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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 Conditional, Lambda
from proveit.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InClass, InSet
from proveit.physics.quantum import QmultCodomain, bra_varphi, ket_varphi, varphi
In [2]:
# build up the expression from sub-expressions
expr = Lambda(Hspace, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = InClass(bra_varphi, QmultCodomain), condition = InSet(ket_varphi, Hspace)), InClass(Hspace, 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())
\mathcal{H} \mapsto \left\{\forall_{\varphi~|~\lvert \varphi \rangle \in \mathcal{H}}~\left(\langle \varphi \rvert \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \textrm{ if } \mathcal{H} \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
0Lambdaparameter: 20
body: 2
1ExprTuple20
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 13
operands: 7
5Literal
6ExprTuple8
7ExprTuple20, 9
8Lambdaparameter: 24
body: 10
9Literal
10Conditionalvalue: 11
condition: 12
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17, 18
15Literal
16ExprTuple19, 20
17Operationoperator: 21
operand: 24
18Literal
19Operationoperator: 22
operand: 24
20Variable
21Literal
22Literal
23ExprTuple24
24Variable