fixed conflicts

index.md

@@ -18,38 +18,38 @@ fixes are encouraged.
 
 ## Front matter
 
-  - [Preface]({{ site.baseurl }}{% link out/Preface.md %})
+  - [Preface]({{ site.baseurl }}{% link out/plta/Preface.md %})
 
 ## Part 1: Logical Foundations
 
 (This part is ready for review. Please comment!)
 
-  - [Naturals: Natural numbers]({{ site.baseurl }}{% link out/Naturals.md %})
+  - [Naturals: Natural numbers]({{ site.baseurl }}{% link out/plta/Naturals.md %})
   - [Properties: Proof by induction](Properties)
-  - [Relations: Inductive definition of relations]({{ site.baseurl }}{% link out/Relations.md %})
-  - [Equality: Equality and equational reasoning]({{ site.baseurl }}{% link out/Equality.md %})
-  - [Isomorphism: Isomorphism and embedding]({{ site.baseurl }}{% link out/Isomorphism.md %})
-  - [Connectives: Conjunction, disjunction, and implication]({{ site.baseurl }}{% link out/Connectives.md %})
-  - [Negation: Negation, with intuitionistic and classical Logic]({{ site.baseurl }}{% link out/Negation.md %})
-  - [Quantifiers: Universals and existentials]({{ site.baseurl }}{% link out/Quantifiers.md %})
-  - [Lists: Lists and higher-order functions]({{ site.baseurl }}{% link out/Lists.md %})
-  - [Decidable: Booleans and decision procedures]({{ site.baseurl }}{% link out/Decidable.md %})
+  - [Relations: Inductive definition of relations]({{ site.baseurl }}{% link out/plta/Relations.md %})
+  - [Equality: Equality and equational reasoning]({{ site.baseurl }}{% link out/plta/Equality.md %})
+  - [Isomorphism: Isomorphism and embedding]({{ site.baseurl }}{% link out/plta/Isomorphism.md %})
+  - [Connectives: Conjunction, disjunction, and implication]({{ site.baseurl }}{% link out/plta/Connectives.md %})
+  - [Negation: Negation, with intuitionistic and classical Logic]({{ site.baseurl }}{% link out/plta/Negation.md %})
+  - [Quantifiers: Universals and existentials]({{ site.baseurl }}{% link out/plta/Quantifiers.md %})
+  - [Lists: Lists and higher-order functions]({{ site.baseurl }}{% link out/plta/Lists.md %})
+  - [Decidable: Booleans and decision procedures]({{ site.baseurl }}{% link out/plta/Decidable.md %})
 
 ## Part 2: Programming Language Foundations
 
 (This part is not yet ready for review.)
 
-  - [Lambda: Lambda: Introduction to Lambda Calculus]({{ site.baseurl }}{% link out/Lambda.md %})
-  - [LambdaProp: Properties of Simply-Typed Lambda Calculus]({{ site.baseurl }}{% link out/LambdaProp.md %})
-  - [DeBruijn: Inherently typed De Bruijn representation]({{ site.baseurl }}{% link out/DeBruijn.md %})
-  - [Extensions: Extensions to simply-typed lambda calculus]({{ site.baseurl }}{% link out/Extensions.md %})
-  - [Inference: Bidirectional type inference]({{ site.baseurl }}{% link out/Inference.md %})
-  - [Untyped: Untyped lambda calculus with full normalisation]({{ site.baseurl }}{% link out/Untyped.md %})
+  - [Lambda: Lambda: Introduction to Lambda Calculus]({{ site.baseurl }}{% link out/plta/Lambda.md %})
+  - [LambdaProp: Properties of Simply-Typed Lambda Calculus]({{ site.baseurl }}{% link out/plta/LambdaProp.md %})
+  - [DeBruijn: Inherently typed De Bruijn representation]({{ site.baseurl }}{% link out/plta/DeBruijn.md %})
+  - [Extensions: Extensions to simply-typed lambda calculus]({{ site.baseurl }}{% link out/plta/Extensions.md %})
+  - [Inference: Bidirectional type inference]({{ site.baseurl }}{% link out/plta/Inference.md %})
+  - [Untyped: Untyped lambda calculus with full normalisation]({{ site.baseurl }}{% link out/plta/Untyped.md %})
 
 ## Backmatter
 
-  - [Acknowledgements]({{ site.baseurl }}{% link out/Acknowledgements.md %})
-  - [Fonts: Test page for fonts]({{ site.baseurl }}{% link out/Fonts.md %})
+  - [Acknowledgements]({{ site.baseurl }}{% link out/plta/Acknowledgements.md %})
+  - [Fonts: Test page for fonts]({{ site.baseurl }}{% link out/plta/Fonts.md %})
 
 [sf]: https://softwarefoundations.cis.upenn.edu/
 [wen]: https://github.com/wenkokke

src/plta/Acknowledgements.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Acknowledgements/
 ---
 
+\begin{code}
+module plta.Acknowledgements where
+\end{code}
+
 Thank you to the following.
 
