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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, ExprRange, IndexedVar, Lambda, Variable, l, m
from proveit.numbers import one
from proveit.physics.quantum import I
from proveit.physics.quantum.circuits import Gate
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, [ExprRange(sub_expr2, Gate(operation = I).with_implicit_representation(), one, m), ExprRange(sub_expr2, IndexedVar(A, [sub_expr1, sub_expr2]), one, l)])
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())
{_{-}b} \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, ..\left(m - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},A_{{_{-}b}, 1}, A_{{_{-}b}, 2}, \ldots, A_{{_{-}b}, l}\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 18
body: 2
1ExprTuple18
2ExprTuple3, 4
3ExprRangelambda_map: 5
start_index: 8
end_index: 6
4ExprRangelambda_map: 7
start_index: 8
end_index: 9
5Lambdaparameter: 19
body: 10
6Variable
7Lambdaparameter: 19
body: 12
8Literal
9Variable
10Operationoperator: 13
operands: 14
11ExprTuple19
12IndexedVarvariable: 15
indices: 16
13Literal
14NamedExprsoperation: 17
15Variable
16ExprTuple18, 19
17Literal
18Variable
19Variable