# # # The Nim Compiler # (c) Copyright 2013 Andreas Rumpf # # See the file "copying.txt", included in this # distribution, for details about the copyright. # ## This module implements the signature matching for resolving ## the call to overloaded procs, generic procs and operators. import ast, astalgo, semdata, types, msgs, renderer, lookups, semtypinst, magicsys, idents, lexer, options, parampatterns, trees, linter, lineinfos, lowerings, modulegraphs, concepts import std/[intsets, strutils, tables] when defined(nimPreviewSlimSystem): import std/assertions type MismatchKind* = enum kUnknown, kAlreadyGiven, kUnknownNamedParam, kTypeMismatch, kVarNeeded, kMissingParam, kExtraArg, kPositionalAlreadyGiven, kGenericParamTypeMismatch, kMissingGenericParam, kExtraGenericParam MismatchInfo* = object kind*: MismatchKind # reason for mismatch arg*: int # position of provided arguments that mismatches formal*: PSym # parameter that mismatches against provided argument # its position can differ from `arg` because of varargs TCandidateState* = enum csEmpty, csMatch, csNoMatch CandidateError* = object sym*: PSym firstMismatch*: MismatchInfo diagnostics*: seq[string] enabled*: bool CandidateErrors* = seq[CandidateError] TCandidate* = object c*: PContext exactMatches*: int # also misused to prefer iters over procs genericMatches: int # also misused to prefer constraints subtypeMatches: int intConvMatches: int # conversions to int are not as expensive convMatches: int state*: TCandidateState callee*: PType # may not be nil! calleeSym*: PSym # may be nil calleeScope*: int # scope depth: # is this a top-level symbol or a nested proc? call*: PNode # modified call bindings*: TypeMapping # maps types to types magic*: TMagic # magic of operation baseTypeMatch: bool # needed for conversions from T to openarray[T] # for example matchedErrorType*: bool # match is considered successful after matching # error type to avoid cascading errors # this is used to prevent instantiations. genericConverter*: bool # true if a generic converter needs to # be instantiated coerceDistincts*: bool # this is an explicit coercion that can strip away # a distrinct type typedescMatched*: bool isNoCall*: bool # misused for generic type instantiations C[T] inferredTypes: seq[PType] # inferred types during the current signature # matching. they will be reset if the matching # is not successful. may replace the bindings # table in the future. diagnostics*: seq[string] # \ # when diagnosticsEnabled, the matching process # will collect extra diagnostics that will be # displayed to the user. # triggered when overload resolution fails # or when the explain pragma is used. may be # triggered with an idetools command in the # future. # to prefer closest father object type inheritancePenalty: int firstMismatch*: MismatchInfo # mismatch info for better error messages diagnosticsEnabled*: bool TTypeRelFlag* = enum trDontBind trNoCovariance trBindGenericParam # bind tyGenericParam even with trDontBind trIsOutParam TTypeRelFlags* = set[TTypeRelFlag] const isNilConversion = isConvertible # maybe 'isIntConv' fits better? maxInheritancePenalty = high(int) div 2 proc markUsed*(c: PContext; info: TLineInfo, s: PSym; checkStyle = true) proc markOwnerModuleAsUsed*(c: PContext; s: PSym) proc initCandidateAux(ctx: PContext, callee: PType): TCandidate {.inline.} = result = TCandidate(c: ctx, exactMatches: 0, subtypeMatches: 0, convMatches: 0, intConvMatches: 0, genericMatches: 0, state: csEmpty, firstMismatch: MismatchInfo(), callee: callee, call: nil, baseTypeMatch: false, genericConverter: false, inheritancePenalty: -1 ) proc initCandidate*(ctx: PContext, callee: PType): TCandidate = result = initCandidateAux(ctx, callee) result.calleeSym = nil result.bindings = initTypeMapping() proc put(c: var TCandidate, key, val: PType) {.inline.} = ## Given: proc foo[T](x: T); foo(4) ## key: 'T' ## val: 'int' (typeof(4)) when false: let old = idTableGet(c.bindings, key) if old != nil: echo "Putting ", typeToString(key), " ", typeToString(val), " and old is ", typeToString(old) if typeToString(old) == "float32": writeStackTrace() if c.c.module.name.s == "temp3": echo "binding ", key, " -> ", val idTablePut(c.bindings, key, val.skipIntLit(c.c.idgen)) proc typeRel*(c: var TCandidate, f, aOrig: PType, flags: TTypeRelFlags = {}): TTypeRelation proc matchGenericParam(m: var TCandidate, formal: PType, n: PNode) = var arg = n.typ if m.c.inGenericContext > 0: # don't match yet-unresolved generic instantiations while arg != nil and arg.kind == tyGenericParam: arg = idTableGet(m.bindings, arg) if arg == nil or arg.containsUnresolvedType: m.state = csNoMatch return # fix up the type to get ready to match formal: var formalBase = formal while formalBase.kind == tyGenericParam and formalBase.genericParamHasConstraints: formalBase = formalBase.genericConstraint if formalBase.kind == tyStatic and arg.kind != tyStatic: # maybe call `paramTypesMatch` here, for now be conservative if n.kind in nkSymChoices: n.flags.excl nfSem let evaluated = m.c.semTryConstExpr(m.c, n, formalBase.skipTypes({tyStatic})) if evaluated != nil: arg = newTypeS(tyStatic, m.c, son = evaluated.typ) arg.n = evaluated elif formalBase.kind == tyTypeDesc: if arg.kind != tyTypeDesc: arg = makeTypeDesc(m.c, arg) else: arg = arg.skipTypes({tyTypeDesc}) let tm = typeRel(m, formal, arg) if tm in {isNone, isConvertible}: m.state = csNoMatch m.firstMismatch.kind = kGenericParamTypeMismatch return proc matchGenericParams*(m: var TCandidate, binding: PNode, callee: PSym) = ## matches explicit generic instantiation `binding` against generic params of ## proc symbol `callee` ## state is set to `csMatch` if all generic params match, `csEmpty` if ## implicit generic parameters are missing (matches but cannot instantiate), ## `csNoMatch` if a constraint fails or param count doesn't match let c = m.c let typeParams = callee.ast[genericParamsPos] let paramCount = typeParams.len let bindingCount = binding.len-1 if bindingCount > paramCount: m.state = csNoMatch m.firstMismatch.kind = kExtraGenericParam m.firstMismatch.arg = paramCount + 1 return for i in 1..bindingCount: matchGenericParam(m, typeParams[i-1].typ, binding[i]) if m.state == csNoMatch: m.firstMismatch.arg = i m.firstMismatch.formal = typeParams[i-1].sym return # not enough generic params given, check if remaining have defaults: for i in bindingCount ..< paramCount: let param = typeParams[i] assert param.kind == nkSym let paramSym = param.sym if paramSym.ast != nil: matchGenericParam(m, param.typ, paramSym.ast) if m.state == csNoMatch: m.firstMismatch.arg = i + 1 m.firstMismatch.formal = paramSym return elif tfImplicitTypeParam in paramSym.typ.flags: # not a mismatch, but can't create sym m.state = csEmpty return else: m.state = csNoMatch m.firstMismatch.kind = kMissingGenericParam m.firstMismatch.arg = i + 1 m.firstMismatch.formal = paramSym return m.state = csMatch proc copyingEraseVoidParams(m: TCandidate, t: var PType) = ## if `t` is a proc type with void parameters, copies it and erases them assert t.kind == tyProc let original = t var copied = false for i in 1 ..< original.len: var f = original[i] var isVoidParam = f.kind == tyVoid if not isVoidParam: let prev = idTableGet(m.bindings, f) if prev != nil: f = prev isVoidParam = f.kind == tyVoid if isVoidParam: if not copied: # keep first i children t = copyType(original, m.c.idgen, t.owner) t.setSonsLen(i) t.n = copyNode(original.n) t.n.sons = original.n.sons t.n.sons.setLen(i) copied = true elif copied: t.add(f) t.n.add(original.n[i]) proc initCandidate*(ctx: PContext, callee: PSym, binding: PNode, calleeScope = -1, diagnosticsEnabled = false): TCandidate = result = initCandidateAux(ctx, callee.typ) result.calleeSym = callee if callee.kind in skProcKinds and calleeScope == -1: result.calleeScope = cmpScopes(ctx, callee) else: result.calleeScope = calleeScope result.diagnostics = @[] # if diagnosticsEnabled: @[] else: nil result.diagnosticsEnabled = diagnosticsEnabled result.magic = result.calleeSym.magic result.bindings = initTypeMapping() if binding != nil and callee.kind in routineKinds: matchGenericParams(result, binding, callee) let genericMatch = result.state if genericMatch != csNoMatch: result.state = csEmpty if genericMatch == csMatch: # csEmpty if not fully instantiated # instantiate the type, emulates old compiler behavior # wouldn't be needed if sigmatch could handle complex cases, # examples are in texplicitgenerics # might be buggy, see rest of generateInstance if problems occur let typ = ctx.instantiateOnlyProcType(ctx, result.bindings, callee, binding.info) result.callee = typ else: # createThread[void] requires this if the above branch is