Proofs

A proof is a series of claims that lead to a conclusion. Some proofs are conditional, which means that the claims can only be made under certain conditions. Click on a statement to see the proof

Do Control Map At Unchanged 19
if the following are true:
  • expression state at time 19 = "return"
  • Control Map at time 19 = [ entry 0: (pair ("if", False)), [ ] ]

then Control Map at time 20 = [ entry 0: (pair ("if", False)), [ ] ]


Do Control Map At Unchanged 20
if the following are true:
  • expression state at time 20 = "iterate_args"
  • Control Map at time 20 = [ entry 0: (pair ("if", False)), [ ] ]

then Control Map at time 21 = [ entry 0: (pair ("if", False)), [ ] ]


Do Control Map At Unchanged 21
if the following are true:
  • expression state at time 21 = "call_function_begin"
  • Control Map at time 21 = [ entry 0: (pair ("if", False)), [ ] ]

then Control Map at time 22 = [ entry 0: (pair ("if", False)), [ ] ]


Do Set Key Value 22 0
result of storing (pair ("if", False)) at key: 0 in map: [ entry 0: (pair ("if", False)), [ ] ] = [ entry 0: (pair ("if", False)), [ ] ]

Elif False Control Map Example
if the following are true:
  • the line at time 22 = 3
  • the tab at time 22 = 0
  • statement at line 3, tab 0 = elif __eq__(7, 9):
  • expression state at time 22 = "end_expr"
  • Return Value at time 22 = False
  • Control Map at time 22 = [ entry 0: (pair ("if", False)), [ ] ]

then Control Map at time 23 = [ entry 0: (pair ("if", False)), [ ] ]


Write Skip Line Control Map At 23
if the following are true:
  • the line at time 23 = 4
  • the tab at time 23 = 0
  • statement at line 4, tab 1 = a = 8
  • Control Map at time 23 = [ entry 0: (pair ("if", False)), [ ] ]

then Control Map at time 24 = [ entry 0: (pair ("if", False)), [ ] ]


Do Get Key Value 24 0
value at 0 in map [ entry 0: (pair ("if", False)), [ ] ] = pair ("if", False)

Get Key Value Control Map At 24
if Control Map at time 24 = [ entry 0: (pair ("if", False)), [ ] ], then value at 0 in map (Control Map at time 24) = pair ("if", False)

Write Stmt Control Map At Unchanged 24
if the following are true:
  • the line at time 24 = 5
  • the tab at time 24 = 0
  • statement at line 5, tab 0 = else:
  • Control Map at time 24 = [ entry 0: (pair ("if", False)), [ ] ]

then Control Map at time 25 = [ entry 0: (pair ("if", False)), [ ] ]


Write Stmt Control Map At Unchanged 25
if the following are true:
  • the line at time 25 = 6
  • the tab at time 25 = 1
  • statement at line 6, tab 1 = a = 9
  • Control Map at time 25 = [ entry 0: (pair ("if", False)), [ ] ]

then Control Map at time 26 = [ entry 0: (pair ("if", False)), [ ] ]


Do Has Key 26 0
map [ entry 0: (pair ("if", False)), [ ] ] contains key 0 = True

Get Decrement Key Value Control Map At 26
if Control Map at time 26 = [ entry 0: (pair ("if", False)), [ ] ], then value at (1 - 1) in map (Control Map at time 26) = pair ("if", False)

Write Stmt Control Map At Unchanged Expr0
if the following are true:
  • the line at time 0 = 1
  • the tab at time 0 = 0
  • statement at line 1, tab 0 = if __eq__(7, 7):
  • expression state at time 0 = "not_expr"
  • Control Map at time 0 = [ ]

then Control Map at time 1 = [ ]


Do Control Map At Unchanged 1
if the following are true:
  • expression state at time 1 = "begin_expr"
  • Control Map at time 1 = [ ]

then Control Map at time 2 = [ ]


Do Control Map At Unchanged 2
if the following are true:
  • expression state at time 2 = "iterate_args"
  • Control Map at time 2 = [ ]

then Control Map at time 3 = [ ]


Do Control Map At Unchanged 3
if the following are true:
  • expression state at time 3 = "begin_expr"
  • Control Map at time 3 = [ ]

then Control Map at time 4 = [ ]


