logo

Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

In [1]:
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, X
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import Qmult, bra_varphi, ket_varphi, var_ket_psi, var_ket_v, varphi
from proveit.physics.quantum.algebra import Hspace
In [2]:
# build up the expression from sub-expressions
expr = Lambda(var_ket_psi, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = Equals(Qmult(var_ket_psi, bra_varphi), Lambda(var_ket_v, Conditional(ScalarMult(Qmult(bra_varphi, var_ket_v), var_ket_psi), InSet(var_ket_v, Hspace)))), condition = InSet(ket_varphi, Hspace)), InSet(var_ket_psi, X)))
Out[2]:
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\lvert \psi \rangle \mapsto \left\{\forall_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\left(\lvert \psi \rangle \thinspace \langle \varphi \rvert\right) = \left[\lvert v \rangle \mapsto \left\{\left(\langle \varphi \rvert \thinspace \lvert v \rangle\right) \cdot \lvert \psi \rangle \textrm{ if } \lvert v \rangle \in \mathcal{H}\right..\right]\right) \textrm{ if } \lvert \psi \rangle \in X\right..
In [5]:
stored_expr.style_options()
Out[5]:
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Lambdaparameter: 30
body: 2
1ExprTuple30
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 27
operands: 7
5Literal
6ExprTuple8
7ExprTuple30, 9
8Lambdaparameter: 38
body: 10
9Variable
10Conditionalvalue: 11
condition: 12
11Operationoperator: 13
operands: 14
12Operationoperator: 27
operands: 15
13Literal
14ExprTuple16, 17
15ExprTuple18, 31
16Operationoperator: 32
operands: 19
17Lambdaparameter: 35
body: 21
18Operationoperator: 22
operand: 38
19ExprTuple30, 34
20ExprTuple35
21Conditionalvalue: 23
condition: 24
22Literal
23Operationoperator: 25
operands: 26
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple29, 30
27Literal
28ExprTuple35, 31
29Operationoperator: 32
operands: 33
30Variable
31Variable
32Literal
33ExprTuple34, 35
34Operationoperator: 36
operand: 38
35Variable
36Literal
37ExprTuple38
38Variable