parser.mly

(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
(*  Copyright 2010-2014   --   INRIA - CNRS - Paris-Sud University  *)
(*                                                                  *)
(*  This software is distributed under the terms of the GNU Lesser  *)
(*  General Public License version 2.1, with the special exception  *)
(*  on linking described in file LICENSE.                           *)
(*                                                                  *)
(********************************************************************)

%{
module Incremental = struct
  let stack = Stack.create ()
  let open_file inc = Stack.push inc stack
  let close_file () = ignore (Stack.pop stack)
  let open_theory id = (Stack.top stack).Ptree.open_theory id
  let close_theory () = (Stack.top stack).Ptree.close_theory ()
  let open_module id = (Stack.top stack).Ptree.open_module id
  let close_module () = (Stack.top stack).Ptree.close_module ()
  let open_namespace n = (Stack.top stack).Ptree.open_namespace n
  let close_namespace l b = (Stack.top stack).Ptree.close_namespace l b
  let new_decl loc d = (Stack.top stack).Ptree.new_decl loc d
  let new_pdecl loc d = (Stack.top stack).Ptree.new_pdecl loc d
  let use_clone loc use = (Stack.top stack).Ptree.use_clone loc use
end

  open Ptree

  let infix  s = "infix "  ^ s
  let prefix s = "prefix " ^ s
  let mixfix s = "mixfix " ^ s

  let qualid_last = function Qident x | Qdot (_, x) -> x.id

  let floc s e = Loc.extract (s,e)

  let add_lab id l = { id with id_lab = l }

  let id_anonymous loc = { id = "_"; id_lab = []; id_loc = loc }

  let mk_id id s e = { id = id; id_lab = []; id_loc = floc s e }

  let mk_pat d s e = { pat_desc = d; pat_loc = floc s e }

  let mk_pp d s e = { pp_desc = d; pp_loc = floc s e }

  let mk_expr d s e = { expr_desc = d; expr_loc = floc s e }

  let variant_union v1 v2 = match v1, v2 with
    | _, [] -> v1
    | [], _ -> v2
    | _, ({pp_loc = loc},_)::_ -> Loc.errorm ~loc
        "multiple `variant' clauses are not allowed"

  let empty_spec = {
    sp_pre     = [];
    sp_post    = [];
    sp_xpost   = [];
    sp_reads   = [];
    sp_writes  = [];
    sp_variant = [];
    sp_checkrw = false;
    sp_diverge = false;
  }

  let spec_union s1 s2 = {
    sp_pre     = s1.sp_pre @ s2.sp_pre;
    sp_post    = s1.sp_post @ s2.sp_post;
    sp_xpost   = s1.sp_xpost @ s2.sp_xpost;
    sp_reads   = s1.sp_reads @ s2.sp_reads;
    sp_writes  = s1.sp_writes @ s2.sp_writes;
    sp_variant = variant_union s1.sp_variant s2.sp_variant;
    sp_checkrw = s1.sp_checkrw || s2.sp_checkrw;
    sp_diverge = s1.sp_diverge || s2.sp_diverge;
  }

(* dead code
  let add_init_mark e =
    let init = { id = "Init"; id_lab = []; id_loc = e.expr_loc } in
    { e with expr_desc = Emark (init, e) }
*)

  let small_integer i =
    try match i with
      | Number.IConstDec s -> int_of_string s
      | Number.IConstHex s -> int_of_string ("0x"^s)
      | Number.IConstOct s -> int_of_string ("0o"^s)
      | Number.IConstBin s -> int_of_string ("0b"^s)
    with Failure _ -> raise Error

  let error_param loc =
    Loc.errorm ~loc "cannot determine the type of the parameter"

  let error_loc loc = Loc.error ~loc Error

  let () = Exn_printer.register (fun fmt exn -> match exn with
    | Error -> Format.fprintf fmt "syntax error"
    | _ -> raise exn)
%}