Do Control Map At Unchanged 4
if the following are true:
  • expression state at time 4 = "return"
  • Control Map at time 4 = [ ]

then Control Map at time 5 = [ ]


Do Control Map At Unchanged 5
if the following are true:
  • expression state at time 5 = "iterate_args"
  • Control Map at time 5 = [ ]

then Control Map at time 6 = [ ]


Do Control Map At Unchanged 6
if the following are true:
  • expression state at time 6 = "begin_expr"
  • Control Map at time 6 = [ ]

then Control Map at time 7 = [ ]


Do Control Map At Unchanged 7
if the following are true:
  • expression state at time 7 = "return"
  • Control Map at time 7 = [ ]

then Control Map at time 8 = [ ]


Do Control Map At Unchanged 8
if the following are true:
  • expression state at time 8 = "iterate_args"
  • Control Map at time 8 = [ ]

then Control Map at time 9 = [ ]


Do Control Map At Unchanged 9
if the following are true:
  • expression state at time 9 = "call_function_begin"
  • Control Map at time 9 = [ ]

then Control Map at time 10 = [ ]


Do Set Key Value 10 0
result of storing (pair ("if", True)) at key: 0 in map: [ ] = [ entry 0: (pair ("if", True)), [ ] ]

Write Test Call End Control Map 10
if the following are true:
  • the line at time 10 = 1
  • the tab at time 10 = 0
  • statement at line 1, tab 0 = if __eq__(7, 7):
  • expression state at time 10 = "end_expr"
  • Return Value at time 10 = True
  • Control Map at time 10 = [ ]

then Control Map at time 11 = [ entry 0: (pair ("if", True)), [ ] ]


Write Stmt Control Map At Unchanged 11
if the following are true:
  • the line at time 11 = 2
  • the tab at time 11 = 1
  • statement at line 2, tab 1 = a = 7
  • Control Map at time 11 = [ entry 0: (pair ("if", True)), [ ] ]

then Control Map at time 12 = [ entry 0: (pair ("if", True)), [ ] ]


Do Get Key Value 12 0
value at 0 in map [ entry 0: (pair ("if", True)), [ ] ] = pair ("if", True)

Get Decrement Key Value Control Map At 12
if Control Map at time 12 = [ entry 0: (pair ("if", True)), [ ] ], then value at (1 - 1) in map (Control Map at time 12) = pair ("if", True)

Write Decrement Tab Control Map 12
if the following are true:
  • the line at time 12 = 3
  • the tab at time 12 = 1
  • statement at line 3, tab 0 = elif __eq__(3, 3):
  • Control Map at time 12 = [ entry 0: (pair ("if", True)), [ ] ]

then Control Map at time 13 = [ entry 0: (pair ("if", True)), [ ] ]


Do Get Key Value 13 0
value at 0 in map [ entry 0: (pair ("if", True)), [ ] ] = pair ("if", True)

Get Key Value Control Map At 13
if Control Map at time 13 = [ entry 0: (pair ("if", True)), [ ] ], then value at 0 in map (Control Map at time 13) = pair ("if", True)

Write Stmt Control Map At Unchanged Expr13
if the following are true:
  • the line at time 13 = 3
  • the tab at time 13 = 0
  • statement at line 3, tab 0 = elif __eq__(3, 3):
  • expression state at time 13 = "not_expr"
  • Control Map at time 13 = [ entry 0: (pair ("if", True)), [ ] ]

then Control Map at time 14 = [ entry 0: (pair ("if", True)), [ ] ]


Write Skip Line Control Map At 14
if the following are true:
  • the line at time 14 = 4
  • the tab at time 14 = 0
  • statement at line 4, tab 1 = a = 8
  • Control Map at time 14 = [ entry 0: (pair ("if", True)), [ ] ]

then Control Map at time 15 = [ entry 0: (pair ("if", True)), [ ] ]


Do Get Key Value 15 0
value at 0 in map [ entry 0: (pair ("if", True)), [ ] ] = pair ("if", True)

Get Key Value Control Map At 15
if Control Map at time 15 = [ entry 0: (pair ("if", True)), [ ] ], then value at 0 in map (Control Map at time 15) = pair ("if", True)

Write Stmt Control Map At Unchanged 15
if the following are true:
  • the line at time 15 = 5
  • the tab at time 15 = 0
  • statement at line 5, tab 0 = else:
  • Control Map at time 15 = [ entry 0: (pair ("if", True)), [ ] ]

then Control Map at time 16 = [ entry 0: (pair ("if", True)), [ ] ]


