59 lines
1.7 KiB
Lean4
59 lines
1.7 KiB
Lean4
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import Spa.Language.Base
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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 Mathlib.Data.Finset.Sort
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import Mathlib.Data.String.Basic
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namespace Spa
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structure Program where
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rootStmt : Stmt
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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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abbrev State : Type := p.graph.Index
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def initialState : p.State := (buildCfg p.rootStmt).wrapInput
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def finalState : p.State := (buildCfg p.rootStmt).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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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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exact tr
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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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theorem states_complete (s : p.State) : s ∈ p.states := p.graph.mem_indices s
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theorem states_nodup : p.states.Nodup := p.graph.nodup_indices
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def code (st : p.State) : List BasicStmt := p.graph.nodes st
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def incoming (s : p.State) : List p.State := p.graph.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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(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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end Program
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end Spa
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