diff options
Diffstat (limited to 'proofs/signatures/th_arrays.plf')
| -rwxr-xr-x | proofs/signatures/th_arrays.plf | 34 |
1 files changed, 23 insertions, 11 deletions
diff --git a/proofs/signatures/th_arrays.plf b/proofs/signatures/th_arrays.plf index 8334f51de..5ed3d2f6f 100755 --- a/proofs/signatures/th_arrays.plf +++ b/proofs/signatures/th_arrays.plf @@ -7,44 +7,56 @@ ; sorts -(declare array (! s1 sort (! s2 sort sort))) ; s1 is index, s2 is element +(declare Array (! s1 sort (! s2 sort sort))) ; s1 is index, s2 is element ; functions (declare write (! s1 sort (! s2 sort - (term (arrow (array s1 s2) + (term (arrow (Array s1 s2) (arrow s1 - (arrow s2 (array s1 s2)))))))) + (arrow s2 (Array s1 s2)))))))) (declare read (! s1 sort (! s2 sort - (term (arrow (array s1 s2) + (term (arrow (Array s1 s2) (arrow s1 s2)))))) ; inference rules + +; read( a[i] = b, i ) == b (declare row1 (! s1 sort (! s2 sort - (! t1 (term (array s1 s2)) + (! t1 (term (Array s1 s2)) (! t2 (term s1) (! t3 (term s2) - (th_holds (= _ (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t3)) t2) - t3)))))))) - + (th_holds (= _ + (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t3)) t2) t3)))))))) (declare row (! s1 sort (! s2 sort (! t2 (term s1) (! t3 (term s1) - (! t1 (term (array s1 s2)) + (! t1 (term (Array s1 s2)) (! t4 (term s2) (! u (th_holds (not (= _ t2 t3))) (th_holds (= _ (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t4)) t3) (apply _ _ (apply _ _ (read s1 s2) t1) t3))))))))))) +(declare negativerow (! s1 sort + (! s2 sort + (! t2 (term s1) + (! t3 (term s1) + (! t1 (term (Array s1 s2)) + (! t4 (term s2) + (! u (th_holds (not (= _ + (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t4)) t3) + (apply _ _ (apply _ _ (read s1 s2) t1) t3)))) + (th_holds (= _ t2 t3)))))))))) + (declare ext (! s1 sort (! s2 sort - (! t1 (term (array s1 s2)) - (! t2 (term (array s1 s2)) + (! t1 (term (Array s1 s2)) + (! t2 (term (Array s1 s2)) (! u1 (! k (term s1) (! u2 (th_holds (or (= _ t1 t2) (not (= _ (apply _ _ (apply _ _ (read s1 s2) t1) k) (apply _ _ (apply _ _ (read s1 s2) t2) k))))) (holds cln))) |