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 A, ExprRange, Function, IndexedVar, Lambda, R, Variable, k, p
from proveit.logic import InvImage
from proveit.numbers import one
from proveit.physics.quantum.circuits import MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = [Function(p, [sub_expr1]), sub_expr2]
expr = Lambda(sub_expr1, [ExprRange(sub_expr2, MultiQubitElem(element = IndexedVar(A, sub_expr3), targets = Function(InvImage(p), [IndexedVar(R, sub_expr3)])), one, k)])

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())

{_{-}b} \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{A_{p\left({_{-}b}\right), 1}~\mbox{on}~p^{\leftarrow}\left(R_{p\left({_{-}b}\right), 1}\right)} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{A_{p\left({_{-}b}\right), 2}~\mbox{on}~p^{\leftarrow}\left(R_{p\left({_{-}b}\right), 2}\right)} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{A_{p\left({_{-}b}\right), k}~\mbox{on}~p^{\leftarrow}\left(R_{p\left({_{-}b}\right), k}\right)} & \qw 
} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 24 body: 1
1	ExprTuple	2
2	ExprRange	lambda_map: 3 start_index: 4 end_index: 5
3	Lambda	parameter: 21 body: 7
4	Literal
5	Variable
6	ExprTuple	21
7	Operation	operator: 8 operands: 9
8	Literal
9	NamedExprs	element: 10 targets: 11
10	IndexedVar	variable: 12 indices: 19
11	Operation	operator: 13 operand: 17
12	Variable
13	Operation	operator: 15 operand: 22
14	ExprTuple	17
15	Literal
16	ExprTuple	22
17	IndexedVar	variable: 18 indices: 19
18	Variable
19	ExprTuple	20, 21
20	Operation	operator: 22 operand: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable