ec65229050
Source.Expr now has intLit and add. Compile and correctness theorem
both extend.
The add case of compile_correct exercises the compositional structure:
- IH on e1 (with extended suffix) gives the multistep for the first
operand's evaluation.
- IH on e2 (with extended prefix) gives the multistep for the second.
- A single .add step at the boundary closes the trace.
- Each intermediate state's PC is computed via array-size arithmetic
threaded through omega.
New supporting lemmas:
step_add - per-instruction step for .add
compile_add_get_op - the instruction at the end of compile (.add e1 e2)
is .add. Extracted so the dependent-rewrite issue
with array bound proofs is contained in one place.
Engineering knowledge gained (recurring patterns when extending):
- Array.getElem_append_left/right take the bound as an explicit positional
arg, not via (h := ...).
- rw on indices that appear in dependent bound proofs fails with "motive
not type correct"; factor the lookup into a separate lemma.
- convert tactic appears not to be available; rw + exact substitutes.
- simp + omega closes most arithmetic on Array.size after expansion.
- step lemmas with implicit args (a, b) need explicit (a := _) in calls
where context doesn't determine them.
Adding a constructor still follows the v0.1 recipe — one Source
constructor, one Eval rule, one compile arm, one step_X helper, one
compile_X_get_op lemma, one case in compile_correct's induction. Each
case is ~25-40 lines of proof.
Zero sorries / axioms / admits.
24 lines
653 B
Text
24 lines
653 B
Text
import TsmLean.Core.Syntax
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namespace TsmLean.Compile.Source
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/-! # Source language for compilation (v0.2).
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Integer literals + addition. The minimal "tree of operations" that
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exercises the compositional structure of the correctness proof. -/
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inductive Expr where
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| intLit : Int → Expr
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| add : Expr → Expr → Expr
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deriving Repr, Inhabited
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abbrev Value := TsmLean.Core.Value
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inductive Eval : Expr → Value → Prop where
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| intLit (n : Int) : Eval (.intLit n) (.vInt n)
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| add {e1 e2 a b}
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(h1 : Eval e1 (.vInt a))
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(h2 : Eval e2 (.vInt b)) :
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Eval (.add e1 e2) (.vInt (a + b))
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end TsmLean.Compile.Source
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