refactor: extract abstract Expression interface (#30)

## Description

The codebase currently couples the engine and plugins directly to `lambda.Expression`.
This PR introduces an abstract `expr.Expression` interface to enable future support for multiple evaluation modes.

- Add `pkg/expr/expr.go` with an `Expression` interface requiring a `String()` method.
- Update `lambda.Expression` to embed `expr.Expression`.
- Add `String()` method to `Abstraction`, `Application`, and `Variable` types.
- Update plugins to use `String()` instead of `lambda.Stringify()`.

### Decisions

- The `expr.Expression` interface is minimal (only `String()`) to avoid over-constraining future expression types.
- The engine still stores `*lambda.Expression` directly rather than `expr.Expression`, because Go's interface semantics require pointer indirection for in-place mutation during reduction.
- Future evaluation modes will implement their own concrete types satisfying `expr.Expression`.

## Benefits

- Establishes a foundation for supporting multiple evaluation modes (SKI combinators, typed lambda calculus, etc.).
- Plugins now use the abstract `String()` method, making them more decoupled from the lambda-specific implementation.
- Prepares the codebase for a Reducer interface abstraction in a future PR.

## Checklist

- [x] Code follows conventional commit format.
- [x] Branch follows naming convention (`<type>/<description>`).
- [x] Tests pass (if applicable).
- [ ] Documentation updated (if applicable).

Reviewed-on: #30
Co-authored-by: M.V. Hutz <git@maximhutz.me>
Co-committed-by: M.V. Hutz <git@maximhutz.me>

cmd/lambda/lambda.go

@@ -8,7 +8,6 @@ import (
 	"git.maximhutz.com/max/lambda/internal/engine"
 	"git.maximhutz.com/max/lambda/internal/plugins"
 	"git.maximhutz.com/max/lambda/pkg/convert"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
 	"git.maximhutz.com/max/lambda/pkg/saccharine"
 )
 
@@ -32,7 +31,7 @@ func main() {
 
 	// Compile expression to lambda calculus.
 	compiled := convert.SaccharineToLambda(ast)
-	logger.Info("compiled λ expression", "tree", lambda.Stringify(compiled))
+	logger.Info("compiled λ expression", "tree", compiled.String())
 
 	// Create reduction engine.
 	process := engine.New(options, &compiled)
@@ -62,7 +61,7 @@ func main() {
 	process.Run()
 
 	// Return the final reduced result.
-	result := lambda.Stringify(compiled)
+	result := (*process.Expression).String()
 	err = options.Destination.Write(result)
 	cli.HandleError(err)
 }

internal/engine/engine.go

@@ -1,5 +1,5 @@
-// Package "engine" provides an extensible interface for users to interfact with
-// λ-calculus.
+// Package "engine" provides an extensible interface for users to interact with
+// λ-calculus and other expression evaluation modes.
 package engine
 
 import (
@@ -8,7 +8,7 @@ import (
 	"git.maximhutz.com/max/lambda/pkg/lambda"
 )
 
-// A process for reducing one λ-expression.
+// A process for reducing one expression.
 type Engine struct {
 	Config     *config.Config
 	Expression *lambda.Expression
@@ -25,7 +25,7 @@ func New(config *config.Config, expression *lambda.Expression) *Engine {
 }
 
 // Begin the reduction process.
-func (e Engine) Run() {
+func (e *Engine) Run() {
 	e.Emit(StartEvent)
 
 	lambda.ReduceAll(e.Expression, func() {

internal/plugins/debug.go

@@ -4,7 +4,6 @@ import (
 	"log/slog"
 
 	"git.maximhutz.com/max/lambda/internal/engine"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
 )
 
 type Logs struct {
@@ -20,6 +19,5 @@ func NewLogs(logger *slog.Logger, process *engine.Engine) *Logs {
 }
 
 func (t *Logs) Step() {
-	stringified := lambda.Stringify(*t.process.Expression)
-	t.logger.Info("reduction", "tree", stringified)
+	t.logger.Info("reduction", "tree", (*t.process.Expression).String())
 }

internal/plugins/explanation.go

@@ -1,4 +1,4 @@
-// Package "explanation" provides a observer to gather the reasoning during the
+// Package "explanation" provides an observer to gather the reasoning during the
 // reduction, and present a thorough explanation to the user for each step.
 package plugins
 
@@ -6,10 +6,9 @@ import (
 	"fmt"
 
 	"git.maximhutz.com/max/lambda/internal/engine"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
 )
 
-// Track the reductions made by a reduction proess.
+// Track the reductions made by a reduction process.
 type Explanation struct {
 	process *engine.Engine
 }
@@ -24,9 +23,9 @@ func NewExplanation(process *engine.Engine) *Explanation {
 }
 
 func (t *Explanation) Start() {
-	fmt.Println(lambda.Stringify(*t.process.Expression))
+	fmt.Println((*t.process.Expression).String())
 }
 
 func (t *Explanation) Step() {
-	fmt.Println("    =", lambda.Stringify(*t.process.Expression))
+	fmt.Println("    =", (*t.process.Expression).String())
 }

pkg/expr/expr.go

@@ -0,0 +1,11 @@
+// Package expr provides the abstract Expression interface for all evaluatable
+// expression types in the lambda interpreter.
+package expr
+
+// Expression is the base interface for all evaluatable expression types.
+// Different evaluation modes (lambda calculus, SKI combinators, typed lambda
+// calculus, etc.) implement this interface with their own concrete types.
+type Expression interface {
+	// String returns a human-readable representation of the expression.
+	String() string
+}

pkg/lambda/expression.go

@@ -1,6 +1,11 @@
 package lambda
 
+import "git.maximhutz.com/max/lambda/pkg/expr"
+
+// Expression is the interface for all lambda calculus expression types.
+// It embeds the general expr.Expression interface for cross-mode compatibility.
 type Expression interface {
+	expr.Expression
 	Accept(Visitor)
 }
 
@@ -23,6 +28,10 @@ func (a *Abstraction) Accept(v Visitor) {
 	v.VisitAbstraction(a)
 }
 
+func (a *Abstraction) String() string {
+	return Stringify(a)
+}
+
 func NewAbstraction(parameter string, body Expression) *Abstraction {
 	return &Abstraction{parameter: parameter, body: body}
 }
@@ -46,6 +55,10 @@ func (a *Application) Accept(v Visitor) {
 	v.VisitApplication(a)
 }
 
+func (a *Application) String() string {
+	return Stringify(a)
+}
+
 func NewApplication(abstraction Expression, argument Expression) *Application {
 	return &Application{abstraction: abstraction, argument: argument}
 }
@@ -64,6 +77,10 @@ func (v *Variable) Accept(visitor Visitor) {
 	visitor.VisitVariable(v)
 }
 
+func (v *Variable) String() string {
+	return Stringify(v)
+}
+
 func NewVariable(name string) *Variable {
 	return &Variable{value: name}
 }