = case Int -> SubDemand -> Maybe [Demand]
go Int
arity SubDemand
sd of
  Just [Demand]
dmds -> DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
emptyDmdEnv [Demand]
dmds Divergence
topDiv
  Maybe [Demand]
Nothing   -> DmdType
nopDmdType -- Not saturated
  where
    go :: Int -> SubDemand -> Maybe [Demand]
go Int
0 SubDemand
sd                            = Int -> SubDemand -> Maybe [Demand]
viewProd Int
arity SubDemand
sd
    go Int
n (SubDemand -> Maybe (Card, SubDemand)
viewCall -> Just (Card
C_11, SubDemand
sd)) = Int -> SubDemand -> Maybe [Demand]
go (Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1) SubDemand
sd  -- strict calls only!
    go Int
_ SubDemand
_                             = Maybe [Demand]
forall a. Maybe a
Nothing

-- | A special 'DmdTransformer' for dictionary selectors that feeds the demand
-- on the result into the indicated dictionary component (if saturated).
dmdTransformDictSelSig :: StrictSig -> DmdTransformer
-- NB: This currently doesn't handle newtype dictionaries and it's unclear how
-- it could without additional parameters.
dmdTransformDictSelSig :: StrictSig -> DmdTransformer
dmdTransformDictSelSig (StrictSig (DmdType DmdEnv
_ [(Card
_ :* SubDemand
sig_sd)] Divergence
_)) SubDemand
call_sd
   | (Card
n, SubDemand
sd') <- SubDemand -> (Card, SubDemand)
peelCallDmd SubDemand
call_sd
   , Prod [Demand]
sig_ds  <- SubDemand
sig_sd
   = Card -> DmdType -> DmdType
multDmdType Card
n (DmdType -> DmdType) -> DmdType -> DmdType
forall a b. (a -> b) -> a -> b
$
     DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
emptyDmdEnv [Card
C_11 Card -> SubDemand -> Demand
:* [Demand] -> SubDemand
Prod ((Demand -> Demand) -> [Demand] -> [Demand]
forall a b. (a -> b) -> [a] -> [b]
map (SubDemand -> Demand -> Demand
enhance SubDemand
sd') [Demand]
sig_ds)] Divergence
topDiv
   | Bool
otherwise
   = DmdType
nopDmdType -- See Note [Demand transformer for a dictionary selector]
  where
    enhance :: SubDemand -> Demand -> Demand
enhance SubDemand
sd Demand
old | Demand -> Bool
isAbsDmd Demand
old = Demand
old
                   | Bool
otherwise    = Card
C_11 Card -> SubDemand -> Demand
:* SubDemand
sd  -- This is the one!

dmdTransformDictSelSig StrictSig
sig SubDemand
sd = String -> SDoc -> DmdType
forall a. HasCallStack => String -> SDoc -> a
pprPanic String
"dmdTransformDictSelSig: no args" (StrictSig -> SDoc
forall a. Outputable a => a -> SDoc
ppr StrictSig
sig SDoc -> SDoc -> SDoc
$$ SubDemand -> SDoc
forall a. Outputable a => a -> SDoc
ppr SubDemand
sd)

{-
Note [What are demand signatures?]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Demand analysis interprets expressions in the abstract domain of demand
transformers. Given a (sub-)demand that denotes the evaluation context, the
abstract transformer of an expression gives us back a demand type denoting
how other things (like arguments and free vars) were used when the expression
was evaluated. Here's an example:

  f x y =
    if x + expensive
      then \z -> z + y * ...
      else \z -> z * ...

The abstract transformer (let's call it F_e) of the if expression (let's
call it e) would transform an incoming (undersaturated!) head demand 1A into
a demand type like {x-><1L>,y-><L>}<L>. In pictures:

     Demand ---F_e---> DmdType
     <1A>              {x-><1L>,y-><L>}<L>

Let's assume that the demand transformers we compute for an expression are
correct wrt. to some concrete semantics for Core. How do demand signatures fit
in? They are strange beasts, given that they come with strict rules when to
it's sound to unleash them.