(* Tokens *)

%token <string> LIDENT UIDENT
%token <Ptree.integer_constant> INTEGER
%token <string> OP1 OP2 OP3 OP4 OPPREF
%token <Ptree.real_constant> FLOAT
%token <string> STRING
%token <Loc.position> POSITION
%token <string> QUOTE_UIDENT QUOTE_LIDENT OPAQUE_QUOTE_LIDENT

(* keywords *)

%token AS AXIOM CLONE COINDUCTIVE CONSTANT
%token ELSE END EPSILON EXISTS EXPORT FALSE FORALL FUNCTION
%token GOAL IF IMPORT IN INDUCTIVE LEMMA
%token LET MATCH META NAMESPACE NOT PROP PREDICATE
%token THEN THEORY TRUE TYPE USE WITH

(* program keywords *)

%token ABSTRACT ABSURD ANY ASSERT ASSUME BEGIN CHECK
%token DIVERGES DO DONE DOWNTO ENSURES EXCEPTION FOR
%token FUN GHOST INVARIANT LOOP MODEL MODULE MUTABLE
%token PRIVATE RAISE RAISES READS REC REQUIRES RETURNS
%token TO TRY VAL VARIANT WHILE WRITES

(* symbols *)

%token AND ARROW
%token BAR
%token COLON COMMA
%token DOT EQUAL LAMBDA LTGT
%token LEFTPAR LEFTPAR_STAR_RIGHTPAR LEFTSQ
%token LARROW LRARROW OR
%token RIGHTPAR RIGHTSQ
%token UNDERSCORE

%token EOF

(* program symbols *)

%token AMPAMP BARBAR LEFTBRC RIGHTBRC SEMICOLON

(* Precedences *)

%nonassoc IN
%nonassoc below_SEMI
%nonassoc SEMICOLON
%nonassoc LET VAL
%nonassoc prec_no_else
%nonassoc DOT ELSE GHOST
%nonassoc prec_named
%nonassoc COLON

%right ARROW LRARROW
%right OR BARBAR
%right AND AMPAMP
%nonassoc NOT
%left EQUAL LTGT OP1
%nonassoc LARROW
%nonassoc RIGHTSQ    (* stronger than <- for e1[e2 <- e3] *)
%left OP2
%left OP3
%left OP4
%nonassoc prec_prefix_op
%nonassoc LEFTSQ
%nonassoc OPPREF

(* Entry points *)

%start <Ptree.incremental -> unit> open_file
%start <unit> logic_file program_file
%%

open_file:
| (* epsilon *) { Incremental.open_file }

logic_file:
| theory* EOF   { Incremental.close_file () }

theory:
| theory_head theory_decl* END  { Incremental.close_theory () }

theory_head:
| THEORY labels(uident)  { Incremental.open_theory $2 }

theory_decl:
| decl            { Incremental.new_decl  (floc $startpos $endpos) $1 }
| use_clone       { Incremental.use_clone (floc $startpos $endpos) $1 }
| namespace_head theory_decl* END
    { Incremental.close_namespace (floc $startpos($1) $endpos($1)) $1 }

namespace_head:
| NAMESPACE namespace_import uident
   { Incremental.open_namespace $3.id; $2 }

namespace_import:
| (* epsilon *)  { false }
| IMPORT         { true }

(* Declaration *)

decl:
| TYPE with_list1(type_decl)                      { TypeDecl $2 }
| TYPE late_invariant                             { TypeDecl [$2] }
| CONSTANT logic_decl_constant                    { LogicDecl [$2] }
| FUNCTION logic_decl_function with_logic_decl*   { LogicDecl ($2::$3) }
| PREDICATE logic_decl_predicate with_logic_decl* { LogicDecl ($2::$3) }
| inductive with_list1(inductive_decl)            { IndDecl ($1, $2) }
| AXIOM labels(ident) COLON lexpr                 { PropDecl (Kaxiom, $2, $4) }
| LEMMA labels(ident) COLON lexpr                 { PropDecl (Klemma, $2, $4) }
| GOAL labels(ident) COLON lexpr                  { PropDecl (Kgoal, $2, $4) }
| META sident comma_list1(meta_arg)               { Meta ($2, $3) }

