Danila Fedorin
94278a6389
Introduce a finite-height lattice instance for Bool, then build the
reaching-definitions analysis on top of the forward framework:
* Spa/Lattice/Bool.lean: FiniteHeightLattice Bool (the two-element
lattice false ≤ true), making FiniteMap A Bool ks a finite-height
"power set" lattice for free.
* Spa/Analysis/Reaching.lean: DefSet prog = FiniteMap prog.State Bool
prog.states as the per-variable lattice of definition sites, with a
StmtEvaluator whose transfer function performs a strong update
(assignment to k at node s sets k's def-set to {s}).
The analysis computes a least fixed point and produces correct
reaching-definitions sets. Soundness (relating def-sets to actual
execution provenance) is deferred; not yet exposed in Spa.lean.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
25 lines
653 B
Lean4
25 lines
653 B
Lean4
import Spa.Lattice
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import Spa.Fixedpoint
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import Spa.Isomorphism
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import Spa.Lattice.Unit
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import Spa.Lattice.Prod
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import Spa.Lattice.AboveBelow
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import Spa.Lattice.IterProd
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import Spa.Lattice.FiniteMap
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import Spa.Lattice.Bool
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import Spa.Language.Base
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import Spa.Language.Notation
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import Spa.Language.Semantics
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import Spa.Language.Graphs
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import Spa.Language.Traces
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import Spa.Language.Properties
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import Spa.Language
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import Spa.Analysis.Forward.Lattices
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import Spa.Analysis.Forward.Evaluation
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import Spa.Analysis.Forward.Adapters
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import Spa.Analysis.Forward
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import Spa.Showable
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import Spa.Analysis.Utils
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import Spa.Analysis.Sign
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import Spa.Analysis.Constant
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