44 lines
2.2 KiB
Text
44 lines
2.2 KiB
Text
new_frontend
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-- set_option syntaxMaxDepth 100
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-- set_option trace.Elab true
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-- set_option trace.Meta true
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-- set_option trace.Meta.synthInstance false
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def adapt1 {m m' σ σ'} {n n' : Type → Type} [MonadFunctor m m' n n'] [MonadStateAdapter σ σ' m m'] : MonadStateAdapter σ σ' n n' :=
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⟨fun split join => monadMap @(fun α => adaptState split join : forall (α : Type), m α → m' α)⟩ -- monadMap (adaptState split join : m α → m' α)⟩
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def adapt2 {m m' σ σ'} {n n' : Type → Type} [MonadFunctor m m' n n'] [MonadStateAdapter σ σ' m m'] : MonadStateAdapter σ σ' n n' :=
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⟨fun split join => monadMap @(fun α => (adaptState split join : m α → m' α))⟩ -- monadMap (adaptState split join : m α → m' α)⟩
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def adapt3 {m m' σ σ'} {n n' : Type → Type} [MonadFunctor m m' n n'] [MonadStateAdapter σ σ' m m'] : MonadStateAdapter σ σ' n n' :=
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⟨fun split join => monadMap (m:=m) (m':=m') (adaptState split join)⟩
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/-
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The following fails because we cannot synthesize the instance
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```
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[MonadFunctorT
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(λ (β : Type), m (?m_1 σ'' α split join β))
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(λ (β : Type), m' (?m_1 σ'' α split join β))
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n
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(λ {α : Type}, n' α)]
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```
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Note that we have an instance `[MonadFunctorT m m' n n']`. The TC procedure performs eta-reduction, and manage to reduce
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`(λ {α : Type}, n' α)` to `n'`, but it cannot eta-reduce the arguments
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```
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(λ (β : Type), m (?m_1 σ'' α split join β))
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(λ (β : Type), m' (?m_1 σ'' α split join β))
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```
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The reduction is blocked by the metavariable applications `(?m_1 σ'' α split join β)`.
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Remark: eta-expansion would also not solve the problem. The TC procedure would convert the instance
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`[MonadFunctorT m m' n n']`
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into
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`[MonadFunctorT (fun β => m β) (fun β => m' β) (fun α => n α) (fun α => n' α)]`
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but it would fail trying to unify
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```
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?m_1 σ'' α split join β =?= β
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```
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since `?m_1` was not created by the TC procedure. It was created by the elaborator.
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-/
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-- def adapt4 {m m' σ σ'} {n n' : Type → Type} [MonadFunctor m m' n n'] [MonadStateAdapter σ σ' m m'] : MonadStateAdapter σ σ' n n' :=
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-- ⟨fun split join => monadMap (adaptState split join : m _ → m' _)⟩ -- monadMap (adaptState split join : m α → m' α)⟩
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