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 B, Function, IndexedVar, Lambda, S, Variable, p
from proveit.logic import InvImage
from proveit.physics.quantum.circuits import MultiQubitElem

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

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{
& & \gate{B_{p\left({_{-}b}\right), {_{-}a}}~\mbox{on}~p^{\leftarrow}\left(S_{p\left({_{-}b}\right), {_{-}a}}\right)} & \qw 
} \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: 16 body: 2
1	ExprTuple	16
2	Operation	operator: 3 operands: 4
3	Literal
4	NamedExprs	element: 5 targets: 6
5	IndexedVar	variable: 7 indices: 14
6	Operation	operator: 8 operand: 12
7	Variable
8	Operation	operator: 10 operand: 17
9	ExprTuple	12
10	Literal
11	ExprTuple	17
12	IndexedVar	variable: 13 indices: 14
13	Variable
14	ExprTuple	15, 16
15	Operation	operator: 17 operand: 19
16	Variable
17	Variable
18	ExprTuple	19
19	Variable