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-rw-r--r--Source/Dafny/Dafny.atg14
-rw-r--r--Source/Dafny/Parser.cs82
-rw-r--r--Source/Dafny/Resolver.cs35
-rw-r--r--Test/dafny0/EqualityTypes.dfy112
-rw-r--r--Test/dafny0/EqualityTypes.dfy.expect24
5 files changed, 220 insertions, 47 deletions
diff --git a/Source/Dafny/Dafny.atg b/Source/Dafny/Dafny.atg
index 6e939968..f30542d0 100644
--- a/Source/Dafny/Dafny.atg
+++ b/Source/Dafny/Dafny.atg
@@ -299,6 +299,9 @@ bool IsGenericInstantiation() {
return false;
}
}
+/* Returns true if the next thing is of the form:
+ * "<" Type { "," Type } ">"
+ */
bool IsTypeList(ref IToken pt) {
if (pt.kind != _openAngleBracket) {
return false;
@@ -306,6 +309,10 @@ bool IsTypeList(ref IToken pt) {
pt = scanner.Peek();
return IsTypeSequence(ref pt, _closeAngleBracket);
}
+/* Returns true if the next thing is of the form:
+ * Type { "," Type }
+ * followed by an endBracketKind.
+ */
bool IsTypeSequence(ref IToken pt, int endBracketKind) {
while (true) {
if (!IsType(ref pt)) {
@@ -343,7 +350,7 @@ bool IsType(ref IToken pt) {
case _map:
case _imap:
pt = scanner.Peek();
- return IsTypeList(ref pt);
+ return pt.kind != _openAngleBracket || IsTypeList(ref pt);
case _ident:
while (true) {
// invariant: next token is an ident
@@ -362,6 +369,11 @@ bool IsType(ref IToken pt) {
}
case _openparen:
pt = scanner.Peek();
+ if (pt.kind == _closeparen) {
+ // end of type list
+ pt = scanner.Peek();
+ return true;
+ }
return IsTypeSequence(ref pt, _closeparen);
default:
return false;
diff --git a/Source/Dafny/Parser.cs b/Source/Dafny/Parser.cs
index 0c88cc22..76e0ebba 100644
--- a/Source/Dafny/Parser.cs
+++ b/Source/Dafny/Parser.cs
@@ -74,8 +74,8 @@ public class Parser {
public const int _ellipsis = 58;
public const int maxT = 138;
- const bool _T = true;
- const bool _x = false;
+ const bool T = true;
+ const bool x = false;
const int minErrDist = 2;
public Scanner/*!*/ scanner;
@@ -370,6 +370,9 @@ bool IsGenericInstantiation() {
return false;
}
}
+/* Returns true if the next thing is of the form:
+ * "<" Type { "," Type } ">"
+ */
bool IsTypeList(ref IToken pt) {
if (pt.kind != _openAngleBracket) {
return false;
@@ -377,6 +380,10 @@ bool IsTypeList(ref IToken pt) {
pt = scanner.Peek();
return IsTypeSequence(ref pt, _closeAngleBracket);
}
+/* Returns true if the next thing is of the form:
+ * Type { "," Type }
+ * followed by an endBracketKind.
