Lambda interpreter in PHP

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Lambda Interpreter @matyo91 20-03-2025 In PHP

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Why? @matyo91 20-03-2025

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Define a language that allows process data-flows with functional programming principles “ @matyo91 20-03-2025

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What is it about ? @matyo91 20-03-2025

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Alonzo Church ( 1903 - 1995 ) Inventor of Lambda Calculus @matyo91 @matyo91 20-03-2025

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Church Turing @matyo91 @matyo91 20-03-2025

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λ x . x + 1 ( λ x . x + 1 ) ( 5 ) = 5 + 1 = 6 @matyo91 @matyo91 20-03-2025 X X + 1

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λ x . λ y . x+y ( λ x . λ y . x+y ) ( 5 , 6 ) = 5 + 6 = 11 @matyo91 @matyo91 20-03-2025 X X + Y Y

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There are variables. We got a way to build functions. We can apply functions to each others by providing elements of the language itself. All derivatives of lambda calculus language is something defined in terms of this definition. Lambda Calculus @matyo91 20-03-2025 @matyo91

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@matyo91 20-03-2025 @matyo91 Functional Programming Haskell

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Functional Programming in PHP @matyo91 @matyo91 20-03-2025 Grégoire Hébert https://knot.gheb.dev/blog/php- programmation-fonctionnelle

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Functional Programming in PHP @matyo91 @matyo91 20-03-2025

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Combinator @matyo91 @matyo91 20-03-2025 Pol Dellaiera https://github.com/loophp/combinator Name Alias Haskell Lambda calculus JS like A Apply $ λab.ab a => b => a(b) B Bluebird . λabc.a(bc) a => b => c => a(b(c)) Blackbird Blackbird ... λabcd.a(bcd) a => b => c => => d => a(b(c) (d)) C Cardinal flip λabc.acb a => b => c => a(c)(b) I Idiot id λa.a a => a

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Combinator @matyo91 @matyo91 20-03-2025 Name Alias Haskell Lambda calculus JS like K Kestrel const λab.a a => b => a Psi on λabcd.a(bc)(bd) a => b => c => d => a(b(c)) (b(d)) Q Queer (##) λabc.b(ac) a => b => c => b(a(c)) S Starling <*> λabc.ac(bc) a => b => c => a(c)(b(c)) T Thrush (&) λab.ba a => b => b(a)

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λ x . x @matyo91 20-03-2025 @matyo91 Lambda-PHP Igor Wiedler https://github.com/igorw/lambda-php

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@matyo91 20-03-2025 @matyo91 Lambda-PHP

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@matyo91 20-03-2025 @matyo91 Lambda-PHP

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@matyo91 20-03-2025 @matyo91 Lambda-PHP

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@matyo91 20-03-2025 @matyo91 Lambda-PHP

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@matyo91 20-03-2025 @matyo91 Lambda-PHP (bonus) Krivine machine: Alternate interpreter that uses de-bruijn indices (M N, S, E) → (M, (S,(N,E)), E) (λM, (S,N), E) → (M, S, (E,N)) (i+1, S, (E,N)) → (i, S, E) (0, S, (E1,(M,E2))) → (M, S, E2) Binary lambda calculus: Allows encoding lambda calculus programs in binary form which produces extremely small programs. This also defines an I/O mechanism.

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@matyo91 20-03-2025 @matyo91 Symfony Expression Language Damien Alexandre https://jolicode.com/blog/adding-php- function-to-symfony- expressionlanguage-the-simple-way

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@matyo91 20-03-2025 @matyo91 Symfony Expression Language

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:= | | := λ . := @matyo91 20-03-2025 @matyo91 Language Introduction to the Lambda Calculus https://personal.utdallas.edu/~gupta/ courses/apl/lambda.pdf

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@matyo91 20-03-2025 @matyo91 Compiler Transformation Code Generation Parsing Tokens AST The Super Tiny Compiler https://github.com/jamiebuilds/the- super-tiny-compiler

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https://github.com/darkwood-com/flow LambdaFlow @matyo91 20-03-2025 @matyo91 Demo

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@matyo91 20-03-2025 @matyo91 Programming with Nothing Tom Stuart https://tomstu.art/programming-with- nothing

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Hello! I Am Mathieu Ledru You can contact me at @matyo91 20-03-2025 @matyo91 Thanks! Any questions?