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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 A, Conditional, Lambda, X
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, var_ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InClass(Qmult(A, var_ket_psi), QmultCodomain), domain = Hspace), condition = InSet(Qmult(A), LinMap(Hspace, X))), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces))))
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())
\left(\mathcal{H}, X\right) \mapsto \left\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 26
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 16
operand: 7
3Operationoperator: 5
operands: 6
4ExprTuple7
5Literal
6ExprTuple8, 9
7Lambdaparameter: 39
body: 10
8Operationoperator: 30
operands: 11
9Operationoperator: 30
operands: 12
10Conditionalvalue: 13
condition: 14
11ExprTuple36, 15
12ExprTuple29, 15
13Operationoperator: 16
operand: 19
14Operationoperator: 32
operands: 18
15Literal
16Literal
17ExprTuple19
18ExprTuple20, 21
19Lambdaparameter: 40
body: 23
20Operationoperator: 37
operand: 39
21Operationoperator: 25
operands: 26
22ExprTuple40
23Conditionalvalue: 27
condition: 28
24ExprTuple39
25Literal
26ExprTuple36, 29
27Operationoperator: 30
operands: 31
28Operationoperator: 32
operands: 33
29Variable
30Literal
31ExprTuple34, 35
32Literal
33ExprTuple40, 36
34Operationoperator: 37
operands: 38
35Literal
36Variable
37Literal
38ExprTuple39, 40
39Variable
40Variable