Safe Haskell | None |
---|---|

Language | Haskell2010 |

- tcMatchTy :: Type -> Type -> Maybe TCvSubst
- tcMatchTyKi :: Type -> Type -> Maybe TCvSubst
- tcMatchTys :: [Type] -> [Type] -> Maybe TCvSubst
- tcMatchTyKis :: [Type] -> [Type] -> Maybe TCvSubst
- tcMatchTyX :: TCvSubst -> Type -> Type -> Maybe TCvSubst
- tcMatchTysX :: TCvSubst -> [Type] -> [Type] -> Maybe TCvSubst
- tcMatchTyKisX :: TCvSubst -> [Type] -> [Type] -> Maybe TCvSubst
- ruleMatchTyKiX :: TyCoVarSet -> RnEnv2 -> TvSubstEnv -> Type -> Type -> Maybe TvSubstEnv
- roughMatchTcs :: [Type] -> [Maybe Name]
- instanceCantMatch :: [Maybe Name] -> [Maybe Name] -> Bool
- typesCantMatch :: [(Type, Type)] -> Bool
- tcUnifyTy :: Type -> Type -> Maybe TCvSubst
- tcUnifyTyKi :: Type -> Type -> Maybe TCvSubst
- tcUnifyTys :: (TyCoVar -> BindFlag) -> [Type] -> [Type] -> Maybe TCvSubst
- tcUnifyTyKis :: (TyCoVar -> BindFlag) -> [Type] -> [Type] -> Maybe TCvSubst
- tcUnifyTysFG :: (TyVar -> BindFlag) -> [Type] -> [Type] -> UnifyResult
- tcUnifyTyWithTFs :: Bool -> Type -> Type -> Maybe TCvSubst
- data BindFlag
- type UnifyResult = UnifyResultM TCvSubst
- data UnifyResultM a
- = Unifiable a
- | MaybeApart a
- | SurelyApart

- liftCoMatch :: TyCoVarSet -> Type -> Coercion -> Maybe LiftingContext

# Documentation

tcMatchTy :: Type -> Type -> Maybe TCvSubst #

`tcMatchTy t1 t2`

produces a substitution (over fvs(t1))
`s`

such that `s(t1)`

equals `t2`

.
The returned substitution might bind coercion variables,
if the variable is an argument to a GADT constructor.

Precondition: typeKind ty1 `eqType`

typeKind ty2

We don't pass in a set of "template variables" to be bound by the match, because tcMatchTy (and similar functions) are always used on top-level types, so we can bind any of the free variables of the LHS.

tcMatchTyKi :: Type -> Type -> Maybe TCvSubst #

Like `tcMatchTy`

, but allows the kinds of the types to differ,
and thus matches them as well.

:: [Type] | Template |

-> [Type] | Target |

-> Maybe TCvSubst | One-shot; in principle the template variables could be free in the target |

Like `tcMatchTy`

but over a list of types.

Like `tcMatchTyKi`

but over a list of types.

This is similar to `tcMatchTy`

, but extends a substitution

:: TCvSubst | Substitution to extend |

-> [Type] | Template |

-> [Type] | Target |

-> Maybe TCvSubst | One-shot substitution |

Like `tcMatchTys`

, but extending a substitution

:: TCvSubst | Substitution to extend |

-> [Type] | Template |

-> [Type] | Target |

-> Maybe TCvSubst | One-shot substitution |

Like `tcMatchTyKis`

, but extending a substitution

:: TyCoVarSet | template variables |

-> RnEnv2 | |

-> TvSubstEnv | type substitution to extend |

-> Type | Template |

-> Type | Target |

-> Maybe TvSubstEnv |

This one is called from the expression matcher, which already has a MatchEnv in hand

# Rough matching

roughMatchTcs :: [Type] -> [Maybe Name] #

typesCantMatch :: [(Type, Type)] -> Bool #

Given a list of pairs of types, are any two members of a pair surely apart, even after arbitrary type function evaluation and substitution?

tcUnifyTy :: Type -> Type -> Maybe TCvSubst #

Simple unification of two types; all type variables are bindable Precondition: the kinds are already equal

tcUnifyTyKis :: (TyCoVar -> BindFlag) -> [Type] -> [Type] -> Maybe TCvSubst #

Like `tcUnifyTys`

but also unifies the kinds

tcUnifyTysFG :: (TyVar -> BindFlag) -> [Type] -> [Type] -> UnifyResult #

`tcUnifyTysFG bind_tv tys1 tys2`

attepts to find a substitution `s`

(whose
domain elements all respond `BindMe`

to `bind_tv`

) such that
`s(tys1)`

and that of `s(tys2)`

are equal, as witnessed by the returned
Coercions. This version requires that the kinds of the types are the same,
if you unify left-to-right.

:: Bool | True = do two-way unification; False = do one-way matching. See end of sec 5.2 from the paper |

-> Type | |

-> Type | |

-> Maybe TCvSubst |

Unify two types, treating type family applications as possibly unifying with anything and looking through injective type family applications. Precondition: kinds are the same

type UnifyResult = UnifyResultM TCvSubst #

data UnifyResultM a #

liftCoMatch :: TyCoVarSet -> Type -> Coercion -> Maybe LiftingContext #

`liftCoMatch`

is sort of inverse to `liftCoSubst`

. In particular, if
`liftCoMatch vars ty co == Just s`

, then `listCoSubst s ty == co`

,
where `==`

there means that the result of `liftCoSubst`

has the same
type as the original co; but may be different under the hood.
That is, it matches a type against a coercion of the same
"shape", and returns a lifting substitution which could have been
used to produce the given coercion from the given type.
Note that this function is incomplete -- it might return Nothing
when there does indeed exist a possible lifting context.

This function is incomplete in that it doesn't respect the equality
in `eqType`

. That is, it's possible that this will succeed for t1 and
fail for t2, even when t1 `eqType`

t2. That's because it depends on
there being a very similar structure between the type and the coercion.
This incompleteness shouldn't be all that surprising, especially because
it depends on the structure of the coercion, which is a silly thing to do.

The lifting context produced doesn't have to be exacting in the roles of the mappings. This is because any use of the lifting context will also require a desired role. Thus, this algorithm prefers mapping to nominal coercions where it can do so.