removed: copyingEraseVoidParams(result, result.callee) proc newCandidate*(ctx: PContext, callee: PSym, binding: PNode, calleeScope = -1): TCandidate = result = initCandidate(ctx, callee, binding, calleeScope) proc newCandidate*(ctx: PContext, callee: PType): TCandidate = result = initCandidate(ctx, callee) proc copyCandidate(dest: var TCandidate, src: TCandidate) = dest.c = src.c dest.exactMatches = src.exactMatches dest.subtypeMatches = src.subtypeMatches dest.convMatches = src.convMatches dest.intConvMatches = src.intConvMatches dest.genericMatches = src.genericMatches dest.state = src.state dest.callee = src.callee dest.calleeSym = src.calleeSym dest.call = copyTree(src.call) dest.baseTypeMatch = src.baseTypeMatch dest.bindings = src.bindings proc checkGeneric(a, b: TCandidate): int = let c = a.c let aa = a.callee let bb = b.callee var winner = 0 for aai, bbi in underspecifiedPairs(aa, bb, 1): var ma = newCandidate(c, bbi) let tra = typeRel(ma, bbi, aai, {trDontBind}) var mb = newCandidate(c, aai) let trb = typeRel(mb, aai, bbi, {trDontBind}) if tra == isGeneric and trb in {isNone, isInferred, isInferredConvertible}: if winner == -1: return 0 winner = 1 if trb == isGeneric and tra in {isNone, isInferred, isInferredConvertible}: if winner == 1: return 0 winner = -1 result = winner proc sumGeneric(t: PType): int = # count the "genericness" so that Foo[Foo[T]] has the value 3 # and Foo[T] has the value 2 so that we know Foo[Foo[T]] is more # specific than Foo[T]. result = 0 var t = t while true: case t.kind of tyAlias, tySink, tyNot: t = t.skipModifier of tyArray, tyRef, tyPtr, tyDistinct, tyUncheckedArray, tyOpenArray, tyVarargs, tySet, tyRange, tySequence, tyLent, tyOwned, tyVar: t = t.elementType inc result of tyBool, tyChar, tyEnum, tyObject, tyPointer, tyVoid, tyString, tyCstring, tyInt..tyInt64, tyFloat..tyFloat128, tyUInt..tyUInt64, tyCompositeTypeClass, tyBuiltInTypeClass: inc result break of tyGenericBody: t = t.typeBodyImpl of tyGenericInst, tyStatic: t = t.skipModifier inc result of tyOr: var maxBranch = 0 for branch in t.kids: let branchSum = sumGeneric(branch) if branchSum > maxBranch: maxBranch = branchSum inc result, maxBranch break of tyTypeDesc: t = t.elementType if t.kind == tyEmpty: break inc result of tyGenericParam: if t.len > 0: t = t.skipModifier else: inc result break of tyUntyped, tyTyped: break of tyGenericInvocation, tyTuple, tyAnd: result += ord(t.kind == tyAnd) for a in t.kids: if a != nil: result += sumGeneric(a) break of tyProc: if t.returnType != nil: result += sumGeneric(t.returnType) for _, a in t.paramTypes: result += sumGeneric(a) break else: break proc complexDisambiguation(a, b: PType): int = # 'a' matches better if *every* argument matches better or equal than 'b'. var winner = 0 for ai, bi in underspecifiedPairs(a, b, 1): let x = ai.sumGeneric let y = bi.sumGeneric if x != y: if winner == 0: if x > y: winner = 1 else: winner = -1 elif x > y: if winner != 1: # contradiction return 0 else: if winner != -1: return 0 result = winner when false: var x, y: int for i in 1..= firstOrd(nil, f) and getInt(ab.n) <= lastOrd(nil, f): # passing 'nil' to firstOrd/lastOrd here as type checking rules should # not depend on the target integer size configurations! # integer literal in the proper range; we want ``i16 + 4`` to stay an # ``int16`` operation so we declare the ``4`` pseudo-equal to int16 result = isFromIntLit elif a.kind == tyInt and nf == c.config.targetSizeSignedToKind: result = isIntConv elif a.kind == tyUInt and nf == c.config.targetSizeUnsignedToKind: result = isIntConv elif f.kind == tyInt and na in {tyInt8 .. pred(c.config.targetSizeSignedToKind)}: result = isIntConv elif f.kind == tyUInt and na in {tyUInt8 .. pred(c.config.targetSizeUnsignedToKind)}: result = isIntConv elif k >= min and k <= max: result = isConvertible elif a.kind == tyRange and # Make sure the conversion happens between types w/ same signedness (f.kind in {tyInt..tyInt64} and a[0].kind in {tyInt..tyInt64} or f.kind in {tyUInt8..tyUInt32} and a[0].kind in {tyUInt8..tyUInt32}) and a.n[0].intVal >= firstOrd(nil, f) and a.n[1].intVal <= lastOrd(nil, f): # passing 'nil' to firstOrd/lastOrd here as type checking rules should # not depend on the target integer size configurations! result = isConvertible else: result = isNone proc isConvertibleToRange(c: PContext, f, a: PType): bool = if f.kind in {tyInt..tyInt64, tyUInt..tyUInt64} and a.kind in {tyInt..tyInt64, tyUInt..tyUInt64}: case f.kind of tyInt8: result = isIntLit(a) or a.kind in {tyInt8} of tyInt16: result = isIntLit(a) or a.kind in {tyInt8, tyInt16} of tyInt32: result = isIntLit(a) or a.kind in {tyInt8, tyInt16, tyInt32} # This is wrong, but seems like there's a lot of code that relies on it :( of tyInt, tyUInt: result = true # of tyInt: result = isIntLit(a) or a.kind in {tyInt8 .. c.config.targetSizeSignedToKind} of tyInt64: result = isIntLit(a) or a.kind in {tyInt8, tyInt16, tyInt32, tyInt, tyInt64} of tyUInt8: result = isIntLit(a) or a.kind in {tyUInt8} of tyUInt16: result = isIntLit(a) or a.kind in {tyUInt8, tyUInt16} of tyUInt32: result = isIntLit(a) or a.kind in {tyUInt8, tyUInt16, tyUInt32} # of tyUInt: result = isIntLit(a) or a.kind in {tyUInt8 .. c.config.targetSizeUnsignedToKind} of tyUInt64: result = isIntLit(a) or a.kind in {tyUInt8, tyUInt16, tyUInt32, tyUInt64} else: result = false elif f.kind in {tyFloat..tyFloat128}: # `isIntLit` is correct and should be used above as well, see PR: # https://github.com/nim-lang/Nim/pull/11197 result = isIntLit(a) or a.kind in {tyFloat..tyFloat128} else: result = false proc handleFloatRange(f, a: PType): TTypeRelation = if a.kind == f.kind: result = isEqual else: let ab = skipTypes(a, {tyRange}) var k = ab.kind if k == f.kind: result = isSubrange elif isFloatLit(ab): result = isFromIntLit elif isIntLit(ab): result = isConvertible elif k >= tyFloat and k <= tyFloat128: # conversion to "float32" is not as good: if f.kind == tyFloat32: result = isConvertible else: result = isIntConv else: result = isNone proc reduceToBase(f: PType): PType = #[ Returns the lowest order (most general) type that that is compatible with the input. E.g. A[T] = ptr object ... A -> ptr object A[N: static[int]] = array[N, int] ... A -> array ]# case f.kind: of tyGenericParam: if f.len <= 0 or f.skipModifier == nil: result = f else: result = reduceToBase(f.skipModifier) of tyGenericInvocation: result = reduceToBase(f.baseClass) of tyCompositeTypeClass, tyAlias: if not f.hasElementType or f.elementType == nil: result = f else: result = reduceToBase(f.elementType) of tyGenericInst: result = reduceToBase(f.skipModifier) of tyGenericBody: result = reduceToBase(f.typeBodyImpl) of tyUserTypeClass: if f.isResolvedUserTypeClass: result = f.base # ?? idk if this is right else: result = f.skipModifier of tyStatic, tyOwned, tyVar, tyLent, tySink: result = reduceToBase(f.base) of tyInferred: # This is not true "After a candidate type is selected" result = reduceToBase(f.base) of tyRange: result = f.elementType else: result = f proc genericParamPut(c: var TCandidate; last, fGenericOrigin: PType) = if fGenericOrigin != nil and last.kind == tyGenericInst and last.kidsLen-1 == fGenericOrigin.kidsLen: for i in FirstGenericParamAt.. -1: # we can't process individual element type conversions from a # type conversion for the whole tuple # subtype relations need type conversions when inheritance is used return isNone result = minRel(result, m) if f.n != nil and a.n != nil: for i in 0..= isGeneric: result = isInferred #inc c.genericMatches else: result = isNone else: # Note that this typeRel call will save f's resolved type into c.bindings # if f is metatype. result = typeRel(c, f, a) if result <= isSubrange or inconsistentVarTypes(f, a): result = isNone #if result == isEqual: # inc c.exactMatches proc procTypeRel(c: var TCandidate, f, a: PType): TTypeRelation = case a.kind of tyProc: var f = f copyingEraseVoidParams(c, f) if f.signatureLen != a.signatureLen: return result = isEqual # start with maximum; also correct for no # params at all if f.flags * {tfIterator} != a.flags * {tfIterator}: return isNone template checkParam(f, a) = result = minRel(result, procParamTypeRel(c, f, a)) if result == isNone: return # Note: We have to do unification for the parameters before the # return type! for i in 1..