Merge branch 'master' of github.com:wenkokke/sf
Merging in pull requests for typo fixes.
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@ -6,7 +6,7 @@ permalink : /Connectives
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This chapter introduces the basic logical connectives, by observing
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This chapter introduces the basic logical connectives, by observing
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a correspondence between connectives of logic and data types,
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a correspondence between connectives of logic and data types,
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a principal known as *Propositions as Types*.
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a principle known as *Propositions as Types*.
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+ *conjunction* is *product*
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+ *conjunction* is *product*
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+ *disjunction* is *sum*
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+ *disjunction* is *sum*
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@ -402,7 +402,7 @@ as earlier examples have shown.
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## Extensionality {#extensionality}
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## Extensionality {#extensionality}
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Extensionality asserts that they only way to distinguish functions is
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Extensionality asserts that the only way to distinguish functions is
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by applying them; if two functions applied to the same argument always
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by applying them; if two functions applied to the same argument always
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yield the same result, then they are the same functions. It is the
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yield the same result, then they are the same functions. It is the
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converse of `cong-app`, introduced earlier.
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converse of `cong-app`, introduced earlier.
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@ -522,7 +522,7 @@ _ =
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1
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1
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∎
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∎
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\end{code}
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\end{code}
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We did not use the third equation at all, but it will be required
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We did not use the second equation at all, but it will be required
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if we try to subtract a smaller number from a larger one.
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if we try to subtract a smaller number from a larger one.
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\begin{code}
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\begin{code}
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_ =
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_ =
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@ -575,7 +575,7 @@ second argument. This trick goes by the name *currying*.
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Agda, like other functional languages such as
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Agda, like other functional languages such as
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ML and Haskell, is designed to make currying easy to use. Function
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ML and Haskell, is designed to make currying easy to use. Function
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arrows associate to the left and application associates to the right.
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arrows associate to the right and application associates to the left.
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ℕ → ℕ → ℕ stands for ℕ → (ℕ → ℕ)
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ℕ → ℕ → ℕ stands for ℕ → (ℕ → ℕ)
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