Fortunately, we can formalise the rules with Galois connections. Consider
f's strictness signature, {}<1L><L>. It's a single-point approximation of
the actual abstract transformer of f's RHS for arity 2. So, what happens is that
we abstract *once more* from the abstract domain we already are in, replacing
the incoming Demand by a simple lattice with two elements denoting incoming
arity: A_2 = {<2, >=2} (where '<2' is the top element and >=2 the bottom
element). Here's the diagram:

     A_2 -----f_f----> DmdType
      ^                   |
      | α               γ |
      |                   v
  SubDemand --F_f----> DmdType

With
  α(C1(C1(_))) = >=2
  α(_)         =  <2
  γ(ty)        =  ty
and F_f being the abstract transformer of f's RHS and f_f being the abstracted
abstract transformer computable from our demand signature simply by

  f_f(>=2) = {}<1L><L>
  f_f(<2)  = multDmdType C_0N {}<1L><L>

where multDmdType makes a proper top element out of the given demand type.

In practice, the A_n domain is not just a simple Bool, but a Card, which is
exactly the Card with which we have to multDmdType. The Card for arity n
is computed by calling @peelManyCalls n@, which corresponds to α above.

Note [Demand transformer for a dictionary selector]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If we evaluate (op dict-expr) under demand 'd', then we can push the demand 'd'
into the appropriate field of the dictionary. What *is* the appropriate field?
We just look at the strictness signature of the class op, which will be
something like: P(AAA1AAAAA).  Then replace the '1' by the demand 'd'.

For single-method classes, which are represented by newtypes the signature
of 'op' won't look like P(...), so matching on Prod will fail.
That's fine: if we are doing strictness analysis we are also doing inlining,
so we'll have inlined 'op' into a cast.  So we can bale out in a conservative
way, returning nopDmdType.

It is (just.. #8329) possible to be running strictness analysis *without*
having inlined class ops from single-method classes.  Suppose you are using
ghc --make; and the first module has a local -O0 flag.  So you may load a class
without interface pragmas, ie (currently) without an unfolding for the class
ops.   Now if a subsequent module in the --make sweep has a local -O flag
you might do strictness analysis, but there is no inlining for the class op.
This is weird, so I'm not worried about whether this optimises brilliantly; but
it should not fall over.
-}

-- | Remove the demand environment from the signature.
zapDmdEnvSig :: StrictSig -> StrictSig
zapDmdEnvSig :: StrictSig -> StrictSig
zapDmdEnvSig (StrictSig (DmdType DmdEnv
_ [Demand]
ds Divergence
r)) = [Demand] -> Divergence -> StrictSig
mkClosedStrictSig [Demand]
ds Divergence
r

zapUsageDemand :: Demand -> Demand
-- Remove the usage info, but not the strictness info, from the demand
zapUsageDemand :: Demand -> Demand
zapUsageDemand = KillFlags -> Demand -> Demand
kill_usage (KillFlags -> Demand -> Demand) -> KillFlags -> Demand -> Demand
forall a b. (a -> b) -> a -> b
$ KillFlags
    { kf_abs :: Bool
kf_abs         = Bool
True
    , kf_used_once :: Bool
kf_used_once   = Bool
True
    , kf_called_once :: Bool
kf_called_once = Bool
True
    }

-- | Remove all `C_01 :*` info (but not `CM` sub-demands) from the demand
zapUsedOnceDemand :: Demand -> Demand
zapUsedOnceDemand :: Demand -> Demand
zapUsedOnceDemand = KillFlags -> Demand -> Demand
kill_usage (KillFlags -> Demand -> Demand) -> KillFlags -> Demand -> Demand
forall a b. (a -> b) -> a -> b
$ KillFlags
    { kf_abs :: Bool
kf_abs         = Bool
False
    , kf_used_once :: Bool
kf_used_once   = Bool
True
    , kf_called_once :: Bool
kf_called_once = Bool
False
    }

-- | Remove all `C_01 :*` info (but not `CM` sub-demands) from the strictness
--   signature
zapUsedOnceSig :: StrictSig -> StrictSig
zapUsedOnceSig :: StrictSig -> StrictSig
zapUsedOnceSig (StrictSig (DmdType DmdEnv
env [Demand]
ds Divergence
r))
    = DmdType -> StrictSig
StrictSig (DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
env ((Demand -> Demand) -> [Demand] -> [Demand]
forall a b. (a -> b) -> [a] -> [b]
map Demand -> Demand
zapUsedOnceDemand [Demand]
ds) Divergence
r)

data KillFlags = KillFlags
    { KillFlags -> Bool
kf_abs         :: Bool
    , KillFlags -> Bool
kf_used_once   :: Bool
    , KillFlags -> Bool
kf_called_once :: Bool
    }