inductive:
| INDUCTIVE   { Decl.Ind }
| COINDUCTIVE { Decl.Coind }

(* Use and clone *)

use_clone:
| USE use               { ($2, None) }
| CLONE use clone_subst { ($2, Some $3) }

use:
| opt_import tqualid
    { { use_theory = $2; use_import = Some ($1, qualid_last $2) } }
| opt_import tqualid AS uident
    { { use_theory = $2; use_import = Some ($1, $4.id) } }
| EXPORT tqualid
    { { use_theory = $2; use_import = None } }

opt_import:
| (* epsilon *) { false }
| IMPORT        { true  }

clone_subst:
| (* epsilon *)                               { [] }
| WITH comma_list1(subst)  { $2 }

subst:
| NAMESPACE ns     EQUAL ns     { CSns    (floc $startpos $endpos, $2,$4) }
| TYPE qualid type_arg* EQUAL primitive_type
                                { CStsym  (floc $startpos $endpos, $2,$3,$5) }
| CONSTANT  qualid EQUAL qualid { CSfsym  (floc $startpos $endpos, $2,$4) }
| FUNCTION  qualid EQUAL qualid { CSfsym  (floc $startpos $endpos, $2,$4) }
| PREDICATE qualid EQUAL qualid { CSpsym  (floc $startpos $endpos, $2,$4) }
| VAL       qualid EQUAL qualid { CSvsym  (floc $startpos $endpos, $2,$4) }
| LEMMA     qualid              { CSlemma (floc $startpos $endpos, $2) }
| GOAL      qualid              { CSgoal  (floc $startpos $endpos, $2) }

ns:
| uqualid { Some $1 }
| DOT     { None }

(* Meta args *)

meta_arg:
| TYPE primitive_type { PMAty  $2 }
| CONSTANT  qualid    { PMAfs  $2 }
| FUNCTION  qualid    { PMAfs  $2 }
| PREDICATE qualid    { PMAps  $2 }
| PROP      qualid    { PMApr  $2 }
| STRING              { PMAstr $1 }
| INTEGER             { PMAint (small_integer $1) }

(* Type declarations *)

type_decl:
| labels(lident) type_arg* typedefn
  { let model, vis, def, inv = $3 in
    let vis = if model then Abstract else vis in
    { td_ident = $1; td_params = $2;
      td_model = model; td_vis = vis; td_def = def;
      td_inv = inv; td_loc = floc $startpos $endpos } }

late_invariant:
| labels(lident) type_arg* invariant+
  { { td_ident = $1; td_params = $2;
      td_model = false; td_vis = Public; td_def = TDabstract;
      td_inv = $3; td_loc = floc $startpos $endpos } }

type_arg:
| labels(quote_lident) { $1 }

typedefn:
| (* epsilon *)
    { false, Public, TDabstract, [] }
| equal_model visibility bar_list1(typecase) invariant*
    { $1, $2, TDalgebraic $3, $4 }
| equal_model visibility BAR bar_list1(typecase) invariant*
    { $1, $2, TDalgebraic $4, $5 }
| equal_model visibility LEFTBRC record_fields RIGHTBRC invariant*
    { $1, $2, TDrecord $4, $6 }
(* abstract/private is not allowed for alias type *)
| equal_model visibility primitive_type
    { if $2 <> Public then
        Loc.error ~loc:(floc $startpos($2) $endpos($2)) Error;
      $1, Public, TDalias $3, [] }

visibility:
| (* epsilon *) { Public }
| PRIVATE       { Private }
| ABSTRACT      { Abstract }

