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Danila Fedorin
2cfd0a2fb7 Lean migration: Phase 5 (language, CFGs, traces, Program) 
- Spa.Language.Base: Expr/BasicStmt/Stmt + HasVar relations; StringSet
  lifts to Finset String
- Spa.Language.Semantics: Value/Env/Env.Mem, big-step relations,
  LatticeInterpretation (respects-≈ field drops out with =)
- Spa.Language.Graphs: Graph with nodes : Fin size → List BasicStmt
  (Vec lookup lemmas lift to Fin.append_left/right), comp/link/loop/
  skipto/singleton/wrap/buildCfg, predecessors via List.finRange
- Spa.Language.Traces: Trace + EndToEndTrace (Prop-valued)
- Spa.Language.Properties: trace embeddings, loop lemmas,
  buildCfg_sufficient; the 80-line Fin-disjointness block reduces to
  castAdd_ne_natAdd + mathlib list lemmas
- Spa.Language: Program (vars via Finset.sort — toList is noncomputable)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 19:30:42 -07:00
Danila Fedorin
781d7947e0 Lean migration: Phase 4 (IterProd + FiniteMap lattices) 
- Spa.Lattice.IterProd: k-fold product, recursive Lattice instance,
  fixed height k*hA + hB, bot = build of bottoms
- Spa.Lattice.FiniteMap: spine-pinned assoc lists ({l // l.map fst = ks});
  with = the 1100-line Map.agda collapses into positional 'combine'.
  Same lemma inventory (membership, locate, updating, GeneralizedUpdate,
  valuesAt, Provenance-union, le_of_mem_mem) — Nodup is now an explicit
  hypothesis where the Agda Map carried it intrinsically. Fixed height
  |ks|*hB still via transport along the IterProd isomorphism, which no
  longer needs Unique ks (representation is canonical).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 19:12:39 -07:00
Danila Fedorin
4c337afa9c Lean migration: Phase 3 (Unit, Prod, AboveBelow lattices) 
- Spa.Lattice.Unit: PUnit fixed height 0 (lattice lifted from mathlib)
- Spa.Lattice.Prod: chain unzip + FixedHeight (h1+h2) on products
  (componentwise lattice lifted from mathlib's Prod.instLattice)
- Spa.Lattice.AboveBelow: flat lattice via Lattice.mk' (mirrors the Agda
  semilattices+absorption construction), boundedness via rank into Nat,
  Plain x ↦ plainFixedHeight x, height 2

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 18:48:02 -07:00
Danila Fedorin
ae030386b4 Lean migration: Phases 0-2 (core lattice/chain, fixpoint, transport) 
- lean/ lake project pinned to Lean v4.17.0 + mathlib v4.17.0
- Spa.Lattice: fold monotonicity, FixedHeight/BoundedChains (LTSeries-based),
  FiniteHeightLattice, chain-bottom-is-least; the rest of Lattice.agda,
  Chain.agda and Equivalence.agda lift into mathlib (see LEAN_MIGRATION.md)
- Spa.Fixedpoint: gas-based least-fixpoint computation (doStep/fix/aFix)
- Spa.Isomorphism: FixedHeight transport along monotone inverse pairs

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 18:36:43 -07:00
Danila Fedorin
1c2bcc2d92 Require bottom element to actually be bottom; finish proof 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-16 20:15:10 -08:00
Danila Fedorin
da2b6dd5c6 Make code less brittle for when \McL changes 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-16 19:43:10 -08:00
Danila Fedorin
c64504b819 Fix broken code by moving fins to utils 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-16 19:33:56 -08:00
Danila Fedorin
4a9e7492f4 Prove the other direction for associativity 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-16 19:31:39 -08:00
Danila Fedorin
ba57e2558d Add more cases for associativity lemma 2026-02-16 17:43:07 -08:00
Danila Fedorin
1c37141234 Add more properties about lattices 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-16 17:43:07 -08:00
Danila Fedorin
9072da4ab6 Add some cases for associativity lemma 2026-02-16 17:42:59 -08:00
Danila Fedorin
3f923c2d7d Clean up some definitions 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-16 12:57:59 -08:00
Danila Fedorin
01555ee203 Make progress on properties of the dependent product 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-16 01:08:34 -08:00
Danila Fedorin
a083f2f4ae Construct proofs of 'basic' lattices 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-14 14:40:15 -08:00
Danila Fedorin
27f65c10f7 Prove absroption laws 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-14 14:22:27 -08:00
Danila Fedorin
c6e525ad7c Add associativity proofs 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-14 13:47:39 -08:00
Danila Fedorin
ccc3c7d5c7 Add meet/join operation and some properties 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-12 20:16:02 -08:00
