package mc2

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Resolution proofs

This modules defines functions to create and manipulate resolution proofs.

Type declarations

type t

Lazy type for proof trees. Proofs are persistent objects, and can be extended to proof nodes using functions defined later.

and node = {
  1. conclusion : Mc2_core__.Solver_types.clause;

    The conclusion of the proof

  2. step : step;

    The reasoning step used to prove the conclusion


A proof can be expanded into a proof node, which show the first step of the proof.

and step =
  1. | Hypothesis

    The conclusion is a user-provided hypothesis

  2. | Assumption

    The conclusion has been locally assumed by the user


A proof can be expanded into a proof node, which show the first step of the proof.

The type of reasoning steps allowed in a proof.

val conclusion : node -> Mc2_core__.Solver_types.clause
val step : node -> step

Proof building functions

val prove : Mc2_core__.Solver_types.clause -> t

Given a clause, return a proof of that clause.

  • raises Util.Error

    if it does not succeed.

val prove_unsat : Mc2_core__.Solver_types.clause -> t

Given a conflict clause c, returns a proof of the empty clause.

  • raises Util.Error

    if it does not succeed

val prove_atom : Mc2_core__.Solver_types.atom -> t option

Given an atom a, returns a proof of the clause [a] if a is true at level 0

Proof Nodes

val is_leaf : step -> bool

Returns whether the proof node is a leaf, i.e. an hypothesis, an assumption, or a lemma. true if and only if parents returns the empty list.

val expl : step -> string

Returns a short string description for the proof step; for instance "hypothesis" for a Hypothesis (it currently returns the variant name in lowercase).

val parents : step -> t list

Returns the parents of a proof node.

Proof Manipulation

val expand : t -> node

Return the proof step at the root of a given proof.

val fold : ('a -> node -> 'a) -> 'a -> t -> 'a

fold f acc p, fold f over the proof p and all its node. It is guaranteed that f is executed exactly once on each proof node in the tree, and that the execution of f on a proof node happens after the execution on the parents of the nodes.

val iter : (node -> unit) -> t -> unit
val unsat_core : t -> Mc2_core__.Solver_types.clause list

Returns the unsat_core of the given proof, i.e the lists of conclusions of all leafs of the proof. More efficient than using the fold function since it has access to the internal representation of proofs

val debug_step : step CCFormat.printer


val check_step : t -> unit

Check only this proof step

val check : t -> unit

Check the contents of a proof. Mainly for internal use


module H : CCHashtbl.S with type key = Mc2_core__.Solver_types.clause

Hashtable over clauses. Uses the details of the internal representation to achieve the best performances, however hashtables from this module become invalid when solving is restarted, so they should only be live during inspection of a single proof.


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