+ */
bool IsTypeSequence(ref IToken pt, int endBracketKind) {
while (true) {
if (!IsType(ref pt)) {
@@ -414,7 +421,7 @@ bool IsType(ref IToken pt) {
case _map:
case _imap:
pt = scanner.Peek();
- return IsTypeList(ref pt);
+ return pt.kind != _openAngleBracket || IsTypeList(ref pt);
case _ident:
while (true) {
// invariant: next token is an ident
@@ -433,6 +440,11 @@ bool IsType(ref IToken pt) {
}
case _openparen:
pt = scanner.Peek();
+ if (pt.kind == _closeparen) {
+ // end of type list
+ pt = scanner.Peek();
+ return true;
+ }
return IsTypeSequence(ref pt, _closeparen);
default:
return false;
@@ -4377,38 +4389,38 @@ List<Expression/*!*/>/*!*/ decreases, ref Attributes decAttrs, ref Attributes mo
}
static readonly bool[,]/*!*/ set = {
- {_T,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_T, _x,_x,_x,_T, _x,_x,_T,_T, _T,_x,_x,_T, _T,_x,_x,_T, _T,_x,_T,_T, _T,_T,_T,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _T,_x,_x,_T, _T,_T,_x,_x, _T,_x,_x,_T, _T,_T,_T,_T, _T,_T,_x,_T, _T,_x,_x,_T, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_T,_x,_x, _T,_x,_x,_x, _x,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_x,_T, _T,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_T,_T,_x, _x,_T,_x,_x, _x,_x,_x,_T, _T,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_T,_x,_x, _x,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _x,_x,_T,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _T,_T,_x,_x, _T,_x,_T,_x, _x,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_x,_T, _T,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_T,_T,_T, _x,_T,_T,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_x, _T,_T,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _T,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_T,_T,_T, _T,_T,_x,_T, _T,_T,_T,_x, _x,_T,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _T,_T,_x,_x, _T,_x,_x,_x, _x,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_x,_T, _T,_T,_T,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_T,_T,_x, _x,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _T,_x,_x,_T, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_T,_T,_T, _x,_T,_T,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_T,_x, _T,_T,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _T,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_T,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _T,_x,_x,_T, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_T,_T,_T, _x,_T,_T,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _x,_T,_x,_x, _x,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_x, _T,_T,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _T,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_T,_T,_T, _x,_T,_T,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _x,_T,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_x, _T,_T,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _T,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_x, _x,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _T,_x,_x,_T, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_x,_T, _T,_x,_x,_T, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_x,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_T,_T,_T, _x,_T,_T,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _x,_T,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_T,_T,_x, _T,_T,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_T, _T,_T,_x,_x, _T,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_x,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_T,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_T, _T,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_x,_T, _T,_x,_x,_T, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_x,_x,_x},
- {_x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_T,_T,_x, _x,_T,_T,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_T,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _T,_x,_x,_x, _x,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _x,_x,_x,_x, _x,_x,_T,_x, _T,_T,_x,_T, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x, _x,_x,_x,_x},
- {_T,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_x, _T,_T,_x,_x, _T,_x,_x,_x, _x,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_T,_T, _T,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x},
- {_T,_T,_T,_T, _T,_x,_x,_x, _T,_x,_T,_x, _x,_x,_x,_x, _x,_x,_x,_T, _T,_T,_T,_T, _T,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_x, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_x, _T,_T,_x,_x, _T,_x,_x,_x, _x,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_x,_T,_T, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_x,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x, _x,_x,_T,_T, _T,_T,_T,_T, _T,_T,_T,_T, _T,_T,_x,_x}
