Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

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

# 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, IndexedVar(A, [sub_expr1, sub_expr2]), one, l), ExprRange(sub_expr2, Gate(operation = I).with_implicit_representation(), one, m)])

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

{_{-}b} \mapsto \left(A_{{_{-}b}, 1}, A_{{_{-}b}, 2}, \ldots, A_{{_{-}b}, l},\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}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 17 body: 2
1	ExprTuple	17
2	ExprTuple	3, 4
3	ExprRange	lambda_map: 5 start_index: 8 end_index: 6
4	ExprRange	lambda_map: 7 start_index: 8 end_index: 9
5	Lambda	parameter: 18 body: 10
6	Variable
7	Lambda	parameter: 18 body: 12
8	Literal
9	Variable
10	IndexedVar	variable: 13 indices: 14
11	ExprTuple	18
12	Operation	operator: 15 operands: 16
13	Variable
14	ExprTuple	17, 18
15	Literal
16	NamedExprs	operation: 19
17	Variable
18	Variable
19	Literal