autodiff_rewrite_toplevel.cpp

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#include "mim/plug/autodiff/autodiff.h"
#include "mim/plug/autodiff/pass/autodiff_eval.h"
 
namespace mim::plug::autodiff {
 
/// Additionally to the derivation, the pullback is registered and the maps are initialized.
Ref AutoDiffEval::derive_(Ref def) {
    auto lam = def->as_mut<Lam>(); // TODO check if mutable
    world().DLOG("Derive lambda: {}", def);
    auto deriv_ty = autodiff_type_fun_pi(lam->type());
    auto deriv    = world().mut_lam(deriv_ty)->set(lam->sym().str() + "_deriv");
 
    // We first pre-register the derivatives.
    // This knowledge is needed for recursion.
    // (Alternatively, we could also use projections out the variables instead of pre-partial-pullback
    // initialization.)
    derived[lam] = deriv;
 
    auto [arg_ty, ret_pi] = lam->type()->doms<2>();
    auto deriv_all_args   = deriv->var();
    Ref deriv_arg         = deriv->var(0_s)->set("arg");
 
    // We generate the shadow pullbacks dynamically to save work and avoid code duplication.
    // Only the toplevel pullback for arguments and return continuation is special cased.
 
    // TODO: check identity: could use identity tangent(arg_ty) = tangent(augment(arg_ty)) with deriv_arg->type() =
    // augment(arg_ty) We give the argument the identity pullback.
    auto arg_id_pb              = id_pullback(arg_ty);
    partial_pullback[deriv_arg] = arg_id_pb;
    // The return continuation has to formally exist but should never be directly accessed.
    auto ret_var              = deriv->var(1);
    auto ret_pb               = zero_pullback(lam->var(1)->type(), arg_ty);
    partial_pullback[ret_var] = ret_pb;
 
    shadow_pullback[deriv_all_args] = world().tuple({arg_id_pb, ret_pb});
    world().DLOG("pullback for argument {} : {} is {} : {}", deriv_arg, deriv_arg->type(), arg_id_pb,
                 arg_id_pb->type());
    world().DLOG("args shadow pb is {} : {}", shadow_pullback[deriv_all_args], shadow_pullback[deriv_all_args]->type());
 
    // We pre-register the augment replacements.
    // The function and its variables are replaced by their new derived versions.
    // TODO: maybe leave out function call (duplication with derived)
    augmented[def] = deriv;
    world().DLOG("Associate {} with {}", def, deriv);
    world().DLOG("  {} : {}", lam, lam->type());
    world().DLOG("  {} : {}", deriv, deriv->type());
    augmented[lam->var()] = deriv->var();
    world().DLOG("Associate vars {} with {}", lam->var(), deriv->var());
 
    // already contains the correct application of
    // deriv->ret_var() by specification
    // f : cn[R] has a partial derivative (exception to closed rule)
    // f': cn[R, cn[R, cn[A]]]
    //   this is needed for continuations (without closure conversion)
    //   but also essentially for the return continuation
 
    // Here a reminder of types:
    // The expression `e: B` has the implicit function `e_fun: A -> B`
    // The partial pullback is then `e*: B* -> A*`
    // The derivatived version is `e': B' × (B* -> A*)` which is an application of `e'_fun: A' -> B' × (B* -> A*)`
    auto new_body = augment(lam->body(), lam, deriv);
    deriv->set(true, new_body);
 
    return deriv;
}
 
} // namespace mim::plug::autodiff