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Folding Cheat Sheet #1 - first in a series
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Folding over recursively defined data structures for natural numbers and lists.
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Folding Cheat Sheet #1 - first in a series
1.
CHEAT-SHEET Folding #1 βΆ / ππ βΆ /
ππ βΆ / ππ βΆ / ππ π / ππ π / ππ π / ππ π / ππ π @philip_schwarz slides by https://fpilluminated.com/
2.
ππππ π΅ππ =
ππππ | πΊπππ π΅ππ ππππ π³πππ Ξ± = π΅ππ | πͺπππ Ξ± (π³πππ Ξ±) π :: π΅ππ β πΌ π ππππ = π π πΊπππ π = β π π πππππ β· πΌ β πΌ β πΌ β π΅ππ β πΌ πππππ β π ππππ = π πππππ β π πΊπππ π = β πππππ β π π π + π = πππππ πΊπππ π π π Γ π = πππππ ππ₯. π₯ + π ππππ π π β π = πππππ ππ₯. π₯ Γ π πΊπππ ππππ π + β· π΅ππ β π΅ππ β π΅ππ π + ππππ = π π + πΊπππ π = πΊπππ π + π (Γ) β· π΅ππ β π΅ππ β π΅ππ π Γ ππππ = ππππ π Γ πΊπππ π = π Γ π + π (β) β· π΅ππ β π΅ππ β π΅ππ π β ππππ = πΊπππ ππππ π β πΊπππ π = π β π Γ π πππππ β· πΌ β π½ β π½ β π½ β πΌ β π½ πππππ π π π΅ππ = π πππππ π π (πͺπππ π₯ π₯π ) = π π₯ πππππ π π π₯π π :: π³πππ πΌ β π½ π π΅ππ = π π πͺπππ π₯ π₯π = β π₯ (π π₯π ) π π’π β· π³πππ π΅ππ β π΅ππ π π’π π΅ππ = ππππ π π’π πͺπππ π₯ π₯π = π₯ + (π π’π π₯π ) ππππππ β· π³πππ πΌ β π³πππ πΌ β π³πππ πΌ ππππππ π΅ππ π¦π = π¦π ππππππ πͺπππ π₯ π₯π π¦π = πͺπππ π₯ (ππππππ π₯π π¦π ) πππππ‘β β· π³πππ πΌ β π΅ππ πππππ‘β π΅ππ = ππππ πππππ‘β πͺπππ π₯ π₯π = πΊπππ ππππ + (πππππ‘β π₯π ) π π’π π₯π = πππππ + ππππ π₯π πππππ‘β π₯π = πππππ ππ₯. ππ. π + πΊπππ ππππ ππππ π₯π ππππππ π₯π π¦π = πππππ πͺπππ π¦π π₯π Common pattern for many recursive functions over π΅ππ : Common pattern for many recursive functions over π³πππ: π :: πΌ β :: πΌ β πΌ π :: π½ β :: πΌ β π½ Three examples of such functions: Three examples of such functions: The common pattern can be captured in a function: The common pattern can be captured in a function: The three sample functions implemented using πππππ: The three sample functions implemented using πππππ:
3.
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