The invariant held over an empty collection

# Self-authored for the EML case corpus (no external origin). The property test
# asserts that every open position nets to within the risk limit, and it has
# passed on every run for the quarter. How many positions it quantifies over is
# computed below.
#
# The test is careful. It checks the real position book, not a fixture; the
# assertion is a genuine universal over every position; a single breach fails
# the run; and it runs before each trading session.
#
# On the runs under review the position book loaded empty, and a universal over
# an empty collection is true with nothing to check.

62 => sessions_this_quarter
18 => sessions_the_book_loaded_empty
0 => positions_that_breached_the_limit
100 => reported_pass_per_hundred
9 => breaches_that_occurred_on_the_empty_load_days

sessions_this_quarter - sessions_the_book_loaded_empty => sessions_with_a_real_book
int(sessions_the_book_loaded_empty * 10000 / sessions_this_quarter) => empty_load_share_per_myriad

"sessions this quarter           : " + str(sessions_this_quarter) ^0
"  the book loaded empty         : " + str(sessions_the_book_loaded_empty) ^0
"  with a real book              : " + str(sessions_with_a_real_book) ^0
"positions that breached (as seen): " + str(positions_that_breached_the_limit) ^0
"reported pass                   : " + str(reported_pass_per_hundred) + " per hundred" ^0
"breaches on the empty-load days : " + str(breaches_that_occurred_on_the_empty_load_days) ^0
"empty-load share                : " + str(empty_load_share_per_myriad) + " per ten thousand" ^0
"" ^0

# ---- what the test verified ----

"the risk property test" ^0
"  checks : the real position book, not a fixture" ^0
"  assertion : every position nets within the limit" ^0
"  a breach : fails the run" ^0
"  runs : before each trading session" ^0
"  positions seen to breach : " + str(positions_that_breached_the_limit) ^0
"  verdict : PROPERTY HELD" ^0
"" ^0
"  a genuine universal over the real book rather than a" ^0
"  fixture is the part done right here, and it is why a" ^0
"  real breach in a loaded book would fail" ^0
"" ^0

# ---- what the universal quantifies over ----

"'every open position is within the limit'" ^0
"  positions on an empty-load day : 0" ^0
"  a for-all over zero positions : true, nothing to check" ^0
"  what 'the property held' means there : the book was" ^0
"    empty, not that risk was in bounds" ^0
"  what it does not mean : that the real positions were" ^0
"    within the limit" ^0
"" ^0

# ---- why the book was empty ----

"the empty load" ^0
"  why : the position feed timed out and the loader" ^0
"    returned an empty book rather than erroring" ^0
"  sessions affected : " + str(sessions_the_book_loaded_empty) ^0
"  breaches that actually existed those days : " ^0
"    " + str(breaches_that_occurred_on_the_empty_load_days) ^0
"  did the passing test see them : no; they were not in" ^0
"    the empty collection it quantified over" ^0
"  is the pass false : no; it is vacuously true" ^0
"" ^0

# ---- null control ----

# The same sessions, with the test asserting the book is non-empty before
# checking the universal, and treating an empty load as a failed precondition.
100 => nc_pass_when_empty_is_vacuous
0 => nc_pass_when_empty_is_a_failed_precondition
18 => nc_sessions_a_nonempty_assertion_would_flag

"null control - require a non-empty book first" ^0
"  pass when empty is vacuous : " + str(nc_pass_when_empty_is_vacuous) ^0
"  pass when empty is a failed precondition : " ^0
"    " + str(nc_pass_when_empty_is_a_failed_precondition) ^0
"  sessions a non-empty assertion would flag : " ^0
"    " + str(nc_sessions_a_nonempty_assertion_would_flag) ^0
"  no position changed; an empty book stopped satisfying a" ^0
"  property about the positions in it" ^0
"" ^0

# ---- the rule ----

"what a passing risk property guarantees" ^0
"  every position in the book is within the limit :" ^0
"    exactly, a genuine universal, a breach fails the run" ^0
"  risk was within the limit : not addressed; the book" ^0
"    loaded empty, and a for-all over an empty collection is" ^0
"    true with nothing to check - " + str(breaches_that_occurred_on_the_empty_load_days) + " real breaches on the" ^0
"    " + str(sessions_the_book_loaded_empty) + " empty-load days were never quantified over" ^0
"" ^0

"a universal is satisfied by an empty domain, and an empty domain is what a" ^0
"failed load looks like; 'every position is safe' is true precisely when there" ^0
"are no positions to be unsafe, which is when the book did not load" ^0
"" ^0

"It asserts a real universal over the actual book and fails on a breach - held" ^0
"all quarter. The book loaded empty on " + str(sessions_the_book_loaded_empty) + " sessions, where a for-all is" ^0
"vacuously true, so " + str(breaches_that_occurred_on_the_empty_load_days) + " real breaches went unseen, " + str(empty_load_share_per_myriad) + " per ten thousand of" ^0
"sessions checking nothing." ^0