equal_model:
| EQUAL         { false }
| MODEL         { true }

record_fields:
| record_field SEMICOLON?               { [$1] }
| record_field SEMICOLON record_fields  { $1 :: $3 }

field_modifiers:
| (* epsilon *) { false, false }
| MUTABLE       { true,  false }
| GHOST         { false, true  }
| GHOST MUTABLE { true,  true  }
| MUTABLE GHOST { true,  true  }

record_field:
| field_modifiers labels(lident) cast
  { { f_ident = $2; f_mutable = fst $1; f_ghost = snd $1;
      f_pty = $3; f_loc = floc $startpos $endpos } }

typecase:
| labels(uident) params { floc $startpos $endpos, $1, $2 }

(* Logic declarations *)

logic_decl_constant:
| labels(lident_rich) cast preceded(EQUAL,lexpr)?
  { { ld_ident = $1; ld_params = []; ld_type = Some $2;
      ld_def = $3; ld_loc = floc $startpos $endpos } }

logic_decl_function:
| labels(lident_rich) params cast preceded(EQUAL,lexpr)?
  { { ld_ident = $1; ld_params = $2; ld_type = Some $3;
      ld_def = $4; ld_loc = floc $startpos $endpos } }

logic_decl_predicate:
| labels(lident_rich) params preceded(EQUAL,lexpr)?
  { { ld_ident = $1; ld_params = $2; ld_type = None;
      ld_def = $3; ld_loc = floc $startpos $endpos } }

with_logic_decl:
| WITH labels(lident_rich) params cast? preceded(EQUAL,lexpr)?
  { { ld_ident = $2; ld_params = $3; ld_type = $4;
      ld_def = $5; ld_loc = floc $startpos $endpos } }

(* Inductive declarations *)

inductive_decl:
| labels(lident_rich) params inddefn
  { { in_ident = $1; in_params = $2;
      in_def = $3; in_loc = floc $startpos $endpos } }

inddefn:
| (* epsilon *)                 { [] }
| EQUAL BAR? bar_list1(indcase) { $3 }

indcase:
| labels(ident) COLON lexpr { floc $startpos $endpos, $1, $3 }

(* Type expressions *)

primitive_type:
| primitive_type_arg                  { $1 }
| lqualid primitive_type_arg+         { PPTtyapp ($1, $2) }
| primitive_type ARROW primitive_type { PPTarrow ($1, $3) }

primitive_type_arg:
| lqualid                                       { PPTtyapp ($1, []) }
| quote_lident                                  { PPTtyvar ($1, false) }
| opaque_quote_lident                           { PPTtyvar ($1, true) }
| LEFTPAR comma_list2(primitive_type) RIGHTPAR  { PPTtuple $2 }
| LEFTPAR RIGHTPAR                              { PPTtuple [] }
| LEFTPAR primitive_type RIGHTPAR               { PPTparen $2 }

(* Logic expressions *)

