From 6aeb6455cc52172fbb78999b17503d9a66ce7bfb Mon Sep 17 00:00:00 2001 From: Xavier Leroy Date: Mon, 12 Oct 2020 16:36:03 +0200 Subject: Add `string_of_ident` conversion This is the left inverse of `ident_to_string`. Closes: #372 --- exportclight/Clightdefs.v | 110 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 110 insertions(+) (limited to 'exportclight') diff --git a/exportclight/Clightdefs.v b/exportclight/Clightdefs.v index c2b38a92..8af920df 100644 --- a/exportclight/Clightdefs.v +++ b/exportclight/Clightdefs.v @@ -179,3 +179,113 @@ Ltac ident_of_string s := Notation "$ s" := (ltac:(ident_of_string s)) (at level 1, only parsing) : string_scope. + +(** The inverse conversion, from encoded strings to strings *) + +Section DECODE_BITS. + +Variable rec: positive -> string. + +Fixpoint decode_n_bits (n: nat) (l: list bool) (p: positive) : string := + match n with + | O => + match l with + | b7 :: b6 :: b5 :: b4 :: b3 :: b2 :: b1 :: b0 :: _ => + String (Ascii b7 b6 b5 b4 b3 b2 b1 b0) (rec p) + | _ => EmptyString + end + | S n => + match p with + | xO q => decode_n_bits n (false :: l) q + | xI q => decode_n_bits n (true :: l) q + | xH => EmptyString + end + end. + +Definition decode_8_bits := Eval compute in (decode_n_bits 8%nat nil). + +End DECODE_BITS. + +Fixpoint string_of_ident (p: positive) : string := + match p with + | xO (xO (xO (xO (xO (xO p))))) => String "0"%char (string_of_ident p) + | xI (xO (xO (xO (xO (xO p))))) => String "1"%char (string_of_ident p) + | xO (xI (xO (xO (xO (xO p))))) => String "2"%char (string_of_ident p) + | xI (xI (xO (xO (xO (xO p))))) => String "3"%char (string_of_ident p) + | xO (xO (xI (xO (xO (xO p))))) => String "4"%char (string_of_ident p) + | xI (xO (xI (xO (xO (xO p))))) => String "5"%char (string_of_ident p) + | xO (xI (xI (xO (xO (xO p))))) => String "6"%char (string_of_ident p) + | xI (xI (xI (xO (xO (xO p))))) => String "7"%char (string_of_ident p) + | xO (xO (xO (xI (xO (xO p))))) => String "8"%char (string_of_ident p) + | xI (xO (xO (xI (xO (xO p))))) => String "9"%char (string_of_ident p) + | xO (xI (xO (xI (xO (xO p))))) => String "a"%char (string_of_ident p) + | xI (xI (xO (xI (xO (xO p))))) => String "b"%char (string_of_ident p) + | xO (xO (xI (xI (xO (xO p))))) => String "c"%char (string_of_ident p) + | xI (xO (xI (xI (xO (xO p))))) => String "d"%char (string_of_ident p) + | xO (xI (xI (xI (xO (xO p))))) => String "e"%char (string_of_ident p) + | xI (xI (xI (xI (xO (xO p))))) => String "f"%char (string_of_ident p) + | xO (xO (xO (xO (xI (xO p))))) => String "g"%char (string_of_ident p) + | xI (xO (xO (xO (xI (xO p))))) => String "h"%char (string_of_ident p) + | xO (xI (xO (xO (xI (xO p))))) => String "i"%char (string_of_ident p) + | xI (xI (xO (xO (xI (xO p))))) => String "j"%char (string_of_ident p) + | xO (xO (xI (xO (xI (xO p))))) => String "k"%char (string_of_ident p) + | xI (xO (xI (xO (xI (xO p))))) => String "l"%char (string_of_ident p) + | xO (xI (xI (xO (xI (xO p))))) => String "m"%char (string_of_ident p) + | xI (xI (xI (xO (xI (xO p))))) => String "n"%char (string_of_ident p) + | xO (xO (xO (xI (xI (xO p))))) => String "o"%char (string_of_ident p) + | xI (xO (xO (xI (xI (xO p))))) => String "p"%char (string_of_ident p) + | xO (xI (xO (xI (xI (xO p))))) => String "q"%char (string_of_ident p) + | xI (xI (xO (xI (xI (xO p))))) => String "r"%char (string_of_ident p) + | xO (xO (xI (xI (xI (xO p))))) => String "s"%char (string_of_ident p) + | xI (xO (xI (xI (xI (xO p))))) => String "t"%char (string_of_ident p) + | xO (xI (xI (xI (xI (xO p))))) => String "u"%char (string_of_ident p) + | xI (xI (xI (xI (xI (xO p))))) => String "v"%char (string_of_ident p) + | xO (xO (xO (xO (xO (xI p))))) => String "w"%char (string_of_ident p) + | xI (xO (xO (xO (xO (xI p))))) => String "x"%char (string_of_ident p) + | xO (xI (xO (xO (xO (xI p))))) => String "y"%char (string_of_ident p) + | xI (xI (xO (xO (xO (xI p))))) => String "z"%char (string_of_ident p) + | xO (xO (xI (xO (xO (xI p))))) => String "A"%char (string_of_ident p) + | xI (xO (xI (xO (xO (xI p))))) => String "B"%char (string_of_ident p) + | xO (xI (xI (xO (xO (xI p))))) => String "C"%char (string_of_ident p) + | xI (xI (xI (xO (xO (xI p))))) => String "D"%char (string_of_ident p) + | xO (xO (xO (xI (xO (xI p))))) => String "E"%char (string_of_ident p) + | xI (xO (xO (xI (xO (xI p))))) => String "F"%char (string_of_ident p) + | xO (xI (xO (xI (xO (xI p))))) => String "G"%char (string_of_ident p) + | xI (xI (xO (xI (xO (xI p))))) => String "H"%char (string_of_ident p) + | xO (xO (xI (xI (xO (xI p))))) => String "I"%char (string_of_ident p) + | xI (xO (xI (xI (xO (xI p))))) => String "J"%char (string_of_ident p) + | xO (xI (xI (xI (xO (xI p))))) => String "K"%char (string_of_ident p) + | xI (xI (xI (xI (xO (xI p))))) => String "L"%char (string_of_ident p) + | xO (xO (xO (xO (xI (xI p))))) => String "M"%char (string_of_ident p) + | xI (xO (xO (xO (xI (xI p))))) => String "N"%char (string_of_ident p) + | xO (xI (xO (xO (xI (xI p))))) => String "O"%char (string_of_ident p) + | xI (xI (xO (xO (xI (xI p))))) => String "P"%char (string_of_ident p) + | xO (xO (xI (xO (xI (xI p))))) => String "Q"%char (string_of_ident p) + | xI (xO (xI (xO (xI (xI p))))) => String "R"%char (string_of_ident p) + | xO (xI (xI (xO (xI (xI p))))) => String "S"%char (string_of_ident p) + | xI (xI (xI (xO (xI (xI p))))) => String "T"%char (string_of_ident p) + | xO (xO (xO (xI (xI (xI p))))) => String "U"%char (string_of_ident p) + | xI (xO (xO (xI (xI (xI p))))) => String "V"%char (string_of_ident p) + | xO (xI (xO (xI (xI (xI p))))) => String "W"%char (string_of_ident p) + | xI (xI (xO (xI (xI (xI p))))) => String "X"%char (string_of_ident p) + | xO (xO (xI (xI (xI (xI p))))) => String "Y"%char (string_of_ident p) + | xI (xO (xI (xI (xI (xI p))))) => String "Z"%char (string_of_ident p) + | xO (xI (xI (xI (xI (xI p))))) => String "_"%char (string_of_ident p) + | xI (xI (xI (xI (xI (xI p))))) => decode_8_bits string_of_ident p + | _ => EmptyString + end. + +Lemma string_of_ident_of_string: + forall s, string_of_ident (ident_of_string s) = s. +Proof. + induction s as [ | c s]; simpl. +- auto. +- rewrite <- IHs at 2. destruct c as [[] [] [] [] [] [] [] []]; reflexivity. +Qed. + +Corollary ident_of_string_injective: + forall s1 s2, ident_of_string s1 = ident_of_string s2 -> s1 = s2. +Proof. + intros. rewrite <- (string_of_ident_of_string s1), <- (string_of_ident_of_string s2). + congruence. +Qed. -- cgit