include "basics/types.ma".
include "ASM/String.ma".
include "ASM/Arithmetic.ma".
include "common/Errors.ma".

(* identifiers and their generators are tagged to differentiate them, and to
   provide extra type checking. *)

inductive identifier (tag:String) : Type[0] ≝
  an_identifier : Word → identifier tag.
  
record universe (tag:String) : Type[0] ≝
  { next_identifier : Word }.


definition new_universe : ∀tag:String. universe tag ≝
  λtag. mk_universe tag (zero ?).
  
definition fresh : ∀tag. universe tag → res (identifier tag × (universe tag)) ≝
λtag,g.
  let 〈gen, carries〉 ≝ add_with_carries ? (next_identifier ? g) (zero ?) true in
    if get_index_v ?? carries 0 ? then Error ? else
      OK ? 〈an_identifier tag (next_identifier ? g), mk_universe tag gen〉.
// qed.

definition identifier_eq : ∀tag:String. ∀x,y:identifier tag. (x=y) + (x≠y).
#tag * #x * #y lapply (refl ? (eq_bv ? x y)) cases (eq_bv ? x y) in ⊢ (???% → %)
#E [ % | %2 ]
lapply E @eq_bv_elim
[ #H #_ >H @refl | 2,3: #_ #H destruct | #H #_ % #H' destruct /2/ ]
qed.

definition identifier_of_nat : ∀tag:String. nat → identifier tag ≝
  λtag,n. an_identifier tag (bitvector_of_nat ? n).


(* Maps from identifiers to arbitrary types. *)

include "ASM/BitVectorTrie.ma".

inductive identifier_map (tag:String) (A:Type[0]) : Type[0] ≝ an_id_map : BitVectorTrie A 16 → identifier_map tag A.
definition empty_map : ∀tag:String. ∀A. identifier_map tag A ≝
  λtag,A. an_id_map tag A (Stub A 16).

definition lookup : ∀tag,A. identifier_map tag A → identifier tag → option A ≝
  λtag,A,m,l. lookup_opt A 16 (match l with [ an_identifier l' ⇒ l' ])
                              (match m with [ an_id_map m' ⇒ m' ]).

definition add : ∀tag,A. identifier_map tag A → identifier tag → A → identifier_map tag A ≝
λtag,A,m,l,a. an_id_map tag A (insert A 16 (match l with [ an_identifier l' ⇒ l' ]) a
                                           (match m with [ an_id_map m' ⇒ m' ])).