The Programming Languages Zoo

A potpourri of programming languages

lambda

[source] [example]

An implementation of the untyped λ-calculus.

The λ-calculus is an equational theory and so does not by itself enforce a notion of computation. There are several strategies for normalizing redices, which in lambda can be controlled with directives:

We can combine these to get various reduction strategies:

  #eager #lazy
#shallow weak normal form weak head normal form
#deep normal form head normal form

In terms of programming language terminology, weak normal form corresponds approximately to call by value and the weak head normal form to call by name.

Example interaction

The file example.lambda contains an example session which defines booleans, numbers, and lists. You can use it as follows:

$ ./lambda.native -l example.lambda 
pair is defined.
first is defined.
second is defined.
K is defined.
true is defined.
false is defined.
if is defined.
and is defined.
or is defined.
not is defined.
fix is defined.
error is a constant.
nil is defined.
cons is defined.
head is defined.
tail is defined.
match is defined.
map is defined.
fold is defined.
0 is defined.
1 is defined.
2 is defined.
3 is defined.
4 is defined.
5 is defined.
6 is defined.
7 is defined.
8 is defined.
9 is defined.
10 is defined.
succ is defined.
+ is defined.
* is defined.
** is defined.
iszero is defined.
pred is defined.
== is defined.
fact is defined.
<= is defined.
>= is defined.
< is defined.
> is defined.
mu is defined.
/ is defined.
| is defined.
all is defined.
prime is defined.
lambda -- programming languages zoo
Type Ctrl-D to exit
lambda> prime 3
λ x _ . x
lambda> prime 4
λ _ y . y
lambda> prime 5
λ x _ . x
lambda> prime 6
λ _ y . y
lambda> prime 7
λ x _ . x
lambda> + 2 3
λ f x . 2 f (3 f x)
lambda> :eager
I will evaluate eagerly.
lambda> :deep
I will evaluate deeply.
lambda> + 2 3
λ f x . f (f (f (f (f x))))
lambda> :lazy
I will evaluate lazily.
lambda> + 2 3
λ f x . f (f (3 f x))