lexpr:
| mk_pp(lexpr_) { $1 }

lexpr_:
| lexpr_arg_
   { match $1 with (* break the infix relation chain *)
     | PPinfix (l,o,r) -> PPinnfix (l,o,r) | d -> d }
| lexpr ARROW lexpr
   { PPbinop ($1, PPimplies, $3) }
| lexpr LRARROW lexpr
   { PPbinop ($1, PPiff, $3) }
| lexpr OR lexpr
   { PPbinop ($1, PPor, $3) }
| lexpr BARBAR lexpr
   { PPbinop ($1, PPor_asym, $3) }
| lexpr AND lexpr
   { PPbinop ($1, PPand, $3) }
| lexpr AMPAMP lexpr
   { PPbinop ($1, PPand_asym, $3) }
| NOT lexpr
   { PPunop (PPnot, $2) }
| l = lexpr ; o = infix_op ; r = lexpr
   { PPinfix (l, o, r) }
| prefix_op lexpr %prec prec_prefix_op
   { PPidapp (Qident $1, [$2]) }
| lexpr_arg lexpr_arg_loc+ (* FIXME/TODO: "lexpr lexpr_arg" *)
   { let join f (e,a) = mk_pp (PPapply (f,a)) $startpos e in
     (List.fold_left join $1 $2).pp_desc }
| IF lexpr THEN lexpr ELSE lexpr
   { PPif ($2, $4, $6) }
| quant comma_list1(quant_vars) triggers DOT lexpr
   { PPquant ($1, List.concat $2, $3, $5) }
| label lexpr %prec prec_named
   { PPnamed ($1, $2) }
| LET pattern EQUAL lexpr IN lexpr
   { match $2.pat_desc with
     | PPpvar id -> PPlet (id, $4, $6)
     | PPpwild -> PPlet (id_anonymous $2.pat_loc, $4, $6)
     | PPptuple [] -> PPlet (id_anonymous $2.pat_loc,
          { $4 with pp_desc = PPcast ($4, PPTtuple []) }, $6)
     | _ -> PPmatch ($4, [$2, $6]) }
| MATCH lexpr WITH BAR? bar_list1(match_case) END
   { PPmatch ($2, $5) }
| MATCH comma_list2(lexpr) WITH BAR? bar_list1(match_case) END
   { PPmatch (mk_pp (PPtuple $2) $startpos($2) $endpos($2), $5) }
| lexpr cast
   { PPcast ($1, $2) }

lexpr_arg_loc:
| lexpr_arg { $endpos, $1 }

constant:
| INTEGER   { Number.ConstInt $1 }
| FLOAT     { Number.ConstReal $1 }

lexpr_arg:
| mk_pp(lexpr_arg_) { $1 }

lexpr_arg_:
| qualid                              { PPident $1 }
| constant                            { PPconst $1 }
| TRUE                                { PPtrue }
| FALSE                               { PPfalse }
| quote_uident                        { PPident (Qident $1) }
| o = oppref ; a = lexpr_arg          { PPidapp (Qident o, [a]) }
| lexpr_sub                           { $1 }

lexpr_dot:
| lqualid                             { PPident $1 }
| o = oppref ; a = mk_pp(lexpr_dot)   { PPidapp (Qident o, [a]) }
| lexpr_sub                           { $1 }

lexpr_sub:
| mk_pp(lexpr_dot) DOT lqualid_rich                   { PPidapp ($3,[$1]) }
| LEFTPAR lexpr RIGHTPAR                              { $2.pp_desc }
| LEFTPAR RIGHTPAR                                    { PPtuple [] }
| LEFTPAR comma_list2(lexpr) RIGHTPAR                 { PPtuple $2 }
| LEFTBRC field_list1(lexpr) RIGHTBRC                 { PPrecord $2 }
| LEFTBRC lexpr_arg WITH field_list1(lexpr) RIGHTBRC  { PPupdate ($2,$4) }
| lexpr_arg LEFTSQ lexpr RIGHTSQ
   { let id = mk_id (mixfix "[]") $startpos($2) $endpos($2) in
     PPidapp (Qident id, [$1;$3]) }
| lexpr_arg LEFTSQ lexpr LARROW lexpr RIGHTSQ
   { let id = mk_id (mixfix "[<-]") $startpos($2) $endpos($2) in
     PPidapp (Qident id, [$1;$3;$5]) }

quant:
| FORALL  { PPforall }
| EXISTS  { PPexists }
| LAMBDA  { PPlambda }
| EPSILON { Loc.errorm ~loc:(floc $startpos $endpos)
    "epsilon terms are currently not supported in WhyML" }

match_case:
| pattern ARROW lexpr   { $1, $3 }

mk_pp(X):
| d = X   { mk_pp d $startpos $endpos }

(* Triggers *)

triggers:
| (* epsilon *)                      { [] }
| LEFTSQ bar_list1(trigger) RIGHTSQ  { $2 }

