diff options
author | Ryan Lahfa | 2024-06-12 13:59:11 +0200 |
---|---|---|
committer | Ryan Lahfa | 2024-06-12 14:27:11 +0200 |
commit | f3b22b5cca9bc1154f55a81c9a82dc491074067d (patch) | |
tree | 4a3f54ee8e95dbeed37a3f3d78ec0d0ac1de7883 /backends | |
parent | e60d525fe3dffa035d2a551af624747dca6e1c1e (diff) |
backends/lean: introduce `HasIntPred` automation
`HasIntPred` enable generation of facts based on specific terms in the
context rather than their types, e.g. if the "length of a list" occurs
in the context, generate the fact 0 ≤ length of that list, which can be
further used for `scalar_tac` automation to discharge bounds goals.
The aim is to use it to simplify various height related computations,
e.g. whenever "height of a (left ; right) tree" is encountered, generate
"height left < height of a (left ; right) tree", etc.
Signed-off-by: Ryan Lahfa <ryan.lahfa@inria.fr>
Diffstat (limited to '')
-rw-r--r-- | backends/lean/Base/Arith/Int.lean | 38 | ||||
-rw-r--r-- | backends/lean/Base/IList/IList.lean | 8 |
2 files changed, 38 insertions, 8 deletions
diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean index 4a3db5f8..a1cb9da3 100644 --- a/backends/lean/Base/Arith/Int.lean +++ b/backends/lean/Base/Arith/Int.lean @@ -21,6 +21,11 @@ class HasIntProp (a : Sort u) where prop_ty : a → Prop prop : ∀ x:a, prop_ty x +/- Terms that induces predicates: if we can find the term `x`, we can introduce `concl` in the context. -/ +class HasIntPred {a: Sort u} (x: a) where + concl : Prop + prop : concl + /- Proposition with implications: if we find P we can introduce Q in the context -/ class PropHasImp (x : Prop) where concl : Prop @@ -106,12 +111,18 @@ def collectInstancesFromMainCtx (k : Expr → MetaM (Option Expr)) : Tactic.Tact let hs := HashSet.empty -- Explore the declarations let decls ← ctx.getDecls - let hs ← decls.foldlM (fun hs d => collectInstances k hs d.toExpr) hs + let hs ← decls.foldlM (fun hs d => do + -- Collect instances over all subexpressions + -- of the inferred type rather than the declaration expression + -- which is often just a name. + let ty ← Lean.Meta.inferType d.toExpr + collectInstances k hs ty + ) hs -- Also explore the goal collectInstances k hs (← Tactic.getMainTarget) -- Helper -def lookupProp (fName : String) (className : Name) (e : Expr) : MetaM (Option Expr) := do +def lookupProp (fName : String) (className : Name) (e : Expr) (instantiateClassFn : Expr → Expr → Array Expr) (instantiateProjectionFn : Expr → Array Expr) : MetaM (Option Expr) := do trace[Arith] fName -- TODO: do we need Lean.observing? -- This actually eliminates the error messages @@ -119,23 +130,31 @@ def lookupProp (fName : String) (className : Name) (e : Expr) : MetaM (Option Ex Lean.observing? do trace[Arith] m!"{fName}: observing: {e}" let ty ← Lean.Meta.inferType e - let hasProp ← mkAppM className #[ty] + let hasProp ← mkAppM className (instantiateClassFn ty e) let hasPropInst ← trySynthInstance hasProp match hasPropInst with | LOption.some i => trace[Arith] "Found {fName} instance" let i_prop ← mkProjection i (Name.mkSimple "prop") - some (← mkAppM' i_prop #[e]) + some (← mkAppM' i_prop (instantiateProjectionFn e)) | _ => none -- Return an instance of `HasIntProp` for `e` if it has some def lookupHasIntProp (e : Expr) : MetaM (Option Expr) := - lookupProp "lookupHasIntProp" ``HasIntProp e + lookupProp "lookupHasIntProp" ``HasIntProp e (fun ty _ => #[ty]) (fun e => #[e]) -- Collect the instances of `HasIntProp` for the subexpressions in the context def collectHasIntPropInstancesFromMainCtx : Tactic.TacticM (HashSet Expr) := do collectInstancesFromMainCtx lookupHasIntProp +-- Return an instance of `HasIntPred` for `e` if it has some +def lookupHasIntPred (e : Expr) : MetaM (Option Expr) := + lookupProp "lookupHasIntPred" ``HasIntPred e (fun _ term => #[term]) (fun _ => #[]) + +-- Collect the instances of `HasIntPred` for the subexpressions in the context +def collectHasIntPredInstancesFromMainCtx : Tactic.TacticM (HashSet Expr) := do + collectInstancesFromMainCtx lookupHasIntPred + -- Return an instance of `PropHasImp` for `e` if it has some def lookupPropHasImp (e : Expr) : MetaM (Option Expr) := do trace[Arith] m!"lookupPropHasImp: {e}" @@ -193,6 +212,13 @@ def introHasIntPropInstances : Tactic.TacticM (Array Expr) := do elab "intro_has_int_prop_instances" : tactic => do let _ ← introHasIntPropInstances +def introHasIntPredInstances : Tactic.TacticM (Array Expr) := do + trace[Arith] "Introducing the HasIntPred instances" + introInstances ``HasIntPred.concl lookupHasIntPred + +elab "intro_has_int_pred_instances" : tactic => do + let _ ← introHasIntPredInstances + def introPropHasImpInstances : Tactic.TacticM (Array Expr) := do trace[Arith] "Introducing the PropHasImp instances" introInstances ``PropHasImp.concl lookupPropHasImp @@ -208,6 +234,8 @@ def intTacPreprocess (extraPreprocess : Tactic.TacticM Unit) : Tactic.TacticM U Tactic.withMainContext do -- Introduce the instances of `HasIntProp` let _ ← introHasIntPropInstances + -- Introduce the instances of `HasIntPred` + let _ ← introHasIntPredInstances -- Introduce the instances of `PropHasImp` let _ ← introPropHasImpInstances -- Extra preprocessing diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean index ca5ee266..9fe2297f 100644 --- a/backends/lean/Base/IList/IList.lean +++ b/backends/lean/Base/IList/IList.lean @@ -19,9 +19,11 @@ theorem len_pos : 0 ≤ (ls : List α).len := by induction ls <;> simp [*] linarith -instance (a : Type u) : Arith.HasIntProp (List a) where - prop_ty := λ ls => 0 ≤ ls.len - prop := λ ls => ls.len_pos +instance (l: List a) : Arith.HasIntPred (l.len) where + concl := 0 ≤ l.len + prop := l.len_pos + +example (l: List a): 0 ≤ l.len := by scalar_tac -- Remark: if i < 0, then the result is none def indexOpt (ls : List α) (i : Int) : Option α := |