2 % (c) The University of Glasgow 2006
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6 {-# OPTIONS_GHC -w #-}
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11 #include "HsVersions.h"
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13 import Unify ( tcMatchTy )
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26 %************************************************************************
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28 Optimising coercions
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30 %************************************************************************
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32 Note [Subtle shadowing in coercions]
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33 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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34 Supose we optimising a coercion
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35 optCoercion (forall (co_X5:t1~t2). ...co_B1...)
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36 The co_X5 is a wild-card; the bound variable of a coercion for-all
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37 should never appear in the body of the forall. Indeed we often
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39 optCoercion ( (t1~t2) => ...co_B1... )
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41 Just because it's a wild-card doesn't mean we are free to choose
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42 whatever variable we like. For example it'd be wrong for optCoercion
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44 forall (co_B1:t1~t2). ...co_B1...
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45 because now the co_B1 (which is really free) has been captured, and
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46 subsequent substitutions will go wrong. That's why we can't use
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47 mkCoPredTy in the ForAll case, where this note appears.
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50 optCoercion :: TvSubst -> Coercion -> NormalCo
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51 -- ^ optCoercion applies a substitution to a coercion,
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52 -- *and* optimises it to reduce its size
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53 optCoercion env co = opt_co env False co
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55 type NormalCo = Coercion
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57 -- * The substitution has been fully applied
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58 -- * For trans coercions (co1 `trans` co2)
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59 -- co1 is not a trans, and neither co1 nor co2 is identity
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60 -- * If the coercion is the identity, it has no CoVars of CoTyCons in it (just types)
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62 type NormalNonIdCo = NormalCo -- Extra invariant: not the identity
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64 opt_co, opt_co' :: TvSubst
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65 -> Bool -- True <=> return (sym co)
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72 -- = pprTrace "opt_co {" (ppr sym <+> ppr co) $
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74 -- pprTrace "opt_co done }" (ppr co1)
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75 -- WARN( not same_co_kind, ppr co <+> dcolon <+> pprEqPred (s1,t1)
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76 -- $$ ppr co1 <+> dcolon <+> pprEqPred (s2,t2) )
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77 = WARN( not (coreEqType co1 simple_result),
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78 (text "env=" <+> ppr env) $$
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79 (text "input=" <+> ppr co) $$
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80 (text "simple=" <+> ppr simple_result) $$
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81 (text "opt=" <+> ppr co1) )
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84 co1 = opt_co' env sym co
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85 same_co_kind = s1 `coreEqType` s2 && t1 `coreEqType` t2
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86 (s,t) = coercionKind (substTy env co)
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87 (s1,t1) | sym = (t,s)
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89 (s2,t2) = coercionKind co1
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91 simple_result | sym = mkSymCoercion (substTy env co)
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92 | otherwise = substTy env co
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95 opt_co' env sym (AppTy ty1 ty2) = mkAppTy (opt_co env sym ty1) (opt_co env sym ty2)
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96 opt_co' env sym (FunTy ty1 ty2) = FunTy (opt_co env sym ty1) (opt_co env sym ty2)
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97 opt_co' env sym (PredTy (ClassP cls tys)) = PredTy (ClassP cls (map (opt_co env sym) tys))
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98 opt_co' env sym (PredTy (IParam n ty)) = PredTy (IParam n (opt_co env sym ty))
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99 opt_co' _ _ co@(PredTy (EqPred {})) = pprPanic "optCoercion" (ppr co)
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101 opt_co' env sym co@(TyVarTy tv)
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102 | Just ty <- lookupTyVar env tv = opt_co' (zapTvSubstEnv env) sym ty
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103 | not (isCoVar tv) = co -- Identity; does not mention a CoVar
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104 | ty1 `coreEqType` ty2 = ty1 -- Identity; ..ditto..
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106 | otherwise = mkSymCoercion co
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108 (ty1,ty2) = coVarKind tv
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110 opt_co' env sym (ForAllTy tv cor)
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111 | isTyVar tv = case substTyVarBndr env tv of
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112 (env', tv') -> ForAllTy tv' (opt_co' env' sym cor)
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114 opt_co' env sym co@(ForAllTy co_var cor)
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116 = WARN( co_var `elemVarSet` tyVarsOfType cor, ppr co )
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117 ForAllTy co_var' cor'
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119 (co1,co2) = coVarKind co_var
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120 co1' = opt_co' env sym co1
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121 co2' = opt_co' env sym co2
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122 cor' = opt_co' env sym cor
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123 co_var' = uniqAway (getTvInScope env) (mkWildCoVar (mkCoKind co1' co2'))
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124 -- See Note [Subtle shadowing in coercions]
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126 opt_co' env sym (TyConApp tc cos)
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127 | Just (arity, desc) <- isCoercionTyCon_maybe tc
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128 = mkAppTys (opt_co_tc_app env sym tc desc (take arity cos))
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129 (map (opt_co env sym) (drop arity cos))
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131 = TyConApp tc (map (opt_co env sym) cos)
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134 opt_co_tc_app :: TvSubst -> Bool -> TyCon -> CoTyConDesc -> [Coercion] -> NormalCo
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135 -- Used for CoercionTyCons only
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136 -- Arguments are *not* already simplified/substituted
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137 opt_co_tc_app env sym tc desc cos
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139 CoAxiom {} -- Do *not* push sym inside top-level axioms
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140 -- e.g. if g is a top-level axiom
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142 -- Then (sym (g ty)) /= g (sym ty) !!
