Proof: Do Stack At Unchanged 29
Let's prove the following theorem:
if the following are true:
- expression state at time 29 = "return"
- stack at time 29 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
then stack at time 30 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
Proof:
Given
1 | expression state at time 29 = "return" |
---|---|
2 | stack at time 29 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
# | Claim | Reason |
---|---|---|
1 | stack at time (29 + 1) = stack at time 29 | if expression state at time 29 = "return", then stack at time (29 + 1) = stack at time 29 |
2 | stack at time (29 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] | if stack at time (29 + 1) = stack at time 29 and stack at time 29 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time (29 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
3 | 29 + 1 = 30 | 29 + 1 = 30 |
4 | stack at time (29 + 1) = stack at time 30 | if 29 + 1 = 30, then stack at time (29 + 1) = stack at time 30 |
5 | stack at time 30 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] | if stack at time (29 + 1) = stack at time 30 and stack at time (29 + 1) = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time 30 = [ program context with variables: [ ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 10 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
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