Imported Upstream version 0.4upstream/0.4

9 files changed, 327 insertions, 3 deletions

diff --git a/Caveats.v b/Caveats.v
index a7967cc..d0ec37a 100644
--- a/Caveats.v
+++ b/Caveats.v
@@ -13,6 +13,7 @@
    with the path to the [aac_tactics] library
 *)
 
+Add Rec LoadPath "." as AAC_tactics. 
 Require Import AAC.
 Require Instances.
 
@@ -370,3 +371,5 @@ to investigate on this in the future *)
 
 End Z.
 
+
+
diff --git a/Makefile b/Makefile
index 1043ce9..03775bc 100644
--- a/Makefile
+++ b/Makefile
@@ -1,24 +1,29 @@
 
 
-FILES :=  coq.mli helper.mli search_monad.mli matcher.mli theory.mli print.mli rewrite.mli \
-	coq.ml helper.ml search_monad.ml matcher.ml theory.ml print.ml rewrite.ml4 \
+FILES := coq.mli helper.mli search_monad.mli matcher.mli theory.mli print.mli  \
+	evm_compute.mli evm_compute.ml  \
+	 coq.ml helper.ml search_monad.ml matcher.ml theory.ml print.ml rewrite.ml4 \
 	aac.mlpack \
 	AAC.v  Instances.v Tutorial.v Caveats.v 
 
 ARGS := -R . AAC_tactics
 
-.PHONY: coq clean
+.PHONY: coq clean doc
 
 world: all doc
 
 all: Makefile.coq
 	$(MAKE) -f Makefile.coq all
 
+install: Makefile.coq
+	$(MAKE) -f Makefile.coq install
+
 coq: Makefile.coq
 	$(MAKE) -f Makefile.coq
 
 doc: Makefile.coq
 	$(MAKE) -f Makefile.coq html
+	$(MAKE) -f Makefile.coq mlihtml
 
 Makefile.coq: Makefile $(VS)
 	coq_makefile $(ARGS) $(FILES) -o Makefile.coq
diff --git a/Tutorial.v b/Tutorial.v
index 76006ca..6356a10 100644
--- a/Tutorial.v
+++ b/Tutorial.v
@@ -397,3 +397,36 @@ Section Examples.
 End Examples.
 
 
+Section Match. 
+  (* The following example is inspired by a question by Francois
+  Pottier, wokring in the context of separation logic. *)
+
+  Variable T : Type. 
+  Variable star : T -> T -> T. 
+  Hypothesis P : T -> Prop. 
+
+  Context (starA : Associative eq star).   
+  Context (starC : Commutative eq star).   
+
+  Hypothesis P_hereditary_left : forall a b, P (star a b) -> P a. 
+  Hypothesis P_hereditary_right : forall a b, P (star a b) -> P b. 
+  
+  Notation "a * b" := (star a b). 
+
+  Ltac crush :=
+    match goal with 
+        H: P ?R' |- P ?R =>
+        let h := fresh in
+        aac_match (fun x => x * R) R' h;
+          rewrite <- h in H;
+          try eauto using P_hereditary_right
+    end.    
+
+  Goal forall a b c, P (c * a * c * b) -> P (b * a). 
+  Proof. intros.  crush.  Qed. 
+
+  Goal forall a b c, exists d,  P (d * a * c * b) -> P (b * d) /\ b = d. 
+  Proof. intros.  eexists. intros.  split. crush. reflexivity. Qed. 
+
+End Match. 
+
diff --git a/aac.mlpack b/aac.mlpack
index 0c12567..60d5298 100644
--- a/aac.mlpack
+++ b/aac.mlpack
@@ -4,4 +4,5 @@ Search_monad
 Matcher
 Theory
 Print
+Evm_compute
 Rewrite
diff --git a/coq.ml b/coq.ml
index 7371913..132fbf7 100644
--- a/coq.ml
+++ b/coq.ml
@@ -148,6 +148,8 @@ module Leibniz = struct
   let path = ["Coq"; "Init"; "Logic"]
   let eq_refl = lazy (init_constant path "eq_refl")
   let eq_refl ty x = lapp eq_refl [| ty;x|]
+  let eq ty = Term.mkApp (init_constant path "eq", [| ty |])
+
 end
 
 module Option = struct
diff --git a/coq.mli b/coq.mli
index a0f2ce0..53d42eb 100644
--- a/coq.mli
+++ b/coq.mli
@@ -79,6 +79,7 @@ end
 
 module Leibniz : sig
   val eq_refl : Term.types -> Term.constr -> Term.constr
+  val eq : Term.types -> Term.constr
 end
 