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143 | sym -> mkSymCoercion the_co
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144 | otherwise -> the_co
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146 the_co = TyConApp tc (map (opt_co env False) cos)
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147 -- Note that the_co does *not* have sym pushed into it
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150 | sym -> opt_trans opt_co2 opt_co1 -- sym (g `o` h) = sym h `o` sym g
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151 | otherwise -> opt_trans opt_co1 opt_co2
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154 | sym -> mkUnsafeCoercion ty2' ty1'
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155 | otherwise -> mkUnsafeCoercion ty1' ty2'
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157 CoSym -> opt_co env (not sym) co1
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158 CoLeft -> opt_lr fst
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159 CoRight -> opt_lr snd
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160 CoCsel1 -> opt_csel fstOf3
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161 CoCsel2 -> opt_csel sndOf3
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162 CoCselR -> opt_csel thirdOf3
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164 CoInst -- See if the first arg is already a forall
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165 -- ...then we can just extend the current substitution
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166 | Just (tv, co1_body) <- splitForAllTy_maybe co1
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167 -> opt_co (extendTvSubst env tv ty2') sym co1_body
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169 -- See if is *now* a forall
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170 | Just (tv, opt_co1_body) <- splitForAllTy_maybe opt_co1
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171 -> substTyWith [tv] [ty2'] opt_co1_body -- An inefficient one-variable substitution
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174 -> TyConApp tc [opt_co1, ty2']
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180 ty1' = substTy env co1
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181 ty2' = substTy env co2
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183 -- These opt_cos have the sym pushed into them
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184 opt_co1 = opt_co env sym co1
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185 opt_co2 = opt_co env sym co2
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187 the_unary_opt_co = TyConApp tc [opt_co1]
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189 opt_lr sel = case splitAppTy_maybe opt_co1 of
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190 Nothing -> the_unary_opt_co
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192 opt_csel sel = case splitCoPredTy_maybe opt_co1 of
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193 Nothing -> the_unary_opt_co
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197 opt_transL :: [NormalCo] -> [NormalCo] -> [NormalCo]
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198 opt_transL = zipWith opt_trans
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200 opt_trans :: NormalCo -> NormalCo -> NormalCo
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202 | isIdNormCo co1 = co2
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203 | otherwise = opt_trans1 co1 co2
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205 opt_trans1 :: NormalNonIdCo -> NormalCo -> NormalCo
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206 -- First arg is not the identity
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208 | isIdNormCo co2 = co1
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209 | otherwise = opt_trans2 co1 co2
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211 opt_trans2 :: NormalNonIdCo -> NormalNonIdCo -> NormalCo
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212 -- Neither arg is the identity
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213 opt_trans2 (TyConApp tc [co1a,co1b]) co2
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214 | tc `hasKey` transCoercionTyConKey
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215 = opt_trans1 co1a (opt_trans2 co1b co2)
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217 opt_trans2 co1 co2
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218 | Just co <- opt_trans_rule co1 co2
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221 opt_trans2 co1 (TyConApp tc [co2a,co2b])
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222 | tc `hasKey` transCoercionTyConKey
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223 , Just co1_2a <- opt_trans_rule co1 co2a
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224 = if isIdNormCo co1_2a
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226 else opt_trans2 co1_2a co2b
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229 = mkTransCoercion co1 co2
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232 opt_trans_rule :: NormalNonIdCo -> NormalNonIdCo -> Maybe NormalCo
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233 opt_trans_rule (TyConApp tc1 args1) (TyConApp tc2 args2)
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235 = case isCoercionTyCon_maybe tc1 of
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237 -> Just (TyConApp tc1 (opt_transL args1 args2))
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238 Just (arity, desc)
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239 | arity == length args1
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240 -> opt_trans_rule_equal_tc desc args1 args2
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242 -> case opt_trans_rule_equal_tc desc
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243 (take arity args1)
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244 (take arity args2) of
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245 Just co -> Just $ mkAppTys co $
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246 opt_transL (drop arity args1) (drop arity args2)
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247 Nothing -> Nothing
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249 -- Push transitivity inside apply
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250 opt_trans_rule co1 co2
