Learn BINARY-LAMBDA-CALCULUS with Real Code Examples

Updated Nov 26, 2025

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Code Sample Descriptions

Hello World in Binary Lambda Calculus

0100011010010110100100100110100011010010...

(Note: Actual Hello World programs in BLC are extremely long binary strings representing λ-terms. They are usually provided as `.blc` binary files rather than text.)

A 'Hello World' program encoded as a binary λ-term. BLC programs are typically stored as binary files, not human-readable text.

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Identity Function

01

(Note: `01` represents a simple λ-term in BLC for the identity function)

Binary Lambda Calculus encoding of the identity function λx.x

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Self-Application

001

(Note: Encoded as a minimal BLC binary string)

A λ-term that applies a function to itself: λx.xx

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Boolean True

0001

(Note: Binary λ-term for true)

Binary encoding of λx.λy.x (Boolean True)

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Boolean False

0010

(Note: Binary λ-term for false)

Binary encoding of λx.λy.y (Boolean False)

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Logical AND

0001010...

(Note: Real AND is encoded as longer binary sequences)

Binary encoding of logical AND in BLC using λ-terms

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Logical OR

0001101...

(Note: Real OR is encoded as longer binary sequences)

Binary encoding of logical OR in BLC using λ-terms

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Church Numeral 0

00000

(Note: Represents λf.λx.x in binary λ-calculus)

Binary encoding of the Church numeral 0

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Church Numeral 1

00001

(Note: Represents λf.λx.f x in binary λ-calculus)

Binary encoding of the Church numeral 1

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Successor Function

000101001...

(Note: Encoded as a longer binary sequence representing λn.λf.λx.f (n f x))

Binary encoding of the successor function on Church numerals

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Code Sample Descriptions

Hello World in Binary Lambda Calculus

0100011010010110100100100110100011010010...

(Note: Actual Hello World programs in BLC are extremely long binary strings representing λ-terms. They are usually provided as `.blc` binary files rather than text.)

A 'Hello World' program encoded as a binary λ-term. BLC programs are typically stored as binary files, not human-readable text.

Let’s Try →

Identity Function

01

(Note: `01` represents a simple λ-term in BLC for the identity function)

Binary Lambda Calculus encoding of the identity function λx.x

Let’s Try →

Self-Application

001

(Note: Encoded as a minimal BLC binary string)

A λ-term that applies a function to itself: λx.xx

Let’s Try →

Boolean True

0001

(Note: Binary λ-term for true)

Binary encoding of λx.λy.x (Boolean True)

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Boolean False

0010

(Note: Binary λ-term for false)

Binary encoding of λx.λy.y (Boolean False)

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Logical AND

0001010...

(Note: Real AND is encoded as longer binary sequences)

Binary encoding of logical AND in BLC using λ-terms

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Logical OR

0001101...

(Note: Real OR is encoded as longer binary sequences)

Binary encoding of logical OR in BLC using λ-terms

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Church Numeral 0

00000

(Note: Represents λf.λx.x in binary λ-calculus)

Binary encoding of the Church numeral 0

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Church Numeral 1

00001

(Note: Represents λf.λx.f x in binary λ-calculus)

Binary encoding of the Church numeral 1

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Successor Function

000101001...

(Note: Encoded as a longer binary sequence representing λn.λf.λx.f (n f x))

Binary encoding of the successor function on Church numerals

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