parser.mly

(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
(*  Copyright 2010-2016   --   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.                           *)
(*                                                                  *)
(********************************************************************)

%{
  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

  let use_as q = function Some x -> x | None -> qualid_last q

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

  let model_label = Ident.create_label "model"
  let model_projected = Ident.create_label "model_projected"

  let is_model_label l = match l with
    | Lstr lab -> Ident.lab_equal lab model_label ||
                  Ident.lab_equal lab model_projected
    | Lpos _ -> false

  let model_lab_present labels = List.exists is_model_label labels

  let is_model_trace_label l = match l with
    | Lstr lab -> Strings.has_prefix "model_trace:" lab.Ident.lab_string
    | Lpos _ -> false

  let model_trace_lab_present labels = List.exists is_model_trace_label labels

  let add_model_trace name labels =
    if model_lab_present labels && not (model_trace_lab_present labels) then
      (Lstr (Ident.create_label ("model_trace:" ^ name)))::labels
    else
      labels

  let add_lab id l = { id with id_lab = add_model_trace id.id_str l }

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

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

  let get_op s e = Qident (mk_id (mixfix "[]") s e)
  let set_op s e = Qident (mk_id (mixfix "[<-]") s e)
  let sub_op s e = Qident (mk_id (mixfix "[_.._]") s e)
  let above_op s e = Qident (mk_id (mixfix "[_..]") s e)
  let below_op s e = Qident (mk_id (mixfix "[.._]") s e)

  let mk_pat  d s e = { pat_desc  = d; pat_loc  = floc s e }
  let mk_term d s e = { term_desc = d; term_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
    | _, ({term_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_str = "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 <Number.integer_constant> INTEGER
%token <string> OP1 OP2 OP3 OP4 OPPREF
%token <Number.real_constant> FLOAT
%token <string> STRING
%token <Loc.position> POSITION
%token <string> QUOTE_LIDENT

(* keywords *)

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

(* program keywords *)

%token ABSTRACT ABSURD ANY ASSERT ASSUME AT BEGIN CHECK
%token DIVERGES DO DONE DOWNTO ENSURES EXCEPTION FOR
%token FUN GHOST INVARIANT LABEL MODULE MUTABLE OLD
%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 DOTDOT EQUAL 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 BY SO
%right OR BARBAR
%right AND AMPAMP
%nonassoc NOT
%right EQUAL LTGT OP1
%nonassoc AT OLD
%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 <Pmodule.pmodule Stdlib.Mstr.t> mlw_file
%%

(* Modules and scopes *)

mlw_file:
| mlw_module* EOF
    { Typing.close_file () }
| module_decl+ EOF
    { let loc = floc $startpos($2) $endpos($2) in
      Typing.close_module loc; Typing.close_file () }

mlw_module:
| module_head module_decl* END
    { Typing.close_module (floc $startpos($3) $endpos($3)) }

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

scope_head:
| SCOPE boption(IMPORT) uident
    { Typing.open_scope (floc $startpos $endpos) $3; $2 }

module_decl:
| scope_head module_decl* END
    { Typing.close_scope (floc $startpos($1) $endpos($1)) ~import:$1 }
| d = pure_decl | d = prog_decl | d = meta_decl
    { Typing.add_decl (floc $startpos $endpos) d }
| use_clone { () }

(* Use and clone *)

use_clone:
| USE EXPORT tqualid
    { Typing.add_decl (floc $startpos $endpos) (Duse $3) }
| CLONE EXPORT tqualid clone_subst
    { Typing.add_decl (floc $startpos $endpos) (Dclone ($3, $4)) }
| USE boption(IMPORT) tqualid option(preceded(AS, uident))
    { let loc = floc $startpos $endpos in
      Typing.open_scope loc (use_as $3 $4);
      Typing.add_decl loc (Duse $3);
      Typing.close_scope loc ~import:$2 }
| CLONE boption(IMPORT) tqualid option(preceded(AS, uident)) clone_subst
    { let loc = floc $startpos $endpos in
      Typing.open_scope loc (use_as $3 $4);
      Typing.add_decl loc (Dclone ($3, $5));
      Typing.close_scope loc ~import:$2 }