kill_usage_card :: KillFlags -> Card -> Card
kill_usage_card :: KillFlags -> Card -> Card
kill_usage_card KillFlags
kfs Card
C_00 | KillFlags -> Bool
kf_abs KillFlags
kfs       = Card
C_0N
kill_usage_card KillFlags
kfs Card
C_10 | KillFlags -> Bool
kf_abs KillFlags
kfs       = Card
C_1N
kill_usage_card KillFlags
kfs Card
C_01 | KillFlags -> Bool
kf_used_once KillFlags
kfs = Card
C_0N
kill_usage_card KillFlags
kfs Card
C_11 | KillFlags -> Bool
kf_used_once KillFlags
kfs = Card
C_1N
kill_usage_card KillFlags
_   Card
n                       = Card
n

kill_usage :: KillFlags -> Demand -> Demand
kill_usage :: KillFlags -> Demand -> Demand
kill_usage KillFlags
kfs (Card
n :* SubDemand
sd) = KillFlags -> Card -> Card
kill_usage_card KillFlags
kfs Card
n Card -> SubDemand -> Demand
:* KillFlags -> SubDemand -> SubDemand
kill_usage_sd KillFlags
kfs SubDemand
sd

kill_usage_sd :: KillFlags -> SubDemand -> SubDemand
kill_usage_sd :: KillFlags -> SubDemand -> SubDemand
kill_usage_sd KillFlags
kfs (Call Card
n SubDemand
sd)
  | KillFlags -> Bool
kf_called_once KillFlags
kfs      = Card -> SubDemand -> SubDemand
mkCall (Card -> Card -> Card
lubCard Card
C_1N Card
n) (KillFlags -> SubDemand -> SubDemand
kill_usage_sd KillFlags
kfs SubDemand
sd)
  | Bool
otherwise               = Card -> SubDemand -> SubDemand
mkCall Card
n                (KillFlags -> SubDemand -> SubDemand
kill_usage_sd KillFlags
kfs SubDemand
sd)
kill_usage_sd KillFlags
kfs (Prod [Demand]
ds) = [Demand] -> SubDemand
Prod ((Demand -> Demand) -> [Demand] -> [Demand]
forall a b. (a -> b) -> [a] -> [b]
map (KillFlags -> Demand -> Demand
kill_usage KillFlags
kfs) [Demand]
ds)
kill_usage_sd KillFlags
_   SubDemand
sd        = SubDemand
sd

{- *********************************************************************
*                                                                      *
               TypeShape and demand trimming
*                                                                      *
********************************************************************* -}


data TypeShape -- See Note [Trimming a demand to a type]
               --     in GHC.Core.Opt.DmdAnal
  = TsFun TypeShape
  | TsProd [TypeShape]
  | TsUnk

trimToType :: Demand -> TypeShape -> Demand
-- See Note [Trimming a demand to a type] in GHC.Core.Opt.DmdAnal
trimToType :: Demand -> TypeShape -> Demand
trimToType (Card
n :* SubDemand
sd) TypeShape
ts
  = Card
n Card -> SubDemand -> Demand
:* SubDemand -> TypeShape -> SubDemand
go SubDemand
sd TypeShape
ts
  where
    go :: SubDemand -> TypeShape -> SubDemand
go (Prod [Demand]
ds)   (TsProd [TypeShape]
tss)
      | [Demand] -> [TypeShape] -> Bool
forall a b. [a] -> [b] -> Bool
equalLength [Demand]
ds [TypeShape]
tss    = [Demand] -> SubDemand
Prod ((Demand -> TypeShape -> Demand)
-> [Demand] -> [TypeShape] -> [Demand]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Demand -> TypeShape -> Demand
trimToType [Demand]
ds [TypeShape]
tss)
    go (Call Card
n SubDemand
sd) (TsFun TypeShape
ts) = Card -> SubDemand -> SubDemand
mkCall Card
n (SubDemand -> TypeShape -> SubDemand
go SubDemand
sd TypeShape
ts)
    go sd :: SubDemand
sd@Poly{}   TypeShape
_          = SubDemand
sd
    go SubDemand
_           TypeShape
_          = SubDemand
topSubDmd

