Expression of type Lambda

from the theory of proveit.physics.quantum.QPE

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, k, t
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, Add(t, one))), InSet(k, Interval(zero, subtract(two_pow_t, one)))))

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())

k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t + 1} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 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: 30 body: 2
1	ExprTuple	30
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	30, 11
9	Operation	operator: 33 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	30, 19
15	Literal
16	ExprTuple	20, 21
17	Literal
18	Operation	operator: 22 operands: 23
19	Operation	operator: 25 operands: 24
20	Literal
21	Operation	operator: 25 operands: 26
22	Literal
23	ExprTuple	37, 27, 28, 29, 30
24	ExprTuple	38, 39
25	Literal
26	ExprTuple	31, 32
27	Literal
28	Literal
29	Literal
30	Variable
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operand: 39
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39
37	Literal
38	Variable
39	Literal