= f0 and a1 <= f1: isConvertible elif a0 <= f1 and f0 <= a1: # X..Y and C..D overlap iff (X <= D and C <= Y) isConvertible else: isNone if f.isOrdinalType: checkRange(firstOrd(nil, a), lastOrd(nil, a), firstOrd(nil, f), lastOrd(nil, f)) else: checkRange(firstFloat(a), lastFloat(a), firstFloat(f), lastFloat(f)) proc matchUserTypeClass*(m: var TCandidate; ff, a: PType): PType = var c = m.c typeClass = ff.skipTypes({tyUserTypeClassInst}) body = typeClass.n[3] matchedConceptContext = TMatchedConcept() prevMatchedConcept = c.matchedConcept prevCandidateType = typeClass[0][0] if prevMatchedConcept != nil: matchedConceptContext.prev = prevMatchedConcept matchedConceptContext.depth = prevMatchedConcept.depth + 1 if prevMatchedConcept.depth > 4: localError(m.c.graph.config, body.info, $body & " too nested for type matching") return nil openScope(c) matchedConceptContext.candidateType = a typeClass[0][0] = a c.matchedConcept = addr(matchedConceptContext) defer: c.matchedConcept = prevMatchedConcept typeClass[0][0] = prevCandidateType closeScope(c) var typeParams: seq[(PSym, PType)] = @[] if ff.kind == tyUserTypeClassInst: for i in 1..<(ff.len - 1): var typeParamName = ff.base[i-1].sym.name typ = ff[i] param: PSym = nil alreadyBound = idTableGet(m.bindings, typ) if alreadyBound != nil: typ = alreadyBound template paramSym(kind): untyped = newSym(kind, typeParamName, c.idgen, typeClass.sym, typeClass.sym.info, {}) block addTypeParam: for prev in typeParams: if prev[1].id == typ.id: param = paramSym prev[0].kind param.typ = prev[0].typ break addTypeParam case typ.kind of tyStatic: param = paramSym skConst param.typ = typ.exactReplica #copyType(typ, c.idgen, typ.owner) if typ.n == nil: param.typ.flags.incl tfInferrableStatic else: param.ast = typ.n of tyFromExpr: param = paramSym skVar param.typ = typ.exactReplica #copyType(typ, c.idgen, typ.owner) else: param = paramSym skType param.typ = if typ.isMetaType: newTypeS(tyInferred, c, typ) else: makeTypeDesc(c, typ) typeParams.add((param, typ)) addDecl(c, param) var oldWriteHook = default typeof(m.c.config.writelnHook) diagnostics: seq[string] = @[] errorPrefix: string flags: TExprFlags = {} collectDiagnostics = m.diagnosticsEnabled or sfExplain in typeClass.sym.flags if collectDiagnostics: oldWriteHook = m.c.config.writelnHook # XXX: we can't write to m.diagnostics directly, because # Nim doesn't support capturing var params in closures diagnostics = @[] flags = {efExplain} m.c.config.writelnHook = proc (s: string) = if errorPrefix.len == 0: errorPrefix = typeClass.sym.name.s & ":" let msg = s.replace("Error:", errorPrefix) if oldWriteHook != nil: oldWriteHook msg diagnostics.add msg var checkedBody = c.semTryExpr(c, body.copyTree, flags) if collectDiagnostics: m.c.config.writelnHook = oldWriteHook for msg in diagnostics: m.diagnostics.add msg m.diagnosticsEnabled = true if checkedBody == nil: return nil # The inferrable type params have been identified during the semTryExpr above. # We need to put them in the current sigmatch's binding table in order for them # to be resolvable while matching the rest of the parameters for p in typeParams: put(m, p[1], p[0].typ) if ff.kind == tyUserTypeClassInst: result = generateTypeInstance(c, m.bindings, typeClass.sym.info, ff) else: result = ff.exactReplica #copyType(ff, c.idgen, ff.owner) result.n = checkedBody proc shouldSkipDistinct(m: TCandidate; rules: PNode, callIdent: PIdent): bool = # XXX This is bad as 'considerQuotedIdent' can produce an error! if rules.kind == nkWith: for r in rules: if considerQuotedIdent(m.c, r) == callIdent: return true return false else: for r in rules: if considerQuotedIdent(m.c, r) == callIdent: return false return true proc maybeSkipDistinct(m: TCandidate; t: PType, callee: PSym): PType = if t != nil and t.kind == tyDistinct and t.n != nil and shouldSkipDistinct(m, t.n, callee.name): result = t.base else: result = t proc tryResolvingStaticExpr(c: var TCandidate, n: PNode, allowUnresolved = false, allowCalls = false, expectedType: PType = nil): PNode = # Consider this example: # type Value[N: static[int]] = object # proc foo[N](a: Value[N], r: range[0..(N-1)]) # Here, N-1 will be initially nkStaticExpr that can be evaluated only after # N is bound to a concrete value during the matching of the first param. # This proc is used to evaluate such static expressions. let instantiated = replaceTypesInBody(c.c, c.bindings, n, nil, allowMetaTypes = allowUnresolved) if not allowCalls and instantiated.kind in nkCallKinds: return nil result = c.c.semExpr(c.c, instantiated) proc inferStaticParam*(c: var TCandidate, lhs: PNode, rhs: BiggestInt): bool = # This is a simple integer arithimetic equation solver, # capable of deriving the value of a static parameter in # expressions such as (N + 5) / 2 = rhs # # Preconditions: # # * The input of this proc must be semantized # - all templates should be expanded # - aby constant folding possible should already be performed # # * There must be exactly one unresolved static parameter # # Result: # # The proc will return true if the static types was successfully # inferred. The result will be bound to the original static type # in the TCandidate. # if lhs.kind in nkCallKinds and lhs[0].kind == nkSym: case lhs[0].sym.magic of mAddI, mAddU, mInc, mSucc: if lhs[1].kind == nkIntLit: return inferStaticParam(c, lhs[2], rhs - lhs[1].intVal) elif lhs[2].kind == nkIntLit: return inferStaticParam(c, lhs[1], rhs - lhs[2].intVal) of mDec, mSubI, mSubU, mPred: if lhs[1].kind == nkIntLit: return inferStaticParam(c, lhs[2], lhs[1].intVal - rhs) elif lhs[2].kind == nkIntLit: return inferStaticParam(c, lhs[1], rhs + lhs[2].intVal) of mMulI, mMulU: if lhs[1].kind == nkIntLit: if rhs mod lhs[1].intVal == 0: return inferStaticParam(c, lhs[2], rhs div lhs[1].intVal) elif lhs[2].kind == nkIntLit: if rhs mod lhs[2].intVal == 0: return inferStaticParam(c, lhs[1], rhs div lhs[2].intVal) of mDivI, mDivU: if lhs[1].kind == nkIntLit: if lhs[1].intVal mod rhs == 0: return inferStaticParam(c, lhs[2], lhs[1].intVal div rhs) elif lhs[2].kind == nkIntLit: return inferStaticParam(c, lhs[1], lhs[2].intVal * rhs) of mShlI: if lhs[2].kind == nkIntLit: return inferStaticParam(c, lhs[1], rhs shr lhs[2].intVal) of mShrI: if lhs[2].kind == nkIntLit: return inferStaticParam(c, lhs[1], rhs shl lhs[2].intVal) of mAshrI: if lhs[2].kind == nkIntLit: return inferStaticParam(c, lhs[1], ashr(rhs, lhs[2].intVal)) of mUnaryMinusI: return inferStaticParam(c, lhs[1], -rhs) of mUnaryPlusI: return inferStaticParam(c, lhs[1], rhs) else: discard elif lhs.kind == nkSym and lhs.typ.kind == tyStatic and (lhs.typ.n == nil or idTableGet(c.bindings, lhs.typ) == nil): var inferred = newTypeS(tyStatic, c.c, lhs.typ.elementType) inferred.n = newIntNode(nkIntLit, rhs) put(c, lhs.typ, inferred) if c.c.matchedConcept != nil: # inside concepts, binding is currently done with # direct mutation of the involved types: lhs.typ.n = inferred.n return true return false proc failureToInferStaticParam(conf: ConfigRef; n: PNode) = let staticParam = n.findUnresolvedStatic let name = if staticParam != nil: staticParam.sym.name.s else: "unknown" localError(conf, n.info, "cannot infer the value of the static param '" & name & "'") proc inferStaticsInRange(c: var TCandidate, inferred, concrete: PType): TTypeRelation = let lowerBound = tryResolvingStaticExpr(c, inferred.n[0], allowUnresolved = true) let upperBound = tryResolvingStaticExpr(c, inferred.n[1], allowUnresolved = true) template doInferStatic(e: PNode, r: Int128) = var exp = e var rhs = r if inferStaticParam(c, exp, toInt64(rhs)): return isGeneric else: failureToInferStaticParam(c.c.config, exp) result = isNone if lowerBound.kind == nkIntLit: if upperBound.kind == nkIntLit: if lengthOrd(c.c.config, concrete) == upperBound.intVal - lowerBound.intVal + 1: return isGeneric else: return isNone doInferStatic(upperBound, lengthOrd(c.c.config, concrete) + lowerBound.intVal - 1) elif upperBound.kind == nkIntLit: doInferStatic(lowerBound, getInt(upperBound) + 1 - lengthOrd(c.c.config, concrete)) template subtypeCheck() = case result of isIntConv: result = isNone of isSubrange: discard # XXX should be isNone with preview define, warnings of isConvertible: if f.last.skipTypes(abstractInst).kind != tyOpenArray: # exclude var openarray which compiler supports result = isNone of isSubtype: if f.last.skipTypes(abstractInst).kind in { tyRef, tyPtr, tyVar, tyLent, tyOwned}: # compiler can't handle subtype conversions with pointer indirection result = isNone else: discard proc isCovariantPtr(c: var TCandidate, f, a: PType): bool = # this proc is always called for a pair of matching types assert f.kind == a.kind template baseTypesCheck(lhs, rhs: PType): bool = lhs.kind notin {tyPtr, tyRef, tyVar, tyLent, tyOwned} and typeRel(c, lhs, rhs, {trNoCovariance}) == isSubtype case f.kind of tyRef, tyPtr, tyOwned: return baseTypesCheck(f.base, a.base) of tyGenericInst: let body = f.base return body == a.base and a.len == 3 and tfWeakCovariant notin body[0].flags and baseTypesCheck(f[1], a[1]) else: return false