Properties
Properties are true expressions. They are used to prove theorems
a = a
(a + b) + c = a + (b + c)
a + b = b + a
a + 0 = a
a - b = a + (b ⋅ (-1))
a + (a ⋅ (-1)) = 0
(a ⋅ b) ⋅ c = a ⋅ (b ⋅ c)
a ⋅ b = b ⋅ a
a ⋅ 0 = 0
a ⋅ 1 = a
a / 1 = a
a / b = a ⋅ (1 / b)
a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c)
1 + 2 = 3
value of cell 0 at time t = 0
expression a + b =
__add__(a, b)expression a * b =
__mul__(a, b)expression a == b =
__eq__(a, b)expression a > b =
__gt__(a, b)expression a < b =
__lt__(a, b)type of
x = e = "assign"type of
elif e: = "elif"type of
else: = "else"(pair ("while", x)) describes a loop = True
(pair ("if", x)) describes a loop = False
is
x = expr an assign statement = Trueis
if expr: an if statement = Trueis
while expr: a while statement = Trueresult of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ [ constant of value x, ys ], rest ], values stack is[ values, v_rest ], variables isvars, and control map iscontrol = result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ ys, rest ], values stack is[ [ x, values ], v_rest ], variables isvars, and control map iscontrol
result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ [ variable of value x, ys ], rest ], values stack is[ values, v_rest ], variables isvars, and control map iscontrol = result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ ys, rest ], values stack is[ [ value at x in map vars, values ], v_rest ], variables isvars, and control map iscontrol
result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ [ function call with name: name and arguments: args, ys ], rest ], values stack isvals, variables isvars, and control map iscontrol = result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ args, [ [ function call with name: name and arguments: args, ys ], rest ] ], values stack is[ [ ], vals ], variables isvars, and control map iscontrol
result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ [ ], [ [ function call with name: "__add__" and arguments: args, ys ], rest ] ], values stack is[ [ a, [ b, [ ] ] ], [ next_level, other_levels ] ], variables isvars, and control map iscontrol = result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ ys, rest ], values stack is[ [ b + a, next_level ], other_levels ], variables isvars, and control map iscontrol
result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ [ ], [ [ function call with name: "__eq__" and arguments: args, ys ], rest ] ], values stack is[ [ a, [ b, [ ] ] ], [ next_level, other_levels ] ], variables isvars, and control map iscontrol = result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ ys, rest ], values stack is[ [ b = a, next_level ], other_levels ], variables isvars, and control map iscontrol
result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ [ ], [ [ function call with name: "__lt__" and arguments: args, ys ], rest ] ], values stack is[ [ a, [ b, [ ] ] ], [ next_level, other_levels ] ], variables isvars, and control map iscontrol = result of executing a Python program where statements is stmts, line is i, tab isj, expression stack is[ ys, rest ], values stack is[ [ b < a, next_level ], other_levels ], variables isvars, and control map iscontrol
get expression from (assign statement with target c and expression (constant of value x)) = constant of value x
get expression from (assign statement with target c and expression (variable of value x)) = variable of value x
get expression from (assign statement with target c and expression (function call with name: a and arguments: b)) = function call with name: a and arguments: b
get target from (assign statement with target (variable of value v) and expression c) = v
get expression from
if test: = testget expression from
while test: = testbyte at ID: x, cell #0 at time t = 0
"A" in decimal = 65
"B" in decimal = 66
target_1.target_2 =
getattr(target1, target2)getattr(target_1, target_2) = value = setattr(target_1, target_2, value)object[key] = __getitem__(object, key)__getitem__(object, key) = value = __setitem__(object, key, value)the first token in (pair (name, some)) = name
(trio ("for", line, ex)) describes a loop = True
sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ] = [ 1, [ ] ]
reverse of s = result of dumping s to [ ]
reverse of remaining stack [ x, [ ] ] and already reversed stack ys = [ x, ys ]