 module Option : sig
diff --git a/evm_compute.ml b/evm_compute.ml
new file mode 100644
index 0000000..b10a9cd
--- /dev/null
+++ b/evm_compute.ml
@@ -0,0 +1,221 @@
+(*i camlp4deps: "parsing/grammar.cma" i*)
+(*i camlp4use: "pa_extend.cmp" i*)
+
+
+let pp_constr fmt x = Pp.pp_with fmt (Printer.pr_constr x)
+let pp_list pp fmt l = List.iter (fun x -> Format.fprintf fmt "%a; " pp x) l
+let pp_list_nl pp fmt l = List.iter (fun x -> Format.fprintf fmt "%a;\n" pp x) l
+let pp_constrs fmt l = (pp_list pp_constr) fmt l
+
+type constr = Term.constr
+
+module Replace (X : sig val eq: Term.constr -> Term.constr -> bool 
+			val subst : (Term.constr * Term.constr) list end) =
+  struct
+
+    (* assumes that [c] and [t] have no outer casts, and all
+       applications have been flattened *)    
+    let rec find l (t: constr) =
+      match l with 
+      | [] -> None
+      | (c,c') :: q -> 
+	begin 
+	  match Term.kind_of_term c, Term.kind_of_term t with 
+	  | Term.App (f1,args1), Term.App (f2, args2) -> 
+	    let l1 = Array.length args1 in 
+	    let l2 = Array.length args2 in 
+	    if l1 <= l2 && X.eq c (Term.mkApp (f2, Array.sub args2 0 l1)) 
+	    then
+	      (* we must return the array of arguments, to make the
+		 substitution in them too *)
+	      Some (c',Array.sub args2 l1 (l2 - l1))
+	    else 
+	      find q t
+	  | _, _ -> 
+	    if X.eq c t 
+	    then Some (c', [| |]) 
+	    else find q t	      
+	end
+	  
+	  
+    let replace_terms t = 
+      let rec aux (k:int) t =
+	match find X.subst t with 
+	| Some (t',v) -> 
+	  let v' = Array.map (Term.map_constr_with_binders (succ) aux k) v in
+	  Term.mkApp (Term.lift k t', v')
+	| None -> 
+	  Term.map_constr_with_binders succ aux k t
+      in aux 0 t
+	  
+  end
+
+let nowhere =
+  { Tacexpr.onhyps = Some [];
+    Tacexpr.concl_occs = Glob_term.no_occurrences_expr
+  }
+
+let mk_letin
+    (name:string)
+    (c: constr)
+    (k : Names .identifier -> Proof_type.tactic)
+: Proof_type.tactic =
+  fun goal ->
+    let name = (Names.id_of_string name) in
+    let name =  Tactics.fresh_id [] name goal in
+    let letin = (Tactics.letin_tac None  (Names.Name name) c None nowhere) in
+      Tacticals.tclTHEN letin (k name) goal
+
+let assert_tac
+    (name:string)
+    (c: constr)
+    (by:Proof_type.tactic)
+    (k : Names.identifier -> Proof_type.tactic)
+: Proof_type.tactic =
+  fun goal ->
+    let name = (Names.id_of_string name) in
+    let name =  Tactics.fresh_id [] name goal in
+    let t = (Tactics.assert_tac  (Names.Name name) c) in
+      Tacticals.tclTHENS t [by; (k name)] goal
+
+
+(* The contrib name is used to locate errors when loading constrs *)
+let contrib_name = "evm_compute"
+
+(* Getting constrs (primitive Coq terms) from existing Coq
+   libraries. *)
+let find_constant contrib dir s =
+  Libnames.constr_of_global (Coqlib.find_reference contrib dir s)
+
+let init_constant dir s = find_constant contrib_name dir s
+
+module Leibniz = struct
+  let path = ["Coq"; "Init"; "Logic"]
+    
+  let eq_refl t x= 
+    Term.mkApp (init_constant path "eq_refl", [| t; x|])
+
+  let eq t x y = 
+    Term.mkApp (init_constant path "eq", [| t; x ; y|])
+      
+  let eq_ind_r ty x p px y yx =
+    Term.mkApp (init_constant path "eq_ind_r", [|ty;x;p;px;y;yx|])
+end
+
+let mk_vm_cast t c = Term.mkCast (c,Term.VMcast,t)
+
+let mk_let  
+    (name:Names.identifier)
+    (c: constr)
+    (t: constr)
+    (k : Names.identifier -> constr) =
+  Term.mkNamedLetIn name c t (Term.subst_vars [name] (k name))
+
+let mk_fun
+    (name:Names.identifier)
+    (t: constr)
+    (k : Names.identifier -> constr) =
+  Term.mkNamedLambda name t (Term.subst_vars [name] (k name))
+
+let rec has_evar x =
+  match Term.kind_of_term x with
+    | Term.Evar _ -> true
+    | Term.Rel _ | Term.Var _ | Term.Meta _ | Term.Sort _ | Term.Const _ | Term.Ind _ | Term.Construct _ ->
+      false
+    | Term.Cast (t1, _, t2) | Term.Prod (_, t1, t2) | Term.Lambda (_, t1, t2) ->
+      has_evar t1 || has_evar t2
+    | Term.LetIn (_, t1, t2, t3) ->
+      has_evar t1 || has_evar t2 || has_evar t3
+    | Term.App (t1, ts) ->
+      has_evar t1 || has_evar_array ts
+    | Term.Case (_, t1, t2, ts) ->
+      has_evar t1 || has_evar t2 || has_evar_array ts
