initial commit

Co-authored-by: Yannick Forster <[email protected]>
Co-authored-by: Théo Winterhalter <[email protected]>

template-coq/_TemplateCoqProject.in

@@ -24,6 +24,7 @@ src/plugin_core.mli
 src/plugin_core.ml
 
 theories/Loader.v
+theories/Lib.v
 theories/All.v
 
 # A checker of well-formedness in MetaCoq and Coq

template-coq/theories/All.v

@@ -16,4 +16,5 @@ From MetaCoq.Template Require Export
      UnivSubst     (* Substitution of universe instances *)
      Typing        (* Typing judgment *)
      TemplateMonad (* The TemplateMonad *)
-     Loader        (* The plugin *).
+     Loader        (* The plugin *)
+     Lib           (* Meta-programming facilities *).

template-coq/theories/Ast.v

@@ -538,7 +538,7 @@ Notation closed t := (closedn 0 t).
 
 Fixpoint noccur_between k n (t : term) : bool :=
   match t with
-  | tRel i => Nat.ltb i k && Nat.leb (k + n) i
+  | tRel i => Nat.ltb i k || Nat.leb (k + n) i
   | tEvar ev args => List.forallb (noccur_between k n) args
   | tLambda _ T M | tProd _ T M => noccur_between k n T && noccur_between (S k) n M
   | tApp u v => noccur_between k n u && List.forallb (noccur_between k n) v

template-coq/theories/AstUtils.v

@@ -7,6 +7,8 @@ From MetaCoq.Template Require Import Ast.
 Require Import ssreflect ssrbool.
 Require Import ZArith.
 
+#[local] Set Universe Polymorphism.
+
 (** Raw term printing *)
 
