This library provides both type level and runtime versions of a lazy functional language.
- static, all constants
- lazy, things only run if needed
- functional, all things are functions
- curryed, we can use partial application
- type inference
- can fit into MCU's (specially the typelevel layer), => the C++11 base.
cout<<beta(toInt(length(list(1,2,3,"ok!"))))<<endl;
cout<<beta(toInt(foldl(mul)(n2)(list(n2,n3))))<<endl;output:
4
12
- full rewrite
- reversed execution queue order for smaller stacks
- full relly on
decltype(...), along withconstexprto obtain the type-level/compile-time versions - use
beta(...)function for expression reduction
This pseudo-language uses C++11 compiler and works both at typelevel and runtime.
Exploring functional paradigm
Extend C++ compiler
Use typelevel for small MCU's
implemented so far:
flip - λfab.fba used function f with arguments in reverse order
pair - λabf.fab construct pair or values to deliver to function f
fst - λo.o(λab.a) get first element of a pair
snd - λo.o(λab.b) get second element of a pair
_true - select first option λab.a
_false - select second option λab.b
_and - functional boolean and
_or - functional boolean or
_not - functional negation
beq - boolean equality
using Church encoded numerals
succ - successor of a nominal
pred - predecessor or a nominal
n0 .. n9 - predefined numerals
is0 - check if numeral is N0
_add - sum 2 numerals
sub - subtract 2 numeral
mul - multiply 2 numerals
_pow - numerals power
eq - check numeral equality
neq - check numeral inequality
leq - check numeral <= relation
geq - check numeral >= relation
lt - check numeral < relation
gt - check numeral > relation
head - get first element of a list
tail - get ramaining of a list (but the head)
cons - construct a list node
nil - empty list
null - check if list is empty
length - get list length (numeral)
index - get element at index
drop - drop elements from list head
init - get list of all but last element
last - get last element of a list
reverse - reverse list order
take - take elements from list start
nats - list of all natural numbers as numerals (infinit list)
range - range of numerals (list)
concat - join 2 lists
_map - map a function over list elements
filter - filter list elements
foldl - left fold a list with a function and start value
foldr - right fold a list with a function and start value
zip - join 2 lists in a list of pairs with minimal length
use:
constexpr turn any code into a compile time value
decltype get type of expression
S:= - λfgo.f(g o)
K:= - λab.a
I:= - λo.o
B:= - λfgo.f(go)
C:= - λfab.fba
M:= - λo.oo
L:= - CBM
Y:= - SLL
T:= - λof.fo
V:= - λabf.fab
Bb:= - BBB
beta perform full beta reduction, returns the same if irreducible
step perform beta reduction step, return None if irreducible
expr expression builder, returns a chain of function application
toBool convert expression to c++ bool
toInt convert expression to c++ int (numeral to c++ int)
list build a polymorphic list
example
constexpr const auto l1=list(1,2,"Ok");//compile time list build
const auto l2=list(1,2,"Ok");//runtime list build<< using c++ operator<<(...) for printing
https://www.angelfire.com/tx4/cus/combinator/birds.html
https://users.monash.edu/~lloyd/tildeFP/Lambda/Examples/const-list/
https://sincereflattery.blog/2021/04/26/lists-in-the-lambda-calculus/
https://blog.ploeh.dk/2018/06/04/church-encoded-maybe/
https://www.cl.cam.ac.uk/~rmk35/lambda_calculus/lambda_calculus.html
https://github.com/neu-rah/lpp
https://www.youtube.com/watch?v=3kMvXXGXaws
https://sookocheff.com/post/fp/evaluating-lambda-expressions/
https://groups.seas.harvard.edu/courses/cs152/2021sp/lectures/sld07-lambdacalc.pdf
https://gist.github.com/typesafedev/3465fab6320b39aa09b701a51f394f2d
https://codegolf.stackexchange.com/questions/231911/we-all-know-how-to-ski-but-can-you-bckw
https://en.wikipedia.org/wiki/B,_C,_K,_W_system