Write Skip Line Control Map At 16
if the following are true:
  • the line at time 16 = 6
  • the tab at time 16 = 0
  • statement at line 6, tab 1 = a = 9
  • Control Map at time 16 = [ entry 0: (pair ("if", True)), [ ] ]

then Control Map at time 17 = [ entry 0: (pair ("if", True)), [ ] ]


Do Set Key Value 0 0
result of storing 0 at key: a in map: [ ] = [ entry a: 0, [ ] ]

Write Assign Const Stack At 0
if the following are true:
  • the line at time 0 = 1
  • the tab at time 0 = 0
  • statement at line 1, tab 0 = a = 0
  • 0 is constant
  • stack at time 0 = [ ]

then stack at time 1 = [ ]


Write Assign Const Object Store At 0
if the following are true:
  • the line at time 0 = 1
  • the tab at time 0 = 0
  • statement at line 1, tab 0 = a = 0
  • 0 is constant
  • Python Object Store at time 0 = [ ]

then Python Object Store at time 1 = [ ]


Write Stmt Control Map At Unchanged 0
if the following are true:
  • the line at time 0 = 1
  • the tab at time 0 = 0
  • statement at line 1, tab 0 = a = 0
  • Control Map at time 0 = [ ]

then Control Map at time 1 = [ ]


Write Stmt Class Defs At Unchanged 0
if the following are true:
  • the line at time 0 = 1
  • the tab at time 0 = 0
  • statement at line 1, tab 0 = a = 0
  • Class Map at time 0 = [ ]

then Class Map at time 1 = [ ]


Write Set Name Expr At on State 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"

then the expression at time 2 = __lt__(a, 2)


Write Set Name Expr State At on State 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"

then expression state at time 2 = "begin_expr"


Write Set Name Line At on State 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"

then the line at time 2 = 2


Write Set Name Tab At on State 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"

then the tab at time 2 = 0


Write Set Name Value Stack At on State 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"

then Value Stack at time 2 = [ ]


Write Set Name Parent Stack At on State 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"

then parent stack at time 2 = [ ]


Write Set Name Arg Stack At on State 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"

then arguments stack at time 2 = [ ]


Write Stmt Object Store At Unchanged Expr1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"
  • Python Object Store at time 1 = [ ]

then Python Object Store at time 2 = [ ]


Write Stmt Control Map At Unchanged Expr1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 1 = "not_expr"
  • Control Map at time 1 = [ ]

then Control Map at time 2 = [ ]


Write Stmt Class Defs At Unchanged 1
if the following are true:
  • the line at time 1 = 2
  • the tab at time 1 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • Class Map at time 1 = [ ]

then Class Map at time 2 = [ ]


Do Object Store At Unchanged 2
if the following are true:
  • expression state at time 2 = "begin_expr"
  • Python Object Store at time 2 = [ ]

then Python Object Store at time 3 = [ ]


Do Control Map At Unchanged 2
if the following are true:
  • expression state at time 2 = "begin_expr"
  • Control Map at time 2 = [ ]

then Control Map at time 3 = [ ]


Do Class Defs At Unchanged 2
if the following are true:
  • expression state at time 2 = "begin_expr"
  • Class Map at time 2 = [ ]

then Class Map at time 3 = [ ]


Do Object Store At Unchanged 3
if the following are true:
  • expression state at time 3 = "iterate_args"
  • Python Object Store at time 3 = [ ]

then Python Object Store at time 4 = [ ]


Do Control Map At Unchanged 3
if the following are true:
  • expression state at time 3 = "iterate_args"
  • Control Map at time 3 = [ ]

then Control Map at time 4 = [ ]


Do Class Defs At Unchanged 3
if the following are true:
  • expression state at time 3 = "iterate_args"
  • Class Map at time 3 = [ ]

then Class Map at time 4 = [ ]


Do Get Key Value 4 0
value at a in map [ entry a: 0, [ ] ] = 0

Do Object Store At Unchanged 4
if the following are true:
  • expression state at time 4 = "begin_expr"
  • Python Object Store at time 4 = [ ]

then Python Object Store at time 5 = [ ]


