[Rafael-SOWNet]

Part of #2195: item 2, comparisons over Complex, with the three-valued logic the thread arrived at.

A comparison over Complex was refused (The binary operator GreaterThan is not defined for the types 'System.Numerics.Complex'). So piecewise and provided compiled over double but not over Complex. Over double, a comparison with NaN was false, which made not (x > 1) true at NaN. Evaluation says it has no truth value there.

Now a compiled statement has the truth value evaluation gives it:

• A comparison over Complex, double or float holds or fails where both sides are real, and has no truth value where one is NaN or not real.
• The connectives follow Kleene's tables, as evaluation's do: (i > 1) or true is true, (i > 1) and false is false, and not (i > 1) has none.
• A provided whose predicate has no truth value has no value, and nor has an Iverson bracket. A piecewise passes over such a case, as evaluation does: piecewise(1 provided x > 0, 3) is 3 at i.
• Compiled to bool?, a statement with no truth value is null. Compiled to bool, it is false, as one that does not hold.

Integer types compare as before. The connectives are explicit methods in ThreeValuedLogic, not .NET's lifted operators, so the tables are written down. They are named the trimmer-safe way the operator tables already are.

	2.6.0	now
not (x > 1), double -> bool, at NaN	True	False
x > 1, Complex -> bool, at i	UncompilableNodeException	False
x > 1 or true, Complex -> bool, at i	UncompilableNodeException	True
x provided x > 1, Complex -> Complex, at 2 and at i	UncompilableNodeException	2, NaN

Tests: ThreeValuedCompilationTest compiles 14 statements over Complex and over double to bool?. Each is compared with evaluation at 2, 1, 1/2, i, 1 + i and NaN. The AOT smoke test checks the same in the interpreter a native build compiles to. Full suite 17898/0, interactive trio, AOT smoke 66/0, all frameworks build.

Still open on #2195: item 1, booleans and branches in FastExpression, and mod over Complex.

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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

[codecov]

Codecov Report

❌ Patch coverage is 91.25000% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.58%. Comparing base (f950af8) to head (60883f0).
⚠️ Report is 2 commits behind head on master.

Files with missing lines	Patch %	Lines
...Functions/Compilation/IntoLinq/ThreeValuedLogic.cs	90.56%	5 Missing ⚠️
...ctions/Compilation/IntoLinq/CompilationProtocol.cs	92.59%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2208      +/-   ##
==========================================
+ Coverage   86.55%   86.58%   +0.03%     
==========================================
  Files         301      302       +1     
  Lines       66878    66950      +72     
  Branches    19428    19464      +36     
==========================================
+ Hits        57888    57971      +83     
+ Misses       4888     4878      -10     
+ Partials     4102     4101       -1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.14% <91.25%> (+0.03%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...ctions/Compilation/IntoLinq/CompilationProtocol.cs	90.24% <92.59%> (+0.92%)	⬆️
...Functions/Compilation/IntoLinq/ThreeValuedLogic.cs	90.56% <90.56%> (ø)

... and 2 files with indirect coverage changes

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