{-
************************************************************************
*                                                                      *
                     'seq'ing demands
*                                                                      *
************************************************************************
-}

seqDemand :: Demand -> ()
seqDemand :: Demand -> ()
seqDemand (Card
_ :* SubDemand
sd) = SubDemand -> ()
seqSubDemand SubDemand
sd

seqSubDemand :: SubDemand -> ()
seqSubDemand :: SubDemand -> ()
seqSubDemand (Prod [Demand]
ds)   = [Demand] -> ()
seqDemandList [Demand]
ds
seqSubDemand (Call Card
_ SubDemand
sd) = SubDemand -> ()
seqSubDemand SubDemand
sd
seqSubDemand (Poly Card
_)    = ()

seqDemandList :: [Demand] -> ()
seqDemandList :: [Demand] -> ()
seqDemandList = (Demand -> () -> ()) -> () -> [Demand] -> ()
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (() -> () -> ()
seq (() -> () -> ()) -> (Demand -> ()) -> Demand -> () -> ()
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Demand -> ()
seqDemand) ()

seqDmdType :: DmdType -> ()
seqDmdType :: DmdType -> ()
seqDmdType (DmdType DmdEnv
env [Demand]
ds Divergence
res) =
  DmdEnv -> ()
seqDmdEnv DmdEnv
env () -> () -> ()
`seq` [Demand] -> ()
seqDemandList [Demand]
ds () -> () -> ()
`seq` Divergence
res Divergence -> () -> ()
`seq` ()

seqDmdEnv :: DmdEnv -> ()
seqDmdEnv :: DmdEnv -> ()
seqDmdEnv DmdEnv
env = ([Demand] -> ()) -> DmdEnv -> ()
forall elt key. ([elt] -> ()) -> UniqFM key elt -> ()
seqEltsUFM [Demand] -> ()
seqDemandList DmdEnv
env

seqStrictSig :: StrictSig -> ()
seqStrictSig :: StrictSig -> ()
seqStrictSig (StrictSig DmdType
ty) = DmdType -> ()
seqDmdType DmdType
ty

{-
************************************************************************
*                                                                      *
                     Outputable and Binary instances
*                                                                      *
************************************************************************
-}