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

single_clone_subst:
| TYPE qualid ty_var* EQUAL ty  { CStsym  ($2,$3,$5) }
| TYPE qualid                   { CStsym  ($2, [], PTtyapp ($2, [])) }
| CONSTANT  qualid EQUAL qualid { CSfsym  ($2,$4) }
| CONSTANT  qualid              { CSfsym  ($2,$2) }
| FUNCTION  qualid EQUAL qualid { CSfsym  ($2,$4) }
| FUNCTION  qualid              { CSfsym  ($2,$2) }
| PREDICATE qualid EQUAL qualid { CSpsym  ($2,$4) }
| PREDICATE qualid              { CSpsym  ($2,$2) }
| VAL       qualid EQUAL qualid { CSvsym  ($2,$4) }
| VAL       qualid              { CSvsym  ($2,$2) }
| AXIOM     qualid              { CSaxiom ($2) }
| LEMMA     qualid              { CSlemma ($2) }
| GOAL      qualid              { CSgoal  ($2) }

(* Meta declarations *)

meta_decl:
| META sident comma_list1(meta_arg)  { Dmeta ($2, $3) }

meta_arg:
| TYPE      ty      { Mty $2 }
| CONSTANT  qualid  { Mfs $2 }
| FUNCTION  qualid  { Mfs $2 }
| PREDICATE qualid  { Mps $2 }
| AXIOM     qualid  { Max $2 }
| LEMMA     qualid  { Mlm $2 }
| GOAL      qualid  { Mgl $2 }
| STRING            { Mstr $1 }
| INTEGER           { Mint (small_integer $1) }

(* Theory declarations *)

pure_decl:
| TYPE with_list1(type_decl)                { Dtype $2 }
| CONSTANT  constant_decl                   { Dlogic [$2] }
| FUNCTION  function_decl  with_logic_decl* { Dlogic ($2::$3) }
| PREDICATE predicate_decl with_logic_decl* { Dlogic ($2::$3) }
| INDUCTIVE   with_list1(inductive_decl)    { Dind (Decl.Ind, $2) }
| COINDUCTIVE with_list1(inductive_decl)    { Dind (Decl.Coind, $2) }
| AXIOM labels(ident) COLON term            { Dprop (Decl.Paxiom, $2, $4) }
| LEMMA labels(ident) COLON term            { Dprop (Decl.Plemma, $2, $4) }
| GOAL  labels(ident) COLON term            { Dprop (Decl.Pgoal, $2, $4) }

(* Type declarations *)

type_decl:
| labels(lident) ty_var* typedefn invariant*
  { let (vis, mut), def = $3 in
    { td_ident = $1; td_params = $2;
      td_vis = vis; td_mut = mut;
      td_inv = $4; td_def = def;
      td_loc = floc $startpos $endpos } }

ty_var:
| labels(quote_lident) { $1 }

typedefn:
| (* epsilon *)
    { (Abstract, false), TDrecord [] }
| EQUAL vis_mut bar_list1(type_case)
    { $2, TDalgebraic $3 }
| EQUAL vis_mut LEFTBRC loption(semicolon_list1(type_field)) RIGHTBRC
    { $2, TDrecord $4 }
| EQUAL vis_mut ty
    { $2, TDalias $3 }

vis_mut:
| (* epsilon *)     { Public, false }
| MUTABLE           { Public, true  }
| abstract          { $1, false }
| abstract MUTABLE  { $1, true }
| MUTABLE abstract  { $2, true }

abstract:
| PRIVATE           { Private }
| ABSTRACT          { Abstract }

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

field_modifiers:
| MUTABLE       { true,  false }
| GHOST         { false, true  }
| GHOST MUTABLE { true,  true  }
| MUTABLE GHOST { true,  true  }