 To the inventors of Agda, for giving us a new playground.

src/plta/Connectives.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Connectives/
 ---
 
+\begin{code}
+module plta.Connectives where
+\end{code}
+
 This chapter introduces the basic logical connectives, by observing
 a correspondence between connectives of logic and data types,
 a principle known as *Propositions as Types*.
@@ -21,8 +25,8 @@ a principle known as *Propositions as Types*.
 import Relation.Binary.PropositionalEquality as Eq
 open Eq using (_≡_; refl; sym; trans; cong)
 open Eq.≡-Reasoning
-open import Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_)
-open Isomorphism.≃-Reasoning
+open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_)
+open plta.Isomorphism.≃-Reasoning
 open import Data.Nat using (ℕ; zero; suc; _+_; _*_)
 open import Data.Nat.Properties.Simple using (+-suc)
 open import Function using (_∘_)
@@ -820,4 +824,3 @@ This chapter uses the following unicode.
     ₁  U+2081  SUBSCRIPT ONE (\_1)
     ₂  U+2082  SUBSCRIPT TWO (\_2)
     ⇔  U+21D4  LEFT RIGHT DOUBLE ARROW (\<=>)
-

src/plta/DeBruijn.lagda

@@ -4,12 +4,12 @@ layout    : page
 permalink : /DeBruijn/
 ---
 
-## Imports
-
 \begin{code}
-module DeBruijn where
+module plta.DeBruijn where
 \end{code}
 
+## Imports
+
 \begin{code}
 import Relation.Binary.PropositionalEquality as Eq
 open Eq using (_≡_; refl; sym; trans; cong)
@@ -476,5 +476,3 @@ normalise (suc g) L with progress L
 ...    | step {M} L⟶M with normalise g M
 ...        | normal h M⟶*N                =  normal (suc h) (L ⟶⟨ L⟶M ⟩ M⟶*N)
 \end{code}
-
-

src/plta/Decidable.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Decidable/
 ---
 
+\begin{code}
+module plta.Decidable where
+\end{code}
+
 We have a choice as to how to represent relations:
 as an inductive data type of *evidence* that the relation holds,
 or as a function that *computes* whether the relation holds.
@@ -563,4 +567,3 @@ import Relation.Nullary.Sum using (_⊎-dec_)
 ## Unicode
 
     ᵇ  U+1D47  MODIFIER LETTER SMALL B  (\^b)
-

src/plta/Equality.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Equality/
 ---
 
+\begin{code}
+module plta.Equality where
+\end{code}
+
 Much of our reasoning has involved equality.  Given two terms `M`
 and `N`, both of type `A`, we write `M ≡ N` to assert that `M` and `N`
 are interchangeable.  So far we have treated equality as a primitive,

src/plta/Extensions.lagda

@@ -4,12 +4,13 @@ layout    : page
 permalink : /Extensions/
 ---
 
-## Imports
-
 \begin{code}
-module Extensions where
+module plta.Extensions where
 \end{code}
 
+
+## Imports
+
 \begin{code}
 import Relation.Binary.PropositionalEquality as Eq
 open Eq using (_≡_; refl; sym; trans; cong)
@@ -600,5 +601,3 @@ normalise (suc g) L with progress L
 ...    | step {M} L⟶M with normalise g M
 ...        | normal h M⟶*N                =  normal (suc h) (L ⟶⟨ L⟶M ⟩ M⟶*N)
 \end{code}
-
-

src/plta/Fonts.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Fonts/
 ---
 
+\begin{code}
+module plta.Fonts where
+\end{code}
+
 Test page for fonts.
 
 Agda:
@@ -55,4 +59,3 @@ Indented code:
     ------------
     ⌊⌋⌈⌉
     ----
-

src/plta/Inference.lagda

@@ -4,12 +4,13 @@ layout    : page
 permalink : /Inference/
 ---
 
-## Imports
-
 \begin{code}
-module Inference where
+module plta.Inference where
 \end{code}
 
