Prompt Dsl

Categorical Prompt DSL

A domain-specific language for composable prompt engineering with categorical foundations.

Core Algebraic Structure

The Prompt DSL treats prompts as objects in a category:

• Objects: Prompt types (system, user, context, etc.)
• Morphisms: Prompt transformations
• Composition: Sequential prompt chaining
• Tensor: Parallel prompt combination
• Exponential: Prompt templates (parameterized prompts)

Basic DSL Primitives

from dataclasses import dataclass
from typing import TypeVar, Generic, Callable, List
from abc import ABC, abstractmethod

T = TypeVar('T')
U = TypeVar('U')

@dataclass
class Prompt:
    """Base prompt type - object in Prompt category."""
    content: str
    role: str = "user"
    metadata: dict = None
    
    def __post_init__(self):
        self.metadata = self.metadata or {}

# Prompt constructors
def system(content: str) -> Prompt:
    return Prompt(content=content, role="system")

def user(content: str) -> Prompt:
    return Prompt(content=content, role="user")

def assistant(content: str) -> Prompt:
    return Prompt(content=content, role="assistant")

def context(content: str) -> Prompt:
    return Prompt(content=content, role="context", metadata={"type": "context"})

Composition Operators

class PromptExpr(ABC):
    """Abstract prompt expression in the DSL."""
    
    @abstractmethod
    def render(self, ctx: dict = None) -> List[Prompt]:
        pass
    
    # Sequential composition: p1 >> p2
    def __rshift__(self, other: 'PromptExpr') -> 'PromptExpr':
        return Sequence(self, other)
    
    # Parallel composition: p1 | p2
    def __or__(self, other: 'PromptExpr') -> 'PromptExpr':
        return Parallel(self, other)
    
    # Repetition: p * n
    def __mul__(self, n: int) -> 'PromptExpr':
        return Repeat(self, n)
    
    # Conditional: p.when(predicate)
    def when(self, predicate: Callable[[dict], bool]) -> 'PromptExpr':
        return Conditional(self, predicate)

@dataclass
class Literal(PromptExpr):
    """Literal prompt value."""
    prompt: Prompt
    
    def render(self, ctx: dict = None) -> List[Prompt]:
        return [self.prompt]

@dataclass
class Sequence(PromptExpr):
    """Sequential composition: first >> second."""
    first: PromptExpr
    second: PromptExpr
    
    def render(self, ctx: dict = None) -> List[Prompt]:
        return self.first.render(ctx) + self.second.render(ctx)

@dataclass
class Parallel(PromptExpr):
    """Parallel composition: left | right."""
    left: PromptExpr
    right: PromptExpr
    
    def render(self, ctx: dict = None) -> List[Prompt]:
        # Interleave prompts
        l = self.left.render(ctx)
        r = self.right.render(ctx)
        result = []
        for i in range(max(len(l), len(r))):
            if i < len(l): result.append(l[i])
            if i < len(r): result.append(r[i])
        return result

@dataclass
class Repeat(PromptExpr):
    """Repetition: expr * count."""
    expr: PromptExpr
    count: int
    
    def render(self, ctx: dict = None) -> List[Prompt]:
        result = []
        for _ in range(self.count):
            result.extend(self.expr.render(ctx))
        return result

@dataclass
class Conditional(PromptExpr):
    """Conditional: expr.when(predicate)."""
    expr: PromptExpr
    predicate: Callable[[dict], bool]
    
    def render(self, ctx: dict = None) -> List[Prompt]:
        if self.predicate(ctx or {}):
            return self.expr.render(ctx)
        return []

Template System (Exponential Objects)

@dataclass
class Template(PromptExpr):
    """
    Parameterized prompt template.
    
    Represents exponential object: Context → Prompt
    """
    template_str: str
    role: str = "user"
    
    def render(self, ctx: dict = None) -> List[Prompt]:
        ctx = ctx or {}
        content = self.template_str.format(**ctx)
        return [Prompt(content=content, role=self.role)]
    
    # Curry: fix some parameters
    def partial(self, **kwargs) -> 'Template':
        """Partial application of template parameters."""
        new_template = self.template_str
        for k, v in kwargs.items():
            new_template = new_template.replace(f"{{{k}}}", str(v))
        return Template(new_template, self.role)

# Template constructors
def template(content: str, role: str = "user") -> Template:
    return Template(content, role)

def system_template(content: str) -> Template:
    return Template(content, "system")

# Example templates
qa_template = template(
    "Question: {question}\nProvide a detailed answer."
)

analysis_template = template(
    "Analyze the following {subject}:\n{content}\n\nFocus on: {focus}"
)

Functor Operations

def fmap(f: Callable[[str], str], expr: PromptExpr) -> PromptExpr:
    """
    Functor map: apply transformation to prompt content.
    