{- Note [Demand notation]
~~~~~~~~~~~~~~~~~~~~~~~~~
This Note should be kept up to date with the documentation of `-fstrictness`
in the user's guide.

For pretty-printing demands, we use quite a compact notation with some
abbreviations. Here's the BNF:

  card ::= B    {}
        |  A    {0}
        |  M    {0,1}
        |  L    {0,1,n}
        |  1    {1}
        |  S    {1,n}

  d    ::= card sd                  The :* constructor, just juxtaposition
        |  card                     abbreviation: Same as "card card",
                                                  in code @polyDmd card@

  sd   ::= card                     @Poly card@
        |  P(d,d,..)                @Prod [d1,d2,..]@
        |  Ccard(sd)                @Call card sd@

So, L can denote a 'Card', polymorphic 'SubDemand' or polymorphic 'Demand',
but it's always clear from context which "overload" is meant. It's like
return-type inference of e.g. 'read'.

Examples are in the haddock for 'Demand'.

This is the syntax for demand signatures:

  div ::= <empty>      topDiv
       |  x            exnDiv
       |  b            botDiv

  sig ::= {x->dx,y->dy,z->dz...}<d1><d2><d3>...<dn>div
                  ^              ^   ^   ^      ^   ^
                  |              |   |   |      |   |
                  |              \---+---+------/   |
                  |                  |              |
             demand on free        demand on      divergence
               variables           arguments      information
           (omitted if empty)                     (omitted if
                                                no information)


-}

-- | See Note [Demand notation]
-- Current syntax was discussed in #19016.
instance Outputable Card where
  ppr :: Card -> SDoc
ppr Card
C_00 = Char -> SDoc
char Char
'A' -- "Absent"
  ppr Card
C_01 = Char -> SDoc
char Char
'M' -- "Maybe"
  ppr Card
C_0N = Char -> SDoc
char Char
'L' -- "Lazy"
  ppr Card
C_11 = Char -> SDoc
char Char
'1' -- "exactly 1"
  ppr Card
C_1N = Char -> SDoc
char Char
'S' -- "Strict"
  ppr Card
C_10 = Char -> SDoc
char Char
'B' -- "Bottom"

-- | See Note [Demand notation]
instance Outputable Demand where
  ppr :: Demand -> SDoc
ppr dmd :: Demand
dmd@(Card
n :* SubDemand
sd)
    | Card -> Bool
isAbs Card
n          = Card -> SDoc
forall a. Outputable a => a -> SDoc
ppr Card
n   -- If absent, sd is arbitrary
    | Demand
dmd Demand -> Demand -> Bool
forall a. Eq a => a -> a -> Bool
== Card -> Demand
polyDmd Card
n = Card -> SDoc
forall a. Outputable a => a -> SDoc
ppr Card
n   -- Print UU as just U
    | Bool
otherwise        = Card -> SDoc
forall a. Outputable a => a -> SDoc
ppr Card
n SDoc -> SDoc -> SDoc
<> SubDemand -> SDoc
forall a. Outputable a => a -> SDoc
ppr SubDemand
sd

-- | See Note [Demand notation]
instance Outputable SubDemand where
  ppr :: SubDemand -> SDoc
ppr (Poly Card
sd)   = Card -> SDoc
forall a. Outputable a => a -> SDoc
ppr Card
sd
  ppr (Call Card
n SubDemand
sd) = Char -> SDoc
char Char
'C' SDoc -> SDoc -> SDoc
<> Card -> SDoc
forall a. Outputable a => a -> SDoc
ppr Card
n SDoc -> SDoc -> SDoc
<> SDoc -> SDoc
parens (SubDemand -> SDoc
forall a. Outputable a => a -> SDoc
ppr SubDemand
sd)
  ppr (Prod [Demand]
ds)   = Char -> SDoc
char Char
'P' SDoc -> SDoc -> SDoc
<> SDoc -> SDoc
parens ([Demand] -> SDoc
forall {a}. Outputable a => [a] -> SDoc
fields [Demand]
ds)
    where
      fields :: [a] -> SDoc
fields []     = SDoc
empty
      fields [a
x]    = a -> SDoc
forall a. Outputable a => a -> SDoc
ppr a
x
      fields (a
x:[a]
xs) = a -> SDoc
forall a. Outputable a => a -> SDoc
ppr a
x SDoc -> SDoc -> SDoc
<> Char -> SDoc
char Char
',' SDoc -> SDoc -> SDoc
<> [a] -> SDoc
fields [a]
xs

instance Outputable Divergence where
  ppr :: Divergence -> SDoc
ppr Divergence
Diverges = Char -> SDoc
char Char
'b' -- for (b)ottom
  ppr Divergence
ExnOrDiv = Char -> SDoc
char Char
'x' -- for e(x)ception
  ppr Divergence
Dunno    = SDoc
empty

instance Outputable DmdType where
  ppr :: DmdType -> SDoc
ppr (DmdType DmdEnv
fv [Demand]
ds Divergence
res)
    = [SDoc] -> SDoc
hsep [[SDoc] -> SDoc
hcat ((Demand -> SDoc) -> [Demand] -> [SDoc]
forall a b. (a -> b) -> [a] -> [b]
map (SDoc -> SDoc
angleBrackets (SDoc -> SDoc) -> (Demand -> SDoc) -> Demand -> SDoc
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Demand -> SDoc
forall a. Outputable a => a -> SDoc
ppr) [Demand]
ds) SDoc -> SDoc -> SDoc
<> Divergence -> SDoc
forall a. Outputable a => a -> SDoc
ppr Divergence
res,
