Proof: Do Stack At Unchanged 75
Let's prove the following theorem:
if the following are true:
- expression state at time 75 = "begin_expr"
- stack at time 75 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
then stack at time 76 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ]
Proof:
Given
1 | expression state at time 75 = "begin_expr" |
---|---|
2 | stack at time 75 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
# | Claim | Reason |
---|---|---|
1 | stack at time (75 + 1) = stack at time 75 | if expression state at time 75 = "begin_expr", then stack at time (75 + 1) = stack at time 75 |
2 | stack at time (75 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] | if stack at time (75 + 1) = stack at time 75 and stack at time 75 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time (75 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
3 | 75 + 1 = 76 | 75 + 1 = 76 |
4 | stack at time (75 + 1) = stack at time 76 | if 75 + 1 = 76, then stack at time (75 + 1) = stack at time 76 |
5 | stack at time 76 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] | if stack at time (75 + 1) = stack at time 76 and stack at time (75 + 1) = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ], then stack at time 76 = [ program context with variables: [ entry joe: (Python reference 0), [ ] ] and expression state: (expression state with parent stack: [ ] arguments: [ ] values: [ ] line: 12 tab: 0) and control map: [ entry 0: (pair ("class", "Dog")), [ ] ], [ ] ] |
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