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, N, Variable, n
from proveit.numbers import Add, Interval, one, subtract
from proveit.physics.quantum.circuits import Input, MultiQubitElem

# 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, MultiQubitElem(element = Input(state = IndexedVar(A, sub_expr1), part = sub_expr2), targets = Interval(Add(IndexedVar(N, subtract(sub_expr1, one)), one), IndexedVar(N, sub_expr1))), one, IndexedVar(n, sub_expr1)).with_wrapping_at(2,6))

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 \begin{array}{l} \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{{_{-}b}}~\mbox{part}~1~\mbox{on}~\{N_{{_{-}b} - 1} + 1~\ldotp \ldotp~N_{{_{-}b}}\}} & \qw 
} \end{array},  \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{{_{-}b}}~\mbox{part}~2~\mbox{on}~\{N_{{_{-}b} - 1} + 1~\ldotp \ldotp~N_{{_{-}b}}\}} & \qw 
} \end{array}, \ldots,  \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{{_{-}b}}~\mbox{part}~n_{{_{-}b}}~\mbox{on}~\{N_{{_{-}b} - 1} + 1~\ldotp \ldotp~N_{{_{-}b}}\}} & \qw 
} \end{array} \end{array}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 28 body: 1
1	ExprRange	lambda_map: 2 start_index: 32 end_index: 3
2	Lambda	parameter: 16 body: 5
3	IndexedVar	variable: 6 index: 28
4	ExprTuple	16
5	Operation	operator: 7 operands: 8
6	Variable
7	Literal
8	NamedExprs	element: 9 targets: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	NamedExprs	state: 15 part: 16
13	Literal
14	ExprTuple	17, 18
15	IndexedVar	variable: 19 index: 28
16	Variable
17	Operation	operator: 26 operands: 20
18	IndexedVar	variable: 23 index: 28
19	Variable
20	ExprTuple	22, 32
21	ExprTuple	28
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Literal