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, l
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
expr = Lambda(l, Conditional(Mult(frac(one, four), frac(one, Exp(_diff_l_scaled_delta_floor, two))), InSet(l, _neg_domain)))

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())

l \mapsto \left\{\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 29 body: 2
1	ExprTuple	29
2	Conditional	value: 3 condition: 4
3	Operation	operator: 37 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	29, 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	53, 16
12	Literal
13	ExprTuple	53, 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	Operation	operator: 44 operands: 20
18	Operation	operator: 39 operands: 21
19	Operation	operator: 48 operand: 25
20	ExprTuple	23, 50
21	ExprTuple	24, 53
22	ExprTuple	25
23	Operation	operator: 39 operands: 26
24	Operation	operator: 48 operand: 31
25	Operation	operator: 39 operands: 28
26	ExprTuple	29, 30
27	ExprTuple	31
28	ExprTuple	32, 53
29	Variable
30	Operation	operator: 48 operand: 35
31	Operation	operator: 44 operands: 34
32	Variable
33	ExprTuple	35
34	ExprTuple	50, 36
35	Operation	operator: 37 operands: 38
36	Operation	operator: 39 operands: 40
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	51, 43
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operand: 52
43	Operation	operator: 48 operand: 53
44	Literal
45	ExprTuple	50, 51
46	Literal
47	ExprTuple	52
48	Literal
49	ExprTuple	53
50	Literal
51	Literal
52	Literal
53	Literal