Building a Logic Scheme Compiler: A Practical Guide

Building a Logic Scheme Compiler: A Practical Guide### Overview

Building a compiler for a Logic Scheme — a dialect of Scheme extended with logic-programming features (like unification, logical variables, and backtracking) — blends functional-language compiler construction with concepts from logic programming (Prolog, miniKanren). This guide walks through design decisions, implementation strategies, optimization techniques, and practical examples to help you build a working Logic Scheme compiler that targets either a stack-based VM, native code, or an intermediate representation such as LLVM IR.

1. Define the Language: Syntax and Semantics

A precise language definition is the foundation. Decide which Scheme features and which logic extensions you’ll support.

Key features to specify:

Core Scheme: lambda, define, let, if, begin, pair/list ops, numeric and boolean primitives.
Tail calls and proper tail recursion.
First-class continuations? (call/cc)
Logic extensions: logical variables, unification (=), fresh, conde (disjunction/interleaving), run/run* queries, constraints?
Evaluation model: eager (Scheme-style) with embedded logic search. Explain semantics for mixed evaluation (functional expressions vs. relational goals).

Short facts

Start with a small core (lambda, application, primitives, and a few logic forms).
Clearly separate functional evaluation from relational search semantics.

2. Frontend: Parsing and AST

Parsing Scheme syntax is straightforward if you accept S-expressions. The parser should convert source text into AST nodes representing both Scheme and logic constructs.

AST node types to include:

Literal, Symbol, Lambda, Application, If, Let, Define, Set!, Quote
Logic nodes: Fresh, Unify, Goal-Invoke (call to a relation), Conjunction, Disjunction, Negation-as-failure (if supported)

Practical tip: represent logic goals as first-class AST nodes that can be passed around and composed.

3. Semantic Analysis and Name Resolution

Perform lexical analysis and scope resolution:

Symbol table for bindings; support for nested lexical scopes.
Distinguish between logical variables and regular variables at this stage or defer to runtime marking.
Type/shape checks for primitives and built-in relations if desired.

Error reporting: supply clear messages for unbound identifiers, arity mismatches, and misuse of logic constructs in pure-functional contexts.

4. Intermediate Representation (IR)

Design an IR that captures both evaluation and search. Options:

CPS-style IR: simplifies control-flow, useful for continuations and backtracking.
A two-tier IR: functional IR for pure evaluation and goal IR for logic search and unification.

IR operations for logic:

allocate_logic_var, unify(var, term), fail, succeed, push_choice, pop_choice, goto_choice
goal_apply(relation, args), fresh_scope_enter/exit

Example minimal IR fragment (pseudocode):

ALLOC_VAR v1 LOAD_CONST 5 -> t1 UNIFY v1, t1 PUSH_CHOICE L1 CALL_GOAL rel_add, (v1, v2, result) POP_CHOICE L1: FAIL

5. Runtime: Representations and the Unification Engine

Runtime decisions shape performance and correctness.

Data representation:

Tagged pointers for immediate vs heap values.
Logical variables: represent as references that can be unbound (self-pointing) or point to a term.
Use union-find with path compression for fast dereferencing of variables.

Unification algorithm:

Implement a standard occurs-check-optional algorithm (omit occurs-check for speed, but provide a safe mode).
Unify(term a, term b):
- Dereference both.
- If same pointer => success.
- If either is an unbound var => bind to the other (record binding on trail).
- If both are compound with same functor/arity => recursively unify fields.
- Else => fail.

Trail and backtracking:

Record variable bindings and allocations on a trail.
On backtrack, unwind the trail to restore bindings and free allocations.
Maintain a choicepoint stack with failure continuation and trail pointer snapshot.

Memory management:

Use a garbage collector aware of logical variable references (roots include continuations, choicepoints).
Alternatively, rely on reference counting with careful cycle handling (more complex).

6. Search Strategies and Goal Scheduling

Choice of search strategy impacts completeness and performance:

Depth-first search (DFS) with chronological backtracking — simple, memory-light, but may diverge.
Interleaving / fair search (like miniKanren’s interleaving) — prevents starvation, more complex.
Breadth-first or iterative deepening for certain problems.