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

(* Logic declarations *)

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

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

predicate_decl:
| labels(lident_rich) params preceded(EQUAL,term)?
  { { 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,term)?
  { { 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 ind_defn
  { { in_ident = $1; in_params = $2;
      in_def = $3; in_loc = floc $startpos $endpos } }

ind_defn:
| (* epsilon *)             { [] }
| EQUAL bar_list1(ind_case) { $2 }

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

(* Type expressions *)

ty:
| ty_arg          { $1 }
| lqualid ty_arg+ { PTtyapp ($1, $2) }
| ty ARROW ty     { PTarrow ($1, $3) }

ty_arg:
| lqualid                           { PTtyapp ($1, []) }
| quote_lident                      { PTtyvar $1 }
| LEFTPAR comma_list2(ty) RIGHTPAR  { PTtuple $2 }
| LEFTPAR RIGHTPAR                  { PTtuple [] }
| LEFTPAR ty RIGHTPAR               { PTparen $2 }
| LEFTBRC ty RIGHTBRC               { PTpure $2 }

cast:
| COLON ty  { $2 }

(* Parameters and 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) }
| ty_arg
    { [floc $startpos $endpos, None, false, $1] }
| LEFTPAR GHOST ty RIGHTPAR
    { [floc $startpos $endpos, None, true, $3] }
| ty_arg label label*
    { match $1 with
      | PTtyapp (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
    { let l,i = $1 in [l, i, false, None] }
| ty_arg
    { match $1 with
      | PTtyapp (Qident id, [])
      | PTparen (PTtyapp (Qident id, [])) ->
             [floc $startpos $endpos, Some id, false, None]
      | _ -> [floc $startpos $endpos, None, false, Some $1] }
| LEFTPAR GHOST ty RIGHTPAR
    { match $3 with
      | PTtyapp (Qident id, []) ->
             [floc $startpos $endpos, Some id, true, None]
      | _ -> [floc $startpos $endpos, None, true, Some $3] }
| ty_arg label label*
    { match $1 with
      | PTtyapp (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* binder_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 binder_var*
    { List.rev_append $1 ($2 :: $3) }
| anon_binder binder_var*
    { $1 :: $2 }

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

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

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

(* Logical terms *)

mk_term(X): d = X { mk_term d $startpos $endpos }

term: t = mk_term(term_) { t }

term_:
| term_arg_
    { match $1 with (* break the infix relation chain *)
      | Tinfix (l,o,r) -> Tinnfix (l,o,r)
      | Tbinop (l,o,r) -> Tbinnop (l,o,r)
      | d -> d }
| NOT term
    { Tnot $2 }
| OLD term
    { Tat ($2, mk_id "0" $startpos($1) $endpos($1)) }
| term AT uident
    { Tat ($1, $3) }
| prefix_op term %prec prec_prefix_op
    { Tidapp (Qident $1, [$2]) }
| l = term ; o = bin_op ; r = term
    { Tbinop (l, o, r) }
| l = term ; o = infix_op_1 ; r = term
    { Tinfix (l, o, r) }
| l = term ; o = infix_op_234 ; r = term
    { Tidapp (Qident o, [l; r]) }
| term_arg located(term_arg)+ (* FIXME/TODO: "term term_arg" *)
    { let join f (a,_,e) = mk_term (Tapply (f,a)) $startpos e in
      (List.fold_left join $1 $2).term_desc }
| IF term THEN term ELSE term
    { Tif ($2, $4, $6) }
| LET pattern EQUAL term IN term
    { let cast ty = { $4 with term_desc = Tcast ($4, ty) } in
      let pat, def = match $2.pat_desc with
        | Ptuple [] -> { $2 with pat_desc = Pwild }, cast (PTtuple [])
        | Pcast ({pat_desc = (Pvar (_,false)|Pwild)} as p, ty) -> p, cast ty
        | _ -> $2, $4 in
      match pat.pat_desc with
      | Pvar (id,false) -> Tlet (id, def, $6)
      | Pwild -> Tlet (id_anonymous pat.pat_loc, def, $6)
      | _ -> Tmatch (def, [pat, $6]) }
| LET labels(lident_op_id) EQUAL term IN term
    { Tlet ($2, $4, $6) }
| LET labels(lident) mk_term(lam_defn) IN term
    { Tlet ($2, $3, $5) }
| LET labels(lident_op_id) mk_term(lam_defn) IN term
    { Tlet ($2, $3, $5) }
| MATCH term WITH match_cases(term) END
    { Tmatch ($2, $4) }
| MATCH comma_list2(term) WITH match_cases(term) END
    { Tmatch (mk_term (Ttuple $2) $startpos($2) $endpos($2), $4) }
| quant comma_list1(quant_vars) triggers DOT term
    { Tquant ($1, List.concat $2, $3, $5) }
| FUN binders ARROW term
    { Tquant (Dterm.DTlambda, $2, [], $4) }
| EPSILON
    { Loc.errorm "Epsilon terms are currently not supported in WhyML" }
| label term %prec prec_named
    { Tnamed ($1, $2) }
| term cast
    { Tcast ($1, $2) }