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251 | Just (co1a, co1b) <- splitAppTy_maybe co1
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252 , Just (co2a, co2b) <- etaApp_maybe co2
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253 = Just (mkAppTy (opt_trans co1a co2a) (opt_trans co1b co2b))
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255 | Just (co2a, co2b) <- splitAppTy_maybe co2
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256 , Just (co1a, co1b) <- etaApp_maybe co1
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257 = Just (mkAppTy (opt_trans co1a co2a) (opt_trans co1b co2b))
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259 -- Push transitivity inside (s~t)=>r
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260 -- We re-use the CoVar rather than using mkCoPredTy
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261 -- See Note [Subtle shadowing in coercions]
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262 opt_trans_rule co1 co2
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263 | Just (cv1,r1) <- splitForAllTy_maybe co1
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265 , Just (s1,t1) <- coVarKind_maybe cv1
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266 , Just (s2,t2,r2) <- etaCoPred_maybe co2
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267 = Just (ForAllTy (mkCoVar (coVarName cv1) (mkCoKind (opt_trans s1 s2) (opt_trans t1 t2)))
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270 | Just (cv2,r2) <- splitForAllTy_maybe co2
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272 , Just (s2,t2) <- coVarKind_maybe cv2
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273 , Just (s1,t1,r1) <- etaCoPred_maybe co1
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274 = Just (ForAllTy (mkCoVar (coVarName cv2) (mkCoKind (opt_trans s1 s2) (opt_trans t1 t2)))
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277 -- Push transitivity inside forall
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278 opt_trans_rule co1 co2
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279 | Just (tv1,r1) <- splitTypeForAll_maybe co1
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280 , Just (tv2,r2) <- etaForAll_maybe co2
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281 , let r2' = substTyWith [tv2] [TyVarTy tv1] r2
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282 = Just (ForAllTy tv1 (opt_trans2 r1 r2'))
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284 | Just (tv2,r2) <- splitTypeForAll_maybe co2
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285 , Just (tv1,r1) <- etaForAll_maybe co1
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286 , let r1' = substTyWith [tv1] [TyVarTy tv2] r1
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287 = Just (ForAllTy tv1 (opt_trans2 r1' r2))
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289 opt_trans_rule co1 co2
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290 {- Omitting for now, because unsound
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291 | Just (sym1, (ax_tc1, ax1_args, ax_tvs, ax_lhs, ax_rhs)) <- co1_is_axiom_maybe
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292 , Just (sym2, (ax_tc2, ax2_args, _, _, _)) <- co2_is_axiom_maybe
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297 then substTyWith ax_tvs (opt_transL (map mkSymCoercion ax1_args) ax2_args) ax_rhs
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298 else substTyWith ax_tvs (opt_transL ax1_args (map mkSymCoercion ax2_args)) ax_lhs
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301 | Just (sym, (ax_tc, ax_args, ax_tvs, ax_lhs, _)) <- co1_is_axiom_maybe
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302 , Just cos <- matchesAxiomLhs ax_tvs ax_lhs co2
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305 then mkSymCoercion $ TyConApp ax_tc (opt_transL (map mkSymCoercion cos) ax_args)
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306 else TyConApp ax_tc (opt_transL ax_args cos)
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308 | Just (sym, (ax_tc, ax_args, ax_tvs, ax_lhs, _)) <- isAxiom_maybe co2
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309 , Just cos <- matchesAxiomLhs ax_tvs ax_lhs co1
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312 then mkSymCoercion $ TyConApp ax_tc (opt_transL ax_args (map mkSymCoercion cos))
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313 else TyConApp ax_tc (opt_transL cos ax_args)
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315 co1_is_axiom_maybe = isAxiom_maybe co1
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316 co2_is_axiom_maybe = isAxiom_maybe co2
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318 opt_trans_rule co1 co2 -- Identity rule
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319 | (ty1,_) <- coercionKind co1
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320 , (_,ty2) <- coercionKind co2
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321 , ty1 `coreEqType` ty2
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324 opt_trans_rule _ _ = Nothing
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327 isAxiom_maybe :: Coercion -> Maybe (Bool, (TyCon, [Coercion], [TyVar], Type, Type))
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329 | Just (tc, args) <- splitTyConApp_maybe co
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330 , Just (_, desc) <- isCoercionTyCon_maybe tc
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332 CoAxiom { co_ax_tvs = tvs, co_ax_lhs = lhs, co_ax_rhs = rhs }
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333 -> Just (False, (tc, args, tvs, lhs, rhs))
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334 CoSym | (arg1:_) <- args
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335 -> case isAxiom_maybe arg1 of
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337 Just (sym, stuff) -> Just (not sym, stuff)
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342 matchesAxiomLhs :: [TyVar] -> Type -> Type -> Maybe [Type]
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343 matchesAxiomLhs tvs ty_tmpl ty
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344 = case tcMatchTy (mkVarSet tvs) ty_tmpl ty of
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346 Just subst -> Just (map (substTyVar subst) tvs)
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349 opt_trans_rule_equal_tc :: CoTyConDesc -> [Coercion] -> [Coercion] -> Maybe Coercion