+
+## Imports
+
 \begin{code}
 import Relation.Binary.PropositionalEquality as Eq
 open Eq using (_≡_; refl; sym; trans; cong; cong₂; _≢_)
@@ -24,8 +25,7 @@ open import Data.Sum using (_⊎_; inj₁; inj₂)
 open import Function using (_∘_)
 open import Relation.Nullary using (¬_; Dec; yes; no)
 open import Relation.Nullary.Negation using (¬?)
-open import DeBruijn using (Type; `ℕ; _⇒_)
-import DeBruijn as DB
+open import plta.DeBruijn as DB using (Type; `ℕ; _⇒_)
 
 pattern [_]       w        =  w ∷ []
 pattern [_,_]     w x      =  w ∷ x ∷ []
@@ -426,5 +426,3 @@ _ = refl
 _ : ∥ ⊢fourCh ∥⁺ ≡ DB.fourCh′
 _ = refl
 \end{code}
-
-

src/plta/Isomorphism.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Isomorphism/
 ---
 
+\begin{code}
+module plta.Isomorphism where
+\end{code}
+
 This section introduces isomorphism as a way of asserting that two
 types are equal, and embedding as a way of asserting that one type is
 smaller than another.  We apply isomorphisms in the next chapter

src/plta/Lambda.lagda

@@ -4,6 +4,11 @@ layout    : page
 permalink : /Lambda/
 ---
 
+
+\begin{code}
+module plta.Lambda where
+\end{code}
+
 [Parts of this chapter take their text from chapter _Stlc_
 of _Software Foundations_ (_Programming Language Foundations_).
 Those parts will be revised.]
@@ -48,8 +53,6 @@ four.
 ## Imports
 
 \begin{code}
-module Lambda where
-
 open import Relation.Binary.PropositionalEquality using (_≡_; _≢_; refl)
 open import Data.String using (String; _≟_)
 open import Data.Nat using (ℕ; zero; suc)

src/plta/LambdaProp.lagda

@@ -4,6 +4,11 @@ layout    : page
 permalink : /LambdaProp/
 ---
 
+
+\begin{code}
+module plta.LambdaProp where
+\end{code}
+
 [Parts of this chapter take their text from chapter _Stlc_
 of _Software Foundations_ (_Programming Language Foundations_).
 Those parts will be revised.]
@@ -25,8 +30,6 @@ types without needing to develop a separate inductive definition of the
 ## Imports
 
 \begin{code}
-module LambdaProp where
-
 open import Relation.Binary.PropositionalEquality using (_≡_; _≢_; refl)
 open import Data.String using (String; _≟_)
 open import Data.Nat using (ℕ; zero; suc)
@@ -37,7 +40,7 @@ open import Data.Product
 open import Data.Sum using (_⊎_; inj₁; inj₂)
 open import Relation.Nullary using (¬_; Dec; yes; no)
 open import Function using (_∘_)
-open import Lambda
+open import plta.Lambda
 \end{code}
 
 
@@ -822,5 +825,3 @@ false, give a counterexample.
   - Progress
 
   - Preservation
-
-

src/plta/Lists.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Lists/
 ---
 
+\begin{code}
+module plta.Lists where
+\end{code}
+
 This chapter discusses the list data type.  It gives further examples
 of many of the techniques we have developed so far, and provides
 examples of polymorphic types and higher-order functions.
@@ -19,7 +23,7 @@ open import Data.Nat.Properties using
   (+-assoc; +-identityˡ; +-identityʳ; *-assoc; *-identityˡ; *-identityʳ)
 open import Relation.Nullary using (¬_)
 open import Data.Product using (_×_) renaming (_,_ to ⟨_,_⟩)
-open import Isomorphism using (_≃_)
+open import plta.Isomorphism using (_≃_)
 open import Function using (_∘_)
 open import Level using (Level)
 \end{code}

src/plta/Modules.lagda

@@ -7,6 +7,10 @@ permalink : /Modules/
 ** Turn this into a Setoid example. Copy equivalence relation and setoid
 from the standard library. **
 
+\begin{code}
+module plta.Modules where
+\end{code}
+
 This chapter introduces modules as a way of structuring proofs,
 and proves some general results which will be useful later.
 
@@ -17,18 +21,15 @@ import Relation.Binary.PropositionalEquality as Eq
 open Eq using (_≡_; refl; sym; trans; cong)
 open Eq.≡-Reasoning
 open import Data.Nat using (ℕ; zero; suc; _+_; _*_; _∸_; _≤_; s≤s; z≤n)
--- open import Data.Nat.Properties using
---   (+-assoc; +-identityˡ; +-identityʳ; *-assoc; *-identityˡ; *-identityʳ)
 open import Relation.Nullary using (¬_)
 open import Data.Product using (_×_) renaming (_,_ to ⟨_,_⟩)
-open import Isomorphism using (_≃_)
+open import plta.Isomorphism using (_≃_)
 open import Function using (_∘_)
 open import Level using (Level)
 open import Data.Maybe using (Maybe; just; nothing)
 open import Data.List using (List; []; _∷_; _++_; map; foldr; downFrom)
 open import Data.List.All using (All; []; _∷_)
 open import Data.List.Any using (Any; here; there)
--- open import Data.List.Any.Membership.Propositional using (_∈_)
 \end{code}
 