lam_defn:
| binders EQUAL term  { Tquant (Dterm.DTlambda, $1, [], $3) }

term_arg: mk_term(term_arg_) { $1 }
term_dot: mk_term(term_dot_) { $1 }

term_arg_:
| qualid                    { Tident $1 }
| numeral                   { Tconst $1 }
| TRUE                      { Ttrue }
| FALSE                     { Tfalse }
| o = oppref ; a = term_arg { Tidapp (Qident o, [a]) }
| term_sub_                 { $1 }

term_dot_:
| lqualid                   { Tident $1 }
| o = oppref ; a = term_dot { Tidapp (Qident o, [a]) }
| term_sub_                 { $1 }

term_sub_:
| term_dot DOT lqualid_rich                         { Tidapp ($3,[$1]) }
| LEFTPAR term RIGHTPAR                             { $2.term_desc }
| LEFTPAR RIGHTPAR                                  { Ttuple [] }
| LEFTPAR comma_list2(term) RIGHTPAR                { Ttuple $2 }
| LEFTBRC field_list1(term) RIGHTBRC                { Trecord $2 }
| LEFTBRC term_arg WITH field_list1(term) RIGHTBRC  { Tupdate ($2,$4) }
| term_arg LEFTSQ term RIGHTSQ
    { Tidapp (get_op $startpos($2) $endpos($2), [$1;$3]) }
| term_arg LEFTSQ term LARROW term RIGHTSQ
    { Tidapp (set_op $startpos($2) $endpos($2), [$1;$3;$5]) }
| term_arg LEFTSQ term DOTDOT term RIGHTSQ
    { Tidapp (sub_op $startpos($2) $endpos($2), [$1;$3;$5]) }
| term_arg LEFTSQ term DOTDOT RIGHTSQ
    { Tidapp (above_op $startpos($2) $endpos($2), [$1;$3]) }
| term_arg LEFTSQ DOTDOT term RIGHTSQ
    { Tidapp (below_op $startpos($2) $endpos($2), [$1;$4]) }

field_list1(X):
| fl = semicolon_list1(separated_pair(lqualid, EQUAL, X)) { fl }

match_cases(X):
| cl = bar_list1(separated_pair(pattern, ARROW, X)) { cl }

quant_vars:
| binder_var+ cast? { List.map (fun (l,i) -> l, i, false, $2) $1 }

triggers:
| (* epsilon *)                                                 { [] }
| LEFTSQ separated_nonempty_list(BAR,comma_list1(term)) RIGHTSQ { $2 }