            if [(Unique, Demand)] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [(Unique, Demand)]
fv_elts then SDoc
empty
            else SDoc -> SDoc
braces ([SDoc] -> SDoc
fsep (((Unique, Demand) -> SDoc) -> [(Unique, Demand)] -> [SDoc]
forall a b. (a -> b) -> [a] -> [b]
map (Unique, Demand) -> SDoc
forall {a} {a}. (Outputable a, Outputable a) => (a, a) -> SDoc
pp_elt [(Unique, Demand)]
fv_elts))]
    where
      pp_elt :: (a, a) -> SDoc
pp_elt (a
uniq, a
dmd) = a -> SDoc
forall a. Outputable a => a -> SDoc
ppr a
uniq SDoc -> SDoc -> SDoc
<> String -> SDoc
text String
"->" SDoc -> SDoc -> SDoc
<> a -> SDoc
forall a. Outputable a => a -> SDoc
ppr a
dmd
      fv_elts :: [(Unique, Demand)]
fv_elts = DmdEnv -> [(Unique, Demand)]
forall key elt. UniqFM key elt -> [(Unique, elt)]
nonDetUFMToList DmdEnv
fv
        -- It's OK to use nonDetUFMToList here because we only do it for
        -- pretty printing

instance Outputable StrictSig where
   ppr :: StrictSig -> SDoc
ppr (StrictSig DmdType
ty) = DmdType -> SDoc
forall a. Outputable a => a -> SDoc
ppr DmdType
ty

instance Outputable TypeShape where
  ppr :: TypeShape -> SDoc
ppr TypeShape
TsUnk        = String -> SDoc
text String
"TsUnk"
  ppr (TsFun TypeShape
ts)   = String -> SDoc
text String
"TsFun" SDoc -> SDoc -> SDoc
<> SDoc -> SDoc
parens (TypeShape -> SDoc
forall a. Outputable a => a -> SDoc
ppr TypeShape
ts)
  ppr (TsProd [TypeShape]
tss) = SDoc -> SDoc
parens ([SDoc] -> SDoc
hsep ([SDoc] -> SDoc) -> [SDoc] -> SDoc
forall a b. (a -> b) -> a -> b
$ SDoc -> [SDoc] -> [SDoc]
punctuate SDoc
comma ([SDoc] -> [SDoc]) -> [SDoc] -> [SDoc]
forall a b. (a -> b) -> a -> b
$ (TypeShape -> SDoc) -> [TypeShape] -> [SDoc]
forall a b. (a -> b) -> [a] -> [b]
map TypeShape -> SDoc
forall a. Outputable a => a -> SDoc
ppr [TypeShape]
tss)

instance Binary Card where
  put_ :: BinHandle -> Card -> IO ()
put_ BinHandle
bh Card
C_00 = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
0
  put_ BinHandle
bh Card
C_01 = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
1
  put_ BinHandle
bh Card
C_0N = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
2
  put_ BinHandle
bh Card
C_11 = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
3
  put_ BinHandle
bh Card
C_1N = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
4
  put_ BinHandle
bh Card
C_10 = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
5
  get :: BinHandle -> IO Card
get BinHandle
bh = do
    Word8
h <- BinHandle -> IO Word8
getByte BinHandle
bh
    case Word8
h of
      Word8
0 -> Card -> IO Card
forall (m :: * -> *) a. Monad m => a -> m a
return Card
C_00
      Word8
1 -> Card -> IO Card
forall (m :: * -> *) a. Monad m => a -> m a
return Card
C_01
      Word8
2 -> Card -> IO Card
forall (m :: * -> *) a. Monad m => a -> m a
return Card
C_0N
      Word8
3 -> Card -> IO Card
forall (m :: * -> *) a. Monad m => a -> m a
return Card
C_11
      Word8
4 -> Card -> IO Card
forall (m :: * -> *) a. Monad m => a -> m a
return Card
C_1N
      Word8
5 -> Card -> IO Card
forall (m :: * -> *) a. Monad m => a -> m a
return Card
C_10
      Word8
_ -> String -> SDoc -> IO Card
forall a. HasCallStack => String -> SDoc -> a
pprPanic String
"Binary:Card" (Int -> SDoc
forall a. Outputable a => a -> SDoc
ppr (Word8 -> Int
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word8
h :: Int))

instance Binary Demand where
  put_ :: BinHandle -> Demand -> IO ()
put_ BinHandle
bh (Card
n :* SubDemand
sd) = BinHandle -> Card -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh Card
n IO () -> IO () -> IO ()
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> BinHandle -> SubDemand -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh SubDemand
sd
  get :: BinHandle -> IO Demand
get BinHandle
bh = Card -> SubDemand -> Demand
(:*) (Card -> SubDemand -> Demand)
-> IO Card -> IO (SubDemand -> Demand)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> BinHandle -> IO Card
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh IO (SubDemand -> Demand) -> IO SubDemand -> IO Demand
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> BinHandle -> IO SubDemand
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh

instance Binary SubDemand where
  put_ :: BinHandle -> SubDemand -> IO ()
put_ BinHandle
bh (Poly Card
sd)   = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
0 IO () -> IO () -> IO ()
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> BinHandle -> Card -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh Card
sd
  put_ BinHandle
bh (Call Card
n SubDemand