Danila Fedorin
05c55498ce Extend proofs to meet as well as join 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-12 17:12:01 -08:00
Danila Fedorin
6b462f1a83 Prove that having a total join function is decidable 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-05 16:54:22 -08:00
Danila Fedorin
7382c632bc Add some proofs about predecessors 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2026-02-05 16:16:12 -08:00
Danila Fedorin
aa32706120 Fix typo 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-12-23 14:07:45 -08:00
Danila Fedorin
4b0541caf5 Use "top" instead of T 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-12-23 14:06:28 -08:00
Danila Fedorin
299938d97e Add decidability proofs for properties 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-12-07 22:25:47 -08:00
Danila Fedorin
927030c337 Prove that having a top and bottom element is decidable 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-12-07 19:28:56 -08:00
Danila Fedorin
ef3c351bb0 Add some utility proofs about uniqueness etc. 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-12-07 19:28:27 -08:00
Danila Fedorin
84c4ea6936 Prove final postulate about cycles in graphs 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-29 22:46:49 -08:00
Danila Fedorin
a277c8f969 Prove walk splitting 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-29 21:34:39 -08:00
Danila Fedorin
d1700f23fa Add some helpers 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-29 13:24:27 -08:00
Danila Fedorin
eb2d64f3b5 Properly state all-paths property using simple walks 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 21:31:54 -08:00
Danila Fedorin
14214ab5e7 Reorder definitions to be in the order the graph is built up 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 17:09:57 -08:00
Danila Fedorin
baece236d3 Re-define 'interior' 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 17:09:14 -08:00
Danila Fedorin
6f642d85e0 Put self-paths into the adjacency graph 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 17:08:56 -08:00
Danila Fedorin
25fa0140f0 Switch to a path definition that allows trivial self-loops 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 16:30:10 -08:00
Danila Fedorin
27621992ad Rename a helper 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 16:25:46 -08:00
Danila Fedorin
e409cceae5 Start on an initial implementation of DAG-based builder 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 16:24:48 -08:00
Danila Fedorin
8cb082e3c5 Delete original builder (lol) 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 16:24:29 -08:00
Danila Fedorin
c199e9616f Factor some code out into Utils 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-11-28 16:22:17 -08:00
Danila Fedorin
f5457d8841 Move proof of least element into FiniteHeightLattice 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-26 13:16:22 +02:00
Danila Fedorin
d99d4a2893 [WIP] Demonstrate partial lattice construction 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 19:51:27 +02:00
Danila Fedorin
fbb98de40f Prove the other absorption law 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 19:26:03 +02:00
Danila Fedorin
706b593d1d Write a lemma to wrangle PartialAbsorb proofs 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 19:14:49 +02:00
Danila Fedorin
45606679f5 Prove one of the absorption laws 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 18:32:23 +02:00
Danila Fedorin
7e099a2561 Delete debugging code 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:18:31 +02:00
Danila Fedorin
2808759338 Add instances of semilattice proofs 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:18:19 +02:00
Danila Fedorin
42bb8f8792 Extend laws on Path' to Path versions 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:17:59 +02:00
Danila Fedorin
05e693594d Prove idempotence of meet and join 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:17:25 +02:00
Danila Fedorin
90e0046707 Prove missing congruence law 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 17:17:01 +02:00
Danila Fedorin
13eee93255 Remove whitespace errors 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 15:26:41 +02:00
Danila Fedorin
6243326665 Prove associativity of meet 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 15:21:59 +02:00
Danila Fedorin
7b2114cd0f Use a convenience function for creating the "greatest path" 
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
 2025-07-25 15:21:43 +02:00