/-
Copyright (c) 2016 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import .clause .prover_state .utils
open tactic monad expr list

namespace super

meta def try_unify_eq_l (c : clause) (i : nat) : tactic clause := do
guard $ clause.literal.is_neg (clause.get_lit c i),
qf ← clause.open_metan c c^.num_quants,
match is_eq (qf.1^.get_lit i)^.formula with
| none := failed
| some (lhs, rhs) := do
unify lhs rhs,
ty ← infer_type lhs,
univ ← infer_univ ty,
refl ← return $ app_of_list (const ``eq.refl [univ]) [ty, lhs],
opened ← clause.open_constn qf.1 i,
clause.meta_closure qf.2 $ clause.close_constn (opened.1^.inst refl) opened.2
end

@[super.inf]
meta def unify_eq_inf : inf_decl := inf_decl.mk 40 $ take given, sequence' $ do
i ← given^.selected,
[inf_if_successful 0 given (do u ← try_unify_eq_l given^.c i, return [u])]

meta def has_refl_r (c : clause) : bool :=
list.bor $ do
literal ← c^.get_lits,
guard literal^.is_pos,
match is_eq literal^.formula with
| some (lhs, rhs) := [decidable.to_bool (lhs = rhs)]
| none := []
end

meta def refl_r_pre : prover unit :=
preprocessing_rule $ take new, return $ filter (λc, ¬has_refl_r c^.c) new

end super