The Coq Proof Assistant

# Library Coq.Numbers.Cyclic.Int63.PrimInt63

Require Export CarryType.
Register bool as kernel.ind_bool.
Register prod as kernel.ind_pair.
Register carry as kernel.ind_carry.
Register comparison as kernel.ind_cmp.
Primitive int := #int63_type.
Register int as num.int63.type.
Variant pos_neg_int63 := Pos (d:int) | Neg (d:int).
Register pos_neg_int63 as num.int63.pos_neg_int63.
Declare Scope uint63_scope.
Definition id_int : int -> int := fun x => x.
Record int_wrapper := wrap_int {int_wrap : int}.
Register wrap_int as num.int63.wrap_int.
Definition printer (x : int_wrapper) : pos_neg_int63 := Pos (int_wrap x).
Definition parser (x : pos_neg_int63) : option int :=
match x with
| Pos p => Some p
| Neg _ => None
end.
Declare Scope int63_scope.
Module Import Int63NotationsInternalA.
Delimit Scope int63_scope with int63.
End Int63NotationsInternalA.
Module Import Uint63NotationsInternalA.
Delimit Scope uint63_scope with uint63.
Bind Scope uint63_scope with int.
End Uint63NotationsInternalA.
Primitive lsl := #int63_lsl.
Primitive lsr := #int63_lsr.
Primitive land := #int63_land.
Primitive lor := #int63_lor.
Primitive lxor := #int63_lxor.
Primitive asr := #int63_asr.
Primitive add := #int63_add.
Primitive sub := #int63_sub.
Primitive mul := #int63_mul.
Primitive mulc := #int63_mulc.
Primitive div := #int63_div.
Primitive mod := #int63_mod.
Primitive divs := #int63_divs.
Primitive mods := #int63_mods.
Primitive eqb := #int63_eq.
Register eqb as num.int63.eqb.
Primitive ltb := #int63_lt.
Primitive leb := #int63_le.
Primitive ltsb := #int63_lts.
Primitive lesb := #int63_les.
Exact arithmetic operations
Primitive addc := #int63_addc.
Primitive addcarryc := #int63_addcarryc.
Primitive subc := #int63_subc.
Primitive subcarryc := #int63_subcarryc.
Primitive diveucl := #int63_diveucl.
Primitive diveucl_21 := #int63_div21.
Primitive addmuldiv := #int63_addmuldiv.
Comparison
Primitive compare := #int63_compare.
Primitive compares := #int63_compares.
Exotic operations
Primitive head0 := #int63_head0.
Primitive tail0 := #int63_tail0.
Module Export PrimInt63Notations.
Export Int63NotationsInternalA.
Export Uint63NotationsInternalA.
End PrimInt63Notations.