diff --git a/src/Connectives.lagda b/src/Connectives.lagda index d8c7ebc4..156b5d02 100644 --- a/src/Connectives.lagda +++ b/src/Connectives.lagda @@ -6,7 +6,7 @@ permalink : /Connectives This chapter introduces the basic logical connectives, by observing a correspondence between connectives of logic and data types, -a principal known as *Propositions as Types*. +a principle known as *Propositions as Types*. + *conjunction* is *product* + *disjunction* is *sum* diff --git a/src/Equality.lagda b/src/Equality.lagda index bd553aa0..20780fdd 100644 --- a/src/Equality.lagda +++ b/src/Equality.lagda @@ -402,7 +402,7 @@ as earlier examples have shown. ## Extensionality {#extensionality} -Extensionality asserts that they only way to distinguish functions is +Extensionality asserts that the only way to distinguish functions is by applying them; if two functions applied to the same argument always yield the same result, then they are the same functions. It is the converse of `cong-app`, introduced earlier. diff --git a/src/Naturals.lagda b/src/Naturals.lagda index 6479507b..86f95c3f 100644 --- a/src/Naturals.lagda +++ b/src/Naturals.lagda @@ -522,7 +522,7 @@ _ = 1 ∎ \end{code} -We did not use the third equation at all, but it will be required +We did not use the second equation at all, but it will be required if we try to subtract a smaller number from a larger one. \begin{code} _ = @@ -575,7 +575,7 @@ second argument. This trick goes by the name *currying*. Agda, like other functional languages such as ML and Haskell, is designed to make currying easy to use. Function -arrows associate to the left and application associates to the right. +arrows associate to the right and application associates to the left. ℕ → ℕ → ℕ stands for ℕ → (ℕ → ℕ)