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|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Numerals in different forms: signed or unsigned, possibly with
fractional part and exponent.
Numerals are represented using raw strings of (hexa)decimal
literals and a separate sign flag.
Note that this representation is not unique, due to possible
multiple leading or trailing zeros, and -0 = +0, for instances.
The reason to keep the numeral exactly as it was parsed is that
specific notations can be declared for specific numerals
(e.g. [Notation "0" := False], or [Notation "00" := (nil,nil)], or
[Notation "2e1" := ...]). Those notations override the generic
interpretation as numeral. So, one has to record the form of the
numeral which exactly matches the notation. *)
type sign = SPlus | SMinus
type num_class = CDec | CHex
type 'a exp = EDec of 'a | EBin of 'a
(** {6 String representation of a natural number } *)
module UnsignedNat :
sig
type t
val of_string : string -> t
(** Convert from a non-empty sequence of digits (which may contain "_")
(or hexdigits when starting with "0x" or "0X") *)
val to_string : t -> string
(** Convert to a non-empty sequence of digit that does not contain "_"
(or hexdigits, starting with "0x", all hexdigits are lower case) *)
val sprint : t -> string
val print : t -> Pp.t
(** [sprint] and [print] returns the numeral as it was parsed, for printing *)
val classify : t -> num_class
val compare : t -> t -> int
end
(** {6 String representation of a signed natural number } *)
module SignedNat :
sig
type t = sign * UnsignedNat.t
val of_string : string -> t
(** Convert from a non-empty sequence of (hex)digits which may contain "_" *)
val to_string : t -> string
(** Convert to a non-empty sequence of (hex)digit that does not contain "_"
(hexadecimals start with "0x" and all hexdigits are lower case) *)
val classify : t -> num_class
val of_bigint : num_class -> Bigint.bigint -> t
val to_bigint : t -> Bigint.bigint
end
(** {6 Unsigned decimal numerals } *)
module Unsigned :
sig
type t
val equal : t -> t -> bool
val is_nat : t -> bool
val to_nat : t -> string option
val sprint : t -> string
val print : t -> Pp.t
(** [sprint] and [print] returns the numeral as it was parsed, for printing *)
val parse : char Stream.t -> t
(** Parse a positive Coq numeral.
Precondition: the first char on the stream is already known to be a digit (\[0-9\]).
Precondition: at least two extra chars after the numeral to parse.
The recognized syntax is:
- integer part: \[0-9\]\[0-9_\]*
- fractional part: empty or .\[0-9_\]+
- exponent part: empty or \[eE\]\[+-\]?\[0-9\]\[0-9_\]*
or
- integer part: 0\[xX\]\[0-9a-fA-F\]\[0-9a-fA-F_\]*
- fractional part: empty or .\[0-9a-fA-F_\]+
- exponent part: empty or \[pP\]\[+-\]?\[0-9\]\[0-9_\]* *)
val parse_string : string -> t option
(** Parse the string as a non negative Coq numeral, if possible *)
val classify : t -> num_class
end
(** {6 Signed decimal numerals } *)
module Signed :
sig
type t = sign * Unsigned.t
val equal : t -> t -> bool
val is_zero : t -> bool
val of_nat : UnsignedNat.t -> t
val of_int : SignedNat.t -> t
val to_int : t -> SignedNat.t option
val is_int : t -> bool
val sprint : t -> string
val print : t -> Pp.t
(** [sprint] and [print] returns the numeral as it was parsed, for printing *)
val parse_string : string -> t option
(** Parse the string as a signed Coq numeral, if possible *)
val of_int_string : string -> t
(** Convert from a string in the syntax of OCaml's int/int64 *)
val of_string : string -> t
(** Convert from a string in the syntax of OCaml's string_of_float *)
val to_string : t -> string
(** Returns a string in the syntax of OCaml's float_of_string *)
val of_bigint : num_class -> Bigint.bigint -> t
val to_bigint : t -> Bigint.bigint option
(** Convert from and to bigint when the denotation of a bigint *)
val of_int_frac_and_exponent : SignedNat.t -> UnsignedNat.t option -> SignedNat.t option -> t
val to_int_frac_and_exponent : t -> SignedNat.t * UnsignedNat.t option * SignedNat.t option
(** n, p and q such that the number is n.p*10^q or n.p*2^q
pre/postcondition: classify n = classify p, classify q = CDec *)
val of_bigint_and_exponent : Bigint.bigint -> Bigint.bigint exp -> t
val to_bigint_and_exponent : t -> Bigint.bigint * Bigint.bigint exp
(** n and p such that the number is n*10^p or n*2^p *)
val classify : t -> num_class
val is_bigger_int_than : t -> UnsignedNat.t -> bool
(** Test if an integer whose absolute value is bounded *)
end
|
