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Inleiding Lambda Calculus 1

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Class notes Logica En Formele Systemen on Lambda Calculus

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  • April 23, 2023
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Inleiding tot Lambda Calculus 1
Type HOC

Class Logica en formele systemen

Les 12

2 fundamentele bewerkingen:

Abstractie: het maken van een functievoorschrift

Toepassen: (of aanroepen) van het functievoorschrift op een parameter.



Syntax of λ-Calculus

Definitie λ-expressies
Laat V een verzameling variabelen zijn V = {x, y, z, ...}
De verzameling van λ expressies wordt als volgt gedefinieerd:

1. alle variabelen (elementen van V ) zijn λ-expressies

2. Als M en N λ-expressies zijn dan is (M)N een λ-expressie (toepassing)
3. Als x ∈ V en M λ-expressie dan is λx.M een λ-expressie (abstractie)
4. Niets anders is een λ-expressie




Currying
In het algemeen:
A1 x...xAn → B wordt A1 → (A2 → ...(An → B)
Deze techniek wordt currying genoemd, genoemd naar een Amerikaanse wiskundige Curry.

Voordeel: Theorie te beperken tot functies met 1 argument

Nadeel: Leesbaarheid




Inleiding tot Lambda Calculus 1 1

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