Do Control Map At Unchanged 4
if the following are true:
  • expression state at time 4 = "begin_expr"
  • Control Map at time 4 = [ ]

then Control Map at time 5 = [ ]


Do Class Defs At Unchanged 4
if the following are true:
  • expression state at time 4 = "begin_expr"
  • Class Map at time 4 = [ ]

then Class Map at time 5 = [ ]


Do Arg Stack At Unchanged 5
if the following are true:
  • expression state at time 5 = "return"
  • arguments stack at time 5 = [ [ 2, [ ] ], [ ] ]

then arguments stack at time 6 = [ [ 2, [ ] ], [ ] ]


Do Class Defs At Unchanged 5
if the following are true:
  • expression state at time 5 = "return"
  • Class Map at time 5 = [ ]

then Class Map at time 6 = [ ]


Do Object Store At Unchanged 5
if the following are true:
  • expression state at time 5 = "return"
  • Python Object Store at time 5 = [ ]

then Python Object Store at time 6 = [ ]


Do Control Map At Unchanged 5
if the following are true:
  • expression state at time 5 = "return"
  • Control Map at time 5 = [ ]

then Control Map at time 6 = [ ]


Do Object Store At Unchanged 6
if the following are true:
  • expression state at time 6 = "iterate_args"
  • Python Object Store at time 6 = [ ]

then Python Object Store at time 7 = [ ]


Do Control Map At Unchanged 6
if the following are true:
  • expression state at time 6 = "iterate_args"
  • Control Map at time 6 = [ ]

then Control Map at time 7 = [ ]


Do Class Defs At Unchanged 6
if the following are true:
  • expression state at time 6 = "iterate_args"
  • Class Map at time 6 = [ ]

then Class Map at time 7 = [ ]


Do Object Store At Unchanged 7
if the following are true:
  • expression state at time 7 = "begin_expr"
  • Python Object Store at time 7 = [ ]

then Python Object Store at time 8 = [ ]


Do Control Map At Unchanged 7
if the following are true:
  • expression state at time 7 = "begin_expr"
  • Control Map at time 7 = [ ]

then Control Map at time 8 = [ ]


Do Class Defs At Unchanged 7
if the following are true:
  • expression state at time 7 = "begin_expr"
  • Class Map at time 7 = [ ]

then Class Map at time 8 = [ ]


Do Arg Stack At Unchanged 8
if the following are true:
  • expression state at time 8 = "return"
  • arguments stack at time 8 = [ [ ], [ ] ]

then arguments stack at time 9 = [ [ ], [ ] ]


Do Class Defs At Unchanged 8
if the following are true:
  • expression state at time 8 = "return"
  • Class Map at time 8 = [ ]

then Class Map at time 9 = [ ]


Do Object Store At Unchanged 8
if the following are true:
  • expression state at time 8 = "return"
  • Python Object Store at time 8 = [ ]

then Python Object Store at time 9 = [ ]


Do Control Map At Unchanged 8
if the following are true:
  • expression state at time 8 = "return"
  • Control Map at time 8 = [ ]

then Control Map at time 9 = [ ]


Do Object Store At Unchanged 9
if the following are true:
  • expression state at time 9 = "iterate_args"
  • Python Object Store at time 9 = [ ]

then Python Object Store at time 10 = [ ]


Do Control Map At Unchanged 9
if the following are true:
  • expression state at time 9 = "iterate_args"
  • Control Map at time 9 = [ ]

then Control Map at time 10 = [ ]


Do Class Defs At Unchanged 9
if the following are true:
  • expression state at time 9 = "iterate_args"
  • Class Map at time 9 = [ ]

then Class Map at time 10 = [ ]


Do Object Store At Unchanged 10
if the following are true:
  • expression state at time 10 = "call_function_begin"
  • the expression at time 10 = __lt__(a, 2)
  • Python Object Store at time 10 = [ ]

then Python Object Store at time 11 = [ ]


Do Arg Stack At Unchanged 10
if the following are true:
  • expression state at time 10 = "call_function_begin"
  • arguments stack at time 10 = [ ]

then arguments stack at time 11 = [ ]


Do Control Map At Unchanged 10
if the following are true:
  • expression state at time 10 = "call_function_begin"
  • Control Map at time 10 = [ ]

then Control Map at time 11 = [ ]