when false: proc maxNumericType(prev, candidate: PType): PType = let c = candidate.skipTypes({tyRange}) template greater(s) = if c.kind in s: result = c case prev.kind of tyInt: greater({tyInt64}) of tyInt8: greater({tyInt, tyInt16, tyInt32, tyInt64}) of tyInt16: greater({tyInt, tyInt32, tyInt64}) of tyInt32: greater({tyInt64}) of tyUInt: greater({tyUInt64}) of tyUInt8: greater({tyUInt, tyUInt16, tyUInt32, tyUInt64}) of tyUInt16: greater({tyUInt, tyUInt32, tyUInt64}) of tyUInt32: greater({tyUInt64}) of tyFloat32: greater({tyFloat64, tyFloat128}) of tyFloat64: greater({tyFloat128}) else: discard template skipOwned(a) = if a.kind == tyOwned: a = a.skipTypes({tyOwned, tyGenericInst}) proc typeRel(c: var TCandidate, f, aOrig: PType, flags: TTypeRelFlags = {}): TTypeRelation = # typeRel can be used to establish various relationships between types: # # 1) When used with concrete types, it will check for type equivalence # or a subtype relationship. # # 2) When used with a concrete type against a type class (such as generic # signature of a proc), it will check whether the concrete type is a member # of the designated type class. # # 3) When used with two type classes, it will check whether the types # matching the first type class (aOrig) are a strict subset of the types matching # the other (f). This allows us to compare the signatures of generic procs in # order to give preferrence to the most specific one: # # seq[seq[any]] is a strict subset of seq[any] and hence more specific. result = isNone assert(f != nil) when declared(deallocatedRefId): let corrupt = deallocatedRefId(cast[pointer](f)) if corrupt != 0: c.c.config.quitOrRaise "it's corrupt " & $corrupt if f.kind == tyUntyped: if aOrig != nil: put(c, f, aOrig) return isGeneric assert(aOrig != nil) var useTypeLoweringRuleInTypeClass = c.c.matchedConcept != nil and not c.isNoCall and f.kind != tyTypeDesc and tfExplicit notin aOrig.flags and tfConceptMatchedTypeSym notin aOrig.flags aOrig = if useTypeLoweringRuleInTypeClass: aOrig.skipTypes({tyTypeDesc}) else: aOrig if aOrig.kind == tyInferred: let prev = aOrig.previouslyInferred if prev != nil: return typeRel(c, f, prev, flags) else: var candidate = f case f.kind of tyGenericParam: var prev = idTableGet(c.bindings, f) if prev != nil: candidate = prev of tyFromExpr: let computedType = tryResolvingStaticExpr(c, f.n).typ case computedType.kind of tyTypeDesc: candidate = computedType.base of tyStatic: candidate = computedType else: # XXX What is this non-sense? Error reporting in signature matching? discard "localError(f.n.info, errTypeExpected)" else: discard result = typeRel(c, aOrig.base, candidate, flags) if result != isNone: c.inferredTypes.add aOrig aOrig.add candidate result = isEqual return template doBind: bool = trDontBind notin flags # var, sink and static arguments match regular modifier-free types var a = maybeSkipDistinct(c, aOrig.skipTypes({tyStatic, tyVar, tyLent, tySink}), c.calleeSym) # XXX: Theoretically, maybeSkipDistinct could be called before we even # start the param matching process. This could be done in `prepareOperand` # for example, but unfortunately `prepareOperand` is not called in certain # situation when nkDotExpr are rotated to nkDotCalls if aOrig.kind in {tyAlias, tySink}: return typeRel(c, f, skipModifier(aOrig), flags) if a.kind == tyGenericInst and skipTypes(f, {tyStatic, tyVar, tyLent, tySink}).kind notin { tyGenericBody, tyGenericInvocation, tyGenericInst, tyGenericParam} + tyTypeClasses: return typeRel(c, f, skipModifier(a), flags) if a.isResolvedUserTypeClass: return typeRel(c, f, a.skipModifier, flags) template bindingRet(res) = if doBind: let bound = aOrig.skipTypes({tyRange}).skipIntLit(c.c.idgen) put(c, f, bound) return res template considerPreviousT(body: untyped) = var prev = idTableGet(c.bindings, f) if prev == nil: body else: return typeRel(c, prev, a, flags) if c.c.inGenericContext > 0 and not c.isNoCall and (tfUnresolved in a.flags or a.kind in tyTypeClasses): # cheap check for unresolved arg, not nested return isNone case a.kind of tyOr: # XXX: deal with the current dual meaning of tyGenericParam c.typedescMatched = true # seq[int|string] vs seq[number] # both int and string must match against number # but ensure that '[T: A|A]' matches as good as '[T: A]' (bug #2219): result = isGeneric for branch in a.kids: let x = typeRel(c, f, branch, flags + {trDontBind}) if x == isNone: return isNone if x < result: result = x return result of tyAnd: # XXX: deal with the current dual meaning of tyGenericParam c.typedescMatched = true # seq[Sortable and Iterable] vs seq[Sortable] # only one match is enough for branch in a.kids: let x = typeRel(c, f, branch, flags + {trDontBind}) if x != isNone: return if x >= isGeneric: isGeneric else: x return isNone of tyIterable: if f.kind != tyIterable: return isNone of tyNot: case f.kind of tyNot: # seq[!int] vs seq[!number] # seq[float] matches the first, but not the second # we must turn the problem around: # is number a subset of int? return typeRel(c, a.elementType, f.elementType, flags) else: # negative type classes are essentially infinite, # so only the `any` type class is their superset return if f.kind == tyAnything: isGeneric else: isNone of tyAnything: if f.kind == tyAnything: return isGeneric else: return isNone of tyUserTypeClass, tyUserTypeClassInst: if c.c.matchedConcept != nil and c.c.matchedConcept.depth <= 4: # consider this: 'var g: Node' *within* a concept where 'Node' # is a concept too (tgraph) inc c.c.matchedConcept.depth let x = typeRel(c, a, f, flags + {trDontBind}) if x >= isGeneric: return isGeneric of tyFromExpr: if c.c.inGenericContext > 0: if not c.isNoCall: # generic type bodies can sometimes compile call expressions # prevent expressions with unresolved types from # being passed as parameters return isNone else: # Foo[templateCall(T)] shouldn't fail early if Foo has a constraint # and we can't evaluate `templateCall(T)` yet return isGeneric else: discard case f.kind of tyEnum: if a.kind == f.kind and sameEnumTypes(f, a): result = isEqual elif sameEnumTypes(f, skipTypes(a, {tyRange})): result = isSubtype of tyBool, tyChar: if a.kind == f.kind: result = isEqual elif skipTypes(a, {tyRange}).kind == f.kind: result = isSubtype of tyRange: if a.kind == f.kind: if f.base.kind == tyNone: return isGeneric result = typeRel(c, base(f), base(a), flags) # bugfix: accept integer conversions here #if result < isGeneric: result = isNone if result notin {isNone, isGeneric}: # resolve any late-bound static expressions # that may appear in the range: let expectedType = base(f) for i in 0..1: if f.n[i].kind == nkStaticExpr: let r = tryResolvingStaticExpr(c, f.n[i], expectedType = expectedType) if r != nil: f.n[i] = r result = typeRangeRel(f, a) else: let f = skipTypes(f, {tyRange}) if f.kind == a.kind and (f.kind != tyEnum or sameEnumTypes(f, a)): result = isIntConv elif isConvertibleToRange(c.c, f, a): result = isConvertible # a convertible to f of tyInt: result = handleRange(c.c, f, a, tyInt8, c.c.config.targetSizeSignedToKind) of tyInt8: result = handleRange(c.c, f, a, tyInt8, tyInt8) of tyInt16: result = handleRange(c.c, f, a, tyInt8, tyInt16) of tyInt32: result = handleRange(c.c, f, a, tyInt8, tyInt32) of tyInt64: result = handleRange(c.c, f, a, tyInt, tyInt64) of tyUInt: result = handleRange(c.c, f, a, tyUInt8, c.c.config.targetSizeUnsignedToKind) of tyUInt8: result = handleRange(c.c, f, a, tyUInt8, tyUInt8) of tyUInt16: result = handleRange(c.c, f, a, tyUInt8, tyUInt16) of tyUInt32: result = handleRange(c.c, f, a, tyUInt8, tyUInt32) of tyUInt64: result = handleRange(c.c, f, a, tyUInt, tyUInt64) of tyFloat: result = handleFloatRange(f, a) of tyFloat32: result = handleFloatRange(f, a) of tyFloat64: result = handleFloatRange(f, a) of tyFloat128: result = handleFloatRange(f, a) of tyVar: let flags = if isOutParam(f): flags + {trIsOutParam} else: flags if aOrig.kind == f.kind and (isOutParam(aOrig) == isOutParam(f)): result = typeRel(c, f.base, aOrig.base, flags) else: result = typeRel(c, f.base, aOrig, flags + {trNoCovariance}) subtypeCheck() of tyLent: if aOrig.kind == f.kind: result = typeRel(c, f.base, aOrig.base, flags) else: result = typeRel(c, f.base, aOrig, flags + {trNoCovariance}) subtypeCheck() of tyArray: a = reduceToBase(a) if a.kind == tyArray: var fRange = f.indexType var aRange = a.indexType if fRange.kind in {tyGenericParam, tyAnything}: var prev = idTableGet(c.bindings, fRange) if prev == nil: if typeRel(c, fRange, aRange) == isNone: return isNone put(c, fRange, a.indexType) fRange = a else: fRange = prev let ff = f[1].skipTypes({tyTypeDesc}) # This typeDesc rule is wrong, see bug #7331 let aa = a[1] #.skipTypes({tyTypeDesc}) if