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Merged
PerAlexandersson merged 1 commit into from
Aug 4, 2026
Merged

Infer derived matrix tactic certificates #337

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22 changes: 11 additions & 11 deletions RealRooted/Tactic/Examples/Matrix.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -99,8 +99,7 @@ example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hfs_len : fs.length = n)
(hfs : IsInterlacingSeqNonneg fs) :
IsInterlacingSeqNonneg ((matPolyAction G fs).filter (· ≠ 0)) := by
rr_matrix0_filter_ne_zero using
G, hG_rect, hG_nonneg, hG_affine, fs, hfs_len, hfs
rr_matrix0_filter_ne_zero

example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hG_rect : ∀ row ∈ G, row.length = n)
Expand Down Expand Up @@ -138,7 +137,7 @@ example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hfs : IsInterlacingSeqNonneg fs) :
IsInterlacingSeq0Nonneg (matPolyAction G fs) ∧
∀ f ∈ matPolyAction G fs, f ≠ 0 → (f ≠ 0 ∧ f.Splits) := by
rr_matrix0_realrooted using G, hG_rect, hG_nonneg, hG_affine, fs, hfs_len, hfs
rr_matrix0_realrooted

example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hG_rect : ∀ row ∈ G, row.length = n)
Expand Down Expand Up @@ -219,8 +218,7 @@ example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hfs : IsInterlacingSeq0Nonneg fs)
(hfs_real : ∀ f ∈ fs, f ≠ 0 → (f ≠ 0 ∧ f.Splits)) :
IsInterlacingSeqNonneg ((matPolyAction G fs).filter (· ≠ 0)) := by
rr_matrix0_filter_ne_zero_weak using
G, hG_rect, hG_nonneg, hG_affine, fs, hfs_len, hfs, hfs_real
rr_matrix0_filter_ne_zero_weak

example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hG_rect : ∀ row ∈ G, row.length = n)
Expand Down Expand Up @@ -402,8 +400,7 @@ example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hfs : IsInterlacingSeq0Nonneg fs)
(hfs_real : ∀ f ∈ fs, f ≠ 0 → (f ≠ 0 ∧ f.Splits)) :
IsInterlacingSeqNonneg ((matPolyAction G fs).filter (· ≠ 0)) := by
rr_row_threshold_matrix0_filter_ne_zero_weak using
G, hG_rect, hG_threshold, hG_affine, fs, hfs_len, hfs, hfs_real
rr_row_threshold_matrix0_filter_ne_zero_weak

example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hG_rect : ∀ row ∈ G, row.length = n)
Expand Down Expand Up @@ -442,8 +439,7 @@ example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hfs : IsInterlacingSeqNonneg fs) :
IsInterlacingSeq0Nonneg (matPolyAction G fs) ∧
∀ f ∈ matPolyAction G fs, f ≠ 0 → (f ≠ 0 ∧ f.Splits) := by
rr_row_threshold_matrix0_realrooted using
G, hG_rect, hG_threshold, hG_affine, fs, hfs_len, hfs
rr_row_threshold_matrix0_realrooted

example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hG_rect : ∀ row ∈ G, row.length = n)
Expand Down Expand Up @@ -480,8 +476,7 @@ example {n : ℕ} (G : List (List ℝ[X])) (fs : List ℝ[X])
(hfs_len : fs.length = n)
(hfs : IsInterlacingSeqNonneg fs) :
IsInterlacingSeqNonneg ((matPolyAction G fs).filter (· ≠ 0)) := by
rr_row_threshold_matrix0_filter_ne_zero using
G, hG_rect, hG_threshold, hG_affine, fs, hfs_len, hfs
rr_row_threshold_matrix0_filter_ne_zero

example {G : List (List ℝ[X])}
(hG_threshold : HasRowThresholdLinearStructure G) :
Expand Down Expand Up @@ -566,6 +561,11 @@ example (hfs_len : ([] : List ℝ[X]).length = 0)
IsInterlacingSeq0Nonneg (matPolyAction decoyMatrix []) := by
rr_matrix0

example (hfs_len : ([] : List ℝ[X]).length = 0)
(hfs : IsInterlacingSeqNonneg ([] : List ℝ[X])) :
IsInterlacingSeqNonneg ((matPolyAction decoyMatrix []).filter (· ≠ 0)) := by
rr_matrix0_filter_ne_zero

example (hfs_len : ([] : List ℝ[X]).length = 0)
(hfs : IsInterlacingSeqNonneg ([] : List ℝ[X])) :
IsInterlacingSeq0Nonneg (matPolyAction baseMatrix []) := by
Expand Down
84 changes: 81 additions & 3 deletions RealRooted/Tactic/Matrix.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -37,9 +37,9 @@ The tactics apply `matrix_preserves_interlacing_seq`,
the user supplies the matrix action, rectangularity, entry nonnegativity, and
`2 x 2` Branden conditions.

The bare `rr_matrix0`, `rr_matrix0_weak`, `rr_row_threshold_matrix0`, and
`rr_row_threshold_matrix0_weak` forms infer the matrix and input from the goal.
They use exact local length and input certificates, then the registered matrix
Every `matrix0` form has a bare variant inferring the matrix and input from the
goal; `rr_matrix` and `rr_row_threshold_matrix` require `using`. The bare forms
use exact local length and input certificates, then the registered matrix
certificate attributes. The bare `rr_row_threshold_entry_nonneg` form infers
its matrix from the target.

