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 Conditional, Lambda, m, n
from proveit.logic import And, InClass, InSet, SetOfAll
from proveit.numbers import NaturalPos
from proveit.physics.quantum import m_bit_interval, m_ket_domain, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import register_meas
from proveit.statistics import SampleSpaces

# build up the expression from sub-expressions
expr = Lambda([m, var_ket_psi], Conditional(InClass(SetOfAll(instance_param_or_params = [n], instance_element = register_meas, domain = m_bit_interval), SampleSpaces), And(InSet(m, NaturalPos), InSet(var_ket_psi, m_ket_domain), normalized_var_ket_psi)))

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())

\left(m, \lvert \psi \rangle\right) \mapsto \left\{\left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \psi \rangle} & \meter & \multiqout{3}{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \measure{\begin{array}{c}:\\ \left(m - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{m}} \\
\ghostqin{\lvert \psi \rangle} & \meter & \ghostqout{\lvert n \rangle_{m}}
} \end{array}\right\}_{n \in \{0~\ldotp \ldotp~2^{m} - 1\}} \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces} \textrm{ if } m \in \mathbb{N}^+ ,  \lvert \psi \rangle \in \mathbb{C}^{2^{m}} ,  \left \|\lvert \psi \rangle\right \| = 1\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	85, 78
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 14 operand: 20
10	Literal
11	Operation	operator: 35 operands: 16
12	Operation	operator: 35 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	20
16	ExprTuple	85, 21
17	ExprTuple	78, 22
18	Literal
19	ExprTuple	23, 81
20	Lambda	parameter: 84 body: 25
21	Literal
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operand: 78
24	ExprTuple	84
25	Conditional	value: 30 condition: 31
26	Literal
27	ExprTuple	32, 61
28	Literal
29	ExprTuple	78
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operands: 36
32	Literal
33	Literal
34	ExprTuple	37, 38, 39
35	Literal
36	ExprTuple	84, 40
37	ExprTuple	41
38	ExprTuple	42
39	ExprTuple	43
40	Operation	operator: 75 operands: 44
41	ExprRange	lambda_map: 45 start_index: 81 end_index: 85
42	ExprRange	lambda_map: 46 start_index: 81 end_index: 85
43	ExprRange	lambda_map: 47 start_index: 81 end_index: 85
44	ExprTuple	48, 49
45	Lambda	parameter: 80 body: 50
46	Lambda	parameter: 80 body: 51
47	Lambda	parameter: 80 body: 53
48	Literal
49	Operation	operator: 54 operands: 55
50	Operation	operator: 59 operands: 56
51	Operation	operator: 57 operands: 58
52	ExprTuple	80
53	Operation	operator: 59 operands: 60
54	Literal
55	ExprTuple	61, 62
56	NamedExprs	element: 63 targets: 66
57	Literal
58	NamedExprs	basis: 64
59	Literal
60	NamedExprs	element: 65 targets: 66
61	Operation	operator: 67 operands: 68
62	Operation	operator: 69 operand: 81
63	Operation	operator: 71 operands: 72
64	Literal
65	Operation	operator: 73 operands: 74
66	Operation	operator: 75 operands: 76
67	Literal
68	ExprTuple	77, 85
69	Literal
70	ExprTuple	81
71	Literal
72	NamedExprs	state: 78 part: 80
73	Literal
74	NamedExprs	state: 79 part: 80
75	Literal
76	ExprTuple	81, 85
77	Literal
78	Variable
79	Operation	operator: 82 operands: 83
80	Variable
81	Literal
82	Literal
83	ExprTuple	84, 85
84	Variable
85	Variable