Reorganize proofs to make 'Program' accessible to files in Language/

lean/Spa/Language.lean

@@ -3,64 +3,4 @@ import Spa.Language.Semantics
 import Spa.Language.Graphs
 import Spa.Language.Traces
 import Spa.Language.Properties
-import Mathlib.Data.Finset.Sort
-import Mathlib.Data.String.Basic
-
-namespace Spa
-
-structure Program where
-  rootStmt : Stmt
-  /-- A memoized copy of the control-flow graph. This field is an
-      implementation detail to avoid re-computing `Graph.wrap` and `Stmt.cfg`
-      every time the program's control flow graph is needed -/
-  cfgCache : Thunk Graph := Thunk.mk fun _ => Graph.wrap rootStmt.cfg
-
-namespace Program
-
-variable (p : Program)
-
--- Runtime implementation of `cfg`: read the memoized graph.
-private def cfgImpl : Graph := p.cfgCache.get
-
-@[implemented_by cfgImpl]
-def cfg : Graph := Graph.wrap p.rootStmt.cfg
-
-abbrev State : Type := p.cfg.Index
-
-def initialState : p.State := p.rootStmt.cfg.wrapInput
-
-def finalState : p.State := p.rootStmt.cfg.wrapOutput
-
-noncomputable def trace {ρ : Env} (h : EvalStmt [] p.rootStmt ρ) :
-    Trace p.cfg p.initialState p.finalState [] ρ := by
-  obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := EndToEndTrace.wrap (Stmt.cfg_sufficient h)
-  rw [Graph.wrap_inputs, List.mem_singleton] at h₁
-  rw [Graph.wrap_outputs, List.mem_singleton] at h₂
-  subst h₁; subst h₂
-  exact tr
-
-def vars : List String := p.rootStmt.vars.sort (· ≤ ·)
-
-lemma vars_nodup : p.vars.Nodup := Finset.sort_nodup _ _
-
-def states : List p.State := p.cfg.indices
-
-lemma states_complete (s : p.State) : s ∈ p.states := p.cfg.mem_indices s
-
-lemma states_nodup : p.states.Nodup := p.cfg.nodup_indices
-
-def code (st : p.State) : Option BasicStmt := p.cfg.nodes st
-
-def incoming (s : p.State) : List p.State := p.cfg.predecessors s
-
-lemma incoming_initialState_eq_nil : p.incoming p.initialState = [] :=
-  Graph.wrap_predecessors_eq_nil p.rootStmt.cfg p.initialState
-    (by rw [Graph.wrap_inputs]; exact List.mem_singleton_self _)
-
-lemma mem_incoming_of_edge {s₁ s₂ : p.State}
-    (h : (s₁, s₂) ∈ p.cfg.edges) : s₁ ∈ p.incoming s₂ :=
-  p.cfg.mem_predecessors_of_edge h
-
-end Program
-
-end Spa
+import Spa.Language.Program