Proof: Do Stack At Unchanged 43
Let's prove the following theorem:
if the following are true:
- expression state at time 43 = "begin_expr"
- stack at time 43 = [ 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 44 = [ 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 43 = "begin_expr" |
---|---|
2 | stack at time 43 = [ 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 (43 + 1) = stack at time 43 | if expression state at time 43 = "begin_expr", then stack at time (43 + 1) = stack at time 43 |
2 | stack at time (43 + 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 (43 + 1) = stack at time 43 and stack at time 43 = [ 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 (43 + 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 | 43 + 1 = 44 | 43 + 1 = 44 |
4 | stack at time (43 + 1) = stack at time 44 | if 43 + 1 = 44, then stack at time (43 + 1) = stack at time 44 |
5 | stack at time 44 = [ 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 (43 + 1) = stack at time 44 and stack at time (43 + 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 44 = [ 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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