+(* Copyright (C) 2005, HELM Team.
+ *
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ *
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ *
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
type equality =
int * (* weight *)
- proof *
+ proof * (* proof *)
(Cic.term * (* type *)
Cic.term * (* left side *)
Cic.term * (* right side *)
and proof =
| NoProof
- | BasicProof of Cic.term
- | ProofBlock of
- Cic.substitution * UriManager.uri *
- (* name, ty, eq_ty, left, right *)
- (Cic.name * Cic.term * Cic.term * Cic.term * Cic.term) *
- (Utils.pos * equality) * proof
- | ProofGoalBlock of proof * equality
- | ProofSymBlock of Cic.term Cic.explicit_named_substitution * proof
-
+ | BasicProof of Cic.term (* already a proof of a goal *)
+ | ProofBlock of (* proof of a rewrite step *)
+ Cic.substitution * UriManager.uri * (* eq_ind or eq_ind_r *)
+ (Cic.name * Cic.term) * Cic.term * (Utils.pos * equality) * proof
+ | ProofGoalBlock of proof * proof
+ (* proof of the new meta, proof of the goal from which this comes *)
+ | ProofSymBlock of Cic.term list * proof (* expl.named subst, proof *)
+ | SubProof of Cic.term * int * proof
+ (* parent proof, subgoal, proof of the subgoal *)
type environment = Cic.metasenv * Cic.context * CicUniv.universe_graph
+(** builds the Cic.term encoded by proof *)
+val build_proof_term: proof -> Cic.term
+
+val string_of_proof: proof -> string
exception MatchingFailure
+(** matching between two terms. Can raise MatchingFailure *)
val matching:
Cic.metasenv -> Cic.context -> Cic.term -> Cic.term ->
CicUniv.universe_graph ->
Cic.substitution * Cic.metasenv * CicUniv.universe_graph
+(**
+ special unification that checks if the two terms are "simple", and in
+ such case should be significantly faster than CicUnification.fo_unif
+*)
val unification:
Cic.metasenv -> Cic.context -> Cic.term -> Cic.term ->
CicUniv.universe_graph ->
Cic.substitution * Cic.metasenv * CicUniv.universe_graph
-(**
- Performs the beta expansion of the term "where" w.r.t. "what",
- i.e. returns the list of all the terms t s.t. "(t what) = where".
-*)
-val beta_expand:
- ?metas_ok:bool -> ?match_only:bool -> Cic.term -> Cic.term -> Cic.term ->
- Cic.context -> Cic.metasenv -> CicUniv.universe_graph ->
- (Cic.term * Cic.substitution * Cic.metasenv * CicUniv.universe_graph) list
-
-
(**
scans the context to find all Declarations "left = right"; returns a
list of tuples (proof, (type, left, right), newmetas). Uses
fresh metas...
*)
val find_equalities:
- ?eq_uri:UriManager.uri -> Cic.context -> ProofEngineTypes.proof ->
- equality list * int
+ Cic.context -> ProofEngineTypes.proof -> int list * equality list * int
-
-exception TermIsNotAnEquality;;
+(**
+ searches the library for equalities that can be applied to the current goal
+*)
+val find_library_equalities:
+ HMysql.dbd -> Cic.context -> ProofEngineTypes.status -> int ->
+ UriManager.UriSet.t * (UriManager.uri * equality) list * int
(**
- raises TermIsNotAnEquality if term is not an equation.
- The first Cic.term is a proof of the equation
+ searches the library for theorems that are not equalities (returned by the
+ function above)
*)
-val equality_of_term: ?eq_uri:UriManager.uri -> Cic.term -> Cic.term ->
- equality
+val find_library_theorems:
+ HMysql.dbd -> environment -> ProofEngineTypes.status -> UriManager.UriSet.t ->
+ (Cic.term * Cic.term * Cic.metasenv) list
(**
- superposition_left env target source
- returns a list of new clauses inferred with a left superposition step
- the negative equation "target" and the positive equation "source"
+ searches the context for hypotheses that are not equalities
*)
-(* val superposition_left: environment -> equality -> equality -> equality list *)
+val find_context_hypotheses:
+ environment -> int list -> (Cic.term * Cic.term * Cic.metasenv) list
+
+
+exception TermIsNotAnEquality;;
(**
- superposition_right newmeta env target source
- returns a list of new clauses inferred with a right superposition step
- the positive equations "target" and "source"
- "newmeta" is the first free meta index, i.e. the first number above the
- highest meta index: its updated value is also returned
+ raises TermIsNotAnEquality if term is not an equation.
+ The first Cic.term is a proof of the equation
*)
-(* val superposition_right: *)
-(* int -> environment -> equality -> equality -> int * equality list *)
+val equality_of_term: Cic.term -> Cic.term -> equality
-(* val demodulation: int -> environment -> equality -> equality -> int * equality *)
+val term_is_equality: Cic.term -> bool
+(** tests a sort of alpha-convertibility between the two terms, but on the
+ metavariables *)
+val meta_convertibility: Cic.term -> Cic.term -> bool
+
+(** meta convertibility between two equations *)
val meta_convertibility_eq: equality -> equality -> bool
val is_identity: environment -> equality -> bool
val string_of_equality: ?env:environment -> equality -> string
-(* val subsumption: environment -> equality -> equality -> bool *)
-
val metas_of_term: Cic.term -> int list
+(** ensures that metavariables in equality are unique *)
val fix_metas: int -> equality -> int * equality
-
-val extract_differing_subterms:
- Cic.term -> Cic.term -> (Cic.term * Cic.term) option
-
-val build_proof_term: equality -> Cic.term
-
-val find_library_equalities:
- dbd:Mysql.dbd -> ProofEngineTypes.status -> int -> equality list * int
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