# Functional & Scientific Language Support: R, Julia, Haskell, Erlang/Elixir

## Executive Summary

Supporting R, Julia, Haskell, Erlang, and Elixir requires addressing three distinct computational paradigms: vectorized statistical computing (R/Julia), lazy pure functional (Haskell), and actor-based concurrency (Erlang/Elixir). Static analysis complexity ranges from Julia's tractable multiple dispatch to Haskell's undecidable type inference.

## Architectural Classification

### Language Taxonomy

| Language | Paradigm | Evaluation | Type System | AST Complexity | Analysis Difficulty |
|----------|----------|------------|-------------|----------------|-------------------|
| R | Array programming | Eager, copy-on-write | Dynamic, weak | Moderate | High (NSE) |
| Julia | Multiple dispatch | JIT compiled | Dynamic, optional | Low | Medium |
| Haskell | Pure functional | Lazy | Static, Hindley-Milner | High | Very High |
| Erlang | Actor model | Eager | Dynamic, strong | Low | Medium |
| Elixir | Actor model + metaprogramming | Eager | Dynamic, strong | Moderate | High (macros) |

## Technical Challenges

### R: Non-Standard Evaluation (NSE)

R's NSE makes static analysis fundamentally incomplete:

```r
# Impossible to statically determine what 'select' evaluates
library(dplyr)
df %>% select(!!sym(user_input))  # Symbol injection

# Lazy evaluation in function arguments
f <- function(x) {
  if (FALSE) x  # x never evaluated, but part of AST
}
f(stop("never called"))  # No error
```

Static analysis approach:

```rust
pub struct RStrategy {
    parser: tree_sitter::Parser,
    nse_detector: NSEDetector,
}

impl RStrategy {
    fn detect_nse_patterns(&self, node: &Node) -> NSEComplexity {
        match node.kind() {
            "call" if self.is_tidyverse_verb(node) => {
                NSEComplexity::Unanalyzable  // Cannot determine statically
            }
            "substitute" | "quote" | "eval" => {
                NSEComplexity::MetaProgramming(self.track_quote_depth(node))
            }
            "do.call" => {
                NSEComplexity::DynamicDispatch  // Function name as string
            }
            _ => NSEComplexity::Standard
        }
    }
    
    fn calculate_r_complexity(&self, ast: &AstDag) -> ComplexityMetrics {
        // Vectorization reduces apparent complexity
        let mut metrics = ComplexityMetrics::default();
        
        for node in ast.nodes.iter() {
            match node.kind {
                RKind::VectorOperation => {
                    // apply family = hidden loops
                    metrics.cognitive += 2;
                    metrics.implicit_iteration = true;
                }
                RKind::S3Dispatch => {
                    // UseMethod = runtime polymorphism
                    metrics.dynamic_dispatch += 1;
                }
                RKind::FormulaInterface => {
                    // y ~ x1 + x2 = DSL complexity
                    metrics.dsl_complexity += 1;
                }
                _ => {}
            }
        }
        
        metrics
    }
}
```

### Julia: Multiple Dispatch Resolution

Julia's multiple dispatch creates exponential method resolution complexity:

```julia
# Methods grow combinatorially with type parameters
f(x::Int, y::Float64) = x + y
f(x::Float64, y::Int) = x - y
f(x::T, y::T) where T <: Number = x * y
f(x::Any, y::Any) = string(x, y)

# Which method called? Requires Julia's type inference
result = f(a, b)  # Static analysis must model Julia's dispatch
```

Implementation strategy:

```rust
pub struct JuliaStrategy {
    parser: tree_sitter_julia::Parser,
    method_table: MultiTable<MethodSignature>,
    type_lattice: JuliaTypeLattice,
}

impl JuliaStrategy {
    fn resolve_dispatch(&self, call: &CallNode) -> Vec<PossibleMethod> {
        let arg_types = self.infer_argument_types(call);
        
        // Julia's dispatch algorithm (simplified)
        let candidates = self.method_table
            .find_methods(call.function_name)
            .filter(|m| self.is_applicable(m, &arg_types))
            .collect::<Vec<_>>();
        
        // Sort by specificity (Julia's type lattice)
        candidates.sort_by(|a, b| {
            self.type_lattice.compare_specificity(a.signature, b.signature)
        });
        
        candidates
    }
    
    fn analyze_type_stability(&self, func: &Function) -> TypeStability {
        // Critical for Julia performance
        let return_types = self.abstract_interpret(func);
        
        match return_types.len() {
            1 => TypeStability::Stable,
            2..=5 => TypeStability::UnionSplit(return_types.len()),
            _ => TypeStability::Unstable  // Kills performance
        }
    }
}

struct JuliaComplexity {
    dispatch_complexity: u32,      // Method table size
    type_stability_score: f32,     // 0.0 = unstable, 1.0 = stable
    allocation_pressure: u32,       // Heap allocations in hot loops
    simd_opportunities: u32,        // @simd annotated loops
}
```

