Proof: Do Stack At Unchanged 56
Let's prove the following theorem:
if the following are true:
- expression state at time 56 = "return"
- stack at time 56 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
then stack at time 57 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
Proof:
Given
1 | expression state at time 56 = "return" |
---|---|
2 | stack at time 56 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
# | Claim | Reason |
---|---|---|
1 | stack at time (56 + 1) = stack at time 56 | if expression state at time 56 = "return", then stack at time (56 + 1) = stack at time 56 |
2 | stack at time (56 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] | if stack at time (56 + 1) = stack at time 56 and stack at time 56 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time (56 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
3 | 56 + 1 = 57 | 56 + 1 = 57 |
4 | stack at time (56 + 1) = stack at time 57 | if 56 + 1 = 57, then stack at time (56 + 1) = stack at time 57 |
5 | stack at time 57 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] | if stack at time (56 + 1) = stack at time 57 and stack at time (56 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time 57 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 11 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
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