 Module string_of_term_tree.
@@ -464,3 +466,254 @@ Ltac nth_leb_simpl :=
     replace n' with n in H' by lia; rewrite -> H in H'; injection H'; intros; subst
   | _ => lia || congruence || solve [repeat (f_equal; try lia)]
   end.
+
+(** * Traversal functions. *)
+
+Section TraverseWithBinders.
+Context {Acc : Type} {A : Type} (a : A) (lift : aname -> A -> A).
+
+Definition lift_names : list aname -> A -> A :=
+  fun names a => List.fold_right lift a names.
+
+Definition map_predicate_with_binders (f : A -> term -> term) (p : predicate term) : predicate term :=
+  let a_return := lift_names p.(pcontext) a in
+  {| puinst := p.(puinst) 
+  ;  pparams := List.map (f a) p.(pparams) 
+  ;  pcontext := p.(pcontext)
+  ;  preturn := f a_return p.(preturn) |}.
+
+Definition map_branch_with_binders (f : A -> term -> term) (b : branch term) : branch term := 
+  let a_body := lift_names b.(bcontext) a in
+  {| bcontext := b.(bcontext) ; bbody := f a_body b.(bbody) |}.
+
+(** [map_term_with_binders a lift f t] maps [f] on the immediate subterms of [t].
+    It carries an extra data [a] (typically a lift index) which is processed by [lift] 
+    (which typically add 1 to [a]) at each binder traversal.
+    It is not recursive and the order in which subterms are processed is not specified. *)
+Definition map_term_with_binders (f : A -> term -> term) (t : term) : term :=
+  match t with
+  | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ | tConstruct _ _ _ | tInt _ | tFloat _ | tString _ => t
+  | tEvar n ts => tEvar n (List.map (f a) ts)
+  | tCast b k t => tCast (f a b) k (f a t)
+  | tProd name ty body => tProd name (f a ty) (f (lift name a) body)
+  | tLambda name ty body => tLambda name (f a ty) (f (lift name a) body)
+  | tLetIn name def ty body => tLetIn name (f a def) (f a ty) (f (lift name a) body)
+  | tApp func args => tApp (f a func) (List.map (f a) args)
+  | tProj proj t => tProj proj (f a t)
+  (* For [tFix] and [tCoFix] we have to take care to lift [a] 
+     only when processing the body of the (co)fixpoint. *)
+  | tFix defs i => 
+    let a_body := lift_names (List.map dname defs) a in
+    let on_def := map_def (f a) (f a_body) in
+    tFix (List.map on_def defs) i
+  | tCoFix defs i => 
+    let a_body := lift_names (List.map dname defs) a in
+    let on_def := map_def (f a) (f a_body) in
+    tCoFix (List.map on_def defs) i
+  | tCase ci pred x branches => 
+    tCase ci (map_predicate_with_binders f pred) (f a x) (List.map (map_branch_with_binders f) branches)
+  | tArray l t def ty => tArray l (List.map (f a) t) (f a def) (f a ty)
+  end.
+
+Definition fold_predicate_with_binders (f : A -> Acc -> term -> Acc) (acc : Acc) (p : predicate term) : Acc :=
+  let a_return := lift_names p.(pcontext) a in
+  let acc := List.fold_left (f a) p.(pparams) acc in
+  f a_return acc p.(preturn).
+
+Definition fold_branch_with_binders (f : A -> Acc -> term -> Acc) (acc : Acc) (b : branch term) : Acc := 
+  let a_body := lift_names b.(bcontext) a in
+  f a_body acc b.(bbody).
+
+(** Fold version of [map_term_with_binders]. *)
+Definition fold_term_with_binders (f : A -> Acc -> term -> Acc) (acc : Acc) (t : term) : Acc :=
+  match t with
+  | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ 
+  | tConstruct _ _ _ | tInt _ | tFloat _ | tString _ => acc
+  | tEvar n ts => List.fold_left (f a) ts acc
+  | tCast b k t => let acc := f a acc b in f a acc t
+  | tProd name ty body => let acc := f a acc ty in f (lift name a) acc body
+  | tLambda name ty body => let acc := f a acc ty in f (lift name a) acc body
+  | tLetIn name def ty body => 
+    let acc := f a acc def in 
+    let acc := f a acc ty in 
+    f (lift name a) acc body 
+  | tApp func args => List.fold_left (f a) (func :: args) acc
+  | tProj proj t => f a acc t
+  | tFix defs i => 
+    let a_body := lift_names (List.map dname defs) a in
+    let acc := List.fold_left (f a) (List.map dtype defs) acc in 
+    List.fold_left (f a_body) (List.map dbody defs) acc
+  | tCoFix defs i => 
+    let a_body := lift_names (List.map dname defs) a in
+    let acc := List.fold_left (f a) (List.map dtype defs) acc in 
+    List.fold_left (f a_body) (List.map dbody defs) acc
+  | tCase ci pred x branches => 
+    let acc := fold_predicate_with_binders f acc pred in
+    let acc := f a acc x in
+    List.fold_left (fold_branch_with_binders f) branches acc
+  | tArray l t def ty => 
+    let acc := List.fold_left (f a) t acc in 
+    let acc := f a acc def in 
+    f a acc ty 
+  end.
+
+End TraverseWithBinders.
+
+Section TraverseWithBindersM.
+Import MCMonadNotation.
+
+Context {M : Type -> Type} `{Monad M} {Acc : Type} {A : Type} {a : A} {liftM : aname -> A -> M A}. 
+
+Definition lift_namesM (names : list aname) (a : A) : M A :=
+  let fix loop names a :=
+    match names with 
+    | [] => ret a
+    | n :: names => loop names =<< liftM n a
+    end
+  in 
+  loop (List.rev names) a.
+
+Definition map_defM {A B} (tyf bodyf : A -> M B) (d : def A) : M (def B) :=
+  mlet dtype <- tyf d.(dtype) ;;
+  mlet dbody <- bodyf d.(dbody) ;;
+  ret (mkdef _ d.(dname) dtype dbody d.(rarg)).
+
+Definition map_predicate_with_bindersM (f : A -> term -> M term) (p : predicate term) : M (predicate term) :=
+  mlet a_return <- lift_namesM p.(pcontext) a ;;
+  mlet pparams <- monad_map (f a) p.(pparams) ;;
+  mlet preturn <- f a_return p.(preturn) ;;
+  ret (mk_predicate p.(puinst) pparams p.(pcontext) preturn).