Goal scheduling:

Support conjunction (goals sequentially) and disjunction (create choicepoints).
Consider goal reordering heuristics: evaluate cheaper or more deterministic goals first.
Implement cut-like primitives or pruning mechanisms if needed.

7. Compiler Backends

Pick a target for code generation:

Bytecode for a VM

Define a compact instruction set: LOAD, STORE, CALL, UNIFY, PUSH_CHOICE, JUMP, RETURN.
VM executes stack frames, handles choicepoints, trail, and heap for logical variables.

Native code (via LLVM)

Map IR to LLVM IR; model unification and trail operations as runtime calls.
LLVM gives optimization passes and native performance, but increases complexity.

C as a backend

Emit C code that implements runtime data structures and unification; portable and debuggable.

Example bytecode for a simple query:

PUSH_ENV ALLOC_VAR v1 LOAD_CONST 5 -> R0 UNIFY R0, v1 CALL_GOAL add, (v1, 2, R1) POP_ENV RETURN

8. Optimization Techniques

Inline deterministic relations and primitives.
Specialize unification when one side is ground (no variables).
Use tag tests and fast paths for common cases (integers, small lists).
Reduce allocation via reuse and stack-allocated temporaries for short-lived terms.
Perform static analysis to identify pure code that can be compiled to direct evaluation without backtracking scaffolding.

Benchmarks: measure common logic programs (list append, member, graph search) and standard Scheme tasks.

9. Interfacing Functional and Relational Code

Important to allow smooth interop:

Treat relations as functions returning goals or streams of solutions.
Offer primitives to convert between streams of solutions and lists or continuations.
Example API:
- run* (q) goal -> returns a list of all q satisfying goal
- run 1 (q) goal -> returns first solution

Example: calling a relation from Scheme code compiles to goal invocation with continuations capturing remaining computation.

10. Tooling, Testing, and Debugging

Testing:

Unit tests for unification, trail/backtracking, and search strategies.
Property-based tests (QuickCheck-style) for substitution invariants and completeness.

Debugging aids:

Query tracing with step-by-step unification logs.
Choicepoint inspection and visualization of search trees.
Pretty-printing dereferenced terms and variable binding history.

Profiling:

Track time spent in unification vs evaluation vs GC.
Heap/choicepoint growth metrics.

11. Example: Implementing append/3 and membero

Append in Logic Scheme (pseudo-Scheme):

(define (appendo l s out)   (conde     [(== l '()) (== s out)]     [(fresh (h t res)        (== l (cons h t))        (== out (cons h res))        (appendo t s res))]))

How compilation works:

appendo compiles to a procedure that, when invoked, creates fresh logic vars, emits UNIFY ops, and sets up recursive goal calls with choicepoints for disjunction.

Membero example:

(define (membero x l)   (conde     [(fresh (h t) (== l (cons h t)) (== h x))]     [(fresh (h t) (== l (cons h t)) (membero x t))]))

12. Advanced Topics

Constraint logic programming: integrate finite-domain constraints (FD), disequality constraints, or constraint propagation engines.
Tabling/memoization: avoid recomputation in recursive relations (like SLG resolution).
Parallel search: distribute choicepoints across workers, handle shared trail/heap or implement copy-based workers.
Type systems: optional gradual types or refinement types for better tooling.

13. Example Project Structure

lexer/, parser/
ast/, sema/
ir/, optimizer/
backend/bytecode/, backend/llvm/, runtime/
stdlib/ (built-in relations)
tests/, examples/

14. Final Notes

Start small and iterate: implement a tiny core with unification and a DFS search to validate semantics, then add optimizations and alternate search strategies. Use existing work (miniKanren, µKanren, Prolog implementations) as reference points but adapt architectures to Scheme’s semantics and your chosen backend.

Bold short answer: A working Logic Scheme compiler combines a Scheme frontend with a unification-based runtime, choicepoint/trail backtracking, and a target backend (VM/LLVM/C) — start with a small core and expand.

Building a Logic Scheme Compiler: A Practical Guide