### Haskell: Lazy Evaluation & Type Classes

Haskell's laziness makes complexity analysis non-local:

```haskell
-- Space complexity depends on evaluation order
foldl (+) 0 [1..1000000]  -- O(n) space (thunk accumulation)
foldl' (+) 0 [1..1000000] -- O(1) space (strict)

-- Type class resolution creates hidden complexity
class Monad m => MonadState s m where
  get :: m s
  put :: s -> m ()

-- Instance resolution at compile time
doSomething :: (MonadState Int m, MonadIO m) => m ()
doSomething = do
  n <- get  -- Which instance? Determined by context
  liftIO $ print n
```

Implementation approach:

```rust
pub struct HaskellStrategy {
    parser: tree_sitter_haskell::Parser,
    thunk_analyzer: ThunkAnalyzer,
    typeclass_resolver: TypeClassResolver,
}

impl HaskellStrategy {
    fn analyze_space_complexity(&self, expr: &HaskellExpr) -> SpaceComplexity {
        match expr {
            HaskellExpr::Fold { strict: false, .. } => {
                SpaceComplexity::Linear  // Thunk accumulation
            }
            HaskellExpr::Map { function, list } => {
                // Lazy map = O(1) until forced
                if self.is_immediately_consumed(expr) {
                    SpaceComplexity::Constant
                } else {
                    SpaceComplexity::Linear  // Retains entire list
                }
            }
            HaskellExpr::RecursiveBinding { .. } => {
                // Knot-tying can create space leaks
                self.detect_space_leak_pattern(expr)
            }
            _ => SpaceComplexity::default()
        }
    }
    
    fn calculate_haskell_complexity(&self, ast: &AstDag) -> HaskellMetrics {
        HaskellMetrics {
            cyclomatic: self.count_pattern_branches(ast),
            monadic_depth: self.analyze_monad_stack_depth(ast),
            typeclass_constraints: self.count_constraints(ast),
            lazy_evaluation_sites: self.identify_thunks(ast),
            strict_annotations: self.count_bang_patterns(ast),
        }
    }
}

#[derive(Debug)]
struct HaskellMetrics {
    cyclomatic: u32,              // Pattern match branches
    monadic_depth: u32,            // Monad transformer stack depth
    typeclass_constraints: u32,    // Constraint complexity
    lazy_evaluation_sites: u32,    // Potential thunks
    strict_annotations: u32,       // BangPatterns/StrictData usage
}
```

### Erlang/Elixir: Actor Model Analysis

BEAM languages require process-aware analysis:

```erlang
%% Erlang: Process communication complexity
server_loop(State) ->
    receive
        {request, Pid, Data} ->
            NewState = handle_request(State, Data),
            Pid ! {response, self(), NewState},
            server_loop(NewState);
        stop -> ok;
        _ -> server_loop(State)  % Catch-all = hidden complexity
    end.
```

```elixir
# Elixir: Macro expansion makes static analysis incomplete
defmodule MyDSL do
  defmacro defstate(name, do: block) do
    quote do
      def unquote(name)() do
        GenServer.call(__MODULE__, unquote(name))
      end
      # Macro generates arbitrary code
      unquote(block)
    end
  end
end
```

BEAM-specific implementation:

```rust
pub struct BeamStrategy {
    parser: BeamParser,
    otp_analyzer: OTPBehaviorAnalyzer,
    message_flow_tracer: MessageFlowAnalyzer,
}

enum BeamParser {
    Erlang(tree_sitter_erlang::Parser),
    Elixir(tree_sitter_elixir::Parser),
    Core(CoreErlangParser),  // Analyze compiled .beam
}

impl BeamStrategy {
    fn analyze_actor_complexity(&self, module: &BeamModule) -> ActorComplexity {
        ActorComplexity {
            message_patterns: self.count_receive_clauses(module),
            supervision_depth: self.analyze_supervision_tree(module),
            gen_server_callbacks: self.count_behavior_callbacks(module),
            mailbox_growth_risk: self.detect_mailbox_overflow_patterns(module),
            hot_loops: self.find_tight_receive_loops(module),
        }
    }
    
    fn detect_otp_antipatterns(&self, ast: &AstDag) -> Vec<AntiPattern> {
        let mut antipatterns = vec![];
        
        // Selective receive with growing mailbox
        if self.has_selective_receive_without_timeout(ast) {
            antipatterns.push(AntiPattern::SelectiveReceiveBottleneck);
        }
        
        // Synchronous calls in handle_call
        if self.has_nested_gen_server_calls(ast) {
            antipatterns.push(AntiPattern::DeadlockRisk);
        }
        
        // Large messages between processes
        if let Some(size) = self.estimate_max_message_size(ast) {
            if size > 64 * 1024 {  // 64KB threshold
                antipatterns.push(AntiPattern::LargeMessagePassing(size));
            }
        }
        
        antipatterns
    }
}
```

