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 IndexedVar, Lambda, Variable
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1, varphi
from proveit.physics.quantum.circuits import Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, IndexedVar(varphi, sub_expr1))), ket1)))))

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())

{_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{{_{-}a}}} \cdot \lvert 1 \rangle\right)\right)} 
} \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: 39 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	NamedExprs	state: 4
4	Operation	operator: 16 operands: 5
5	ExprTuple	6, 7
6	Operation	operator: 22 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	30, 11
9	Literal
10	ExprTuple	12, 13
11	Operation	operator: 24 operands: 14
12	Operation	operator: 26 operand: 19
13	Operation	operator: 16 operands: 17
14	ExprTuple	33, 18
15	ExprTuple	19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operand: 30
22	Literal
23	ExprTuple	30, 33
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30
28	Literal
29	Operation	operator: 31 operands: 32
30	Literal
31	Literal
32	ExprTuple	33, 34, 35, 36
33	Literal
34	Literal
35	Literal
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable