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 B, C, ExprRange, IndexedVar, Lambda, S, T, Variable, k, l
from proveit.numbers import one
from proveit.physics.quantum.circuits import MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = [sub_expr1, sub_expr2]
expr = Lambda(sub_expr1, [ExprRange(sub_expr2, MultiQubitElem(element = IndexedVar(B, sub_expr3), targets = IndexedVar(S, sub_expr3)), one, k), ExprRange(sub_expr2, MultiQubitElem(element = IndexedVar(C, sub_expr3), targets = IndexedVar(T, sub_expr3)), one, l)])

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{{_{-}b}, 1}~\mbox{on}~S_{{_{-}b}, 1}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{{_{-}b}, 2}~\mbox{on}~S_{{_{-}b}, 2}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{{_{-}b}, k}~\mbox{on}~S_{{_{-}b}, k}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{C_{{_{-}b}, 1}~\mbox{on}~T_{{_{-}b}, 1}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{C_{{_{-}b}, 2}~\mbox{on}~T_{{_{-}b}, 2}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{C_{{_{-}b}, l}~\mbox{on}~T_{{_{-}b}, l}} & \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: 25 body: 2
1	ExprTuple	25
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: 26 body: 10
6	Variable
7	Lambda	parameter: 26 body: 12
8	Literal
9	Variable
10	Operation	operator: 14 operands: 13
11	ExprTuple	26
12	Operation	operator: 14 operands: 15
13	NamedExprs	element: 16 targets: 17
14	Literal
15	NamedExprs	element: 18 targets: 19
16	IndexedVar	variable: 20 indices: 24
17	IndexedVar	variable: 21 indices: 24
18	IndexedVar	variable: 22 indices: 24
19	IndexedVar	variable: 23 indices: 24
20	Variable
21	Variable
22	Variable
23	Variable
24	ExprTuple	25, 26
25	Variable
26	Variable