+ {T,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,x,x,T, x,x,x,T, x,x,T,T, T,x,x,T, T,x,x,T, T,x,T,T, T,T,T,x, x,T,x,x, x,x,x,x, x,x,T,x, x,x,x,x, x,x,x,x, x,T,x,T, T,x,x,T, T,T,x,x, T,x,x,T, T,T,T,T, T,T,x,T, T,x,x,T, x,x,T,T, T,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,T,x,x, T,x,x,x, x,T,x,T, T,T,T,T, T,T,T,T, T,x,x,T, T,T,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,T,T,x, x,T,x,x, x,x,x,T, T,T,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,T,x,x, x,T,T,T, T,T,T,T, T,T,T,T, T,T,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, x,x,T,x, x,x,x,T, x,x,x,x, x,x,x,x, T,T,x,x, T,x,T,x, x,T,x,T, T,T,T,T, T,T,T,T, T,x,x,T, T,T,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,T,T,T, x,T,T,T, T,x,x,T, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,T, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,x, T,T,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, T,x,x,T, T,T,T,T, T,x,x,x},
+ {T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,T,T,T, T,T,x,T, T,T,T,x, x,T,x,T, x,x,x,x, x,x,x,x, T,T,x,x, T,x,x,x, x,T,x,T, T,T,T,T, T,T,T,T, T,x,x,T, T,T,T,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,x,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,T,T,x, x,T,T,T, T,T,T,T, T,T,T,T, T,T,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,x,x,T, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,x, x,T,x,x, x,x,x,x, x,x,T,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,T,x,T, T,x,x,T, x,x,T,T, T,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,x,x,x},
+ {T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,x,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,T,T,T, x,T,T,T, T,x,x,T, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,T, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,T,T, x,x,x,x, x,x,T,x, T,T,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, T,x,x,T, T,T,T,T, T,x,x,x},
+ {T,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,x,x,T, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,x, x,T,x,x, x,x,x,x, x,x,T,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,T,x,T, T,x,x,T, x,x,T,T, T,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,T,T,T, x,T,T,T, T,x,x,T, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,T, x,T,x,x, x,x,x,x, T,x,T,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,x, T,T,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, T,x,x,T, T,T,T,T, T,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,T,T,T, x,T,T,T, T,x,x,T, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,T, x,T,x,x, x,x,x,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,x, T,T,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, T,x,x,T, T,T,T,T, T,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,x,x,x, x,x,T,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,x,x,T, x,x,x,x, x,x,T,T, T,x,x,x, x,x,x,x, x,x,x,x, x,T,T,x, x,T,x,x, x,x,x,x, x,x,T,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,T,x,T, T,x,x,T, x,x,T,T, T,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,x,x,T, x,x,x,x, x,x,T,T, T,x,x,x, x,x,x,x, x,x,x,x, x,T,T,x, x,T,x,x, x,x,x,x, x,x,T,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,T, T,T,x,T, T,x,x,T, x,x,T,T, T,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,T,T,T, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {x,T,T,T, T,x,x,x, T,x,T,x, x,T,T,T, x,T,T,T, T,x,x,T, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,T, x,T,x,x, x,x,x,x, T,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,T,T,x, T,T,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,T, T,T,x,x, T,x,x,T, T,T,T,T, T,x,x,x},
+ {x,x,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,x,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,x,x,x},
+ {T,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,x,x,T, x,x,x,x, x,x,T,T, T,x,x,x, x,x,x,x, x,x,x,x, x,T,T,x, x,T,x,x, x,x,x,x, x,x,T,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,T,x,T, T,x,x,T, x,x,T,T, T,T,T,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,T,T, T,x,x,x},
+ {x,x,x,x, x,x,x,x, x,x,x,x, x,T,T,x, x,T,T,x, x,x,x,x, x,x,x,x, x,x,T,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, T,x,x,x, x,T,x,x, x,x,x,x, x,x,x,x, x,x,x,T, x,x,x,x, x,x,T,x, T,T,x,T, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,x, x,x,x,T, T,T,x,x, x,x,x,x, x,x,x,x, x,x,x,x},
+ {T,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,x, T,T,x,x, T,x,x,x, x,T,x,T, T,T,T,T, T,T,T,T, T,x,x,T, T,T,T,T, T,T,T,T, T,x,T,T, T,x,T,T, T,T,T,T, T,T,x,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,x,x, x,x,T,T, T,T,T,T, T,T,T,T, T,T,x,x},
+ {T,T,T,T, T,x,x,x, T,x,T,x, x,x,x,x, x,x,x,T, T,T,T,T, T,T,x,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,T,x, T,T,T,T, T,T,T,T, T,T,T,x, T,T,x,x, T,x,x,x, x,T,x,T, T,T,T,T, T,T,T,T, T,x,x,T, T,T,T,T, T,T,T,T, T,x,T,T, x,x,T,T, T,T,T,T, T,T,x,T, T,T,T,T, T,T,T,T, T,T,T,T, T,T,x,x, x,x,T,T, T,T,T,T, T,T,T,T, T,T,x,x}
};
} // end Parser