f.indexType.kind != tyGenericParam and aa.kind == tyEmpty: result = isGeneric else: result = typeRel(c, ff, aa, flags) if result < isGeneric: if nimEnableCovariance and trNoCovariance notin flags and ff.kind == aa.kind and isCovariantPtr(c, ff, aa): result = isSubtype else: return isNone if fRange.rangeHasUnresolvedStatic: if aRange.kind in {tyGenericParam} and aRange.reduceToBase() == aRange: return return inferStaticsInRange(c, fRange, a) elif c.c.matchedConcept != nil and aRange.rangeHasUnresolvedStatic: return inferStaticsInRange(c, aRange, f) elif result == isGeneric and concreteType(c, aa, ff) == nil: return isNone else: if lengthOrd(c.c.config, fRange) != lengthOrd(c.c.config, aRange): result = isNone of tyOpenArray, tyVarargs: # varargs[untyped] is special too but handled earlier. So we only need to # handle varargs[typed]: if f.kind == tyVarargs: if tfVarargs in a.flags: return typeRel(c, f.base, a.elementType, flags) if f[0].kind == tyTyped: return template matchArrayOrSeq(aBase: PType) = let ff = f.base let aa = aBase let baseRel = typeRel(c, ff, aa, flags) if baseRel >= isGeneric: result = isConvertible elif nimEnableCovariance and trNoCovariance notin flags and ff.kind == aa.kind and isCovariantPtr(c, ff, aa): result = isConvertible case a.kind of tyOpenArray, tyVarargs: result = typeRel(c, base(f), base(a), flags) if result < isGeneric: result = isNone of tyArray: if (f[0].kind != tyGenericParam) and (a.elementType.kind == tyEmpty): return isSubtype matchArrayOrSeq(a.elementType) of tySequence: if (f[0].kind != tyGenericParam) and (a.elementType.kind == tyEmpty): return isConvertible matchArrayOrSeq(a.elementType) of tyString: if f.kind == tyOpenArray: if f[0].kind == tyChar: result = isConvertible elif f[0].kind == tyGenericParam and a.len > 0 and typeRel(c, base(f), base(a), flags) >= isGeneric: result = isConvertible else: discard of tySequence, tyUncheckedArray: if a.kind == f.kind: if (f[0].kind != tyGenericParam) and (a.elementType.kind == tyEmpty): result = isSubtype else: let ff = f[0] let aa = a.elementType result = typeRel(c, ff, aa, flags) if result < isGeneric: if nimEnableCovariance and trNoCovariance notin flags and ff.kind == aa.kind and isCovariantPtr(c, ff, aa): result = isSubtype else: result = isNone elif a.kind == tyNil: result = isNone of tyOrdinal: if isOrdinalType(a): var x = if a.kind == tyOrdinal: a.elementType else: a if f[0].kind == tyNone: result = isGeneric else: result = typeRel(c, f[0], x, flags) if result < isGeneric: result = isNone elif a.kind == tyGenericParam: result = isGeneric of tyForward: #internalError("forward type in typeRel()") result = isNone of tyNil: skipOwned(a) if a.kind == f.kind: result = isEqual of tyTuple: if a.kind == tyTuple: result = recordRel(c, f, a, flags) of tyObject: let effectiveArgType = if useTypeLoweringRuleInTypeClass: a else: reduceToBase(a) if effectiveArgType.kind == tyObject: if sameObjectTypes(f, effectiveArgType): c.inheritancePenalty = if tfFinal in f.flags: -1 else: 0 result = isEqual # elif tfHasMeta in f.flags: result = recordRel(c, f, a) elif trIsOutParam notin flags: c.inheritancePenalty = isObjectSubtype(c, effectiveArgType, f, nil) if c.inheritancePenalty > 0: result = isSubtype of tyDistinct: a = a.skipTypes({tyOwned, tyGenericInst, tyRange}) if a.kind == tyDistinct: if sameDistinctTypes(f, a): result = isEqual #elif f.base.kind == tyAnything: result = isGeneric # issue 4435 elif c.coerceDistincts: result = typeRel(c, f.base, a, flags) elif c.coerceDistincts: result = typeRel(c, f.base, a, flags) of tySet: if a.kind == tySet: if f[0].kind != tyGenericParam and a[0].kind == tyEmpty: result = isSubtype else: result = typeRel(c, f[0], a[0], flags) if result < isGeneric: if result <= isConvertible: result = isNone elif tfIsConstructor notin a.flags: # set constructors are a bit special... result = isNone of tyPtr, tyRef: a = reduceToBase(a) if a.kind == f.kind: # ptr[R, T] can be passed to ptr[T], but not the other way round: if a.len < f.len: return isNone for i in 0.. 0 and f.len > 0 and a.base != f.base) let roota = if skipBoth or deptha > depthf: a.skipGenericAlias else: a let rootf = if skipBoth or depthf > deptha: f.skipGenericAlias else: f if a.kind == tyGenericInst: if roota.base == rootf.base: let nextFlags = flags + {trNoCovariance} var hasCovariance = false # YYYY result = isEqual for i in 1.. 0: x = x.last let concpt = f[0].skipTypes({tyGenericBody}) var preventHack = concpt.kind == tyConcept if x.kind == tyOwned and f[0].kind != tyOwned: preventHack = true x = x.last # XXX: This is very hacky. It should be moved back into liftTypeParam if x.kind in {tyGenericInst, tyArray} and c.calleeSym != nil and c.calleeSym.kind in {skProc, skFunc} and c.call != nil and not preventHack: let inst = prepareMetatypeForSigmatch(c.c, c.bindings, c.call.info, f) return typeRel(c, inst, a, flags) if x.kind == tyGenericInvocation: if f[0] == x[0]: for i in 1..= x.len: return let tr = typeRel(c, f[i], x[i], flags) if tr <= isSubtype: return result = isGeneric elif x.kind == tyGenericInst and f[0] == x[0] and x.len - 1 == f.len: for i in 1..= 0: inc c.inheritancePenalty, depth + int(c.inheritancePenalty < 0) # bug #4863: We still need to bind generic alias crap, so # we cannot return immediately: result = if depth == 0: isGeneric else: isSubtype of tyAnd: considerPreviousT: result = isEqual for branch in f.kids: let x = typeRel(c, branch, aOrig, flags) if x < isSubtype: return isNone # 'and' implies minimum matching result: if x < result: result = x if result > isGeneric: result = isGeneric bindingRet result of tyOr: considerPreviousT: result = isNone let oldInheritancePenalty = c.inheritancePenalty var minInheritance = maxInheritancePenalty for branch in f.kids: c.inheritancePenalty = -1 let x = typeRel(c, branch, aOrig, flags) if x >= result: if c.inheritancePenalty > -1: minInheritance = min(minInheritance, c.inheritancePenalty) result = x if result >= isIntConv: if minInheritance < maxInheritancePenalty: c.inheritancePenalty = oldInheritancePenalty + minInheritance if result > isGeneric: result = isGeneric bindingRet result else: result = isNone of tyNot: considerPreviousT: if typeRel(c, f.elementType, aOrig, flags) != isNone: return isNone bindingRet isGeneric of tyAnything: considerPreviousT: var concrete = concreteType(c, a) if concrete != nil and doBind: put(c, f, concrete) return isGeneric of tyBuiltInTypeClass: considerPreviousT: let target = f.genericHead let targetKind = target.kind var effectiveArgType = reduceToBase(a) effectiveArgType = effectiveArgType.skipTypes({tyBuiltInTypeClass}) if targetKind == effectiveArgType.kind: if effectiveArgType.isEmptyContainer: return isNone if targetKind == tyProc: if target.flags * {tfIterator} != effectiveArgType.flags * {tfIterator}: return isNone if tfExplicitCallConv in target.flags and target.callConv != effectiveArgType.callConv: return isNone if doBind: put(c, f, a) return isGeneric else: return isNone of tyUserTypeClassInst, tyUserTypeClass: if f.isResolvedUserTypeClass: result = typeRel(c, f.last, a, flags) else: considerPreviousT: if aOrig == f: return isEqual var matched = matchUserTypeClass(c, f, aOrig) if matched != nil: bindConcreteTypeToUserTypeClass(matched, a) if doBind: put(c, f, matched) result = isGeneric elif a.len > 0 and a.last == f: # Needed for checking `Y` == `Addable` in the following #[ type Addable = concept a, type A a + a is A MyType[T: Addable; Y: static T] = object ]# result = isGeneric else: result = isNone of tyConcept: result = if concepts.conceptMatch(c.c, f, a, c.bindings, nil): isGeneric else: isNone of tyCompositeTypeClass: considerPreviousT: let roota = a.skipGenericAlias let rootf = f.last.skipGenericAlias if a.kind == tyGenericInst and roota.base == rootf.base: for i in 1.. 