logo

Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Function, Lambda, Q
from proveit.logic import Forall
from proveit.physics.quantum.circuits import QcircuitEquiv
from proveit.statistics import Prob
In [2]:
# build up the expression from sub-expressions
expr = Lambda(Q, Forall(instance_param_or_params = [A, B], instance_expr = Function(Q, [Prob(B)]), conditions = [Function(Q, [Prob(A)]), QcircuitEquiv(A, B)]))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
Q \mapsto \left[\forall_{A, B~|~Q\left(\textrm{Pr}\left(A\right)\right), A \cong B}~Q\left(\textrm{Pr}\left(B\right)\right)\right]
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 16
body: 2
1ExprTuple16
2Operationoperator: 3
operand: 5
3Literal
4ExprTuple5
5Lambdaparameters: 19
body: 6
6Conditionalvalue: 7
condition: 8
7Operationoperator: 16
operand: 12
8Operationoperator: 10
operands: 11
9ExprTuple12
10Literal
11ExprTuple13, 14
12Operationoperator: 22
operand: 21
13Operationoperator: 16
operand: 20
14Operationoperator: 18
operands: 19
15ExprTuple21
16Variable
17ExprTuple20
18Literal
19ExprTuple24, 21
20Operationoperator: 22
operand: 24
21Variable
22Literal
23ExprTuple24
24Variable