sessions_this_quarter = 62
sessions_the_book_loaded_empty = 18
positions_that_breached_the_limit = 0
reported_pass_per_hundred = 100
breaches_that_occurred_on_the_empty_load_days = 9
sessions_with_a_real_book = sessions_this_quarter - sessions_the_book_loaded_empty
empty_load_share_per_myriad = int(sessions_the_book_loaded_empty * 10000 / sessions_this_quarter)
print("sessions this quarter           : " + str(sessions_this_quarter))
print("  the book loaded empty         : " + str(sessions_the_book_loaded_empty))
print("  with a real book              : " + str(sessions_with_a_real_book))
print("positions that breached (as seen): " + str(positions_that_breached_the_limit))
print("reported pass                   : " + str(reported_pass_per_hundred) + " per hundred")
print("breaches on the empty-load days : " + str(breaches_that_occurred_on_the_empty_load_days))
print("empty-load share                : " + str(empty_load_share_per_myriad) + " per ten thousand")
print("")
print("the risk property test")
print("  checks : the real position book, not a fixture")
print("  assertion : every position nets within the limit")
print("  a breach : fails the run")
print("  runs : before each trading session")
print("  positions seen to breach : " + str(positions_that_breached_the_limit))
print("  verdict : PROPERTY HELD")
print("")
print("  a genuine universal over the real book rather than a")
print("  fixture is the part done right here, and it is why a")
print("  real breach in a loaded book would fail")
print("")
print("'every open position is within the limit'")
print("  positions on an empty-load day : 0")
print("  a for-all over zero positions : true, nothing to check")
print("  what 'the property held' means there : the book was")
print("    empty, not that risk was in bounds")
print("  what it does not mean : that the real positions were")
print("    within the limit")
print("")
print("the empty load")
print("  why : the position feed timed out and the loader")
print("    returned an empty book rather than erroring")
print("  sessions affected : " + str(sessions_the_book_loaded_empty))
print("  breaches that actually existed those days : ")
print("    " + str(breaches_that_occurred_on_the_empty_load_days))
print("  did the passing test see them : no; they were not in")
print("    the empty collection it quantified over")
print("  is the pass false : no; it is vacuously true")
print("")
nc_pass_when_empty_is_vacuous = 100
nc_pass_when_empty_is_a_failed_precondition = 0
nc_sessions_a_nonempty_assertion_would_flag = 18
print("null control - require a non-empty book first")
print("  pass when empty is vacuous : " + str(nc_pass_when_empty_is_vacuous))
print("  pass when empty is a failed precondition : ")
print("    " + str(nc_pass_when_empty_is_a_failed_precondition))
print("  sessions a non-empty assertion would flag : ")
print("    " + str(nc_sessions_a_nonempty_assertion_would_flag))
print("  no position changed; an empty book stopped satisfying a")
print("  property about the positions in it")
print("")
print("what a passing risk property guarantees")
print("  every position in the book is within the limit :")
print("    exactly, a genuine universal, a breach fails the run")
print("  risk was within the limit : not addressed; the book")
print("    loaded empty, and a for-all over an empty collection is")
print("    true with nothing to check - " + str(breaches_that_occurred_on_the_empty_load_days) + " real breaches on the")
print("    " + str(sessions_the_book_loaded_empty) + " empty-load days were never quantified over")
print("")
print("a universal is satisfied by an empty domain, and an empty domain is what a")
print("failed load looks like; 'every position is safe' is true precisely when there")
print("are no positions to be unsafe, which is when the book did not load")
print("")
print("It asserts a real universal over the actual book and fails on a breach - held")
print("all quarter. The book loaded empty on " + str(sessions_the_book_loaded_empty) + " sessions, where a for-all is")
print("vacuously true, so " + str(breaches_that_occurred_on_the_empty_load_days) + " real breaches went unseen, " + str(empty_load_share_per_myriad) + " per ten thousand of")
print("sessions checking nothing.")

sessions this quarter           : 62
  the book loaded empty         : 18
  with a real book              : 44
positions that breached (as seen): 0
reported pass                   : 100 per hundred
breaches on the empty-load days : 9
empty-load share                : 2903 per ten thousand

the risk property test
  checks : the real position book, not a fixture
  assertion : every position nets within the limit
  a breach : fails the run
  runs : before each trading session
  positions seen to breach : 0
  verdict : PROPERTY HELD

  a genuine universal over the real book rather than a
  fixture is the part done right here, and it is why a
  real breach in a loaded book would fail

'every open position is within the limit'
  positions on an empty-load day : 0
  a for-all over zero positions : true, nothing to check
  what 'the property held' means there : the book was
    empty, not that risk was in bounds
  what it does not mean : that the real positions were
    within the limit

the empty load
  why : the position feed timed out and the loader
    returned an empty book rather than erroring
  sessions affected : 18
  breaches that actually existed those days : 
    9
  did the passing test see them : no; they were not in
    the empty collection it quantified over
  is the pass false : no; it is vacuously true

null control - require a non-empty book first
  pass when empty is vacuous : 100
  pass when empty is a failed precondition : 
    0
  sessions a non-empty assertion would flag : 
    18
  no position changed; an empty book stopped satisfying a
  property about the positions in it

what a passing risk property guarantees
  every position in the book is within the limit :
    exactly, a genuine universal, a breach fails the run
  risk was within the limit : not addressed; the book
    loaded empty, and a for-all over an empty collection is
    true with nothing to check - 9 real breaches on the
    18 empty-load days were never quantified over

a universal is satisfied by an empty domain, and an empty domain is what a
failed load looks like; 'every position is safe' is true precisely when there
are no positions to be unsafe, which is when the book did not load

It asserts a real universal over the actual book and fails on a breach - held
all quarter. The book loaded empty on 18 sessions, where a for-all is
vacuously true, so 9 real breaches went unseen, 2903 per ten thousand of
sessions checking nothing.

Trace event types