%inline bin_op:
| ARROW   { Dterm.DTimplies }
| LRARROW { Dterm.DTiff }
| OR      { Dterm.DTor }
| BARBAR  { Dterm.DTor_asym }
| AND     { Dterm.DTand }
| AMPAMP  { Dterm.DTand_asym }
| BY      { Dterm.DTby }
| SO      { Dterm.DTso }

quant:
| FORALL  { Dterm.DTforall }
| EXISTS  { Dterm.DTexists }

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

(* Program declarations *)

prog_decl:
| VAL ghost kind labels(lident_rich) mk_expr(val_defn) { Dlet ($4, $2, $3, $5) }
| LET ghost kind labels(lident_rich) mk_expr(fun_defn) { Dlet ($4, $2, $3, $5) }
| LET ghost kind labels(lident_rich) const_defn        { Dlet ($4, $2, $3, $5) }
| LET REC with_list1(rec_defn)                         { Drec $3 }
| EXCEPTION labels(uident)            { Dexn ($2, PTtuple [], Ity.MaskVisible) }
| EXCEPTION labels(uident) return     { Dexn ($2, fst $3, snd $3) }

ghost:
| (* epsilon *) { false }
| GHOST         { true }

kind:
| (* epsilon *) { Expr.RKnone }
| FUNCTION      { Expr.RKfunc }
| CONSTANT      { Expr.RKfunc }
| PREDICATE     { Expr.RKpred }
| LEMMA         { Expr.RKlemma }

(* Function definitions *)

rec_defn:
| ghost kind labels(lident_rich) binders ret_opt spec EQUAL spec seq_expr
    { $3, $1, $2, $4, fst $5, snd $5, spec_union $6 $8, $9 }

fun_defn:
| binders ret_opt spec EQUAL spec seq_expr
    { Efun ($1, fst $2, snd $2, spec_union $3 $5, $6) }

val_defn:
| params ret_opt spec
    { Eany ($1, Expr.RKnone, fst $2, snd $2, $3) }

const_defn:
| cast EQUAL seq_expr   { { $3 with expr_desc = Ecast ($3, $1) } }
| EQUAL seq_expr        { $2 }

(* Program expressions *)

mk_expr(X): d = X { mk_expr d $startpos $endpos }

seq_expr:
| expr %prec below_SEMI   { $1 }
| expr SEMICOLON          { $1 }
| expr SEMICOLON seq_expr { mk_expr (Esequence ($1, $3)) $startpos $endpos }