## Complexity Metrics Comparison

| Metric | R | Julia | Haskell | Erlang/Elixir |
|--------|---|-------|---------|---------------|
| Primary Complexity | NSE depth | Dispatch ambiguity | Lazy thunk chains | Message patterns |
| Secondary | Vectorization | Type stability | Typeclass constraints | Supervision depth |
| Cognitive Load | Formula DSLs | Macro complexity | Monad stacks | Actor interactions |
| Dead Code Precision | 40% | 70% | 85% | 60% |

## Parser Technology Selection

```rust
enum ParserBackend {
    TreeSitter {
        language: tree_sitter::Language,
        queries: Vec<tree_sitter::Query>,
    },
    LanguageServer {
        client: LspClient,
        capabilities: ServerCapabilities,
    },
    Hybrid {
        lexical: Box<ParserBackend>,
        semantic: Box<ParserBackend>,
    }
}

impl ParserSelection {
    fn select_optimal(lang: Language) -> ParserBackend {
        match lang {
            Language::R => ParserBackend::Hybrid {
                lexical: Box::new(ParserBackend::TreeSitter {
                    language: tree_sitter_r::language(),
                    queries: r_analysis_queries(),
                }),
                semantic: Box::new(ParserBackend::LanguageServer {
                    client: LspClient::new("R", "languageserver"),
                    capabilities: ServerCapabilities::default(),
                })
            },
            Language::Julia => ParserBackend::TreeSitter {
                language: tree_sitter_julia::language(),
                queries: julia_dispatch_queries(),
            },
            Language::Haskell => ParserBackend::LanguageServer {
                // HLS provides type information essential for analysis
                client: LspClient::new("haskell", "haskell-language-server"),
                capabilities: ServerCapabilities::with_type_info(),
            },
            Language::Erlang => ParserBackend::TreeSitter {
                language: tree_sitter_erlang::language(),
                queries: beam_analysis_queries(),
            },
            Language::Elixir => ParserBackend::Hybrid {
                // Macros require expansion via language server
                lexical: Box::new(ParserBackend::TreeSitter {
                    language: tree_sitter_elixir::language(),
                    queries: elixir_analysis_queries(),
                }),
                semantic: Box::new(ParserBackend::LanguageServer {
                    client: LspClient::new("elixir", "elixir-ls"),
                    capabilities: ServerCapabilities::with_macro_expansion(),
                })
            }
        }
    }
}
```

## Performance Characteristics

| Language | Parse Rate | Semantic Analysis | Memory Usage | Bottleneck |
|----------|------------|-------------------|--------------|------------|
| R | 200K LOC/s | 20K LOC/s | 150MB/100K | NSE resolution |
| Julia | 400K LOC/s | 100K LOC/s | 80MB/100K | Type inference |
| Haskell | 150K LOC/s | 10K LOC/s | 200MB/100K | Type checking |
| Erlang | 500K LOC/s | 300K LOC/s | 50MB/100K | Simple grammar |
| Elixir | 350K LOC/s | 50K LOC/s | 70MB/100K | Macro expansion |

## Implementation Requirements

### Core Implementation (8K LOC)
- Tree-sitter parsers for all languages
- Basic complexity metrics
- Pattern-based dead code detection

### Advanced Features (15K LOC)
- R: NSE tracking, S3/S4 method resolution
- Julia: Multiple dispatch resolution, type stability analysis
- Haskell: Space leak detection, typeclass constraint tracking
- Erlang/Elixir: Message flow analysis, OTP behavior validation

## Validation Benchmarks

| Language | Reference Tool | Target Metric |
|----------|---------------|---------------|
| R | lintr | 80% rule agreement |
| Julia | JET.jl | 90% type stability match |
| Haskell | HLint | 85% suggestion overlap |
| Erlang | dialyzer | 75% discrepancy detection |
| Elixir | credo | 80% issue correlation |

## Critical Implementation Insights

1. **R's NSE breaks traditional AST analysis** - Require hybrid runtime sampling
2. **Julia's performance depends on type stability** - Priority metric over complexity
3. **Haskell's laziness requires space complexity analysis** - Traditional metrics insufficient
4. **BEAM languages need process-aware metrics** - Actor interaction complexity dominates
5. **Macro systems (Elixir) require expansion** - Static analysis inherently incomplete

Total implementation effort: 23K LOC for production support across all five languages.