0 c.typedescMatched = true var aa = a while aa.kind in {tyTypeDesc, tyGenericParam} and aa.len > 0: aa = last(aa) if aa.kind in {tyGenericParam} + tyTypeClasses: # If the constraint is a genericParam or typeClass this isGeneric return isGeneric result = typeRel(c, f.base, aa, flags) if result > isGeneric: result = isGeneric elif c.isNoCall: if doBindGP: let concrete = concreteType(c, a, f) if concrete == nil: return isNone put(c, f, concrete) result = isGeneric else: result = isNone else: # check if 'T' has a constraint as in 'proc p[T: Constraint](x: T)' if f.len > 0 and f[0].kind != tyNone: result = typeRel(c, f[0], a, flags + {trDontBind, trBindGenericParam}) if doBindGP and result notin {isNone, isGeneric}: let concrete = concreteType(c, a, f) if concrete == nil: return isNone put(c, f, concrete) if result in {isEqual, isSubtype}: result = isGeneric elif a.kind == tyTypeDesc: # somewhat special typing rule, the following is illegal: # proc p[T](x: T) # p(int) result = isNone else: result = isGeneric if result == isGeneric: var concrete = a if tfWildcard in a.flags: a.sym.transitionGenericParamToType() a.flags.excl tfWildcard elif doBind: # careful: `trDontDont` (set by `checkGeneric`) is not always respected in this call graph. # typRel having two different modes (binding and non-binding) can make things harder to # reason about and maintain. Refactoring typeRel to not be responsible for setting, or # at least validating, bindings can have multiple benefits. This is debatable. I'm not 100% sure. # A design that allows a proper complexity analysis of types like `tyOr` would be ideal. concrete = concreteType(c, a, f) if concrete == nil: return isNone if doBindGP: put(c, f, concrete) elif result > isGeneric: result = isGeneric elif a.kind == tyEmpty: result = isGeneric elif x.kind == tyGenericParam: result = isGeneric else: # This is the bound type - can't benifit from these tallies let inheritancePenaltyOld = c.inheritancePenalty result = typeRel(c, x, a, flags) # check if it fits c.inheritancePenalty = inheritancePenaltyOld if result > isGeneric: result = isGeneric of tyStatic: let prev = idTableGet(c.bindings, f) if prev == nil: if aOrig.kind == tyStatic: if c.c.inGenericContext > 0 and aOrig.n == nil and not c.isNoCall: # don't match unresolved static value to static param to avoid # faulty instantiations in calls in generic bodies # but not for generic invocations as they only check constraints result = isNone elif f.base.kind notin {tyNone, tyGenericParam}: result = typeRel(c, f.base, a, flags) if result != isNone and f.n != nil: var r = tryResolvingStaticExpr(c, f.n) if r == nil: r = f.n if not exprStructuralEquivalent(r, aOrig.n) and not (aOrig.n != nil and aOrig.n.kind == nkIntLit and inferStaticParam(c, r, aOrig.n.intVal)): result = isNone elif f.base.kind == tyGenericParam: # Handling things like `type A[T; Y: static T] = object` if f.base.len > 0: # There is a constraint, handle it result = typeRel(c, f.base.last, a, flags) else: # No constraint if tfGenericTypeParam in f.flags: result = isGeneric else: # for things like `proc fun[T](a: static[T])` result = typeRel(c, f.base, a, flags) else: result = isGeneric if result != isNone: put(c, f, aOrig) elif aOrig.n != nil and aOrig.n.typ != nil: result = if f.base.kind != tyNone: typeRel(c, f.last, aOrig.n.typ, flags) else: isGeneric if result != isNone: var boundType = newTypeS(tyStatic, c.c, aOrig.n.typ) boundType.n = aOrig.n put(c, f, boundType) else: result = isNone elif prev.kind == tyStatic: if aOrig.kind == tyStatic: result = typeRel(c, prev.last, a, flags) if result != isNone and prev.n != nil: if not exprStructuralEquivalent(prev.n, aOrig.n): result = isNone else: result = isNone else: # XXX endless recursion? #result = typeRel(c, prev, aOrig, flags) result = isNone of tyInferred: let prev = f.previouslyInferred if prev != nil: result = typeRel(c, prev, a, flags) else: result = typeRel(c, f.base, a, flags) if result != isNone: c.inferredTypes.add f f.add a of tyTypeDesc: var prev = idTableGet(c.bindings, f) if prev == nil: # proc foo(T: typedesc, x: T) # when `f` is an unresolved typedesc, `a` could be any # type, so we should not perform this check earlier if c.c.inGenericContext > 0 and a.containsUnresolvedType: # generic type bodies can sometimes compile call expressions # prevent unresolved generic parameters from being passed to procs as # typedesc parameters result = isNone elif a.kind != tyTypeDesc: if a.kind == tyGenericParam and tfWildcard in a.flags: # TODO: prevent `a` from matching as a wildcard again result = isGeneric else: result = isNone elif f.base.kind == tyNone: result = isGeneric else: result = typeRel(c, f.base, a.base, flags) if result != isNone: put(c, f, a) else: if tfUnresolved in f.flags: result = typeRel(c, prev.base, a, flags) elif a.kind == tyTypeDesc: result = typeRel(c, prev.base, a.base, flags) else: result = isNone of tyTyped: if aOrig != nil: put(c, f, aOrig) result = isGeneric of tyError: result = isEqual of tyFromExpr: # fix the expression, so it contains the already instantiated types if f.n == nil or f.n.kind == nkEmpty: return isGeneric if c.c.inGenericContext > 0: # need to delay until instantiation # also prevent infinite recursion below return isNone inc c.c.inGenericContext # to generate tyFromExpr again if unresolved # use prepareNode for consistency with other tyFromExpr in semtypinst: let instantiated = prepareTypesInBody(c.c, c.bindings, f.n) let reevaluated = c.c.semExpr(c.c, instantiated).typ dec c.c.inGenericContext case reevaluated.kind of tyFromExpr: # not resolved result = isNone of tyTypeDesc: result = typeRel(c, reevaluated.base, a, flags) of tyStatic: result = typeRel(c, reevaluated.base, a, flags) if result != isNone and reevaluated.n != nil: if not exprStructuralEquivalent(aOrig.n, reevaluated.n): result = isNone else: # bug #14136: other types are just like 'tyStatic' here: result = typeRel(c, reevaluated, a, flags) if result != isNone and reevaluated.n != nil: if not exprStructuralEquivalent(aOrig.n, reevaluated.n): result = isNone of tyNone: if a.kind == tyNone: result = isEqual else: internalError c.c.graph.config, " unknown type kind " & $f.kind when false: var nowDebug = false var dbgCount = 0 proc typeRel(c: var TCandidate, f, aOrig: PType, flags: TTypeRelFlags = {}): TTypeRelation = if nowDebug: echo f, " <- ", aOrig inc dbgCount if dbgCount == 2: writeStackTrace() result = typeRelImpl(c, f, aOrig, flags) if nowDebug: echo f, " <- ", aOrig, " res ", result proc cmpTypes*(c: PContext, f, a: PType): TTypeRelation = var m = newCandidate(c, f) result = typeRel(m, f, a) proc getInstantiatedType(c: PContext, arg: PNode, m: TCandidate, f: PType): PType = result = idTableGet(m.bindings, f) if result == nil: result = generateTypeInstance(c, m.bindings, arg, f) if result == nil: internalError(c.graph.config, arg.info, "getInstantiatedType") result = errorType(c) proc implicitConv(kind: TNodeKind, f: PType, arg: PNode, m: TCandidate, c: PContext): PNode = result = newNodeI(kind, arg.info) if containsGenericType(f): if not m.matchedErrorType: result.typ = getInstantiatedType(c, arg, m, f).skipTypes({tySink}) else: result.typ = errorType(c) else: result.typ = f.skipTypes({tySink}) # keep varness if arg.typ != nil and arg.typ.kind == tyVar: result.typ = toVar(result.typ, tyVar, c.idgen) else: result.typ = result.typ.skipTypes({tyVar}) if result.typ == nil: internalError(c.graph.config, arg.info, "implicitConv") result.add c.graph.emptyNode if arg.typ != nil and arg.typ.kind == tyLent: let a = newNodeIT(nkHiddenDeref, arg.info, arg.typ.elementType) a.add arg result.add a else: result.add arg proc isLValue(c: PContext; n: PNode, isOutParam = false): bool {.inline.} = let aa = isAssignable(nil, n) case aa of arLValue, arLocalLValue, arStrange: result = true of arDiscriminant: result = c.inUncheckedAssignSection > 0 of arAddressableConst: let sym = getRoot(n) result = strictDefs in c.features and sym != nil and sym.kind == skLet and isOutParam else: result = false proc userConvMatch(c: PContext, m: var TCandidate, f, a: PType, arg: PNode): PNode = result = nil for i in 0.. 0: # don't try to evaluate discard elif arg.kind != nkEmpty: var evaluated = c.semTryConstExpr(c, arg) if evaluated != nil: # Don't build the type in-place because `evaluated` and `arg` may point # to the same object and we'd end up creating recursive types (#9255) let typ = newTypeS(tyStatic, c, son = evaluated.typ) typ.n = evaluated arg = copyTree(arg) # fix #12864 arg.typ = typ a = typ else: if m.callee.kind == tyGenericBody: if f.kind == tyStatic and typeRel(m, f.base, a) != isNone: result = makeStaticExpr(m.c, arg) result.typ.flags.incl tfUnresolved result.typ.n = arg return let oldInheritancePenalty = m.inheritancePenalty var r = typeRel(m, f, a) # This special typing rule for macros and templates is not documented # anywhere and breaks symmetry. It's hard to get rid of though, my # custom seqs example fails to compile without this: if r != isNone and m.calleeSym != nil and m.calleeSym.kind in {skMacro, skTemplate}: # XXX: duplicating this is ugly, but we cannot (!) move this # directly into typeRel using return-like templates incMatches(m, r) if f.kind == tyTyped: return arg elif f.kind == tyTypeDesc: return arg elif f.kind == tyStatic and arg.typ.n != nil: return arg.typ.n else: return argSemantized # argOrig block instantiateGenericRoutine: # In the case where the matched value is a generic proc, we need to # fully instantiate it and then rerun typeRel to make sure it matches. # instantiationCounter is for