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/*******************************************************************************
* Copyright by the contributors to the Dafny Project
* SPDX-License-Identifier: MIT
*******************************************************************************/
include "../Collections/Sequences/Seq.dfy"
include "../Functions.dfy"
include "Unicode.dfy"
include "UnicodeEncodingForm.dfy"
/**
* The Unicode encoding form that assigns each Unicode scalar value to an unsigned byte sequence of one to four bytes
* in length, as specified in Table 3-6 and Table 3-7.
*/
module {:options "-functionSyntax:4"} Utf8EncodingForm refines UnicodeEncodingForm {
type CodeUnit = bv8
//
// Definitions of well-formedness.
//
function IsMinimalWellFormedCodeUnitSubsequence(s: CodeUnitSeq): (b: bool)
{
if |s| == 1 then (
var b := IsWellFormedSingleCodeUnitSequence(s);
assert b ==> forall i | 0 < i < |s| :: !IsMinimalWellFormedCodeUnitSubsequence(s[..i]);
b
)
else if |s| == 2 then (
var b := IsWellFormedDoubleCodeUnitSequence(s);
assert b ==> forall i | 0 < i < |s| :: !IsMinimalWellFormedCodeUnitSubsequence(s[..i]);
b
)
else if |s| == 3 then (
var b := IsWellFormedTripleCodeUnitSequence(s);
assert b ==> forall i | 0 < i < |s| :: !IsMinimalWellFormedCodeUnitSubsequence(s[..i]);
b
)
else if |s| == 4 then (
var b := IsWellFormedQuadrupleCodeUnitSequence(s);
assert b ==> forall i | 0 < i < |s| :: !IsMinimalWellFormedCodeUnitSubsequence(s[..i]);
b
)
else false
}
function IsWellFormedSingleCodeUnitSequence(s: CodeUnitSeq): (b: bool)
requires |s| == 1
{
var firstByte := s[0];
&& 0x00 <= firstByte <= 0x7F
}
function IsWellFormedDoubleCodeUnitSequence(s: CodeUnitSeq): (b: bool)
requires |s| == 2
ensures b ==>
&& !IsWellFormedSingleCodeUnitSequence(s[..1])
{
var firstByte := s[0];
var secondByte := s[1];
&& 0xC2 <= firstByte <= 0xDF
&& 0x80 <= secondByte <= 0xBF
}
function IsWellFormedTripleCodeUnitSequence(s: CodeUnitSeq): (b: bool)
requires |s| == 3
ensures b ==>
&& !IsWellFormedSingleCodeUnitSequence(s[..1])
&& !IsWellFormedDoubleCodeUnitSequence(s[..2])
{
var firstByte := s[0];
var secondByte := s[1];
var thirdByte := s[2];
&& (
|| (firstByte == 0xE0 && 0xA0 <= secondByte <= 0xBF)
|| (0xE1 <= firstByte <= 0xEC && 0x80 <= secondByte <= 0xBF)
|| (firstByte == 0xED && 0x80 <= secondByte <= 0x9F)
|| (0xEE <= firstByte <= 0xEF && 0x80 <= secondByte <= 0xBF)
)
&& 0x80 <= thirdByte <= 0xBF
}
function IsWellFormedQuadrupleCodeUnitSequence(s: CodeUnitSeq): (b: bool)
requires |s| == 4
ensures b ==>
&& !IsWellFormedSingleCodeUnitSequence(s[..1])
&& !IsWellFormedDoubleCodeUnitSequence(s[..2])
&& !IsWellFormedTripleCodeUnitSequence(s[..3])
{
var firstByte := s[0];
var secondByte := s[1];
var thirdByte := s[2];
var fourthByte := s[3];
&& (
|| (firstByte == 0xF0 && 0x90 <= secondByte <= 0xBF)
|| (0xF1 <= firstByte <= 0xF3 && 0x80 <= secondByte <= 0xBF)
|| (firstByte == 0xF4 && 0x80 <= secondByte <= 0x8F)
)
&& 0x80 <= thirdByte <= 0xBF
&& 0x80 <= fourthByte <= 0xBF
}
function SplitPrefixMinimalWellFormedCodeUnitSubsequence(s: CodeUnitSeq):
(maybePrefix: Option<MinimalWellFormedCodeUnitSeq>)
{
if |s| >= 1 && IsWellFormedSingleCodeUnitSequence(s[..1]) then Some(s[..1])
else if |s| >= 2 && IsWellFormedDoubleCodeUnitSequence(s[..2]) then Some(s[..2])
else if |s| >= 3 && IsWellFormedTripleCodeUnitSequence(s[..3]) then Some(s[..3])
else if |s| >= 4 && IsWellFormedQuadrupleCodeUnitSequence(s[..4]) then Some(s[..4])
else None
}
//
// Encoding and decoding.
// See Table 3-6. UTF-8 Bit Distribution of the Unicode Standard 14.0.