trigger:
| comma_list1(lexpr) { $1 }

(* Patterns *)

pattern:
| mk_pat(pattern_)  { $1 }

pattern_:
| pat_conj                      { $1 }
| mk_pat(pat_conj) BAR pattern  { PPpor ($1,$3) }

pat_conj:
| pat_uni                       { $1 }
| comma_list2(mk_pat(pat_uni))  { PPptuple $1 }

pat_uni:
| pat_arg_                          { $1 }
| uqualid pat_arg+                  { PPpapp ($1,$2) }
| mk_pat(pat_uni) AS labels(lident) { PPpas ($1,$3) }

pat_arg:
| mk_pat(pat_arg_)  { $1 }

pat_arg_:
| UNDERSCORE                            { PPpwild }
| labels(lident)                        { PPpvar $1 }
| uqualid                               { PPpapp ($1,[]) }
| LEFTPAR RIGHTPAR                      { PPptuple [] }
| LEFTPAR pattern_ RIGHTPAR             { $2 }
| LEFTBRC field_list1(pattern) RIGHTBRC { PPprec $2 }

mk_pat(X):
| X { mk_pat $1 $startpos $endpos }

(* Binders *)

(* [param] and [binder] below must have the same grammar
   and raise [Error] in the same cases. Interpretaion of
   single-standing untyped [Qident]'s is different: [param]
   treats them as type expressions, [binder], as parameter
   names, whose type must be inferred. *)

params:
| param*  { List.concat $1 }

binders:
| binder+ { List.concat $1 }

param:
| anon_binder
   { error_param (floc $startpos $endpos) }
| primitive_type_arg
   { [floc $startpos $endpos, None, false, $1] }
| LEFTPAR GHOST primitive_type RIGHTPAR
   { [floc $startpos $endpos, None, true, $3] }
| primitive_type_arg label label*
   { match $1 with
      | PPTtyapp (Qident _, []) ->
             error_param (floc $startpos $endpos)
      | _ -> error_loc (floc $startpos($2) $endpos($2)) }
| LEFTPAR binder_vars_rest RIGHTPAR
   { match $2 with [l,_] -> error_param l
      | _ -> error_loc (floc $startpos($3) $endpos($3)) }
| LEFTPAR GHOST binder_vars_rest RIGHTPAR
   { match $3 with [l,_] -> error_param l
      | _ -> error_loc (floc $startpos($4) $endpos($4)) }
| LEFTPAR binder_vars cast RIGHTPAR
   { List.map (fun (l,i) -> l, i, false, $3) $2 }
| LEFTPAR GHOST binder_vars cast RIGHTPAR
   { List.map (fun (l,i) -> l, i, true, $4) $3 }

binder:
| anon_binder
   { error_param (floc $startpos $endpos) }
| primitive_type_arg
   { match $1 with
      | PPTtyapp (Qident id, [])
      | PPTparen (PPTtyapp (Qident id, [])) ->
             [floc $startpos $endpos, Some id, false, None]
      | _ -> [floc $startpos $endpos, None, false, Some $1] }
| LEFTPAR GHOST primitive_type RIGHTPAR
   { match $3 with
      | PPTtyapp (Qident id, []) ->
             [floc $startpos $endpos, Some id, true, None]
      | _ -> [floc $startpos $endpos, None, true, Some $3] }
| primitive_type_arg label label*
   { match $1 with
      | PPTtyapp (Qident id, []) ->
             let id = add_lab id ($2::$3) in
             [floc $startpos $endpos, Some id, false, None]
      | _ -> error_loc (floc $startpos($2) $endpos($2)) }
| LEFTPAR binder_vars_rest RIGHTPAR
   { match $2 with [l,i] -> [l, i, false, None]
      | _ -> error_loc (floc $startpos($3) $endpos($3)) }
| LEFTPAR GHOST binder_vars_rest RIGHTPAR
   { match $3 with [l,i] -> [l, i, true, None]
      | _ -> error_loc (floc $startpos($4) $endpos($4)) }
| LEFTPAR binder_vars cast RIGHTPAR
   { List.map (fun (l,i) -> l, i, false, Some $3) $2 }
| LEFTPAR GHOST binder_vars cast RIGHTPAR
   { List.map (fun (l,i) -> l, i, true, Some $4) $3 }