diff --git a/Source/Dafny/Resolver.cs b/Source/Dafny/Resolver.cs
index 78bc02ff..66d44706 100644
--- a/Source/Dafny/Resolver.cs
+++ b/Source/Dafny/Resolver.cs
@@ -2180,7 +2180,8 @@ namespace Microsoft.Dafny
proxy.T = new ObjectType();
return true;
}
- return !(t is TypeProxy); // all other proxies indicate the type has not yet been determined
+ // all other proxies indicate the type has not yet been determined, provided their type parameters have been
+ return !(t is TypeProxy) && t.TypeArgs.All(tt => IsDetermined(tt.Normalize()));
}
ISet<TypeProxy> UnderspecifiedTypeProxies = new HashSet<TypeProxy>();
bool CheckTypeIsDetermined(IToken tok, Type t, string what) {
@@ -2752,6 +2753,14 @@ namespace Microsoft.Dafny
foreach (var v in s.BoundVars) {
CheckEqualityTypes_Type(v.Tok, v.Type);
}
+ // do substatements and subexpressions, except attributes and ensures clauses, since they are not compiled
+ foreach (var ss in s.SubStatements) {
+ Visit(ss, st);
+ }
+ if (s.Range != null) {
+ Visit(s.Range, st);
+ }
+ return false; // we're done
}
return true;
}
@@ -2810,6 +2819,18 @@ namespace Microsoft.Dafny
foreach (var bv in e.BoundVars) {
CheckEqualityTypes_Type(bv.tok, bv.Type);
}
+ } else if (expr is MemberSelectExpr) {
+ var e = (MemberSelectExpr)expr;
+ if (e.Member is Function || e.Member is Method) {
+ var i = 0;
+ foreach (var tp in ((ICallable)e.Member).TypeArgs) {
+ var actualTp = e.TypeApplication[e.Member.EnclosingClass.TypeArgs.Count + i];
+ if (tp.MustSupportEquality && !actualTp.SupportsEquality) {
+ Error(e.tok, "type parameter {0} ({1}) passed to {5} '{2}' must support equality (got {3}){4}", i, tp.Name, e.Member.Name, actualTp, TypeEqualityErrorMessageHint(actualTp), e.Member.WhatKind);
+ }
+ i++;
+ }
+ }
} else if (expr is FunctionCallExpr) {
var e = (FunctionCallExpr)expr;
Contract.Assert(e.Function.TypeArgs.Count <= e.TypeArgumentSubstitutions.Count);
@@ -2832,7 +2853,7 @@ namespace Microsoft.Dafny
i++;
}
return false; // we've done what there is to be done
- } else if (expr is SetDisplayExpr || expr is MultiSetDisplayExpr || expr is MapDisplayExpr || expr is MultiSetFormingExpr) {
+ } else if (expr is SetDisplayExpr || expr is MultiSetDisplayExpr || expr is MapDisplayExpr || expr is MultiSetFormingExpr || expr is StaticReceiverExpr) {
// This catches other expressions whose type may potentially be illegal
CheckEqualityTypes_Type(expr.tok, expr.Type);
}
@@ -2848,11 +2869,8 @@ namespace Microsoft.Dafny
} else if (type is SetType) {
var st = (SetType)type;
var argType = st.Arg;
- if (!st.Finite) {
- Error(tok, "isets do not support equality: {0}", st);
- }
if (!argType.SupportsEquality) {
- Error(tok, "set argument type must support equality (got {0}){1}", argType, TypeEqualityErrorMessageHint(argType));
+ Error(tok, "{2}set argument type must support equality (got {0}){1}", argType, TypeEqualityErrorMessageHint(argType), st.Finite ? "" : "i");
}
CheckEqualityTypes_Type(tok, argType);
@@ -2865,11 +2883,8 @@ namespace Microsoft.Dafny
} else if (type is MapType) {
var mt = (MapType)type;
- if (!mt.Finite) {
- Error(tok, "imaps do not support equality: {0}", mt);
- }
if (!mt.Domain.SupportsEquality) {
- Error(tok, "map domain type must support equality (got {0}){1}", mt.Domain, TypeEqualityErrorMessageHint(mt.Domain));
+ Error(tok, "{2}map domain type must support equality (got {0}){1}", mt.Domain, TypeEqualityErrorMessageHint(mt.Domain), mt.Finite ? "" : "i");
}
CheckEqualityTypes_Type(tok, mt.Domain);
CheckEqualityTypes_Type(tok, mt.Range);
diff --git a/Test/dafny0/EqualityTypes.dfy b/Test/dafny0/EqualityTypes.dfy
index b2812759..c510cfb1 100644
--- a/Test/dafny0/EqualityTypes.dfy
+++ b/Test/dafny0/EqualityTypes.dfy
@@ -241,3 +241,115 @@ module Deep {
var m1 := map[ko := 5]; // error: bad type
}
}
+
+//--------------------------
+
+module UnderspecifiedTypeParameters {
+ method UP<T>()
+ function method UG<T>(): int
+ method Callee<T(==)>()
+ class TakesParam<U> { }
+
+ method MPG()
+ {
+ var g := UG(); // error: type parameter underspecified
+ UP(); // error: type parameter underspecified
+ }
+ method M() {
+ var zs: set; // error: type is underspecified
+ Callee<(int)>();
+ Callee<set>(); // error: type is underspecified
+ Callee<()>();
+ // The following
+ Callee<TakesParam>(); // error: type is underspecified
+ }
+}
+
+module EqualitySupportingTypes {
+ method P<T>()
+ function method G<T>(): int
+ class AClass<V(==),Y> {
+ static function method H<W,X(==)>(): bool
+ static method Q<A,B(==)>()
+ }
+
+ method Callee<T(==)>()
+ function method FCallee<T>(): T
+
+ datatype Dt = Dt(f: int -> int)
+ codatatype Stream<T> = Cons(T, Stream)
+
+ method M<ArbitraryTypeArg>()
+ {
+ Callee<Dt>(); // error: Dt is not an equality-supporting type
+ Callee<Stream<int>>(); // error: specified type does not support equality
+
+ // set<X> is allowed in a non-ghost context only if X is equality supporting.
