docs: document remaining packages and simplify AST types (#45)

## Summary

- Added doc comments across the codebase: `pkg/lambda`, `pkg/saccharine`, `pkg/codec`, `pkg/engine`, `pkg/iterator`, `pkg/set`, `pkg/convert`, `internal/registry`, and `cmd/lambda`.
- Made lambda and saccharine expression structs use public fields instead of getters, matching `go/ast` conventions.
- Removed superfluous constructors for saccharine and lambda expression/statement types in favor of struct literals.
- Consolidated saccharine token constructors into a single `NewToken` function.
- Removed the unused `trace` package.

## Test plan

- [x] `go build ./...` passes.
- [x] `go test ./...` passes.
- [ ] Verify `go doc` output renders correctly for documented packages.

Reviewed-on: #45
Co-authored-by: M.V. Hutz <git@maximhutz.me>
Co-committed-by: M.V. Hutz <git@maximhutz.me>

pkg/convert/saccharine_to_lambda.go

@@ -1,3 +1,5 @@
+// Package convert defined some standard conversions between various types of
+// representations.
 package convert
 
 import (
@@ -8,7 +10,7 @@ import (
 )
 
 func encodeAtom(n *saccharine.Atom) lambda.Expression {
-	return lambda.NewVariable(n.Name)
+	return lambda.Variable{Name: n.Name}
 }
 
 func encodeAbstraction(n *saccharine.Abstraction) lambda.Expression {
@@ -19,13 +21,13 @@ func encodeAbstraction(n *saccharine.Abstraction) lambda.Expression {
 	// If the function has no parameters, it is a thunk. Lambda calculus still
 	// requires _some_ parameter exists, so generate one.
 	if len(parameters) == 0 {
-		freeVars := result.GetFree()
+		freeVars := lambda.GetFree(result)
 		freshName := lambda.GenerateFreshName(freeVars)
 		parameters = append(parameters, freshName)
 	}
 
 	for i := len(parameters) - 1; i >= 0; i-- {
-		result = lambda.NewAbstraction(parameters[i], result)
+		result = lambda.Abstraction{Parameter: parameters[i], Body: result}
 	}
 
 	return result
@@ -41,7 +43,7 @@ func encodeApplication(n *saccharine.Application) lambda.Expression {
 	}
 
 	for _, argument := range arguments {
-		result = lambda.NewApplication(result, argument)
+		result = lambda.Application{Abstraction: result, Argument: argument}
 	}
 
 	return result
@@ -53,22 +55,22 @@ func reduceLet(s *saccharine.LetStatement, e lambda.Expression) lambda.Expressio
 	if len(s.Parameters) == 0 {
 		value = encodeExpression(s.Body)
 	} else {
-		value = encodeAbstraction(saccharine.NewAbstraction(s.Parameters, s.Body))
+		value = encodeAbstraction(&saccharine.Abstraction{Parameters: s.Parameters, Body: s.Body})
 	}
 
-	return lambda.NewApplication(
-		lambda.NewAbstraction(s.Name, e),
-		value,
-	)
+	return lambda.Application{
+		Abstraction: lambda.Abstraction{Parameter: s.Name, Body: e},
+		Argument:    value,
+	}
 }
 
 func reduceDeclare(s *saccharine.DeclareStatement, e lambda.Expression) lambda.Expression {
-	freshVar := lambda.GenerateFreshName(e.GetFree())
+	freshVar := lambda.GenerateFreshName(lambda.GetFree(e))
 
-	return lambda.NewApplication(
-		lambda.NewAbstraction(freshVar, e),
-		encodeExpression(s.Value),
-	)
+	return lambda.Application{
+		Abstraction: lambda.Abstraction{Parameter: freshVar, Body: e},
+		Argument:    encodeExpression(s.Value),
+	}
 }
 
 func reduceStatement(s saccharine.Statement, e lambda.Expression) lambda.Expression {
@@ -110,24 +112,27 @@ func encodeExpression(s saccharine.Expression) lambda.Expression {
 func decodeExression(l lambda.Expression) saccharine.Expression {
 	switch l := l.(type) {
 	case lambda.Variable:
-		return saccharine.NewAtom(l.Name())
+		return &saccharine.Atom{Name: l.Name}
 	case lambda.Abstraction:
-		return saccharine.NewAbstraction(
-			[]string{l.Parameter()},
-			decodeExression(l.Body()))
+		return &saccharine.Abstraction{
+			Parameters: []string{l.Parameter},
+			Body:       decodeExression(l.Body)}
 	case lambda.Application:
-		return saccharine.NewApplication(
-			decodeExression(l.Abstraction()),
-			[]saccharine.Expression{decodeExression(l.Argument())})
+		return &saccharine.Application{
+			Abstraction: decodeExression(l.Abstraction),
+			Arguments:   []saccharine.Expression{decodeExression(l.Argument)}}
 	default:
 		panic(fmt.Errorf("unknown expression type: %T", l))
 	}
 }
 
+// Lambda2Saccharine converts a pure lambda calculus expression into its
+// Saccharine counterpart.
 func Lambda2Saccharine(l lambda.Expression) (saccharine.Expression, error) {
 	return decodeExression(l), nil
 }
 
+// Saccharine2Lambda desugars a saccharine expression into pure lambda calculus.
 func Saccharine2Lambda(s saccharine.Expression) (lambda.Expression, error) {
 	return encodeExpression(s), nil
 }