    Preserves structure: fmap(id) = id, fmap(g . f) = fmap(g) . fmap(f)
    """
    @dataclass
    class Mapped(PromptExpr):
        original: PromptExpr
        transform: Callable[[str], str]
        
        def render(self, ctx: dict = None) -> List[Prompt]:
            prompts = self.original.render(ctx)
            return [
                Prompt(
                    content=self.transform(p.content),
                    role=p.role,
                    metadata=p.metadata
                )
                for p in prompts
            ]
    
    return Mapped(expr, f)

# Example transformations
uppercase = lambda expr: fmap(str.upper, expr)
prefix = lambda pre: lambda expr: fmap(lambda s: f"{pre}\n{s}", expr)
suffix = lambda suf: lambda expr: fmap(lambda s: f"{s}\n{suf}", expr)

Natural Transformations

def role_transform(from_role: str, to_role: str) -> Callable[[PromptExpr], PromptExpr]:
    """
    Natural transformation changing prompt roles.
    
    Naturality: role_transform commutes with fmap.
    """
    @dataclass
    class RoleTransformed(PromptExpr):
        original: PromptExpr
        from_role: str
        to_role: str
        
        def render(self, ctx: dict = None) -> List[Prompt]:
            prompts = self.original.render(ctx)
            return [
                Prompt(
                    content=p.content,
                    role=self.to_role if p.role == self.from_role else p.role,
                    metadata=p.metadata
                )
                for p in prompts
            ]
    
    return lambda expr: RoleTransformed(expr, from_role, to_role)

# Transform user prompts to system prompts
user_to_system = role_transform("user", "system")

Monad Structure

@dataclass
class PromptM(Generic[T]):
    """
    Prompt monad for sequencing prompt effects.
    
    return: T → PromptM[T]
    bind: PromptM[T] → (T → PromptM[U]) → PromptM[U]
    """
    value: T
    prompts: List[Prompt]
    
    @staticmethod
    def pure(value: T) -> 'PromptM[T]':
        """Monadic return."""
        return PromptM(value=value, prompts=[])
    
    def bind(self, f: Callable[[T], 'PromptM[U]']) -> 'PromptM[U]':
        """Monadic bind (>>=)."""
        result = f(self.value)
        return PromptM(
            value=result.value,
            prompts=self.prompts + result.prompts
        )
    
    def map(self, f: Callable[[T], U]) -> 'PromptM[U]':
        """Functor map."""
        return PromptM(value=f(self.value), prompts=self.prompts)
    
    # Syntactic sugar
    def __rshift__(self, f: Callable[[T], 'PromptM[U]']) -> 'PromptM[U]':
        return self.bind(f)

def emit(prompt: Prompt) -> PromptM[None]:
    """Emit a prompt in the monad."""
    return PromptM(value=None, prompts=[prompt])

def emit_user(content: str) -> PromptM[None]:
    return emit(user(content))

def emit_system(content: str) -> PromptM[None]:
    return emit(system(content))

DSL Combinators

# Choice combinator: try first, fallback to second
def choice(primary: PromptExpr, fallback: PromptExpr) -> PromptExpr:
    @dataclass
    class Choice(PromptExpr):
        primary: PromptExpr
        fallback: PromptExpr
        
        def render(self, ctx: dict = None) -> List[Prompt]:
            result = self.primary.render(ctx)
            return result if result else self.fallback.render(ctx)
    
    return Choice(primary, fallback)

# Optional combinator
def optional(expr: PromptExpr) -> PromptExpr:
    return choice(expr, Literal(Prompt("")))

# Many combinator: zero or more
def many(expr: PromptExpr, separator: str = "\n") -> PromptExpr:
    @dataclass
    class Many(PromptExpr):
        expr: PromptExpr
        items_key: str = "items"
        separator: str = "\n"
        
        def render(self, ctx: dict = None) -> List[Prompt]:
            ctx = ctx or {}
            items = ctx.get(self.items_key, [])
            result = []
            for item in items:
                item_ctx = {**ctx, "item": item}
                result.extend(self.expr.render(item_ctx))
            return result
    
    return Many(expr, separator=separator)

Complete Example

# Build a complex prompt using the DSL
analysis_prompt = (
    Literal(system("You are an expert analyst."))
    >> Template("Analyze the following {topic}:", role="user")
    >> Template("{content}", role="context")
    >> Literal(user("Provide:"))
    >> (
        Literal(user("1. Key insights"))
        >> Literal(user("2. Potential issues"))
        >> Literal(user("3. Recommendations"))
    ).when(lambda ctx: ctx.get("detailed", False))
)

# Render with context
prompts = analysis_prompt.render({
    "topic": "market trends",
    "content": "Q4 sales increased 15%...",
    "detailed": True
})

# Convert to API format
messages = [{"role": p.role, "content": p.content} for p in prompts]

Categorical Guarantees

The Prompt DSL ensures:

1. Associativity: (a >> b) >> c = a >> (b >> c)
2. Identity: Empty prompt is identity for composition
3. Functor Laws: fmap preserves identity and composition
4. Naturality: Role transforms commute with content maps
5. Monad Laws: pure and bind satisfy left/right identity and associativity

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