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76 lines
2.9 KiB
OCaml
76 lines
2.9 KiB
OCaml
(*
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MSAT is free software, using the Apache license, see file LICENSE
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Copyright 2014 Guillaume Bury
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Copyright 2014 Simon Cruanes
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*)
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module type S = sig
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(** Signature for a module handling proof by resolution from sat solving traces *)
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(** {3 Type declarations} *)
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exception Insuficient_hyps
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(** Raised when a complete resolution derivation cannot be found using the current hypotheses. *)
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type atom
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type clause
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type lemma
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(** Abstract types for atoms, clauses and theoriy-specific lemmas *)
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type proof_node = {
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conclusion : clause;
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step : step;
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}
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and proof = unit -> proof_node
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and step =
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| Hypothesis
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| Lemma of lemma
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| Resolution of proof * proof * atom
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(** Lazy type for proof trees. *)
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(** {3 Resolution helpers} *)
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val to_list : clause -> atom list
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(** Returns the sorted list of atoms of a clause. *)
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val merge : atom list -> atom list -> atom list
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(** Merge two sorted atom list using a suitable comparison function. *)
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val resolve : atom list -> atom list * atom list
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(** Performs a "resolution step" on a sorted list of atoms.
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[resolve (List.merge l1 l2)] where [l1] and [l2] are sorted atom lists should return the pair
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[\[a\], l'], where [l'] is the result of the resolution of [l1] and [l2] over [a]. *)
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(** {3 Proof building functions} *)
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val has_been_proved : clause -> bool
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(** Returns [true] if the clause is part of the current proof graph. This function does not alter
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the proof graph (contrary to [is_proven]). *)
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val is_proven : clause -> bool
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(** Checks if the given clause has a derivation in the current state. Whatever the result,
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new proven clauses (including the given clause) may be added to the proof graph. In particular,
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hyptohesis and theory lemmas always have trivial derivations, and as such [is_proven c] (where [c]
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is a hypothesis or lemma) will always return [true] and add it to the proof graph. *)
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val prove : clause -> unit
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(** Same as 'learn', but works on single clauses instead of vectors. *)
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val learn : clause Vec.t -> unit
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(** Learn and build proofs for the clause in the vector. Clauses in the vector should be in the order they were learned. *)
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val assert_can_prove_unsat : clause -> unit
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(** [assert_can_prove_unsat c] tries and prove the empty clause from [c]. [c] may be a learnt clause not yet proved.
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@raise Insuficient_hyps if it is impossible. *)
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val prove_unsat : clause -> proof
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(** Given a conflict clause [c], returns a proof of the empty clause. Same as [assert_can_prove_unsat] but returns
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the proof if it succeeds.
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@raise Insuficient_hyps if it does not succeed. *)
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val unsat_core : proof -> clause list
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(** Returns the unsat_core of the given proof, i.e the lists of conclusions of all leafs of the proof. *)
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val print_dot : Format.formatter -> proof -> unit
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(** Print the given proof in dot format on the given formatter. *)
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end
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