safety to avoid any infinite loop, # I don't have any example when it is needed. # lastBindingCount is used to check whether m.bindings remains the same, # because in that case there is no point in continuing. var instantiationCounter = 0 var lastBindingCount = -1 while r in {isBothMetaConvertible, isInferred, isInferredConvertible} and lastBindingCount != m.bindings.len and instantiationCounter < 100: lastBindingCount = m.bindings.len inc(instantiationCounter) if arg.kind in {nkProcDef, nkFuncDef, nkIteratorDef} + nkLambdaKinds: result = c.semInferredLambda(c, m.bindings, arg) elif arg.kind != nkSym: return nil elif arg.sym.kind in {skMacro, skTemplate}: return nil else: if arg.sym.ast == nil: return nil let inferred = c.semGenerateInstance(c, arg.sym, m.bindings, arg.info) result = newSymNode(inferred, arg.info) arg = result r = typeRel(m, f, arg.typ) case r of isConvertible: if f.skipTypes({tyRange}).kind in {tyInt, tyUInt}: inc(m.convMatches) inc(m.convMatches) result = implicitConv(nkHiddenStdConv, f, arg, m, c) of isIntConv: # I'm too lazy to introduce another ``*matches`` field, so we conflate # ``isIntConv`` and ``isIntLit`` here: if f.skipTypes({tyRange}).kind notin {tyInt, tyUInt}: inc(m.intConvMatches) inc(m.intConvMatches) result = implicitConv(nkHiddenStdConv, f, arg, m, c) of isSubtype: inc(m.subtypeMatches) if f.kind == tyTypeDesc: result = arg else: result = implicitConv(nkHiddenSubConv, f, arg, m, c) of isSubrange: inc(m.subtypeMatches) if f.kind in {tyVar}: result = arg else: result = implicitConv(nkHiddenStdConv, f, arg, m, c) of isInferred: # result should be set in above while loop: assert result != nil inc(m.genericMatches) of isInferredConvertible: # result should be set in above while loop: assert result != nil inc(m.convMatches) result = implicitConv(nkHiddenStdConv, f, result, m, c) of isGeneric: inc(m.genericMatches) if arg.typ == nil: result = arg elif skipTypes(arg.typ, abstractVar-{tyTypeDesc}).kind == tyTuple or cmpInheritancePenalty(oldInheritancePenalty, m.inheritancePenalty) > 0: result = implicitConv(nkHiddenSubConv, f, arg, m, c) elif arg.typ.isEmptyContainer: result = arg.copyTree result.typ = getInstantiatedType(c, arg, m, f) else: result = arg of isBothMetaConvertible: # result should be set in above while loop: assert result != nil inc(m.convMatches) result = arg of isFromIntLit: # too lazy to introduce another ``*matches`` field, so we conflate # ``isIntConv`` and ``isIntLit`` here: inc(m.intConvMatches, 256) result = implicitConv(nkHiddenStdConv, f, arg, m, c) of isEqual: inc(m.exactMatches) result = arg let ff = skipTypes(f, abstractVar-{tyTypeDesc}) if ff.kind == tyTuple or (arg.typ != nil and skipTypes(arg.typ, abstractVar-{tyTypeDesc}).kind == tyTuple): result = implicitConv(nkHiddenSubConv, f, arg, m, c) of isNone: # do not do this in ``typeRel`` as it then can't infer T in ``ref T``: if a.kind == tyFromExpr: return nil elif a.kind == tyError: inc(m.genericMatches) m.matchedErrorType = true return arg elif a.kind == tyVoid and f.matchesVoidProc and argOrig.kind == nkStmtList: # lift do blocks without params to lambdas # now deprecated message(c.config, argOrig.info, warnStmtListLambda) let p = c.graph let lifted = c.semExpr(c, newProcNode(nkDo, argOrig.info, body = argOrig, params = nkFormalParams.newTree(p.emptyNode), name = p.emptyNode, pattern = p.emptyNode, genericParams = p.emptyNode, pragmas = p.emptyNode, exceptions = p.emptyNode), {}) if f.kind == tyBuiltInTypeClass: inc m.genericMatches put(m, f, lifted.typ) inc m.convMatches return implicitConv(nkHiddenStdConv, f, lifted, m, c) result = userConvMatch(c, m, f, a, arg) # check for a base type match, which supports varargs[T] without [] # constructor in a call: if result == nil and f.kind == tyVarargs: if f.n != nil: # Forward to the varargs converter result = localConvMatch(c, m, f, a, arg) elif f[0].kind == tyTyped: inc m.genericMatches result = arg else: r = typeRel(m, base(f), a) case r of isGeneric: inc(m.convMatches) result = copyTree(arg) result.typ = getInstantiatedType(c, arg, m, base(f)) m.baseTypeMatch = true of isFromIntLit: inc(m.intConvMatches, 256) result = implicitConv(nkHiddenStdConv, f[0], arg, m, c) m.baseTypeMatch = true of isEqual: inc(m.convMatches) result = copyTree(arg) m.baseTypeMatch = true of isSubtype: # bug #4799, varargs accepting subtype relation object inc(m.subtypeMatches) if base(f).kind == tyTypeDesc: result = arg else: result = implicitConv(nkHiddenSubConv, base(f), arg, m, c) m.baseTypeMatch = true else: result = userConvMatch(c, m, base(f), a, arg) if result != nil: m.baseTypeMatch = true proc staticAwareTypeRel(m: var TCandidate, f: PType, arg: var PNode): TTypeRelation = if f.kind == tyStatic and f.base.kind == tyProc: # The ast of the type does not point to the symbol. # Without this we will never resolve a `static proc` with overloads let copiedNode = copyNode(arg) copiedNode.typ = exactReplica(copiedNode.typ) copiedNode.typ.n = arg arg = copiedNode typeRel(m, f, arg.typ) proc paramTypesMatch*(m: var TCandidate, f, a: PType, arg, argOrig: PNode): PNode = if arg == nil or arg.kind notin nkSymChoices: result = paramTypesMatchAux(m, f, a, arg, argOrig) else: # symbol kinds that don't participate in symchoice type disambiguation: let matchSet = {low(TSymKind)..high(TSymKind)} - {skModule, skPackage} var best = -1 result = arg var actingF = f if f.kind == tyVarargs: if m.calleeSym.kind in {skTemplate, skMacro}: actingF = f[0] if actingF.kind in {tyTyped, tyUntyped}: var bestScope = -1 counts = 0 for i in 0.. bestScope: best = i bestScope = thisScope counts = 0 elif thisScope == bestScope: inc counts if best == -1: result = nil elif counts > 0: m.genericMatches = 1 best = -1 else: # CAUTION: The order depends on the used hashing scheme. Thus it is # incorrect to simply use the first fitting match. However, to implement # this correctly is inefficient. We have to copy `m` here to be able to # roll back the side effects of the unification algorithm. let c = m.c var x = newCandidate(c, m.callee) # potential "best" y = newCandidate(c, m.callee) # potential competitor with x z = newCandidate(c, m.callee) # buffer for copies of m x.calleeSym = m.calleeSym y.calleeSym = m.calleeSym z.calleeSym = m.calleeSym for i in 0.. -1 and result != nil: # only one valid interpretation found: markUsed(m.c, arg.info, arg[best].sym) onUse(arg.info, arg[best].sym) result = paramTypesMatchAux(m, f, arg[best].typ, arg[best], argOrig) when false: if m.calleeSym != nil and m.calleeSym.name.s == "[]": echo m.c.config $ arg.info, " for ", m.calleeSym.name.s, " ", m.c.config $ m.calleeSym.info writeMatches(m) proc setSon(father: PNode, at: int, son: PNode) = let oldLen = father.len if oldLen <= at: setLen(father.sons, at + 1) father[at] = son # insert potential 'void' parameters: #for i in oldLen.. 1: m.callee.n[1].sym else: nil # current routine parameter container: PNode = nil # constructed container let firstArgBlock = findFirstArgBlock(m, n) while a < n.len: c.openShadowScope if a >= formalLen-1 and f < formalLen and m.callee.n[f].typ.isVarargsUntyped: formal = m.callee.n[f].sym incl(marker, formal.position) if n[a].kind == nkHiddenStdConv: doAssert n[a][0].kind == nkEmpty and n[a][1].kind in {nkBracket, nkArgList} # Steal the container and pass it along setSon(m.call, formal.position + 1, n[a][1]) else: if container.isNil: container = newNodeIT(nkArgList, n[a].info, arrayConstr(c, n.info)) setSon(m.call, formal.position + 1, container) else: incrIndexType(container.typ) container.add n[a] elif n[a].kind == nkExprEqExpr: # named param m.firstMismatch.kind = kUnknownNamedParam # check if m.callee has such a param: prepareNamedParam(n[a], c) if n[a][0].kind != nkIdent: localError(c.config, n[a].info, "named parameter has to be an identifier") noMatch() formal = getNamedParamFromList(m.callee.n, n[a][0].ident) if formal == nil: # no error message! noMatch() if containsOrIncl(marker, formal.position): m.firstMismatch.kind = kAlreadyGiven # already in namedParams, so no match # we used to produce 'errCannotBindXTwice' here but see # bug #3836 of why that is not sound (other overload with # different parameter names could match later on): when false: localError(n[a].info, errCannotBindXTwice, formal.name.s) noMatch() m.baseTypeMatch = false m.typedescMatched = false n[a][1] = prepareOperand(c, formal.typ, n[a][1]) n[a].typ = n[a][1].typ arg = paramTypesMatch(m, formal.typ, n[a].typ, n[a][1], n[a][1]) m.firstMismatch.kind = kTypeMismatch if arg == nil: noMatch() checkConstraint(n[a][1]) if m.baseTypeMatch: #assert(container == nil) container = newNodeIT(nkBracket, n[a].info, arrayConstr(c, arg)) container.add arg