Proof: Write Class Def 0
Let's prove the following theorem:
if the following are true:
- the line at time 0 = 1
- the tab at time 0 = 0
- statement at line 1, tab 0 =
class Animal:
- Class Map at time 0 = [ ]
then Class Map at time 1 = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ]
Proof:
Given
1 | the line at time 0 = 1 |
---|---|
2 | the tab at time 0 = 0 |
3 | statement at line 1, tab 0 = class Animal: |
4 | Class Map at time 0 = [ ] |
# | Claim | Reason |
---|---|---|
1 | Class Map at time (0 + 1) = result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) | if the line at time 0 = 1 and the tab at time 0 = 0 and statement at line 1, tab 0 = class Animal: , then Class Map at time (0 + 1) = result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) |
2 | result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) = result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: [ ] | if Class Map at time 0 = [ ], then result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) = result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: [ ] |
3 | result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: [ ] = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] | result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: [ ] = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] |
4 | result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] | if result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) = result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: [ ] and result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: [ ] = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ], then result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] |
5 | Class Map at time (0 + 1) = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] | if Class Map at time (0 + 1) = result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) and result of storing [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ] at key: "Animal" in map: (Class Map at time 0) = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ], then Class Map at time (0 + 1) = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] |
6 | 0 + 1 = 1 | 0 + 1 = 1 |
7 | Class Map at time (0 + 1) = Class Map at time 1 | if 0 + 1 = 1, then Class Map at time (0 + 1) = Class Map at time 1 |
8 | Class Map at time 1 = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] | if Class Map at time (0 + 1) = Class Map at time 1 and Class Map at time (0 + 1) = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ], then Class Map at time 1 = [ entry "Animal": [ entry "bases": [ ], [ entry "methods": [ ], [ entry "line": 1, [ ] ] ] ], [ ] ] |
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