Danila Fedorin
e2df847139
Convert every theorem to lemma (mathlib's default) except the headline results a reader of each module seeks out: analyze_correct (Forward/Sign/Constant), aFix_eq/aFix_le (Fixedpoint), trace (Language), and Stmt.cfg_sufficient (Language/Properties). lemma and theorem are interchangeable keywords, so no references change. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
59 lines
1.6 KiB
Lean4
59 lines
1.6 KiB
Lean4
import Spa.Language.Base
|
||
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
|
||
|
||
namespace Program
|
||
|
||
variable (p : Program)
|
||
|
||
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
|
||
|
||
theorem 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) : List 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
|