setSon(m.call, formal.position + 1, container) if f != formalLen - 1: container = nil else: setSon(m.call, formal.position + 1, arg) inc f else: # unnamed param if f >= formalLen: # too many arguments? if tfVarargs in m.callee.flags: # is ok... but don't increment any counters... # we have no formal here to snoop at: n[a] = prepareOperand(c, n[a]) if skipTypes(n[a].typ, abstractVar-{tyTypeDesc}).kind==tyString: m.call.add implicitConv(nkHiddenStdConv, getSysType(c.graph, n[a].info, tyCstring), copyTree(n[a]), m, c) else: m.call.add copyTree(n[a]) elif formal != nil and formal.typ.kind == tyVarargs: m.firstMismatch.kind = kTypeMismatch # beware of the side-effects in 'prepareOperand'! So only do it for # varargs matching. See tests/metatype/tstatic_overloading. m.baseTypeMatch = false m.typedescMatched = false incl(marker, formal.position) n[a] = prepareOperand(c, formal.typ, n[a]) arg = paramTypesMatch(m, formal.typ, n[a].typ, n[a], nOrig[a]) if arg != nil and m.baseTypeMatch and container != nil: container.add arg incrIndexType(container.typ) checkConstraint(n[a]) else: noMatch() else: m.firstMismatch.kind = kExtraArg noMatch() else: if m.callee.n[f].kind != nkSym: internalError(c.config, n[a].info, "matches") noMatch() if flexibleOptionalParams in c.features and a >= firstArgBlock: f = max(f, m.callee.n.len - (n.len - a)) formal = m.callee.n[f].sym m.firstMismatch.kind = kTypeMismatch if containsOrIncl(marker, formal.position) and container.isNil: m.firstMismatch.kind = kPositionalAlreadyGiven # positional param already in namedParams: (see above remark) when false: localError(n[a].info, errCannotBindXTwice, formal.name.s) noMatch() if formal.typ.isVarargsUntyped: if container.isNil: container = newNodeIT(nkArgList, n[a].info, arrayConstr(c, n.info)) setSon(m.call, formal.position + 1, container) else: incrIndexType(container.typ) container.add n[a] else: m.baseTypeMatch = false m.typedescMatched = false n[a] = prepareOperand(c, formal.typ, n[a]) arg = paramTypesMatch(m, formal.typ, n[a].typ, n[a], nOrig[a]) if arg == nil: noMatch() if formal.typ.isVarargsTyped and m.calleeSym.kind in {skTemplate, skMacro}: if container.isNil: container = newNodeIT(nkBracket, n[a].info, arrayConstr(c, n.info)) setSon(m.call, formal.position + 1, implicitConv(nkHiddenStdConv, formal.typ, container, m, c)) else: incrIndexType(container.typ) container.add n[a] f = max(f, formalLen - n.len + a + 1) elif m.baseTypeMatch: assert formal.typ.kind == tyVarargs #assert(container == nil) if container.isNil: container = newNodeIT(nkBracket, n[a].info, arrayConstr(c, arg)) container.typ.flags.incl tfVarargs else: incrIndexType(container.typ) container.add arg setSon(m.call, formal.position + 1, implicitConv(nkHiddenStdConv, formal.typ, container, m, c)) #if f != formalLen - 1: container = nil # pick the formal from the end, so that 'x, y, varargs, z' works: f = max(f, formalLen - n.len + a + 1) elif formal.typ.kind != tyVarargs or container == nil: setSon(m.call, formal.position + 1, arg) inc f container = nil else: # we end up here if the argument can be converted into the varargs # formal (e.g. seq[T] -> varargs[T]) but we have already instantiated # a container #assert arg.kind == nkHiddenStdConv # for 'nim check' # this assertion can be off localError(c.config, n[a].info, "cannot convert $1 to $2" % [ typeToString(n[a].typ), typeToString(formal.typ) ]) noMatch() checkConstraint(n[a]) if m.state == csMatch and not (m.calleeSym != nil and m.calleeSym.kind in {skTemplate, skMacro}): c.mergeShadowScope else: c.closeShadowScope inc a # for some edge cases (see tdont_return_unowned_from_owned test case) m.firstMismatch.arg = a m.firstMismatch.formal = formal proc partialMatch*(c: PContext, n, nOrig: PNode, m: var TCandidate) = # for 'suggest' support: var marker = initIntSet() matchesAux(c, n, nOrig, m, marker) proc matches*(c: PContext, n, nOrig: PNode, m: var TCandidate) = if m.magic in {mArrGet, mArrPut}: m.state = csMatch m.call = n # Note the following doesn't work as it would produce ambiguities. # Instead we patch system.nim, see bug #8049. when false: inc m.genericMatches inc m.exactMatches return # initCandidate may have given csNoMatch if generic params didn't match: if m.state == csNoMatch: return var marker = initIntSet() matchesAux(c, n, nOrig, m, marker) if m.state == csNoMatch: return # check that every formal parameter got a value: for f in 1.. 1: t.newSons 1 proc argtypeMatches*(c: PContext, f, a: PType, fromHlo = false): bool = var m = newCandidate(c, f) let res = paramTypesMatch(m, f, a, c.graph.emptyNode, nil) #instantiateGenericConverters(c, res, m) # XXX this is used by patterns.nim too; I think it's better to not # instantiate generic converters for that if not fromHlo: res != nil else: # pattern templates do not allow for conversions except from int literal res != nil and m.convMatches == 0 and m.intConvMatches in [0, 256] proc instTypeBoundOp*(c: PContext; dc: PSym; t: PType; info: TLineInfo; op: TTypeAttachedOp; col: int): PSym = var m = newCandidate(c, dc.typ) if col >= dc.typ.len: localError(c.config, info, "cannot instantiate: '" & dc.name.s & "'") return nil var f = dc.typ[col] if op == attachedDeepCopy: if f.kind in {tyRef, tyPtr}: f = f.elementType else: if f.kind in {tyVar}: f = f.elementType if typeRel(m, f, t) == isNone: result = nil localError(c.config, info, "cannot instantiate: '" & dc.name.s & "'") else: result = c.semGenerateInstance(c, dc, m.bindings, info) if op == attachedDeepCopy: assert sfFromGeneric in result.flags include suggest when not declared(tests): template tests(s: untyped) = discard tests: var dummyOwner = newSym(skModule, getIdent("test_module"), nil, unknownLineInfo) proc `|` (t1, t2: PType): PType = result = newType(tyOr, dummyOwner) result.rawAddSon(t1) result.rawAddSon(t2) proc `&` (t1, t2: PType): PType = result = newType(tyAnd, dummyOwner) result.rawAddSon(t1) result.rawAddSon(t2) proc `!` (t: PType): PType = result = newType(tyNot, dummyOwner) result.rawAddSon(t) proc seq(t: PType): PType = result = newType(tySequence, dummyOwner) result.rawAddSon(t) proc array(x: int, t: PType): PType = result = newType(tyArray, dummyOwner) var n = newNodeI(nkRange, unknownLineInfo) n.add newIntNode(nkIntLit, 0) n.add newIntNode(nkIntLit, x) let range = newType(tyRange, dummyOwner) result.rawAddSon(range) result.rawAddSon(t) suite "type classes": let int = newType(tyInt, dummyOwner) float = newType(tyFloat, dummyOwner) string = newType(tyString, dummyOwner) ordinal = newType(tyOrdinal, dummyOwner) any = newType(tyAnything, dummyOwner) number = int | float var TFoo = newType(tyObject, dummyOwner) TFoo.sym = newSym(skType, getIdent"TFoo", dummyOwner, unknownLineInfo) var T1 = newType(tyGenericParam, dummyOwner) T1.sym = newSym(skType, getIdent"T1", dummyOwner, unknownLineInfo) T1.sym.position = 0 var T2 = newType(tyGenericParam, dummyOwner) T2.sym = newSym(skType, getIdent"T2", dummyOwner, unknownLineInfo) T2.sym.position = 1 setup: var c = newCandidate(nil, nil) template yes(x, y) = test astToStr(x) & " is " & astToStr(y): check typeRel(c, y, x) == isGeneric template no(x, y) = test astToStr(x) & " is not " & astToStr(y): check typeRel(c, y, x) == isNone yes seq(any), array(10, int) | seq(any) # Sure, seq[any] is directly included yes seq(int), seq(any) yes seq(int), seq(number) # Sure, the int sequence is certainly # part of the number sequences (and all sequences) no seq(any), seq(float) # Nope, seq[any] includes types that are not seq[float] (e.g. seq[int]) yes seq(int|string), seq(any) # Sure yes seq(int&string), seq(any) # Again yes seq(int&string), seq(int) # A bit more complicated # seq[int&string] is not a real type, but it's analogous to # seq[Sortable and Iterable], which is certainly a subset of seq[Sortable] no seq(int|string), seq(int|float) # Nope, seq[string] is not included in not included in # the seq[int|float] set no seq(!(int|string)), seq(string) # A sequence that is neither seq[int] or seq[string] # is obviously not seq[string] no seq(!int), seq(number) # Now your head should start to hurt a bit # A sequence that is not seq[int] is not necessarily a number sequence # it could well be seq[string] for example yes seq(!(int|string)), seq(!string) # all sequnece types besides seq[int] and seq[string] # are subset of all sequence types that are not seq[string] no seq(!(int|string)), seq(!(string|TFoo)) # Nope, seq[TFoo] is included in the first set, but not in the second no seq(!string), seq(!number) # Nope, seq[int] in included in the first set, but not in the second yes seq(!number), seq(any) yes seq(!int), seq(any) no seq(any), seq(!any) no seq(!int), seq(!any) yes int, ordinal no string, ordinal