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, b
from proveit.logic import And, InClass, InSet, Set, SetOfAll
from proveit.numbers import one, zero
from proveit.physics.quantum import QubitSpace, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import qubit_meas
from proveit.statistics import SampleSpaces

# build up the expression from sub-expressions
expr = Lambda(var_ket_psi, Conditional(InClass(SetOfAll(instance_param_or_params = [b], instance_element = qubit_meas, domain = Set(zero, one)), SampleSpaces), And(InSet(var_ket_psi, QubitSpace), 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())

\lvert \psi \rangle \mapsto \left\{\left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right\}_{b \in \left\{0, 1\right\}} \underset{{\scriptscriptstyle c}}{\in} \textrm{SampleSpaces} \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{2} ,  \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	parameter: 50 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operand: 17
9	Literal
10	Operation	operator: 31 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	ExprTuple	17
14	ExprTuple	50, 18
15	Literal
16	ExprTuple	19, 49
17	Lambda	parameter: 55 body: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operand: 50
20	Conditional	value: 25 condition: 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	50
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Literal
28	Literal
29	Literal
30	ExprTuple	33, 34, 35
31	Literal
32	ExprTuple	55, 36
33	ExprTuple	37
34	ExprTuple	38
35	ExprTuple	39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operands: 43
38	Operation	operator: 44 operands: 45
39	Operation	operator: 46 operands: 47
40	Literal
41	ExprTuple	48, 49
42	Literal
43	NamedExprs	state: 50
44	Literal
45	NamedExprs	basis: 51
46	Literal
47	NamedExprs	state: 52
48	Literal
49	Literal
50	Variable
51	Literal
52	Operation	operator: 53 operand: 55
53	Literal
54	ExprTuple	55
55	Variable