+    | Term.Fix ((_, tr)) | Term.CoFix ((_, tr)) ->
+      has_evar_prec tr
+and has_evar_array x =
+  Util.array_exists has_evar x
+and has_evar_prec (_, ts1, ts2) =
+  Util.array_exists has_evar ts1 || Util.array_exists has_evar ts2
+
+let evm_compute eq blacklist = fun gl -> 
+  (* the type of the conclusion of the goal is [concl] *)
+  let concl = Tacmach.pf_concl gl in 
+
+  let extra = 
+    List.fold_left (fun acc (id,body,ty) -> 
+      match body with 
+	| None -> acc
+	| Some body -> if has_evar body then (Term.mkVar id :: acc) else acc)
+      [] (Tacmach.pf_hyps gl) in 
+
+  (* the set of evars that appear in the goal *)
+  let evars = Evd.evar_list (Tacmach.project gl) concl in 
+  
+  (* the arguments of the function are: the constr that are blacklisted, then the evars  *)
+  let args = extra @ blacklist @ (List.map (fun x -> Term.mkEvar x) evars) in 
+  
+  let argsv = Array.of_list args in 
+
+  let context = (Termops.rel_list 0 (List.length args)) in 
+
+  (* we associate to each argument the proper de bruijn index *)
+  let (subst: (Term.constr * Term.constr) list) = List.combine args context in 
+  
+  let module R = Replace(struct let eq = eq let subst = subst end) in 
+  
+  let t = R.replace_terms concl in 
+  
+  (* we have to retype both the blacklist and the evars to know how to build the final product *)
+  let rel_context = List.map (fun x -> Names.Anonymous, None, Tacmach.pf_type_of gl x) args in 
+  
+  (* the abstraction *)
+  let t = Term.it_mkLambda_or_LetIn t (List.rev rel_context) in 
+  
+  let typeof_t = (Tacmach.pf_type_of gl t) in 
+
+  (* the normal form of the head function *)
+  let nft = Vnorm.cbv_vm (Tacmach.pf_env gl) t typeof_t in 
+  
+
+  let (!!) x = Tactics.fresh_id [] ((Names.id_of_string x)) gl in
+
+  (* p = [fun x => x a_i] which corresponds to the type of the goal when applied to [t] *)
+  let p = mk_fun (!! "x") typeof_t (fun x -> Term.mkApp (Term.mkVar x,argsv)) in 
+  
+  let proof_term pnft = begin  
+    mk_let (!! "nft") nft typeof_t (fun nft -> let nft' = Term.mkVar nft in
+    mk_let (!! "t") t typeof_t (fun t -> let t' = Term.mkVar t in 	
+    mk_let (!! "H") (mk_vm_cast (Leibniz.eq typeof_t t' nft') (Leibniz.eq_refl typeof_t nft')) (Leibniz.eq typeof_t t' nft')
+   (fun h -> 
+    (* typeof_t -> Prop *)
+    let body = Leibniz.eq_ind_r typeof_t 
+      nft' p pnft t' (Term.mkVar h) 
+    in 
+    Term.mkCast (body, Term.DEFAULTcast, Term.mkApp (t', argsv))
+  )))
+  end in 
+  
+  try 
+    assert_tac "subgoal" (Term.mkApp (p,[| nft |]))
+      Tacticals.tclIDTAC
+      (fun subgoal -> 
+	(* We use the tactic [exact_no_check]. It has two consequences:
+	- first, it means that in theory we could produce ill typed proof terms, that fail to type check at Qed; 
+	- second, it means that we are able to use vm_compute and vm_compute casts, that will be checkable at Qed time when all evars have been instantiated. 
+	*)
+	Tactics.exact_no_check (proof_term (Term.mkVar subgoal))  
+      ) gl
+  with 
+    | e ->
+      Tacticals.tclFAIL 0 (Pp.str (Printf.sprintf "evm_compute failed with an exception %s" (Printexc.to_string e))) gl
+      
+;;
+
+let evm_compute_in eq blacklist h = fun gl -> 
+  let concl = Tacmach.pf_concl gl in 
+  Tacticals.tclTHENLIST
+    [Tactics.revert [h];
+     evm_compute eq (concl :: blacklist);
+     Tactics.introduction h
+    ]
+    gl
diff --git a/evm_compute.mli b/evm_compute.mli
new file mode 100644
index 0000000..f50c0db
--- /dev/null
+++ b/evm_compute.mli
@@ -0,0 +1,11 @@
+
+
+(** [evm_compute eq blacklist] performs a vm_compute step with the
+    following provisos: evars can appear in the goal; terms that are
+    equal (modulo eq) to terms in the blacklist are abstracted
+    before-hand. *)
+val evm_compute : (Term.constr -> Term.constr -> bool) -> Term.constr list -> Proof_type.tactic 
+
+
+(** [evm_compute eq blacklist h] performs an evm_compute step in the hypothesis h *)
+val evm_compute_in : (Term.constr -> Term.constr -> bool) -> Term.constr list -> Names.identifier ->  Proof_type.tactic 
diff --git a/rewrite.ml4 b/rewrite.ml4
index 6229262..383d706 100644
--- a/rewrite.ml4
+++ b/rewrite.ml4
@@ -32,6 +32,10 @@ let push_anomaly msg = function
   | Util.Anomaly _ as e -> raise e
   | _ -> Coq.anomaly msg
 