//
function EncodeScalarValue(v: Unicode.ScalarValue): (m: MinimalWellFormedCodeUnitSeq)
{
if v <= 0x7F then EncodeScalarValueSingleByte(v)
else if v <= 0x7FF then EncodeScalarValueDoubleByte(v)
else if v <= 0xFFFF then EncodeScalarValueTripleByte(v)
else EncodeScalarValueQuadrupleByte(v)
}
function EncodeScalarValueSingleByte(v: Unicode.ScalarValue): (m: MinimalWellFormedCodeUnitSeq)
requires 0 <= v <= 0x7F
ensures |m| == 1
ensures IsWellFormedSingleCodeUnitSequence(m)
{
// v = 0000 0000 / 0xxx xxxx
var x := (v & 0x7F) as bv7;
// encoded = 0xxx xxxx
var firstByte := x as CodeUnit;
[firstByte]
}
function EncodeScalarValueDoubleByte(v: Unicode.ScalarValue): (s: CodeUnitSeq)
requires 0x80 <= v <= 0x7FF
ensures |s| == 2
ensures IsWellFormedDoubleCodeUnitSequence(s)
{
// v = 0000 0yyy / yyxx xxxx
var x := (v & 0x3F) as bv6;
var y := ((v & 0x7C0) >> 6) as bv5;
// encoded = 110y yyyy / 10xx xxxx
var firstByte := 0xC0 | y as CodeUnit;
var secondByte := 0x80 | x as CodeUnit;
[firstByte, secondByte]
}
function EncodeScalarValueTripleByte(v: Unicode.ScalarValue): (s: CodeUnitSeq)
requires 0x800 <= v <= 0xFFFF
ensures |s| == 3
ensures IsWellFormedTripleCodeUnitSequence(s)
{
// v = zzzz yyyy / yyxx xxxx
var x := (v & 0x3F) as bv6;
var y := ((v & 0xFC0) >> 6) as bv6;
var z := ((v & 0xF000) >> 12) as bv4;
// encoded = 1110 zzzz / 10yy yyyy / 10xx xxxx
var firstByte := 0xE0 | z as CodeUnit;
var secondByte := 0x80 | y as CodeUnit;
var thirdByte := 0x80 | x as CodeUnit;
[firstByte, secondByte, thirdByte]
}
function EncodeScalarValueQuadrupleByte(v: Unicode.ScalarValue): (s: CodeUnitSeq)
requires 0x10000 <= v <= 0x10FFFF
ensures |s| == 4
ensures IsWellFormedQuadrupleCodeUnitSequence(s)
{
// v = 000u uuuu / zzzz yyyy / yyxx xxxx
// 1 1122
assert v <= 0x1FFFFF;
var x := (v & 0x3F) as bv6;
var y := ((v & 0xFC0) >> 6) as bv6;
var z := ((v & 0xF000) >> 12) as bv4;
var u2 := ((v & 0x30000) >> 16) as bv2;
var u1 := ((v & 0x1C0000) >> 18) as bv3;
// encoded = 1111 0uuu / 10uu zzzz / 10yy yyyy / 10xx xxxx
// 111 22
var firstByte := 0xF0 | u1 as CodeUnit;
var secondByte := 0x80 | ((u2 as CodeUnit) << 4) | z as CodeUnit;
var thirdByte := 0x80 | y as CodeUnit;
var fourthByte := 0x80 | x as CodeUnit;
[firstByte, secondByte, thirdByte, fourthByte]
}
function DecodeMinimalWellFormedCodeUnitSubsequence(m: MinimalWellFormedCodeUnitSeq): (v: Unicode.ScalarValue)
{
if |m| == 1 then DecodeMinimalWellFormedCodeUnitSubsequenceSingleByte(m)
else if |m| == 2 then DecodeMinimalWellFormedCodeUnitSubsequenceDoubleByte(m)
else if |m| == 3 then DecodeMinimalWellFormedCodeUnitSubsequenceTripleByte(m)
else assert |m| == 4; DecodeMinimalWellFormedCodeUnitSubsequenceQuadrupleByte(m)
}
function DecodeMinimalWellFormedCodeUnitSubsequenceSingleByte(m: MinimalWellFormedCodeUnitSeq): (v: Unicode.ScalarValue)
requires |m| == 1
ensures 0 <= v <= 0x7F
ensures EncodeScalarValueSingleByte(v) == m
{
var firstByte := m[0];
var x := firstByte as bv7;
x as Unicode.ScalarValue
}
function DecodeMinimalWellFormedCodeUnitSubsequenceDoubleByte(m: MinimalWellFormedCodeUnitSeq): (v: Unicode.ScalarValue)
requires |m| == 2
ensures 0x80 <= v <= 0x7FF
ensures EncodeScalarValueDoubleByte(v) == m
{
var firstByte := m[0];
var secondByte := m[1];
var y := (firstByte & 0x1F) as bv24;
var x := (secondByte & 0x3F) as bv24;
(y << 6) | x as Unicode.ScalarValue
}
function DecodeMinimalWellFormedCodeUnitSubsequenceTripleByte(m: MinimalWellFormedCodeUnitSeq): (v: Unicode.ScalarValue)
requires |m| == 3
ensures 0x800 <= v <= 0xFFFF
ensures EncodeScalarValueTripleByte(v) == m
{
var firstByte := m[0];
var secondByte := m[1];
var thirdByte := m[2];
var z := (firstByte & 0xF) as bv24;
var y := (secondByte & 0x3F) as bv24;
var x := (thirdByte & 0x3F) as bv24;
assert {:split_here} true;
(z << 12) | (y << 6) | x as Unicode.ScalarValue
}
function DecodeMinimalWellFormedCodeUnitSubsequenceQuadrupleByte(m: MinimalWellFormedCodeUnitSeq): (v: Unicode.ScalarValue)
requires |m| == 4
ensures 0x10000 <= v <= 0x10FFFF
ensures EncodeScalarValueQuadrupleByte(v) == m
{
var firstByte := m[0];
var secondByte := m[1];
var thirdByte := m[2];
var fourthByte := m[3];
var u1 := (firstByte & 0x7) as bv24;
var u2 := ((secondByte & 0x30) >> 4) as bv24;
var z := (secondByte & 0xF) as bv24;
var y := (thirdByte & 0x3F) as bv24;
var x := (fourthByte & 0x3F) as bv24;
assert {:split_here} true;
(u1 << 18) | (u2 << 16) | (z << 12) | (y << 6) | x as Unicode.ScalarValue
}
}
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