sd) = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
1 IO () -> IO () -> IO ()
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> BinHandle -> Card -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh Card
n IO () -> IO () -> IO ()
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> BinHandle -> SubDemand -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh SubDemand
sd
  put_ BinHandle
bh (Prod [Demand]
ds)   = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
2 IO () -> IO () -> IO ()
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> BinHandle -> [Demand] -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh [Demand]
ds
  get :: BinHandle -> IO SubDemand
get BinHandle
bh = do
    Word8
h <- BinHandle -> IO Word8
getByte BinHandle
bh
    case Word8
h of
      Word8
0 -> Card -> SubDemand
Poly (Card -> SubDemand) -> IO Card -> IO SubDemand
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> BinHandle -> IO Card
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh
      Word8
1 -> Card -> SubDemand -> SubDemand
mkCall (Card -> SubDemand -> SubDemand)
-> IO Card -> IO (SubDemand -> SubDemand)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> BinHandle -> IO Card
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh IO (SubDemand -> SubDemand) -> IO SubDemand -> IO SubDemand
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> BinHandle -> IO SubDemand
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh
      Word8
2 -> [Demand] -> SubDemand
Prod ([Demand] -> SubDemand) -> IO [Demand] -> IO SubDemand
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> BinHandle -> IO [Demand]
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh
      Word8
_ -> String -> SDoc -> IO SubDemand
forall a. HasCallStack => String -> SDoc -> a
pprPanic String
"Binary:SubDemand" (Int -> SDoc
forall a. Outputable a => a -> SDoc
ppr (Word8 -> Int
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word8
h :: Int))

instance Binary StrictSig where
  put_ :: BinHandle -> StrictSig -> IO ()
put_ BinHandle
bh (StrictSig DmdType
aa) = BinHandle -> DmdType -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh DmdType
aa
  get :: BinHandle -> IO StrictSig
get BinHandle
bh = DmdType -> StrictSig
StrictSig (DmdType -> StrictSig) -> IO DmdType -> IO StrictSig
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> BinHandle -> IO DmdType
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh

instance Binary DmdType where
  -- Ignore DmdEnv when spitting out the DmdType
  put_ :: BinHandle -> DmdType -> IO ()
put_ BinHandle
bh (DmdType DmdEnv
_ [Demand]
ds Divergence
dr) = BinHandle -> [Demand] -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh [Demand]
ds IO () -> IO () -> IO ()
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> BinHandle -> Divergence -> IO ()
forall a. Binary a => BinHandle -> a -> IO ()
put_ BinHandle
bh Divergence
dr
  get :: BinHandle -> IO DmdType
get BinHandle
bh = DmdEnv -> [Demand] -> Divergence -> DmdType
DmdType DmdEnv
emptyDmdEnv ([Demand] -> Divergence -> DmdType)
-> IO [Demand] -> IO (Divergence -> DmdType)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> BinHandle -> IO [Demand]
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh IO (Divergence -> DmdType) -> IO Divergence -> IO DmdType
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> BinHandle -> IO Divergence
forall a. Binary a => BinHandle -> IO a
get BinHandle
bh

instance Binary Divergence where
  put_ :: BinHandle -> Divergence -> IO ()
put_ BinHandle
bh Divergence
Dunno    = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
0
  put_ BinHandle
bh Divergence
ExnOrDiv = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
1
  put_ BinHandle
bh Divergence
Diverges = BinHandle -> Word8 -> IO ()
putByte BinHandle
bh Word8
2
  get :: BinHandle -> IO Divergence
get BinHandle
bh = do
    Word8
h <- BinHandle -> IO Word8
getByte BinHandle
bh
    case Word8
h of
      Word8
0 -> Divergence -> IO Divergence
forall (m :: * -> *) a. Monad m => a -> m a
return Divergence
Dunno
      Word8
1 -> Divergence -> IO Divergence
forall (m :: * -> *) a. Monad m => a -> m a
return Divergence
ExnOrDiv
      Word8
2 -> Divergence -> IO Divergence
forall (m :: * -> *) a. Monad m => a -> m a
return Divergence
Diverges
      Word8
_ -> String -> SDoc -> IO Divergence
forall a. HasCallStack => String -> SDoc -> a
pprPanic String
"Binary:Divergence" (Int -> SDoc
forall a. Outputable a => a -> SDoc
ppr (Word8 -> Int
forall a b. (Integral a, Num b) => a -> b
fromIntegral Word8
h :: Int))