+ // Ditto for multiset<X> and map<X,Y>.
+ var s3x: set<Dt>; // error: this type not allowed in a non-ghost context
+ var is3x: iset<Dt>; // error: this type not allowed in a non-ghost context
+ var mast: multiset<ArbitraryTypeArg>; // error: this type not allowed in a non-ghost context
+ var qt: seq<Stream<int>>; // allowed
+ var mp0: map<Dt,int>; // error: this type not allowed in a non-ghost context
+ var mp1: map<int,Dt>; // allowed
+ var imp0: imap<Dt,int>; // error: this type not allowed in a non-ghost context
+ var imp1: imap<int,Dt>; // allowed
+
+ var S := FCallee<set>(); // this gives s:set<?>
+ if 4 in S { // this constrains the type further to be s:set<int>
+ }
+
+ var xy: set<set<int>>;
+ var xz: set<set<Stream<int>>>; // error: set type argument must support equality
+
+ Callee<set<Stream<int>>>(); // bogus: a set shouldn't ever be allowed to take a Stream as an argument (this check seems to be missing for explicit type arguments) -- Note: language definition should be changed, because it doesn't make sense for it to talk about a type appearing in a ghost or non-ghost context. Instead, set/iset/multiset/map/imap should always be allowed to take any type argument, but these types may or may not support equality.
+ var xg := G<set<Stream<int>>>();
+
+ var ac0: AClass<int,int>;
+ var ac1: AClass<Stream<int>,int>; // error: type parameter 0 is required to support equality
+ var ac2: AClass<int,Stream<int>>;
+ var xd0 := ac0.H<real,real>();
+ var xd1 := ac1.H<Stream<real>,real>(); // error (remnant of the fact that the type of ac1 is not allowed)
+ var xd2 := ac2.H<real,Stream<real>>(); // error: type parameter 1 is required to support equality
+ var xe0 := ac0.H<real,real>;
+ var xe1 := ac1.H<Stream<real>,real>; // error (remnant of the fact that the type of ac1 is not allowed)
+ var xe2 := ac2.H<real,Stream<real>>; // error: type parameter 1 is required to support equality
+ var xh0 := AClass<int,int>.H<real,real>();
+ var xh1 := AClass<int,int>.H<Stream<real>,real>();
+ var xh2 := AClass<int,int>.H<real,Stream<real>>(); // error: type parameter 1 is required to support equality
+ var xk0 := AClass<real,real>.H<int,int>;
+ var xk1 := AClass<Stream<real>,real>.H<int,int>; // error: class type param 0 wants an equality-supporting type
+ var xk2 := AClass<real,Stream<real>>.H<int,int>;
+ AClass<Stream<int>,int>.Q<real,real>(); // error: class type param 0 wants an equality-supporting type
+ AClass<int,Stream<int>>.Q<real,real>();
+ AClass<int,Stream<int>>.Q<Stream<real>,real>();
+ AClass<int,Stream<int>>.Q<real,Stream<real>>(); // error: method type param 1 wants an equality-supporting type
+
+/*************************** TESTS YET TO COME
+ var ac8: AClass<real,real>;
+ var xd8 := (if 5/0 == 3 then ac0 else ac8).H<real,real>(); // error: this should be checked by the verifier
+
+ AClass<int,set<Stream<int>>>.Q<real,real>(); // error: cannot utter "set<Stream<int>>" Or is that okay???
+ AClass<int,int>.Q<set<Stream<real>>,real>(); // error: cannot utter "set<Stream<real>>" Or is that okay???
+ var xi0 := AClass<int,set<Stream<int>>>.H<real,real>(); // error: cannot utter "set<Stream<int>>" Or is that okay???
