this is pure compile time, so "data" here are C++ types
Some examples:
Float::Type phi=1.618;using MCU_8BITS=True;
using idx_t=MCU_BITS::Bind<As<uint8_t>>::Bind<Int>::App::Type;
//alternative syntax:
using sz_t=Expr<MCU_8BITS,As<uint8_t>,Int>::App::Type;
//syntactic sugar
using port_t=If<MCU_8BITS>::Then<Char>::Else<Int>::App::Type;Using a curry template that can turn any c++ template of types into a curried version, adding ::Bind member types. This also reduces the original template to a single type, making it possible to compose and combine them again in new operations.
Just because non-curried version are so easy to write in C++, but we absolutely need them currying.
Function application is Lazy.
| name | lambda | description |
|---|---|---|
| I | λx.x | Identity |
| M | λf.ff | Self application |
| K | λab.a | first = functional boolean True |
| KI | λba.a | second = functional boolean false |
| C | λfab.fba | flip = functional negation |
| B | λfgo.f(g o) | function composition |
| V | λabf.fab | pair = functional data structure |
| V | λabf.fab | pair = functional data structure |
| Y | λf.(λo.f(o o)) (λo.f(o o)) | Recursion |
Id o - identity
Flip f a b - swap 2 arguments of a given function f a b -> f b a
Pair a b f - data constructor, holds a pair of 2 types to deliver them later to the reader function f (Pair a b) f -> f a b
Fst p - get the first of a pair p
Snd p - get the second of a pair p
provides a c++ primitive type wrapper
As< type >
extract with ::Type
StaticValue< type , value >
extract with ::value() static function
note: can only host constexpr values
StaticText< pointer to some static text >
a specialization for handling strings as dependent types in C++11
curry< «return type», «func. type», «func. ptr», «nr of arguments», [«bounded arguments type list...»] >
(this is an experimental feature expect heavy changes).
transform a C++ constexpr returning function into a lambda curried function that can be used as a lambda term.
//define
inline int _test(int a,int b) {return a*b;}
using test=curry<int,decltype(&_test),_test,2>;
//use
cout<<"call c++ function test(3,5) "<<test::Bind<StaticValue<int,3>>::Bind<StaticValue<int,5>>::value()<<endl;
cout<<"call c++ function Expr<test,3,5> "<<Expr<test,StaticValue<int,3>,StaticValue<int,5>>::value()<<endl;implemented operators And, Or, Not, BEq (boolean equality) along with functional boolean versions True and False
N0 .. N9 for convenience
Succ n get the successor of numeral n
Pred n get the predecessor of numeral n
Is0 n check if numeral n is zero
using Peano numbers to convert Numeral to constexpr values
toInt< type >() a convenience to print numerals
numerals will yield the corresponding value
Add a b a+b
Sub a b a-b
Mul a b a*b
Pow b e b^e
Fact n n!
Eq, LEq, GEq, LT, GT, NEq
Nil empty list.
Cons h t use o as list t head
Head l get list l first element (fails compilation if empty).
Tail l get list l tail, yields empty list when empty.
Null l check if l is empty.
Drop n l drops first n (as numeral) elements from the list l
Concat a b join to lists
Length l length of a list
Index l i get liost element by index/composition
Last l get last element of list or Nil
Init l list without last element
Reverse reverse a finite list
NatsN n numerals infinite list starting at n
Nats numerals infinite list starting at N1
TakeR n l take n elements of a list in reverse order
Take n l take n elements of a list
Range s e list of numerals from s to e
Map f l map a function f over list l
Filter f l filter a list l with function f
FoldL f n l fold left a list l using 'binary' function f starting with n
FoldR f n l right fold a list l using 'binary' function f starting with n
Zip a b build a list of pairs from elements of lists A and B, until one of them ends.
List< elements[,..] >
utility to construct lists as:
using L1=List<A,B,C>;
using same_as_L1=Const::Bind<A>::Bind<Const::Bind<B>::Bind<Const::Bind<C>::Bind<Nil>>>;
using or_this_way=Expr<Cons,A,Expr<Cons,B,Expr<Cons,C,Nil>>>;Curry template
for currying template<typename...> class
Lambda Calculus
http://www.allisons.org/ll/FP/Lambda/
Collected Lambda Calculus Functions
https://jwodder.freeshell.org/lambda.html
Lambda Calculus Examples
http://users.monash.edu/~lloyd/tildeFP/Lambda/Examples/
Lazy or Eager? Order of Evaluation in Lambda Calculus and OCaml - The Always Learning Marty
https://thealmarty.com/2018/09/03/lazy-or-eager-order-of-evaluation-in-lambda-calculus-and-ocaml/
Lambda the Ultimate | Programming Languages Weblog
http://lambda-the-ultimate.org/
lists.lam
http://languagemachine.sourceforge.net/lists.html
Lambda calculus definition
https://en.wikipedia.org/wiki/Lambda_calculus_definition
Fixed-point combinator
https://en.wikipedia.org/wiki/Fixed-point_combinator