reverse of remaining stack [ x, xs ] and already reversed stack ys = reverse of remaining stack xs and already reversed stack [ x, ys ]
reverse of remaining stack [ ] and already reversed stack [ ] = [ ]
reverse of xs = reverse of remaining stack xs and already reversed stack [ ]
result of dumping [ y, ys ] to xs = result of dumping ys to [ y, xs ]
result of dumping [ ] to xs = xs
result of appending y to xs = result of dumping (result of dumping xs to [ ]) to [ y, [ ] ]
result of appending y to xs = reverse of [ y, reverse of xs ]
compare bit 0 and bit 0 = [ 1, [ 0, [ ] ] ]
compare bit 1 and bit 0 = [ 0, [ 1, [ ] ] ]
compare bit 0 and bit 1 = [ 0, [ 0, [ ] ] ]
compare bit 1 and bit 1 = [ 1, [ 0, [ ] ] ]
compare bit stack [ x, [ ] ] and bit stack [ y, [ ] ] = compare bit x and bit y
minimum value of stack [ x, [ ] ] = x
maximum value in stack [ x, [ ] ] = x
[] = []
index of value value in numbers = index of value value in numbers with current index [ 0, [ ] ]
index of value v in els = index of value v in els with current index 0
index of value v in els = output of the index_compute function where the input stack is els, value is v, and index is 0
index of value val in els = index of value val in els with current index 0
index of the mininum value in stack els = index of value (minimum value of stack els) in els
index of the maximum value in stack els = index of value (maximum value in stack els) in els
bit xs minus bit 0 = xs
bit [ 1, xs ] minus bit 1 = [ 0, xs ]
bit [ 0, xs ] minus bit 1 = [ 1, bit xs minus bit 1 ]
remaining elements after xs is popped at index idx = remaining elements after xs is popped at index idx and visited stack is [ ]
remaining elements after [ x, xs ] is popped at index [ 0, [ ] ] and visited stack is ys = result of dumping xs to ys
remaining elements after [ x, xs ] is popped at index [ 1, [ ] ] and visited stack is result = remaining elements after xs is popped at index [ 0, [ ] ] and visited stack is [ x, result ]
remaining elements after [ x, xs ] is popped at index [ y0, [ y1, ys ] ] and visited stack is result = remaining elements after xs is popped at index (bit [ y0, [ y1, ys ] ] minus bit 1) and visited stack is [ x, result ]
remaining elements after [ x, xs ] is popped at index 0 and visited stack is ys = reverse of (result of dumping xs to ys)
remaining elements after [ x, xs ] is popped at index 0 and visited stack is ys = result of dumping ys to xs
remaining elements after [ x, xs ] is popped at index idx and visited stack is v = remaining elements after xs is popped at index (idx - 1) and visited stack is [ x, v ]
stack after popping a value from stack xs at index idx = reverse of (stack after popping a value from stack xs at index idx in traversed elements: [ ])
stack after popping a value from stack [ x, xs ] at index 0 in traversed elements: result = result of dumping xs to result
stack after popping a value from stack [ x, xs ] at index idx in traversed elements: result = stack after popping a value from stack xs at index (idx - 1) in traversed elements: [ x, result ]
result of sorting [ ] with sorted stack sl = sl
result of sorting [ el, rem ] with sorted stack sl = result of sorting (remaining elements after [ el, rem ] is popped at index (index of the maximum value in stack [ el, rem ])) with sorted stack [ maximum value in stack [ el, rem ], sl ]
result of sorting els = result of sorting els with sorted stack [ ]
the element at index 0 of stack [ x, y ] = x
the element at index i of stack [ x, y ] = the element at index (i - 1) of stack y
the element at index 0 of stack (pair (x, y)) = x
the element at index 1 of stack (pair (x, y)) = y
result of storing value at index idx of stack elements = set index idx of remaining stack elements to value with visited : [ ]
set index 0 of remaining stack [ x, rest ] to value with visited : visited = result of dumping [ value, visited ] to rest
set index idx of remaining stack [ x, rest ] to value with visited : y = set index (idx - 1) of remaining stack rest to value with visited : [ x, y ]
length of stack xs = length of remaining stack xs with count 0
length of remaining stack [ ] with count count = count
length of remaining stack [ x, y ] with count count = length of remaining stack y with count (count + 1)
stack [ ] contains x = False