evaluation


How am I misunderstanding call-by-need evaluation?


First of all, I never studied these things or anything, so I may be asking very silly questions, which I am sorry for, but please go easy on me :)
I'm playing around with implementing lambda calculus, with call-by-need evaluation. I'm trying to follow this paper on the subject, where the relevant bit seems to be the natural semantics described on page 28.
Anyway, what I don't understand about this evaluation strategy is that, as far as I understand, the actual substitution only happens when evaluating variables. Abstractions evaluate to themselves, as these are the values, and applications only add new entries to the cache.
But given that, how exactly one go about evaluating a term like
(λx.λy.x y) λa.a
According to the natural semantics, described in the linked paper, the first evaluation step would be to add the entry x -> λa.a to the cache, and evaluate the body of the abstraction on the lhs of the application, which is λy.x y. But this is a value, so the evaluation ends. At which point we have a term that is not closed, and a non-empty heap. While we know exactly that this term should evaluate to λy.(λa.a) y.
What am I misunderstanding? How does this work in languages that actually use this evaluation strategy?
Your reduction is right. The point is that the call by need strategy addressed in that paper is only a weak strategy, in the sense that it will never reduce under a lambda expression. This is evident in Fig.1, where the expression \x.M is a value.
At the end of the reduction, if you want to obtain a lambda term explicitly, you still need to unwind the cache (frequently called environment in the literature), that amounts to substitute the associations in the cache inside your term:
λy.x y [x -> λa.a] = λy.(λa.a) y
as expected.

Related Links

Math notation understanding
What criterias do you look for in a WAF (web application firewall)?
Predictionio evaluation fails with Text Classification template
Evaluation of APL direct functions
Modelica Evaluation Order
how compilers evaluate mathematical expressions? [closed]
What does “top-level evaluation” mean?
Boolean expression evaluation with a given context
Is relying on short-circuit evaluation good design? [closed]
Objectively evaluating new GUI toolkits
what are evaluation techniques for HCI projects (without involving users, or psychologist)?
Evaluating developers [closed]
Options to Common Criteria
What are some useful criteria for deciding on which software package to go for?
Having to set objectives for developers, even though objectives don't work [closed]
How would you go about evaluating a programmer? [closed]

Categories

HOME
openacc
window.open
gaussian
watson-iot
pandoc
hiveql
yuv
swap
symfony-3.2
oms
suitecrm
chef-recipe
tracking
dat.gui
beacon
aws-devicefarm
conditional-formatting
combinations
connectiq
jira-zephyr
my.cnf
jopendocument
android-cursorloader
multiple-inheritance
marionette
request-uri
federated
ipython-parallel
xlib
andengine
android-scrollview
javax
android-geofence
respect-validation
strategy-pattern
queryover
lex
ssdp
logan-square
spring-ide
import.io
dna-sequence
bioperl
node-java
aot
iban
acceleo
group
esprima
android-tabs
networkstream
xcode7.1
db2-zos
jcalendar
android-progressbar
periodic-processing
hana-sql-script
wordpress-plugin
javapackager
libgcrypt
winforms-interop
minko
uiblureffect
information-hiding
powershell-v1.0
azure-worker-roles
visual-c#-express-2010
mvcgrid
dateadd
new-operator
fastcgi-mono-server
object-oriented-database
mysql-error-1146
sygic
ie-developer-tools
kendo-window
angularjs-select2
typography
leap-year
gmail-imap
nx
blotter
configurationsection
nude.js
session-hijacking
noise-reduction
oaw
numerical-computing
data-formats

Resources

Mobile Apps Dev
Database Users
javascript
java
csharp
php
android
MS Developer
developer works
python
ios
c
html
jquery
RDBMS discuss
Cloud Virtualization
Database Dev&Adm
javascript
java
csharp
php
python
android
jquery
ruby
ios
html
Mobile App
Mobile App
Mobile App