playground/coq/binN.v

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Coq

(*
- N: https://coq.inria.fr/library/Coq.Numbers.BinNums.html
- Z: https://coq.inria.fr/library/Coq.Numbers.BinNums.html
- positive: https://coq.inria.fr/library/Coq.Numbers.BinNums.html
*)
Print Nat.
Require Import Nat.
Print Nat.
Print t.
Unset Printing Notations.
Check ~True.
Set Printing Notations.
Print nat.
(*
Inductive nat : Set :=
| O : nat
| S : nat -> nat.
*)
Require Import BinNums.
Print positive.
(*
Inductive positive : Set :=
| xI : positive -> positive
| xO : positive -> positive
| xH : positive.
*)
(*Require Import BinNat.*)
Print N.
(*
Inductive N : Set :=
| N0 : N
| Npos : positive -> N.
*)
(*Require Import ZArith.*)
Print Z.
(*
Inductive Z : Set :=
| Z0 : Z
| Zpos : positive -> Z
| Zneg : positive -> Z.
*)
Require Import Reals.
Print R.
Require Import QArith.
Print Q.
(*
Record Q : Set := Qmake {
Qnum : Z;
Qden : positive
}.
*)
Check 6%positive.
Check 6%Q.
Check 6%R.
Check 6%N.
Check 6%Z.
Compute 6%xpositive.
Unset Printing Notations.
Check 6%nat.
Set Printing Notations.