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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, Conditional, Function, Lambda, Q
from proveit.logic import And
from proveit.physics.quantum.circuits import QcircuitEquiv
from proveit.statistics import Prob
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Function(Q, [Prob(B)]), And(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())
\left(A, B\right) \mapsto \left\{Q\left(\textrm{Pr}\left(B\right)\right) \textrm{ if } Q\left(\textrm{Pr}\left(A\right)\right) ,  A \cong B\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 14
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 11
operand: 7
3Operationoperator: 5
operands: 6
4ExprTuple7
5Literal
6ExprTuple8, 9
7Operationoperator: 17
operand: 16
8Operationoperator: 11
operand: 15
9Operationoperator: 13
operands: 14
10ExprTuple16
11Variable
12ExprTuple15
13Literal
14ExprTuple19, 16
15Operationoperator: 17
operand: 19
16Variable
17Literal
18ExprTuple19
19Variable