lambda is a programming language purely based on the (untyped) lambda calculus and its beta-reduction.
Installation can (and should) be done with stack, so stack must be installed prior. If you are on Linux, you can install stack via your distributions package manager, on macOS it can be installed via brew and for windows there exists a dedicated installer. See https://docs.haskellstack.org/en/stable/install_and_upgrade/ for detailed instructions.
Next clone the repository (or download and extract it somewhere)
# clone
git clone https://github.com/christofsteel/lambda.git
Now enter the cloned repository lambda and install it (If you downloaded the zip you have to enter the extracted folder. It is usually called lambda-master)
cd lambda
stack init
stack install
There are three ways to run lambda
- Call with a file
lambda -f examples/exampleA.l
- Call with a string
lambda "let I=\x.x; printNF I I"
- Open a REPL
lambda -r
See lambda --help for a complete list of arguments
The basic syntax for creating term is,
- any alphanumeric string is a variable. In addition the
'and the_symbol are allowed. (e.g.a,x',8,ab_8) The_symbol on its own is no Variable - a
\followed by one or more variables, then a.and another term is an abstraction. (e.g.\x.x,\x y.x) - a
p q,(\x.x.) q),p q s)
Parentheses are optional. If they are not present, the binding of operators follow the usual conventions for lambda calculus.
To form a program you can use the following commands
| Command | Description |
|---|---|
import File |
Imports a file and executes it |
let Variable = Term |
Defines a Variable to be expanded to a Term in later commands |
print Text |
Prints Text without a newline |
printLN Text |
Prints Text with a newline |
printT Term |
Prints the definition of a Term |
printNF Term |
Calculates the normal form for a Term and prints it |
printNFMax Int Term |
As printNF but only computes a given number of steps |
traceNF Term |
Calculates the normal form for a Term and prints every step |
traceNFMax Int Term |
As traceNF but only computes a given number of steps |
step Variable |
Applies beta reduction on the term stored in the Variable |
set Option Value |
Sets an Option to a Value (see below) |
get Option |
Prints the value for an Option |
addRev Variable |
Notes, that terms corresponding to the Variable will be printed as the Variable, not as the Term |
delRev Variable |
Removes the Variable from the above list |
showRev |
Shows all variables, that will not be shown as lambdaterms |
The following Options exist and can be set with set
| Option | Possible Values | Default Value | Descrition |
|---|---|---|---|
utf8 |
True, False |
False |
Show a real lambda, beta and arrow |
explicit |
True, False |
False |
Shows every parentheses |
pnat |
True, False |
True |
Interpret natural numbers as church numerals |
rnat |
True, False |
False |
If a Term looks like a church numeral, show the number |
ps1 |
Any String | LAMBDA |
Prompt to show in REPL mode |
steps |
Any natural number | 100 |
Steps to calculate in REPL mode |
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