Do Class Defs At Unchanged 10
if the following are true:
  • expression state at time 10 = "call_function_begin"
  • Class Map at time 10 = [ ]

then Class Map at time 11 = [ ]


Do Set Key Value 11 0
result of storing (pair ("while", 2)) at key: 0 in map: [ ] = [ entry 0: (pair ("while", 2)), [ ] ]

While Test True Store Example
if the following are true:
  • the line at time 11 = 2
  • the tab at time 11 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 11 = "end_expr"
  • Return Value at time 11 = True
  • Control Map at time 11 = [ ]

then Control Map at time 12 = [ entry 0: (pair ("while", 2)), [ ] ]


Write Stmt Class Defs At Unchanged 11
if the following are true:
  • the line at time 11 = 2
  • the tab at time 11 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • Class Map at time 11 = [ ]

then Class Map at time 12 = [ ]


Write Stmt Object Store At Unchanged Expr11
if the following are true:
  • the line at time 11 = 2
  • the tab at time 11 = 0
  • statement at line 2, tab 0 = while __lt__(a, 2):
  • expression state at time 11 = "end_expr"
  • Python Object Store at time 11 = [ ]

then Python Object Store at time 12 = [ ]


Write Set Name Arg Stack At on State 12
if the following are true:
  • the line at time 12 = 3
  • the tab at time 12 = 1
  • statement at line 3, tab 1 = a = __add__(a, 1)
  • expression state at time 12 = "not_expr"

then arguments stack at time 13 = [ ]


Write Stmt Object Store At Unchanged Expr12
if the following are true:
  • the line at time 12 = 3
  • the tab at time 12 = 1
  • statement at line 3, tab 1 = a = __add__(a, 1)
  • expression state at time 12 = "not_expr"
  • Python Object Store at time 12 = [ ]

then Python Object Store at time 13 = [ ]


Write Stmt Control Map At Unchanged 12
if the following are true:
  • the line at time 12 = 3
  • the tab at time 12 = 1
  • statement at line 3, tab 1 = a = __add__(a, 1)
  • Control Map at time 12 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 13 = [ entry 0: (pair ("while", 2)), [ ] ]


Write Stmt Class Defs At Unchanged 12
if the following are true:
  • the line at time 12 = 3
  • the tab at time 12 = 1
  • statement at line 3, tab 1 = a = __add__(a, 1)
  • Class Map at time 12 = [ ]

then Class Map at time 13 = [ ]


Do Object Store At Unchanged 13
if the following are true:
  • expression state at time 13 = "begin_expr"
  • Python Object Store at time 13 = [ ]

then Python Object Store at time 14 = [ ]


Do Control Map At Unchanged 13
if the following are true:
  • expression state at time 13 = "begin_expr"
  • Control Map at time 13 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 14 = [ entry 0: (pair ("while", 2)), [ ] ]


Do Class Defs At Unchanged 13
if the following are true:
  • expression state at time 13 = "begin_expr"
  • Class Map at time 13 = [ ]

then Class Map at time 14 = [ ]


Do Object Store At Unchanged 14
if the following are true:
  • expression state at time 14 = "iterate_args"
  • Python Object Store at time 14 = [ ]

then Python Object Store at time 15 = [ ]


Do Control Map At Unchanged 14
if the following are true:
  • expression state at time 14 = "iterate_args"
  • Control Map at time 14 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 15 = [ entry 0: (pair ("while", 2)), [ ] ]


Do Class Defs At Unchanged 14
if the following are true:
  • expression state at time 14 = "iterate_args"
  • Class Map at time 14 = [ ]

then Class Map at time 15 = [ ]


Do Get Key Value 15 0
value at a in map [ entry a: 0, [ ] ] = 0

Do Object Store At Unchanged 15
if the following are true:
  • expression state at time 15 = "begin_expr"
  • Python Object Store at time 15 = [ ]

then Python Object Store at time 16 = [ ]


Do Control Map At Unchanged 15
if the following are true:
  • expression state at time 15 = "begin_expr"
  • Control Map at time 15 = [ entry 0: (pair ("while", 2)), [ ] ]

then Control Map at time 16 = [ entry 0: (pair ("while", 2)), [ ] ]


Do Class Defs At Unchanged 15
if the following are true:
  • expression state at time 15 = "begin_expr"
  • Class Map at time 15 = [ ]

then Class Map at time 16 = [ ]



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