# Curry–Howard correspondence

If one now abstracts on the peculiarities of this or that formalism, the immediate generalization is the following claim: a proof is a program, the formula it proves is a type for the program. Most informally, this can be seen as an analogy which states that the return type of a function (i.e., the type of values returned by a function) is analogous to a logical theorem, subject to hypotheses corresponding to the types of the argument values passed to the function; and that the program to compute that function is analogous to a proof of that theorem. This sets a form of logic programming on a rigorous foundation: proofs can be represented as programs, and especially as lambda terms, or proofs can be run.

The correspondence has been the starting point of a large spectrum of new research after its discovery, leading in particular to a new class of formal systems designed to act both as a proof system and as a typed functional programming language.

— Wikipedia on Curry–Howard correspondence

2010.03.07 Sunday ACHK

# Past papers 5

“Past papers” means “past HKCEE/HKAL examination papers”. The topic is for Hong Kong students who are facing HKCEE or HKAL. But the general principles can also be used for tackling other public examinations.

— Me@2010.03.06

# 天空堤壩

Talent at its best and character at its worst

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Lord Acton said we should judge talent at its best and character at its worst. For example, if you write one great book and ten bad ones, you still count as a great writer — or at least, a better writer than someone who wrote eleven that were merely good. Whereas if you’re a quiet, law-abiding citizen most of the time but occasionally cut someone up and bury them in your backyard, you’re a bad guy.

— Paul Graham

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— KinOn’s presentation, modified by Me@2010.03.06

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— Translation by Me@2010.03.06

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2010.03.07 Sunday $copyright ACHK$