55 lines
1.6 KiB
Text
55 lines
1.6 KiB
Text
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import data.list data.nat
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open list nat
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structure unification_constraint := {A : Type} (lhs : A) (rhs : A)
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structure unification_hint := (pattern : unification_constraint) (constraints : list unification_constraint)
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namespace toy
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constants (A : Type.{1}) (f h : A → A) (x y z : A)
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definition g [irreducible] (x y : A) : A := f z
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#unify (g x y), (f z)
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definition toy_hint [unify] (x y : A) : unification_hint :=
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unification_hint.mk (unification_constraint.mk (g x y) (f z)) []
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#unify (g x y), (f z)
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print [unify]
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end toy
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namespace add
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constants (n : ℕ)
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#unify (n + 1), succ n
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definition add_zero_hint [unify] (m n : ℕ) [has_add ℕ] [has_one ℕ] [has_zero ℕ] : unification_hint :=
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unification_hint.mk (unification_constraint.mk (m + 1) (succ n)) [unification_constraint.mk m n]
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#unify (n + 1), (succ n)
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print [unify]
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end add
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namespace canonical
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structure Canonical := (carrier : Type) (op : carrier → carrier)
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attribute Canonical.carrier [irreducible]
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constants (A : Type.{1}) (f : A → A) (x : A)
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definition A_canonical : Canonical := Canonical.mk A f
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#unify (Canonical.carrier A_canonical), A
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definition Canonical_hint [unify] (C : Canonical) : unification_hint :=
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unification_hint.mk (unification_constraint.mk (Canonical.carrier C) A) [unification_constraint.mk C A_canonical]
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-- TODO(dhs): we mark carrier as irreducible and prove A_canonical explicitly to work around the fact that
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-- the default_type_context does not recognize the elaborator metavariables as metavariables,
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-- and so cannot perform the assignment.
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#unify (Canonical.carrier A_canonical), A
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print [unify]
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end canonical
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print [unify] canonical
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