-- | Main definitions of the foil that can be
-- reused for specific implementations.
--
-- The original description of this approach
-- is described in the IFL 2022 paper by Maclaurin, Radul, and Paszke
-- [«The Foil: Capture-Avoiding Substitution With No Sharp Edges»](https://doi.org/10.1145/3587216.3587224).
-- This module also introduces 'CoSinkable' class,
-- generalizing handling of patterns, as described in
-- [«Free Foil: Generating Efficient and Scope-Safe Abstract Syntax»](https://arxiv.org/abs/2405.16384).
--
-- Since the representation of scopes and substitutions
-- is either @IntMap@ or @IntSet@, many of the operations
-- have a worst-case complexity of \(O(\min(n,W))\).
-- This means that the operation can become linear in the size of the scope \(n\) with a
-- maximum of \(W\), the number of bits in an 'Int' (32 or 64).
module Control.Monad.Foil (
  -- * Safe scopes, names, and binders
  S(..),
  Scope,
  Name,
  NameBinder,
  emptyScope,
  extendScope,
  extendScopePattern,
  member,
  nameOf,
  namesOfPattern,
  nameId,
  Id,
  RawName,
  withFreshBinder,
  withFresh,
  NameRange(..),
  fullNameRange,
  withFreshIn,
  tryWithFreshIn,
  withFreshPattern,
  withRefreshed,
  withRefreshedIn,
  withRefreshedPattern,
  withRefreshedPattern',
  unsinkName,
  unsinkNamePattern,
  -- * Sets of names and scope restriction
  NameSet,
  emptyNameSet,
  nameSetSingleton,
  nameSetInsert,
  nameSetMember,
  nameSetNull,
  nameSetSize,
  nameSetToList,
  nameSetFromList,
  nameSetOfPattern,
  scopeToNameSet,
  nameSetSubsetOfScope,
  unsinkNameSet,
  withRestrictedScope,
  -- * Safe (co)sinking and renaming
  SinkableK(..),
  Sinkable(..),
  CoSinkable(..),
  -- ** Transporting a pattern's payloads
  PatternTransport,
  verbatimTransport,
  transportUnderBinder,
  transportPayload,
  transportName,
  HasNameBinders(getNameBinders),
  sink,
  sink1,
  sink2,
  sinkabilityProof2,
  sinkContainer,
  extendRenaming,
  extendNameBinderRenaming,
  composeNameBinderRenamings,
  fromNameBinderRenaming,
  extendRenamingNameBinder,
  -- * Safe substitutions
  Substitution,
  lookupSubst,
  identitySubst,
  nullSubst,
  voidSubst,
  addSubst,
  addSubstPattern,
  addSubstList,
  addRename,
  -- * Unification of binders
  UnifyNameBinders(..),
  unifyNameBinders,
  andThenUnifyPatterns,
  andThenUnifyNameBinders,
  UnifiablePattern(..),
  UnifiableInPattern(..),
  AlphaEquiv(..),
  NameBinders,
  emptyNameBinders,
  mergeNameBinders,
  -- ** Eliminating impossible unification
  V2, absurd2,
  -- * Name maps
  NameMap,
  emptyNameMap,
  mapWithName,
  lookupName,
  addNameBinder,
  popNameBinder,
  nameMapToSubstitution,
  nameMapToScope,
  addNameBinders,
  addNameBinderList,
  withFreshNameBinderList,
  withFreshNameBinderListIn,
  NameBinderList(..),
  nameBindersList,
  nameBinderListOf,
  fromNameBindersList,
  snocNameBinderList,
  concatNameBinderLists,
  withThinnedNameBinderList,
  -- * Constraints
  Ext,
  ExtEvidence(..),
  Distinct,
  DistinctEvidence(..),
  assertDistinct,
  assertExt,
  DExt,
  InjectName(..),
) where

import           Control.Monad.Foil.Internal