Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

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
from proveit.linear_algebra import Hspace, InnerProd
from proveit.logic import Equals, InSet
from proveit.physics.quantum import bra_varphi, ket_varphi, var_ket_psi, varphi

# build up the expression from sub-expressions
expr = Lambda(varphi, Conditional(Equals(bra_varphi, Lambda(var_ket_psi, Conditional(InnerProd(ket_varphi, var_ket_psi), InSet(var_ket_psi, Hspace)))), InSet(ket_varphi, Hspace)))

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())

\varphi \mapsto \left\{\langle \varphi \rvert = \left[\lvert \psi \rangle \mapsto \left\{\left \langle \lvert \varphi \rangle, \lvert \psi \rangle\right \rangle \textrm{ if } \lvert \psi \rangle \in \mathcal{H}\right..\right] \textrm{ if } \lvert \varphi \rangle \in \mathcal{H}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 23 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 16 operands: 6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	18, 20
7	Operation	operator: 9 operand: 23
8	Lambda	parameter: 19 body: 11
9	Literal
10	ExprTuple	19
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 21 operand: 23
19	Variable
20	Variable
21	Literal
22	ExprTuple	23
23	Variable