Lambda: fixes spellings of a few words
This commit is contained in:
parent
c5f862ecfa
commit
e3623f18cb
5 changed files with 9 additions and 9 deletions
|
@ -460,7 +460,7 @@ we yield `V`, otherwise we yield `x` unchanged.
|
||||||
|
|
||||||
* For abstractions, we compare `w`, the variable we are substituting for,
|
* For abstractions, we compare `w`, the variable we are substituting for,
|
||||||
with `x`, the variable bound in the abstraction. If they are the same,
|
with `x`, the variable bound in the abstraction. If they are the same,
|
||||||
we yield the abstraction unchanged, otherwise we subsititute inside the body.
|
we yield the abstraction unchanged, otherwise we substitute inside the body.
|
||||||
|
|
||||||
* For application, we recursively substitute in the function
|
* For application, we recursively substitute in the function
|
||||||
and the argument.
|
and the argument.
|
||||||
|
@ -919,7 +919,7 @@ For example
|
||||||
|
|
||||||
give us the types associated with variables ` "z" ` and ` "s" `, respectively.
|
give us the types associated with variables ` "z" ` and ` "s" `, respectively.
|
||||||
The symbol `∋` (pronounced "ni", for "in" backwards) is chosen because
|
The symbol `∋` (pronounced "ni", for "in" backwards) is chosen because
|
||||||
checking that `Γ ∋ x ⦂ A` is anologous to checking whether `x ⦂ A` appears
|
checking that `Γ ∋ x ⦂ A` is analogous to checking whether `x ⦂ A` appears
|
||||||
in a list corresponding to `Γ`.
|
in a list corresponding to `Γ`.
|
||||||
|
|
||||||
If two variables in a context have the same name, then lookup
|
If two variables in a context have the same name, then lookup
|
||||||
|
|
|
@ -360,7 +360,7 @@ we yield `V`, otherwise we yield `x` unchanged.
|
||||||
|
|
||||||
* For abstractions, we compare `w`, the variable we are substituting for,
|
* For abstractions, we compare `w`, the variable we are substituting for,
|
||||||
with `x`, the variable bound in the abstraction. If they are the same,
|
with `x`, the variable bound in the abstraction. If they are the same,
|
||||||
we yield the abstraction unchanged, otherwise we subsititute inside the body.
|
we yield the abstraction unchanged, otherwise we substitute inside the body.
|
||||||
|
|
||||||
In all other cases, we push substitution recursively into
|
In all other cases, we push substitution recursively into
|
||||||
the subterms.
|
the subterms.
|
||||||
|
|
|
@ -402,7 +402,7 @@ we yield `V`, otherwise we yield `x′` unchanged.
|
||||||
|
|
||||||
* For abstractions, we compare `x`, the variable we are substituting for,
|
* For abstractions, we compare `x`, the variable we are substituting for,
|
||||||
with `x′`, the variable bound in the abstraction. If they are the same,
|
with `x′`, the variable bound in the abstraction. If they are the same,
|
||||||
we yield abstraction unchanged, otherwise we subsititute inside the body.
|
we yield abstraction unchanged, otherwise we substitute inside the body.
|
||||||
|
|
||||||
In all other cases, we push substitution recursively into
|
In all other cases, we push substitution recursively into
|
||||||
the subterms.
|
the subterms.
|
||||||
|
|
|
@ -209,7 +209,7 @@ definition may use `plusᶜ` as defined earlier (or may not
|
||||||
|
|
||||||
#### Exercise `primed` (stretch)
|
#### Exercise `primed` (stretch)
|
||||||
|
|
||||||
We can make examples with lambda terms slighly easier to write
|
We can make examples with lambda terms slightly easier to write
|
||||||
by adding the following definitions:
|
by adding the following definitions:
|
||||||
\begin{code}
|
\begin{code}
|
||||||
ƛ′_⇒_ : Term → Term → Term
|
ƛ′_⇒_ : Term → Term → Term
|
||||||
|
@ -466,7 +466,7 @@ we yield `V`, otherwise we yield `x` unchanged.
|
||||||
|
|
||||||
* For abstractions, we compare `y`, the substituted variable,
|
* For abstractions, we compare `y`, the substituted variable,
|
||||||
with `x`, the variable bound in the abstraction. If they are the same,
|
with `x`, the variable bound in the abstraction. If they are the same,
|
||||||
we yield the abstraction unchanged, otherwise we subsititute inside the body.
|
we yield the abstraction unchanged, otherwise we substitute inside the body.
|
||||||
|
|
||||||
* For application, we recursively substitute in the function
|
* For application, we recursively substitute in the function
|
||||||
and the argument.
|
and the argument.
|
||||||
|
@ -758,7 +758,7 @@ steps it is called the diamond property. In symbols:
|
||||||
--------------------
|
--------------------
|
||||||
→ ((M —↠ P) × (N —↠ P)) )
|
→ ((M —↠ P) × (N —↠ P)) )
|
||||||
|
|
||||||
All of the reduction systems studied in this text are determistic.
|
All of the reduction systems studied in this text are deterministic.
|
||||||
In symbols:
|
In symbols:
|
||||||
|
|
||||||
deterministic : ∀ {L M N}
|
deterministic : ∀ {L M N}
|
||||||
|
@ -987,7 +987,7 @@ For example,
|
||||||
|
|
||||||
give us the types associated with variables `` "z" `` and `` "s" ``,
|
give us the types associated with variables `` "z" `` and `` "s" ``,
|
||||||
respectively. The symbol `∋` (pronounced "ni", for "in"
|
respectively. The symbol `∋` (pronounced "ni", for "in"
|
||||||
backwards) is chosen because checking that `Γ ∋ x ⦂ A` is anologous to
|
backwards) is chosen because checking that `Γ ∋ x ⦂ A` is analogous to
|
||||||
checking whether `x ⦂ A` appears in a list corresponding to `Γ`.
|
checking whether `x ⦂ A` appears in a list corresponding to `Γ`.
|
||||||
|
|
||||||
If two variables in a context have the same name, then lookup
|
If two variables in a context have the same name, then lookup
|
||||||
|
|
|
@ -251,7 +251,7 @@ two natural numbers.
|
||||||
|
|
||||||
#### Exercise `primed` (stretch)
|
#### Exercise `primed` (stretch)
|
||||||
|
|
||||||
We can make examples with lambda terms slighly easier to write
|
We can make examples with lambda terms slightly easier to write
|
||||||
by adding the following definitions.
|
by adding the following definitions.
|
||||||
\begin{code}
|
\begin{code}
|
||||||
ƛ′_⇒_ : Term → Term → Term
|
ƛ′_⇒_ : Term → Term → Term
|
||||||
|
|
Loading…
Reference in a new issue