fixed backticks in code spans

This commit is contained in:
Philip Wadler 2017-07-14 10:56:59 +01:00
parent 3de139a5ef
commit a43bdb46c7
4 changed files with 4851 additions and 4851 deletions

File diff suppressed because it is too large Load diff

File diff suppressed because it is too large Load diff

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@ -70,7 +70,7 @@ data Type : Set where
\end{code}
Terms have six constructs. Three are for the core lambda calculus:
* Variables, `\` x`
* Variables, `` ` x ``
* Abstractions, `λ[ x A ] N`
* Applications, `L · M`
and three are for the base type, booleans:
@ -285,7 +285,7 @@ outermost term is now `if_then_else_`, which is typed using `𝔹-E`. The
?2 : ∅ , x 𝔹 ⊢ true 𝔹
Again we fill in the three holes by typing C-c C-r in each. Agda observes
that `\` x`, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
that `` ` x ``, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
`𝔹-I₁` respectively. The `Ax` rule in turn takes an argument, to show
that `(∅ , x 𝔹) x = just 𝔹`, which can in turn be specified with a
hole. After filling in all holes, the term is as above.

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@ -266,7 +266,7 @@ _Proof_: We show, by induction on the proof that `x` appears
free in `M`, that, for all contexts `Γ`, if `M` is well
typed under `Γ`, then `Γ` assigns some type to `x`.
- If the last rule used was `free-\``, then `M = \` x`, and from
- If the last rule used was `` free-` ``, then `M = `` `x ``, and from
the assumption that `M` is well typed under `Γ` we have
immediately that `Γ` assigns a type to `x`.
@ -452,7 +452,7 @@ we show that if `∅ ⊢ V A` then `Γ ⊢ N [ x := V ] B`.
- If `N` is a variable there are two cases to consider,
depending on whether `N` is `x` or some other variable.
- If `N = \` x`, then from `Γ , x A ⊢ x B`
- If `N = `` `x ``, then from `Γ , x A ⊢ x B`
we know that looking up `x` in `Γ , x : A` gives
`just B`, but we already know it gives `just A`;
applying injectivity for `just` we conclude that `A ≡ B`.