Llama is a language that compiles directly to lambda calculus with almost no layer of abstraction
Example
This code successfully compiles to:
(λmkpair.(λfirst.(λgetfirst.(λsecond.(λgetsecond.(λconcat.(λmap.(λsucc.(λpred.(λmult.(λowo.(λwew.concat (concat (map owo succ) " ") (map wew succ)) "Vgdqk ") "Gdmkn+") λm n f x.m (n f) x) λn f x.n 2 (λ_.x) λu.u) λn f x.n f (f x)) λs fn f x.s (λnm nx.f (fn nm) nx) x) λa b f x.a f (b f x)) λp.p second) 0) λp.p first) 0) λa b f.a b
And without literals:
(λmkpair.(λfirst.(λgetfirst.(λsecond.(λgetsecond.(λconcat.(λmap.(λsucc.(λpred.(λmult.(λowo.(λwew.concat (concat (map owo succ) (λf x.f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x)))))))))))))))))))))))))))))))) x)) (map wew succ)) λf x.f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x)))))))))))))))))))))))))))))))) x)))))) λf x.f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (f (λf x.f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))))))))))))))))))) x)))))) λm n f x.m (n f) x) λn f x.n (λg h.h (g f)) (λ_.x) λu.u) λn f x.n f (f x)) λs fn f x.s (λnm nx.f (fn nm) nx) x) λa b f x.a f (b f x)) λp.p second) λa b.b) λp.p first) λa b.a) λa b f.a b
Which reduces to "Henlo, Whirl"
Online compiler and solver soon(tm)
Specs
Variable names follow the regex [A-Za-z_][A-Za-z0-9_]*
Expression
Expressions are one of anything below, Long expressions (the body of a llama for example) consume multiple expressions until they hit the EOF or some token like )
LLama
Llamas work the same as lambdas in lambda calculus
λx.λy.λz.x looks like \x\y\z x in llama
syntax: \name lexpr
Application
Applications work the same as usual, two expressions grouped together is an application
It is always left associative meaning a b c d = ((a b) c) d
syntax: expr expr
Variables
Variables are bound to the closest llama that matches their name, otherwise they are free and applications to it cannot be solved.
Binding should work exactly like it would in a high level programming language like Dart, where variables are bound based on where they were the application took place, not where it was subsituted into.
syntax: name
Parentheses
Parentheses allow you to group expressions together to explicitly control application order
example: a (b c)
syntax: (lexpr)
Comments
Comments start with // and continue until the end of line
example:
~\flutter 1 // The one
Squiggly
The squiggly character is like parentheses that dont need to be closed
example: \f\x f(f(f(f x))) = \f\x f~f~f~f x
syntax: ~lexpr
Definitions
This is the first major difference to lambda calculus, you can procedurally define variables to be used in code preceding it
Only valid inside of a long expression
example:~\a 1 ~\b (succ a) ~\b (succ b) b = 3 (succ not included by default)
syntax: ~\name expr lexpr
The way this works is it puts the lexpr as a body of a llama and applies your expr to it
~\a 1
~\b (succ a)
succ b
turns into
(\a
(\b
succ b
) succ a
) 1
Vectors
Vectors can be created using square brackets
example: [1 2 3] = \f\x f 1~f 2~f 3 x
syntax: [expr...]
Numbers
Numbers use basic church encoding so 1 means \f\x f x and 3 means \f\x f~f~f x
example:
123 // decimal
0x7B // hex
0b1111011 // binary
0o173 // octal
'{' // character
Strings
String literals are equivalent to a vector of char codes
Both character literals and strings support the common escapes \a \b \f \n \r \t \v \\ \" and also number escapes \123 \x7b \b1111011
example: "foo" = ['f' 'o' 'o']
Llama include
Used to include a whole file as a llama, the file must have a main body
syntax: ~"filename"
example:
foo.lm
succ 1
bar.lm
succ \"foo.lm" // result is 3
Definition include
Unlike llama includes, definition includes import definitions and the file cannot have a main body
syntax: ~\"filename"
example:
foo.lm
~\concat(\a\b
\f\x a f ~b f x
)
bar.lm
~\"foo.lm"
concat "foo" "bar" // result is "foobar"
