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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open Ccalgo
open Constr
type rule =
| Ax of axiom
(** if ⊢ t = u :: A, then ⊢ t = u :: A *)
| SymAx of axiom
(** if ⊢ t = u : A, then ⊢ u = t :: A *)
| Refl of ATerm.t (* ⊢ t = t :: A *)
| Trans of proof * proof
(** ⊢ t = u :: A -> ⊢ u = v :: A -> ⊢ t = v :: A *)
| Congr of proof * proof
(** ⊢ f = g :: forall x : A, B -> ⊢ t = u :: A -> f t = g u :: B{t}
Assumes that B{t} ≡ B{u} for this to make sense! *)
| Inject of proof * pconstructor * int * int
(** ⊢ ci v = ci w :: Ind(args) -> ⊢ v = w :: T
where T is the type of the n-th argument of ci, assuming they coincide *)
and proof =
private {p_lhs:ATerm.t;p_rhs:ATerm.t;p_rule:rule}
(** Main proof building function *)
val build_proof :
Environ.env -> Evd.evar_map -> forest ->
[ `Discr of int * pa_constructor * int * pa_constructor
| `Prove of int * int ] -> proof
|