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350 -- Rules for Coercion TyCons only
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352 -- Push transitivity inside instantiation
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353 opt_trans_rule_equal_tc desc [co1,ty1] [co2,ty2]
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355 , ty1 `coreEqType` ty2
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356 , co1 `compatible_co` co2
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357 = Just (mkInstCoercion (opt_trans2 co1 co2) ty1)
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359 opt_trans_rule_equal_tc desc [co1] [co2]
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360 | CoLeft <- desc, is_compat = Just (mkLeftCoercion res_co)
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361 | CoRight <- desc, is_compat = Just (mkRightCoercion res_co)
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362 | CoCsel1 <- desc, is_compat = Just (mkCsel1Coercion res_co)
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363 | CoCsel2 <- desc, is_compat = Just (mkCsel2Coercion res_co)
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364 | CoCselR <- desc, is_compat = Just (mkCselRCoercion res_co)
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366 is_compat = co1 `compatible_co` co2
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367 res_co = opt_trans2 co1 co2
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369 opt_trans_rule_equal_tc _ _ _ = Nothing
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372 compatible_co :: Coercion -> Coercion -> Bool
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373 -- Check whether (co1 . co2) will be well-kinded
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374 compatible_co co1 co2
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375 = x1 `coreEqType` x2
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377 (_,x1) = coercionKind co1
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378 (x2,_) = coercionKind co2
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381 etaForAll_maybe :: Coercion -> Maybe (TyVar, Coercion)
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382 -- Try to make the coercion be of form (forall tv. co)
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384 | Just (tv, r) <- splitForAllTy_maybe co
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385 , not (isCoVar tv) -- Check it is a *type* forall, not a (t1~t2)=>co
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388 | (ty1,ty2) <- coercionKind co
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389 , Just (tv1, _) <- splitTypeForAll_maybe ty1
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390 , Just (tv2, _) <- splitTypeForAll_maybe ty2
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391 , tyVarKind tv1 `eqKind` tyVarKind tv2
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392 = Just (tv1, mkInstCoercion co (mkTyVarTy tv1))
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397 etaCoPred_maybe :: Coercion -> Maybe (Coercion, Coercion, Coercion)
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398 etaCoPred_maybe co
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399 | Just (s,t,r) <- splitCoPredTy_maybe co
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402 -- co :: (s1~t1)=>r1 ~ (s2~t2)=>r2
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403 | (ty1,ty2) <- coercionKind co -- We know ty1,ty2 have same kind
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404 , Just (s1,_,_) <- splitCoPredTy_maybe ty1
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405 , Just (s2,_,_) <- splitCoPredTy_maybe ty2
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406 , typeKind s1 `eqKind` typeKind s2 -- t1,t2 have same kinds
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407 = Just (mkCsel1Coercion co, mkCsel2Coercion co, mkCselRCoercion co)
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412 etaApp_maybe :: Coercion -> Maybe (Coercion, Coercion)
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413 -- Split a coercion g :: t1a t1b ~ t2a t2b
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414 -- into (left g, right g) if possible
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416 | Just (co1, co2) <- splitAppTy_maybe co
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419 | (ty1,ty2) <- coercionKind co
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420 , Just (ty1a, _) <- splitAppTy_maybe ty1
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421 , Just (ty2a, _) <- splitAppTy_maybe ty2
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422 , typeKind ty1a `eqKind` typeKind ty2a
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423 = Just (mkLeftCoercion co, mkRightCoercion co)
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429 splitTypeForAll_maybe :: Type -> Maybe (TyVar, Type)
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430 -- Returns Just only for a *type* forall, not a (t1~t2)=>co
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431 splitTypeForAll_maybe ty
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432 | Just (tv, rty) <- splitForAllTy_maybe ty
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440 isIdNormCo :: NormalCo -> Bool
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441 -- Cheap identity test: look for coercions with no coercion variables at all
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442 -- So it'll return False for (sym g `trans` g)
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443 isIdNormCo ty = go ty
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445 go (TyVarTy tv) = not (isCoVar tv)
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446 go (AppTy t1 t2) = go t1 && go t2
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447 go (FunTy t1 t2) = go t1 && go t2
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448 go (ForAllTy tv ty) = go (tyVarKind tv) && go ty
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449 go (TyConApp tc tys) = not (isCoercionTyCon tc) && all go tys
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450 go (PredTy (IParam _ ty)) = go ty
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451 go (PredTy (ClassP _ tys)) = all go tys
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452 go (PredTy (EqPred t1 t2)) = go t1 && go t2
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