binder_vars:
| binder_vars_head  { List.rev $1 }
| binder_vars_rest  { $1 }

binder_vars_rest:
| binder_vars_head label label* quant_var*
   { List.rev_append (match $1 with
      | (l, Some id) :: bl ->
          let l3 = floc $startpos($3) $endpos($3) in
          (Loc.join l l3, Some (add_lab id ($2::$3))) :: bl
      | _ -> assert false) $4 }
| binder_vars_head anon_binder quant_var*
   { List.rev_append $1 ($2 :: $3) }
| anon_binder quant_var*
   { $1 :: $2 }

binder_vars_head:
| primitive_type {
    let of_id id = id.id_loc, Some id in
    let push acc = function
      | PPTtyapp (Qident id, []) -> of_id id :: acc
      | _ -> Loc.error ~loc:(floc $startpos $endpos) Error in
    match $1 with
      | PPTtyapp (Qident id, l) -> List.fold_left push [of_id id] l
      | _ -> Loc.error ~loc:(floc $startpos $endpos) Error }

quant_vars:
| quant_var+ cast? {
    List.map (function
      | loc, None -> Loc.errorm ~loc "anonymous binders are not allowed here"
      | _, Some i -> i, $2) $1 }

quant_var:
| labels(lident)  { floc $startpos $endpos, Some $1 }
| anon_binder     { $1 }

anon_binder:
| UNDERSCORE      { floc $startpos $endpos, None }

labels(X):
| X label*  { add_lab $1 $2 }

(* Idents *)

ident:
| uident { $1 }
| lident { $1 }

uident:
| UIDENT          { mk_id $1 $startpos $endpos }

lident:
| LIDENT          { mk_id $1 $startpos $endpos }
| lident_keyword  { mk_id $1 $startpos $endpos }

lident_keyword:
| MODEL           { "model" }

quote_uident:
| QUOTE_UIDENT    { mk_id ("'" ^ $1) $startpos $endpos }

quote_lident:
| QUOTE_LIDENT    { mk_id $1 $startpos $endpos }

opaque_quote_lident:
| OPAQUE_QUOTE_LIDENT { mk_id $1 $startpos $endpos }

(* Idents + symbolic operations' names *)

ident_rich:
| uident      { $1 }
| lident_rich { $1 }

lident_rich:
| lident        { $1 }
| lident_op_id  { $1 }

lident_op_id:
| LEFTPAR lident_op RIGHTPAR  { mk_id $2 $startpos $endpos }
| LEFTPAR_STAR_RIGHTPAR       { mk_id (infix "*") $startpos $endpos }

lident_op:
| op_symbol               { infix $1 }
| op_symbol UNDERSCORE    { prefix $1 }
| EQUAL                   { infix "=" }
| OPPREF                  { prefix $1 }
| LEFTSQ RIGHTSQ          { mixfix "[]" }
| LEFTSQ LARROW RIGHTSQ   { mixfix "[<-]" }
| LEFTSQ RIGHTSQ LARROW   { mixfix "[]<-" }

op_symbol:
| OP1   { $1 }
| OP2   { $1 }
| OP3   { $1 }
| OP4   { $1 }

%inline oppref:
| o = OPPREF { mk_id (prefix o)  $startpos $endpos }

prefix_op:
| op_symbol { mk_id (prefix $1)  $startpos $endpos }

%inline infix_op:
| o = OP1   { mk_id (infix o)    $startpos $endpos }
| o = OP2   { mk_id (infix o)    $startpos $endpos }
| o = OP3   { mk_id (infix o)    $startpos $endpos }
| o = OP4   { mk_id (infix o)    $startpos $endpos }
| EQUAL     { mk_id (infix "=")  $startpos $endpos }
| LTGT      { mk_id (infix "<>") $startpos $endpos }