 We assume [extensionality][extensionality].

src/plta/Naturals.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Naturals/
 ---
 
+\begin{code}
+module plta.Naturals where
+\end{code}
+
 The night sky holds more stars than I can count, though fewer than five
 thousand are visible to the naked eye.  The observable universe
 contains about seventy sextillion stars.
@@ -265,7 +269,7 @@ specifies operators to support reasoning about equivalence, and adds
 all the names specified in the `using` clause into the current scope.
 In this case, the names added are `begin_`, `_≡⟨⟩_`, and `_∎`.  We
 will see how these are used below.  We take all these as givens for now,
-but will see how they are defined in Chapter [Equality]({{ site.baseurl }}{% link out/Equality.md %}).
+but will see how they are defined in Chapter [Equality](Equality).
 
 Agda uses underbars to indicate where terms appear in infix or mixfix
 operators. Thus, `_≡_` and `_≡⟨⟩_` are infix (each operator is written
@@ -894,5 +898,3 @@ In place of left, right, up, and down keys, one may also use control characters.
 
 We write `^B` to stand for control-B, and similarly.  One can also navigate
 left and write by typing the digits that appear in the displayed list.
-
-

src/plta/Negation.lagda

@@ -4,13 +4,17 @@ layout    : page
 permalink : /Negation/
 ---
 
+\begin{code}
+module plta.Negation where
+\end{code}
+
 This chapter introduces negation, and discusses intuitionistic
 and classical logic.
 
 ## Imports
 
 \begin{code}
-open import Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_)
+open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_)
 open import Relation.Binary.PropositionalEquality using (_≡_; refl)
 open import Data.Nat using (ℕ; zero; suc)
 open import Data.Empty using (⊥; ⊥-elim)

src/plta/Preface.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Preface/
 ---
 
+\begin{code}
+module plta.Preface where
+\end{code}
+
 This book is an introduction to programming language theory, written
 in Agda.  The authors are [Wen Kokke][wen] and [Philip Wadler][phil].
 
@@ -88,4 +92,3 @@ preparing an Agda file that solves the exercise.  Sometimes it is up to you to
 work out the type of the identifier, but sometimes we give it in the exercise.
 In some cases the type is bound to an identifier with a capital in its
 name, where the identifier you are to define has a small letter instead.
-

src/plta/Properties.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Properties/
 ---
 
+\begin{code}
+module plta.Properties where
+\end{code}
+
 Now that we've defined the naturals and operations upon them, our next
 step is to learn how to prove properties that they satisfy.  As hinted
 by their name, properties of *inductive datatypes* are proved by

src/plta/Quantifiers.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Quantifiers/
 ---
 
+\begin{code}
+module plta.Quantifiers where
+\end{code}
+
 This chapter introduces universal and existential quantification.
 
 ## Imports
@@ -12,8 +16,8 @@ This chapter introduces universal and existential quantification.
 import Relation.Binary.PropositionalEquality as Eq
 open Eq using (_≡_; refl; sym; trans; cong)
 open Eq.≡-Reasoning
-open import Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_)
-open Isomorphism.≃-Reasoning
+open import plta.Isomorphism using (_≃_; ≃-sym; ≃-trans; _≲_)
+open plta.Isomorphism.≃-Reasoning
 open import Data.Nat using (ℕ; zero; suc; _+_; _*_)
 open import Data.Nat.Properties.Simple using (+-suc)
 open import Relation.Nullary using (¬_)

src/plta/Relations.lagda

@@ -4,10 +4,13 @@ layout    : page
 permalink : /Relations/
 ---
 
+\begin{code}
+module plta.Relations where
+\end{code}
+
 After having defined operations such as addition and multiplication,
 the next step is to define relations, such as *less than or equal*.
 
-
 ## Imports
 
 \begin{code}

src/plta/Untyped.lagda

@@ -4,6 +4,10 @@ layout    : page
 permalink : /Untyped/
 ---
 
+\begin{code}
+module plta.Untyped where
+\end{code}
+
 This chapter considers a system that varies, in interesting ways,
 what has gone earlier.  The lambda calculus in this section is
 untyped rather than simply-typed; uses terms that are inherently-scoped
@@ -13,10 +17,6 @@ call-by-value order of reduction.
 
 ## Imports
 
-\begin{code}
-module Untyped where
-\end{code}
-
 \begin{code}
 import Relation.Binary.PropositionalEquality as Eq
 open Eq using (_≡_; refl; sym; trans; cong)