expr: e = mk_expr(expr_) { e }

expr_:
| expr_arg_
    { match $1 with (* break the infix relation chain *)
      | Einfix (l,o,r) -> Einnfix (l,o,r) | d -> d }
| expr AMPAMP expr
    { Eand ($1, $3) }
| expr BARBAR expr
    { Eor ($1, $3) }
| NOT expr
    { Enot $2 }
| prefix_op expr %prec prec_prefix_op
    { Eidapp (Qident $1, [$2]) }
| l = expr ; o = infix_op_1 ; r = expr
    { Einfix (l,o,r) }
| l = expr ; o = infix_op_234 ; r = expr
    { Eidapp (Qident o, [l;r]) }
| expr_arg located(expr_arg)+ (* FIXME/TODO: "expr expr_arg" *)
    { let join f (a,_,e) = mk_expr (Eapply (f,a)) $startpos e in
      (List.fold_left join $1 $2).expr_desc }
| IF seq_expr THEN expr ELSE expr
    { Eif ($2, $4, $6) }
| IF seq_expr THEN expr %prec prec_no_else
    { Eif ($2, $4, mk_expr (Etuple []) $startpos $endpos) }
| expr LARROW expr
    { let loc = floc $startpos $endpos in
      let rec down ll rl = match ll, rl with
        | {expr_desc = Eidapp (q, [e1])}::ll, e2::rl -> (e1,q,e2) :: down ll rl
        | {expr_desc = Eidapp (Qident id, [_;_]); expr_loc = loc}::_, _::_
          when id.id_str = mixfix "[]" -> Loc.errorm ~loc
            "Parallel array assignments are not allowed"
        | {expr_loc = loc}::_, _::_ -> Loc.errorm ~loc
            "Invalid left expression in an assignment"
        | [], [] -> []
        | _ -> Loc.errorm ~loc "Invalid parallel assignment" in
      match $1.expr_desc, $3.expr_desc with
        | Eidapp (Qident id, [e1;e2]), _ when id.id_str = mixfix "[]" ->
            Eidapp (Qident {id with id_str = mixfix "[]<-"}, [e1;e2;$3])
        | Etuple ll, Etuple rl -> Eassign (down ll rl)
        | Etuple _, _ -> Loc.errorm ~loc "Invalid parallel assignment"
        | _, _ -> Eassign (down [$1] [$3]) }
| LET ghost kind let_pattern EQUAL seq_expr IN seq_expr
    { let re_pat pat d = { pat with pat_desc = d } in
      let rec ghostify pat = match pat.pat_desc with
        (* let_pattern marks the opening variable with Ptuple [_] *)
        | Ptuple [{pat_desc = Pvar (id,_)}] -> re_pat pat (Pvar (id,$2))
        | Ptuple (p::pl) -> re_pat pat (Ptuple (ghostify p :: pl))
        | Pas (p,id,gh) -> re_pat pat (Pas (ghostify p, id, gh))
        | Por (p1,p2) -> re_pat pat (Por (ghostify p1, p2))
        | Pcast (p,t) -> re_pat pat (Pcast (ghostify p, t))
        | _ when $2 -> Loc.errorm ~loc:(floc $startpos($2) $endpos($2))
            "illegal ghost qualifier" (* $4 does not start with a Pvar *)
        | _ -> pat in
      let pat = ghostify $4 in
      let kind = match pat.pat_desc with
        | _ when $3 = Expr.RKnone -> $3
        | Pvar (_,_) | Pcast ({pat_desc = Pvar (_,_)},_) -> $3
        | _ -> Loc.errorm ~loc:(floc $startpos($3) $endpos($3))
            "illegal kind qualifier" in
      let cast ty = { $6 with expr_desc = Ecast ($6, ty) } in
      let pat, def = match pat.pat_desc with
        | Ptuple [] -> re_pat pat Pwild, cast (PTtuple [])
        | Pcast ({pat_desc = (Pvar _|Pwild)} as pat, ty) -> pat, cast ty
        | _ -> pat, $6 in
      match pat.pat_desc with
      | Pvar (id, gh) -> Elet (id, gh, kind, def, $8)
      | Pwild -> Elet (id_anonymous pat.pat_loc, false, kind, def, $8)
      | _ -> Ematch (def, [pat, $8]) }
| LET ghost kind labels(lident_op_id) EQUAL seq_expr IN seq_expr
    { Elet ($4, $2, $3, $6, $8) }
| LET ghost kind labels(lident) mk_expr(fun_defn) IN seq_expr
    { Elet ($4, $2, $3, $5, $7) }
| LET ghost kind labels(lident_op_id) mk_expr(fun_defn) IN seq_expr
    { Elet ($4, $2, $3, $5, $7) }
| LET REC with_list1(rec_defn) IN seq_expr
    { Erec ($3, $5) }
| FUN binders spec ARROW spec seq_expr
    { Efun ($2, None, Ity.MaskVisible, spec_union $3 $5, $6) }
| ANY return spec
    { Eany ([], Expr.RKnone, Some (fst $2), snd $2, $3) }
| VAL ghost kind labels(lident_rich) mk_expr(val_defn) IN seq_expr
    { Elet ($4, $2, $3, $5, $7) }
| MATCH seq_expr WITH match_cases(seq_expr) END
    { Ematch ($2, $4) }
| MATCH comma_list2(expr) WITH match_cases(seq_expr) END
    { Ematch (mk_expr (Etuple $2) $startpos($2) $endpos($2), $4) }
| LABEL labels(uident) IN seq_expr
    { Emark ($2, $4) }
| WHILE seq_expr DO loop_annotation seq_expr DONE
    { let inv, var = $4 in Ewhile ($2, inv, var, $5) }
| FOR lident EQUAL seq_expr for_direction seq_expr DO invariant* seq_expr DONE
    { Efor ($2, $4, $5, $6, $8, $9) }
| ABSURD
    { Eabsurd }
| RAISE uqualid expr_arg?
    { Eraise ($2, $3) }
| RAISE LEFTPAR uqualid expr_arg? RIGHTPAR
    { Eraise ($3, $4) }
| TRY seq_expr WITH bar_list1(exn_handler) END
    { Etry ($2, $4) }
| GHOST expr
    { Eghost $2 }
| assertion_kind LEFTBRC term RIGHTBRC
    { Eassert ($1, $3) }
| label expr %prec prec_named
    { Enamed ($1, $2) }
| expr cast
    { Ecast ($1, $2) }

