Turn buildCfg into a method
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@@ -94,7 +94,7 @@ theorem stepTrace {s₁ : prog.State} {ρ₁ ρ₂ : Env}
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theorem walkTrace {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
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(hjoin : ⟦ joinForKey s₁ (result L prog) ⟧ ρ₁)
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(tr : Trace prog.graph s₁ s₂ ρ₁ ρ₂) :
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(tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂) :
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⟦ variablesAt s₂ (result L prog) ⟧ ρ₂ := by
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induction tr with
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| single hbss => exact stepTrace hjoin hbss
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@@ -15,17 +15,17 @@ namespace Program
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variable (p : Program)
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def graph : Graph := Graph.wrap (buildCfg p.rootStmt)
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def cfg : Graph := Graph.wrap p.rootStmt.cfg
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abbrev State : Type := p.graph.Index
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abbrev State : Type := p.cfg.Index
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def initialState : p.State := (buildCfg p.rootStmt).wrapInput
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def initialState : p.State := p.rootStmt.cfg.wrapInput
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def finalState : p.State := (buildCfg p.rootStmt).wrapOutput
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def finalState : p.State := p.rootStmt.cfg.wrapOutput
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theorem trace {ρ : Env} (h : EvalStmt [] p.rootStmt ρ) :
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Trace p.graph p.initialState p.finalState [] ρ := by
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obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := EndToEndTrace.wrap (buildCfg_sufficient h)
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Trace p.cfg p.initialState p.finalState [] ρ := by
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obtain ⟨i₁, h₁, i₂, h₂, tr⟩ := EndToEndTrace.wrap (Stmt.cfg_sufficient h)
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rw [Graph.wrap_inputs, List.mem_singleton] at h₁
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rw [Graph.wrap_outputs, List.mem_singleton] at h₂
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subst h₁; subst h₂
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@@ -35,23 +35,23 @@ def vars : List String := p.rootStmt.vars.sort (· ≤ ·)
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theorem vars_nodup : p.vars.Nodup := Finset.sort_nodup _ _
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def states : List p.State := p.graph.indices
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def states : List p.State := p.cfg.indices
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theorem states_complete (s : p.State) : s ∈ p.states := p.graph.mem_indices s
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theorem states_complete (s : p.State) : s ∈ p.states := p.cfg.mem_indices s
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theorem states_nodup : p.states.Nodup := p.graph.nodup_indices
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theorem states_nodup : p.states.Nodup := p.cfg.nodup_indices
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def code (st : p.State) : List BasicStmt := p.graph.nodes st
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def code (st : p.State) : List BasicStmt := p.cfg.nodes st
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def incoming (s : p.State) : List p.State := p.graph.predecessors s
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def incoming (s : p.State) : List p.State := p.cfg.predecessors s
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theorem incoming_initialState_eq_nil : p.incoming p.initialState = [] :=
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Graph.wrap_predecessors_eq_nil (buildCfg p.rootStmt) p.initialState
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Graph.wrap_predecessors_eq_nil p.rootStmt.cfg p.initialState
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(by rw [Graph.wrap_inputs]; exact List.mem_singleton_self _)
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theorem mem_incoming_of_edge {s₁ s₂ : p.State}
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(h : (s₁, s₂) ∈ p.graph.edges) : s₁ ∈ p.incoming s₂ :=
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p.graph.mem_predecessors_of_edge h
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(h : (s₁, s₂) ∈ p.cfg.edges) : s₁ ∈ p.incoming s₂ :=
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p.cfg.mem_predecessors_of_edge h
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end Program
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@@ -167,10 +167,10 @@ export GGraph (comp link loop skipto singleton wrap loop_inputs loop_outputs)
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end Graph
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open Graph in
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def buildCfg : Stmt → Graph
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def Stmt.cfg : Stmt → Graph
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| .basic bs => singleton [bs]
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| .andThen s₁ s₂ => buildCfg s₁ ⤳ buildCfg s₂
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| .ifElse _ s₁ s₂ => buildCfg s₁ ∙ buildCfg s₂
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| .whileLoop _ s => loop (buildCfg s)
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| .andThen s₁ s₂ => s₁.cfg ⤳ s₂.cfg
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| .ifElse _ s₁ s₂ => s₁.cfg ∙ s₂.cfg
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| .whileLoop _ s => loop s.cfg
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end Spa
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@@ -174,8 +174,8 @@ theorem EndToEndTrace.wrap {g : Graph} {ρ₁ ρ₂ : Env}
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(etr : EndToEndTrace g ρ₁ ρ₂) : EndToEndTrace (Graph.wrap g) ρ₁ ρ₂ :=
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(EndToEndTrace.singleton_nil ρ₁).concat (etr.concat (EndToEndTrace.singleton_nil ρ₂))
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theorem buildCfg_sufficient {s : Stmt} {ρ₁ ρ₂ : Env}
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(h : EvalStmt ρ₁ s ρ₂) : EndToEndTrace (buildCfg s) ρ₁ ρ₂ := by
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theorem Stmt.cfg_sufficient {s : Stmt} {ρ₁ ρ₂ : Env}
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(h : EvalStmt ρ₁ s ρ₂) : EndToEndTrace s.cfg ρ₁ ρ₂ := by
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induction h with
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| basic ρ₁ ρ₂ bs hbs =>
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exact EndToEndTrace.singleton (EvalBasicStmts.cons hbs EvalBasicStmts.nil)
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