+
+Definition map_branch_with_bindersM (f : A -> term -> M term) (b : branch term) : M (branch term) := 
+  mlet a_body <- lift_namesM b.(bcontext) a ;;
+  mlet bbody <- f a_body b.(bbody) ;;
+  ret (mk_branch b.(bcontext) bbody).
+
+(** Monadic variant of [map_term_with_binders]. *)
+Definition map_term_with_bindersM (f : A -> term -> M term) (t : term) : M term :=
+  match t with
+  | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ 
+  | tConstruct _ _ _ | tInt _ | tFloat _ | tString _ => ret t
+  | tEvar n ts => 
+    mlet ts <- monad_map (f a) ts ;; 
+    ret (tEvar n ts)
+  | tCast b k t => 
+    mlet b <- f a b ;;
+    mlet t <- f a t ;;
+    ret (tCast b k t)
+  | tProd name ty body => 
+    mlet ty <- f a ty ;;
+    mlet a_body <- liftM name a ;;
+    mlet body <- f a_body body ;;
+    ret (tProd name ty body)
+  | tLambda name ty body => 
+    mlet ty <- f a ty ;;
+    mlet a_body <- liftM name a ;;
+    mlet body <- f a_body body ;;
+    ret (tLambda name ty body)
+  | tLetIn name def ty body => 
+    mlet def <- f a def ;;
+    mlet ty <- f a ty ;;
+    mlet a_body <- liftM name a ;;
+    mlet body <- f a_body body ;;
+    ret (tLetIn name def ty body)
+  | tApp func args => 
+    mlet func <- f a func ;;
+    mlet args <- monad_map (f a) args ;;
+    ret (tApp func args)
+  | tProj proj t => 
+    mlet t <- f a t ;;
+    ret (tProj proj t)
+  (* For [tFix] and [tCoFix] we have to take care to lift [a] 
+     only when processing the body of the (co)fixpoint. *)
+  | tFix defs i => 
+    mlet a_body <- lift_namesM (List.map dname defs) a ;;
+    let on_def := map_defM (f a) (f a_body) in
+    mlet defs <- monad_map on_def defs ;;
+    ret (tFix defs i)
+  | tCoFix defs i => 
+    mlet a_body <- lift_namesM (List.map dname defs) a ;;
+    let on_def := map_defM (f a) (f a_body) in
+    mlet defs <- monad_map on_def defs ;;
+    ret (tCoFix defs i)
+  | tCase ci pred x branches => 
+    mlet pred <- map_predicate_with_bindersM f pred ;;
+    mlet x <- f a x ;;
+    mlet branches <- monad_map (map_branch_with_bindersM f) branches ;;
+    ret (tCase ci pred x branches)
+  | tArray l t def ty => 
+    mlet t <- monad_map (f a) t ;;
+    mlet def <- f a def ;;
+    mlet ty <- f a ty ;;
+    ret (tArray l t def ty)
+  end.
+
+Definition fold_predicate_with_bindersM (f : A -> Acc -> term -> M Acc) (acc : Acc) (p : predicate term) : M Acc :=
+  mlet a_return <- lift_namesM p.(pcontext) a ;;
+  mlet acc <- monad_fold_left (f a) p.(pparams) acc ;;
+  f a_return acc p.(preturn).
+
+Definition fold_branch_with_bindersM (f : A -> Acc -> term -> M Acc) (acc : Acc) (b : branch term) : M Acc := 
+  mlet a_body <- lift_namesM b.(bcontext) a ;;
+  f a_body acc b.(bbody).
+
+(** Monadic variant of [fold_term_with_binders]. *)
+Definition fold_term_with_bindersM (f : A -> Acc -> term -> M Acc) (acc : Acc) (t : term) : M Acc :=
+  match t with
+  | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ 
+  | tConstruct _ _ _ | tInt _ | tFloat _ | tString _ => ret acc
+  | tEvar n ts => monad_fold_left (f a) ts acc
+  | tCast b k t => mlet acc <- f a acc b ;; f a acc t
+  | tProd name ty body => 
+    mlet a_body <- liftM name a ;;
+    mlet acc <- f a acc ty ;; 
+    f a_body acc body
+  | tLambda name ty body => 
+    mlet a_body <- liftM name a ;;
+    mlet acc <- f a acc ty ;; 
+    f a_body acc body
+  | tLetIn name def ty body => 
+    mlet a_body <- liftM name a ;;
+    mlet def <- f a acc def ;;
+    mlet acc <- f a acc ty ;; 
+    f a_body acc body
+  | tApp func args => monad_fold_left (f a) (func :: args) acc
+  | tProj proj t => f a acc t
+  | tFix defs i => 
+    mlet a_body <- lift_namesM (List.map dname defs) a ;;
+    mlet acc <- monad_fold_left (f a) (List.map dtype defs) acc ;;
+    monad_fold_left (f a_body) (List.map dbody defs) acc
+  | tCoFix defs i => 
+    mlet a_body <- lift_namesM (List.map dname defs) a ;;
+    mlet acc <- monad_fold_left (f a) (List.map dtype defs) acc ;;
+    monad_fold_left (f a_body) (List.map dbody defs) acc
+  | tCase ci pred x branches => 
+    mlet acc <- fold_predicate_with_bindersM f acc pred ;;
+    mlet acc <- f a acc x ;;
+    monad_fold_left (fold_branch_with_bindersM f) branches acc
+  | tArray l t def ty => 
+    mlet acc <- monad_fold_left (f a) t acc ;;
+    mlet acc <- f a acc def ;; 
+    f a acc ty 
+  end.
+
+End TraverseWithBindersM.
+
+
+(** [map_term f t] maps [f] on the immediate subterms of [t].
+    It is not recursive and the order in which subterms are processed is not specified. *)
+Definition map_term (f : term -> term) (t : term) : term :=
+  @map_term_with_binders unit tt (fun _ _ => tt) (fun _ => f) t.   
+
+(** Monadic variant of [map_term]. *)
+Definition map_termM {M} `{Monad M} (f : term -> M term) (t : term) : M term :=
+  @map_term_with_bindersM M _ unit tt (fun _ _ => ret tt) (fun _ => f) t.
+
+(** [fold_term f acc t] folds [f] on the immediate subterms of [t].
+    It is not recursive and the order in which subterms are processed is not specified. *)
+Definition fold_term {Acc} (f : Acc -> term -> Acc) (acc : Acc) (t : term) : Acc :=
+  @fold_term_with_binders Acc unit tt (fun _ _ => tt) (fun _ => f) acc t.
+
+(** Monadic variant of [fold_term]. *)
+Definition fold_termM {M} `{Monad M} {Acc} (f : Acc -> term -> M Acc) (acc : Acc) (t : term) : M Acc :=
+  @fold_term_with_bindersM M _ Acc unit tt (fun _ _ => ret tt) (fun _ => f) acc t.