expr_arg: e = mk_expr(expr_arg_) { e }
expr_dot: e = mk_expr(expr_dot_) { e }

expr_arg_:
| qualid                    { Eident $1 }
| numeral                   { Econst $1 }
| TRUE                      { Etrue }
| FALSE                     { Efalse }
| o = oppref ; a = expr_arg { Eidapp (Qident o, [a]) }
| expr_sub                  { $1 }

expr_dot_:
| lqualid                   { Eident $1 }
| o = oppref ; a = expr_dot { Eidapp (Qident o, [a]) }
| expr_sub                  { $1 }

expr_sub:
| BEGIN single_spec spec seq_expr END
    { Efun ([], None, Ity.MaskVisible, spec_union $2 $3, $4) }
| BEGIN single_spec spec END
    { let e = mk_expr (Etuple []) $startpos $endpos in
      Efun ([], None, Ity.MaskVisible, spec_union $2 $3, e) }
| BEGIN seq_expr END                                { $2.expr_desc }
| LEFTPAR seq_expr RIGHTPAR                         { $2.expr_desc }
| BEGIN END                                         { Etuple [] }
| LEFTPAR RIGHTPAR                                  { Etuple [] }
| LEFTPAR comma_list2(expr) RIGHTPAR                { Etuple $2 }
| LEFTBRC field_list1(expr) RIGHTBRC                { Erecord $2 }
| LEFTBRC expr_arg WITH field_list1(expr) RIGHTBRC  { Eupdate ($2, $4) }
| expr_dot DOT lqualid_rich                         { Eidapp ($3, [$1]) }
| expr_arg LEFTSQ expr RIGHTSQ
    { Eidapp (get_op $startpos($2) $endpos($2), [$1;$3]) }
| expr_arg LEFTSQ expr LARROW expr RIGHTSQ
    { Eidapp (set_op $startpos($2) $endpos($2), [$1;$3;$5]) }
| expr_arg LEFTSQ expr DOTDOT expr RIGHTSQ
    { Eidapp (sub_op $startpos($2) $endpos($2), [$1;$3;$5]) }
| expr_arg LEFTSQ expr DOTDOT RIGHTSQ
    { Eidapp (above_op $startpos($2) $endpos($2), [$1;$3]) }
| expr_arg LEFTSQ DOTDOT expr RIGHTSQ
    { Eidapp (below_op $startpos($2) $endpos($2), [$1;$4]) }

loop_annotation:
| (* epsilon *)
    { [], [] }
| invariant loop_annotation
    { let inv, var = $2 in $1 :: inv, var }
| variant loop_annotation
    { let inv, var = $2 in inv, variant_union $1 var }