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Document Program.lean

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This commit is contained in:
Danila Fedorin
2026-06-29 10:42:01 -05:00
parent fe5098095a
commit 6c05e401c1
1 changed files with 21 additions and 1 deletions
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22
lean/Spa/Language/Program.lean
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@@ -6,10 +6,14 @@ import Mathlib.Data.String.Basic
namespace Spa namespace Spa
/-- A self-contained program to be evaluated, analyzed, and transformed. -/
structure Program where structure Program where
/-- The statement at the top level of the program. Since `Spa.Stmt` contains
sequencing via `Spa.Stmt.andThen`, this can encode any number of
statements. -/
rootStmt : Stmt rootStmt : Stmt
/-- A memoized copy of the control-flow graph. This field is an /-- A memoized copy of the control-flow graph. This field is an
implementation detail to avoid re-computing `Graph.wrap` and `Stmt.cfg` implementation detail to avoid re-computing `Spa.GGraph.wrap` and `Spa.Stmt.cfg`
every time the program's control flow graph is needed -/ every time the program's control flow graph is needed -/
cfgCache : Thunk Graph := Thunk.mk fun _ => Graph.wrap rootStmt.cfg cfgCache : Thunk Graph := Thunk.mk fun _ => Graph.wrap rootStmt.cfg
@@ -20,33 +24,49 @@ variable (p : Program)
-- Runtime implementation of `cfg`: read the memoized graph. -- Runtime implementation of `cfg`: read the memoized graph.
private def cfgImpl : Graph := p.cfgCache.get private def cfgImpl : Graph := p.cfgCache.get
/-- The control flow graph corresponding to this graph. -/
@[implemented_by cfgImpl] @[implemented_by cfgImpl]
def cfg : Graph := Graph.wrap p.rootStmt.cfg def cfg : Graph := Graph.wrap p.rootStmt.cfg
/-- A state in the control flow `Spa.Graph` of this program. -/
abbrev State : Type := p.cfg.Index abbrev State : Type := p.cfg.Index
/-- Variables mentioned or defined in this program. -/
def vars : List String := p.rootStmt.vars.sort (· ≤ ·) def vars : List String := p.rootStmt.vars.sort (· ≤ ·)
/-- `vars` has no duplicates. -/
lemma vars_nodup : p.vars.Nodup := Finset.sort_nodup _ _ lemma vars_nodup : p.vars.Nodup := Finset.sort_nodup _ _
/-- All the states in the program's control flow `Spa.Graph`. -/
def states : List p.State := p.cfg.indices def states : List p.State := p.cfg.indices
/-- All states in the CFG are contained in `states`. -/
lemma states_complete (s : p.State) : s ∈ p.states := p.cfg.mem_indices s lemma states_complete (s : p.State) : s ∈ p.states := p.cfg.mem_indices s
/-- `states` has no duplicates. -/
lemma states_nodup : p.states.Nodup := p.cfg.nodup_indices lemma states_nodup : p.states.Nodup := p.cfg.nodup_indices
/-- Given a node of the program's CFG, return the code at that node.
At this time, for convenience of proofs, the CFGs have at most
one basic statement, and multi-statement basic blocks are encoded
as chains of blocks. Thus, this returns at most one `Spa.BasicStmt`. -/
def code (st : p.State) : Option BasicStmt := p.cfg.nodes st def code (st : p.State) : Option BasicStmt := p.cfg.nodes st
/-- Get the predecessors of a particular CFG node / program state. -/
def incoming (s : p.State) : List p.State := p.cfg.predecessors s def incoming (s : p.State) : List p.State := p.cfg.predecessors s
/-- The entry point of the program's CFG. -/
def initialState : p.State := Graph.wrapInput p.rootStmt.cfg def initialState : p.State := Graph.wrapInput p.rootStmt.cfg
/-- The exit point of the program's CFG. -/
def finalState : p.State := Graph.wrapOutput p.rootStmt.cfg def finalState : p.State := Graph.wrapOutput p.rootStmt.cfg
/-- `incoming` is a faithful representation of edges in the CFG. -/
lemma mem_incoming_of_edge {s₁ s₂ : p.State} lemma mem_incoming_of_edge {s₁ s₂ : p.State}
(h : (s₁, s₂) ∈ p.cfg.edges) : s₁ ∈ p.incoming s₂ := (h : (s₁, s₂) ∈ p.cfg.edges) : s₁ ∈ p.incoming s₂ :=
p.cfg.mem_predecessors_of_edge h p.cfg.mem_predecessors_of_edge h
/-- The `initialState` has no incoming edges (it's the program start). -/
lemma incoming_initialState_eq_nil : p.incoming p.initialState = [] := lemma incoming_initialState_eq_nil : p.incoming p.initialState = [] :=
GGraph.wrap_predecessors_eq_nil p.rootStmt.cfg p.initialState GGraph.wrap_predecessors_eq_nil p.rootStmt.cfg p.initialState
(by rw [Graph.wrap_inputs]; exact List.mem_singleton_self _) (by rw [Graph.wrap_inputs]; exact List.mem_singleton_self _)