+
+
+
+
 module M = Matcher
 
 open Term
@@ -435,6 +439,41 @@ let aac_rewrite  ?abort rew ?(l2r=true) ?(show = false) ?(in_left=true) ?strict
     ) goal
 
 
+(** [aac_match eq (fun x1 ... xn => p) t H] match the term [t] against
+    the pattern, and introduces an hypothesis H of type p = t.  (Note
+    that we have performed the substitution in p).
+*)
+
+let aac_match ~eq pattern term h = fun gl ->
+  let env = Tacmach.pf_env gl in
+  let evar_map = Tacmach.project gl in
+  let carrier = Typing.type_of env evar_map term in   
+  let rel = Coq.Relation.make carrier eq in
+  let equiv,gl = Coq.Equivalence.from_relation gl rel in 
+  (* first, we decompose the pattern as an arity. *)
+  let x_args, pat = Term.decompose_lam pattern in 
+  (* then, we reify the pattern and the term, using the provided equality *)
+  let envs = Theory.Trans.empty_envs () in
+  let left, right,gl = Theory.Trans.t_of_constr gl rel envs (pat,term) in 
+  let gl,ir = Theory.Trans.ir_of_envs gl rel envs in 
+  let solutions = Matcher.matcher (Theory.Trans.ir_to_units ir) left right in 
+  (* then, we pick the first solution   to the matching problem *)
+  let sigma = match Search_monad.choose solutions with
+    | None -> Coq.user_error "no solution to the matching problem"
+    | Some sigma -> sigma
+  in
+  let p_sigma = Matcher.Subst.instantiate sigma left in 
+  let args = List.map (fun (x,t) -> x,Theory.Trans.raw_constr_of_t ir rel [] t) (Matcher.Subst.to_list sigma) in 
+  (* Then, we have to assert the fact that p_sigma is equal to term *)
+  let equation = mkApp (eq, [| Theory.Trans.raw_constr_of_t ir rel [] p_sigma ; term |]) in 
+  let evar_map = Tacmach.project gl in
+  Tacticals.tclTHENLIST 
+    [      
+      Refiner.tclEVARS evar_map;
+      Tactics.assert_by h  equation (by_aac_reflexivity term equiv ir p_sigma right);
+    ] gl
+  
+
 open Coq.Rewrite
 open Tacmach
 open Tacticals
@@ -522,3 +561,11 @@ TACTIC EXTEND _aacu_instances_
 | [ "aacu_instances" orient(l2r) constr(c) aac_args(args) constro(extra)] ->
   [ fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:false ~show:true c gl ]
 END
+
+TACTIC EXTEND _aac_match_
+| [ "aac_match" constr(p) constr(t) ident(h)] ->
+  [ fun gl ->
+    let ty = Tacmach.pf_type_of gl t in 
+    let eq = Coq.Leibniz.eq ty in 
+    aac_match ~eq p t (Names.Name h) gl]
+END