Expand Down Expand Up @@ -143,6 +143,9 @@ syntax (name := rr_matrix0_realrooted_named)
"input_interlacing" ":=" term :
tactic

syntax (name := rr_matrix0_realrooted_inferred)
"rr_matrix0_realrooted" : tactic

syntax (name := rr_matrix0_filter_ne_zero)
"rr_matrix0_filter_ne_zero" " using " term ", "
term ", "
Expand All @@ -164,6 +167,9 @@ syntax (name := rr_matrix0_filter_ne_zero_named)
"input_interlacing" ":=" term :
tactic

syntax (name := rr_matrix0_filter_ne_zero_inferred)
"rr_matrix0_filter_ne_zero" : tactic

syntax (name := rr_matrix0_filter_ne_zero_weak)
"rr_matrix0_filter_ne_zero_weak" " using " term ", "
term ", "
Expand All @@ -187,6 +193,9 @@ syntax (name := rr_matrix0_filter_ne_zero_weak_named)
"input_real_rooted" ":=" term :
tactic

syntax (name := rr_matrix0_filter_ne_zero_weak_inferred)
"rr_matrix0_filter_ne_zero_weak" : tactic

syntax (name := rr_row_threshold_matrix_named)
"rr_row_threshold_matrix" " using "
"n_pos" ":=" term ","
Expand Down Expand Up @@ -283,6 +292,9 @@ syntax (name := rr_row_threshold_matrix0_filter_ne_zero_weak)
term :
tactic

syntax (name := rr_row_threshold_matrix0_filter_ne_zero_weak_inferred)
"rr_row_threshold_matrix0_filter_ne_zero_weak" : tactic

syntax (name := rr_row_threshold_matrix0_realrooted_named)
"rr_row_threshold_matrix0_realrooted" " using "
"matrix" ":=" term ","
Expand All @@ -304,6 +316,9 @@ syntax (name := rr_row_threshold_matrix0_realrooted)
term :
tactic

syntax (name := rr_row_threshold_matrix0_realrooted_inferred)
"rr_row_threshold_matrix0_realrooted" : tactic

syntax (name := rr_row_threshold_matrix0_filter_ne_zero_named)
"rr_row_threshold_matrix0_filter_ne_zero" " using "
"matrix" ":=" term ","
Expand All @@ -325,6 +340,9 @@ syntax (name := rr_row_threshold_matrix0_filter_ne_zero)
term :
tactic

syntax (name := rr_row_threshold_matrix0_filter_ne_zero_inferred)
"rr_row_threshold_matrix0_filter_ne_zero" : tactic

syntax (name := rr_row_threshold_entry_nonneg_named)
"rr_row_threshold_entry_nonneg" " using "
"row_threshold" ":=" term :
Expand Down Expand Up @@ -358,6 +376,35 @@ macro_rules
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption
case hfs_real => assumption))
| `(tactic| rr_matrix0_realrooted) =>
`(tactic|
exact (by
apply RealRooted.matrix_preserves_interlacing_seq0_of_2x2_realRooted
case hfs_len => assumption
case hG_rect => rr_lookup [rr_matrix_rect]
case hG_nonneg => rr_lookup [rr_matrix_nonneg]
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption))
| `(tactic| rr_matrix0_filter_ne_zero) =>
`(tactic|
exact (by
apply RealRooted.matrix_preserves_interlacing_seq0_filter_ne_zero_of_2x2
case hfs_len => assumption
case hG_rect => rr_lookup [rr_matrix_rect]
case hG_nonneg => rr_lookup [rr_matrix_nonneg]
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption))
| `(tactic| rr_matrix0_filter_ne_zero_weak) =>
`(tactic|
exact (by
apply
RealRooted.matrix_preserves_interlacing_seq0_filter_ne_zero_of_2x2_weak
case hfs_len => assumption
case hG_rect => rr_lookup [rr_matrix_rect]
case hG_nonneg => rr_lookup [rr_matrix_nonneg]
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption
case hfs_real => assumption))
| `(tactic| rr_row_threshold_matrix0) =>
`(tactic|
exact (by
Expand All @@ -377,6 +424,37 @@ macro_rules
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption
case hfs_real => assumption))
| `(tactic| rr_row_threshold_matrix0_realrooted) =>
`(tactic|
exact (by
apply
RealRooted.rowThreshold_matrix_preserves_interlacing_seq0_of_2x2_realRooted
case hfs_len => assumption
case hG_rect => rr_lookup [rr_matrix_rect]
case hG_threshold => rr_lookup [rr_matrix_threshold]
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption))
| `(tactic| rr_row_threshold_matrix0_filter_ne_zero) =>
`(tactic|
exact (by
apply
RealRooted.rowThreshold_matrix_preserves_interlacing_seq0_filter_ne_zero_of_2x2
case hfs_len => assumption
case hG_rect => rr_lookup [rr_matrix_rect]
case hG_threshold => rr_lookup [rr_matrix_threshold]
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption))
| `(tactic| rr_row_threshold_matrix0_filter_ne_zero_weak) =>
`(tactic|
exact (by
apply
RealRooted.rowThreshold_matrix_preserves_interlacing_seq0_filter_ne_zero_of_2x2_weak
case hfs_len => assumption
case hG_rect => rr_lookup [rr_matrix_rect]
case hG_threshold => rr_lookup [rr_matrix_threshold]
case hG_affine => rr_lookup [rr_matrix_2x2]
case hfs => assumption
case hfs_real => assumption))
| `(tactic| rr_row_threshold_entry_nonneg) =>
`(tactic|
rr_row_threshold_entry_nonneg using
Expand Down
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