+ var xi1 := AClass<int,int>.H<real,set<Stream<real>>>(); // error: cannot utter "set<Stream<real>>" Or is that okay???
+
+ var x, t, s: seq<int -> int>, fii: int -> int;
+ if s == t {
+ x := 5; // error: assigning to non-ghost variable in ghost context
+ }
+ if fii in s {
+ x := 4; // error: assigning to non-ghost variable in ghost context
+ }
+ if !(fii in s) {
+ x := 3; // error: assigning to non-ghost variable in ghost context
+ }
+
+ ghost var ghostset: set<Stream<int>> := {}; // fine, since this is ghost
+ forall u | 0 <= u < 100
+ ensures var lets: set<Stream<int>> := {}; lets == lets // this is ghost, so the equality requirement doesn't apply
+ {
+ }
+*********************************************/
+ }
+}
diff --git a/Test/dafny0/EqualityTypes.dfy.expect b/Test/dafny0/EqualityTypes.dfy.expect
index 9f277582..1c02f3a0 100644
--- a/Test/dafny0/EqualityTypes.dfy.expect
+++ b/Test/dafny0/EqualityTypes.dfy.expect
@@ -35,4 +35,26 @@ EqualityTypes.dfy(238,24): Error: set argument type must support equality (got C
EqualityTypes.dfy(239,21): Error: multiset argument type must support equality (got Co)
EqualityTypes.dfy(241,8): Error: map domain type must support equality (got Co)
EqualityTypes.dfy(241,14): Error: map domain type must support equality (got Co)
-37 resolution/type errors detected in EqualityTypes.dfy
+EqualityTypes.dfy(255,13): Error: type variable 'T' in the function call to 'UG' could not be determined
+EqualityTypes.dfy(256,4): Error: type '?' to the method 'UP' is not determined
+EqualityTypes.dfy(259,8): Error: the type of this local variable is underspecified
+EqualityTypes.dfy(261,4): Error: type 'set<?>' to the method 'Callee' is not determined
+EqualityTypes.dfy(264,4): Error: type 'TakesParam<?>' to the method 'Callee' is not determined
+EqualityTypes.dfy(284,14): Error: type parameter 0 (T) passed to method Callee must support equality (got Dt)
+EqualityTypes.dfy(285,23): Error: type parameter 0 (T) passed to method Callee must support equality (got Stream<int>)
+EqualityTypes.dfy(289,8): Error: set argument type must support equality (got Dt)
+EqualityTypes.dfy(290,8): Error: iset argument type must support equality (got Dt)
+EqualityTypes.dfy(291,8): Error: multiset argument type must support equality (got ArbitraryTypeArg) (perhaps try declaring type parameter 'ArbitraryTypeArg' on line 282 as 'ArbitraryTypeArg(==)', which says it can only be instantiated with a type that supports equality)
+EqualityTypes.dfy(293,8): Error: map domain type must support equality (got Dt)
+EqualityTypes.dfy(295,8): Error: imap domain type must support equality (got Dt)
+EqualityTypes.dfy(303,8): Error: set argument type must support equality (got Stream<int>)
+EqualityTypes.dfy(309,8): Error: type parameter 0 (V) passed to type AClass must support equality (got Stream<int>)
+EqualityTypes.dfy(312,19): Error: type parameter 0 (V) passed to type AClass must support equality (got Stream<int>)
+EqualityTypes.dfy(313,19): Error: type parameter 1 (X) passed to function H must support equality (got Stream<real>)
+EqualityTypes.dfy(315,19): Error: type parameter 0 (V) passed to type AClass must support equality (got Stream<int>)
+EqualityTypes.dfy(316,19): Error: type parameter 1 (X) passed to function 'H' must support equality (got Stream<real>)
+EqualityTypes.dfy(319,31): Error: type parameter 1 (X) passed to function H must support equality (got Stream<real>)
+EqualityTypes.dfy(321,41): Error: type parameter 0 (V) passed to type AClass must support equality (got Stream<real>)
+EqualityTypes.dfy(323,28): Error: type parameter 0 (V) passed to type AClass must support equality (got Stream<int>)
+EqualityTypes.dfy(326,48): Error: type parameter 1 (B) passed to method Q must support equality (got Stream<real>)
+59 resolution/type errors detected in EqualityTypes.dfy
generated by cgit v1.2.3 (git 2.39.1) at 2024-07-06 06:30:15 +0000