(* Qualified idents *)

qualid:
| ident_rich              { Qident $1 }
| uqualid DOT ident_rich  { Qdot ($1, $3) }

lqualid_rich:
| lident_rich             { Qident $1 }
| uqualid DOT lident_rich { Qdot ($1, $3) }

lqualid:
| lident              { Qident $1 }
| uqualid DOT lident  { Qdot ($1, $3) }

uqualid:
| uident              { Qident $1 }
| uqualid DOT uident  { Qdot ($1, $3) }

(* Theory/Module names *)

tqualid:
| uident                { Qident $1 }
| any_qualid DOT uident { Qdot ($1, $3) }

any_qualid:
| sident                { Qident $1 }
| any_qualid DOT sident { Qdot ($1, $3) }

sident:
| ident   { $1 }
| STRING  { mk_id $1 $startpos $endpos }

label:
| STRING    { Lstr (Ident.create_label $1) }
| POSITION  { Lpos $1 }

(****************************************************************************)

program_file:
| theory_or_module* EOF { Incremental.close_file () }

theory_or_module:
| theory_head theory_decl* END  { Incremental.close_theory () }
| module_head module_decl* END  { Incremental.close_module () }

module_head:
| MODULE labels(uident)  { Incremental.open_module $2 }

module_decl:
| decl            { Incremental.new_decl  (floc $startpos $endpos) $1 }
| pdecl           { Incremental.new_pdecl (floc $startpos $endpos) $1 }
| use_clone       { Incremental.use_clone (floc $startpos $endpos) $1 }
| namespace_head module_decl* END
    { Incremental.close_namespace (floc $startpos($1) $endpos($1)) $1 }

pdecl:
| LET top_ghost labels(lident_rich) EQUAL fun_expr  { Dfun ($3, $2, $5) }
| LET top_ghost labels(lident_rich) fun_defn        { Dfun ($3, $2, $4) }
| LET REC with_list1(rec_defn)                      { Drec $3 }
| VAL top_ghost labels(lident_rich) type_v          { Dval ($3, $2, $4) }
| EXCEPTION labels(uident)                          { Dexn ($2, PPTtuple []) }
| EXCEPTION labels(uident) primitive_type           { Dexn ($2, $3) }

(*
type_c:
| spec arrow_type_v { $2, $1 }
| simple_type_c     { $1 }
*)

type_v:
| arrow_type_v  { $1 }
| cast          { Tpure $1 }

arrow_type_v:
| param params tail_type_c  { Tarrow ($1 @ $2, $3) }

tail_type_c:
| single_spec spec arrow_type_v   { $3, spec_union $1 $2 }
| COLON simple_type_c             { $2 }

simple_type_c:
| primitive_type spec { Tpure $1, $2 }

rec_defn:
| top_ghost labels(lident_rich) binders cast? spec EQUAL spec seq_expr
   { $2, $1, ($3, $4, $8, spec_union $5 $7) }

fun_defn:
| binders cast? spec EQUAL spec seq_expr { ($1, $2, $6, spec_union $3 $5) }

fun_expr:
| FUN binders spec ARROW spec seq_expr { ($2, None, $6, spec_union $3 $5) }

(* Expressions *)

expr:
| mk_expr(expr_)  { $1 }

expr_:
| expr_arg_
   { match $1 with (* break the infix relation chain *)
     | Einfix (l,o,r) -> Einnfix (l,o,r) | d -> d }
| expr LARROW expr
   { match $1.expr_desc with
     | Eidapp (q, [e1]) -> Eassign (e1, q, $3)
     | Eidapp (Qident id, [e1;e2]) when id.id = mixfix "[]" ->