Flean

Flean is an attempt at formalizing floating point numbers in Lean 4.

Goals and Non-Goals

Personally: Learn Lean in a serious but not hard way. I've already learned a lot.

In general, the idea is to (1) model the floating point numbers, (2) characterize their properties via a convenient set of rules, and (3) apply that logic to prove things about Lean's Float by declaring an interface axiomatically.

Goals

• Be capable of matching operations of normal floating points as exactly as possible IEEE 754
• Extensible to different precisions
• Theoretically capable of supporting lots of bounds on Lean's Float

Non-Goals

• Performance
• Fixed-point arithmetic
• Interval arithmetic
• Using SMT solvers to bitblast our way to happiness--which is almost certainly the most practical approach.