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Declaration.lean
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Declaration.lean
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/-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Expr
namespace Lean
/--
Reducibility hints are used in the convertibility checker.
When trying to solve a constraint such a
(f ...) =?= (g ...)
where f and g are definitions, the checker has to decide which one will be unfolded.
If f (g) is opaque, then g (f) is unfolded if it is also not marked as opaque,
Else if f (g) is abbrev, then f (g) is unfolded if g (f) is also not marked as abbrev,
Else if f and g are regular, then we unfold the one with the biggest definitional height.
Otherwise both are unfolded.
The arguments of the `regular` Constructor are: the definitional height and the flag `selfOpt`.
The definitional height is by default computed by the kernel. It only takes into account
other regular definitions used in a definition. When creating declarations using meta-programming,
we can specify the definitional depth manually.
Remark: the hint only affects performance. None of the hints prevent the kernel from unfolding a
declaration during Type checking.
Remark: the ReducibilityHints are not related to the attributes: reducible/irrelevance/semireducible.
These attributes are used by the Elaborator. The ReducibilityHints are used by the kernel (and Elaborator).
Moreover, the ReducibilityHints cannot be changed after a declaration is added to the kernel. -/
inductive ReducibilityHints where
| opaque : ReducibilityHints
| «abbrev» : ReducibilityHints
| regular : UInt32 → ReducibilityHints
deriving Inhabited
@[export lean_mk_reducibility_hints_regular]
def mkReducibilityHintsRegularEx (h : UInt32) : ReducibilityHints :=
ReducibilityHints.regular h
@[export lean_reducibility_hints_get_height]
def ReducibilityHints.getHeightEx (h : ReducibilityHints) : UInt32 :=
match h with
| ReducibilityHints.regular h => h
| _ => 0
namespace ReducibilityHints
def lt : ReducibilityHints → ReducibilityHints → Bool
| «abbrev», «abbrev» => false
| «abbrev», _ => true
| regular d₁, regular d₂ => d₁ < d₂
| regular _, opaque => true
| _, _ => false
def isAbbrev : ReducibilityHints → Bool
| «abbrev» => true
| _ => false
def isRegular : ReducibilityHints → Bool
| regular .. => true
| _ => false
end ReducibilityHints
/-- Base structure for `AxiomVal`, `DefinitionVal`, `TheoremVal`, `InductiveVal`, `ConstructorVal`, `RecursorVal` and `QuotVal`. -/
structure ConstantVal where
name : Name
levelParams : List Name
type : Expr
deriving Inhabited
structure AxiomVal extends ConstantVal where
isUnsafe : Bool
deriving Inhabited
@[export lean_mk_axiom_val]
def mkAxiomValEx (name : Name) (levelParams : List Name) (type : Expr) (isUnsafe : Bool) : AxiomVal := {
name := name,
levelParams := levelParams,
type := type,
isUnsafe := isUnsafe
}
@[export lean_axiom_val_is_unsafe] def AxiomVal.isUnsafeEx (v : AxiomVal) : Bool :=
v.isUnsafe
inductive DefinitionSafety where
| «unsafe» | safe | «partial»
deriving Inhabited, BEq, Repr
structure DefinitionVal extends ConstantVal where
value : Expr
hints : ReducibilityHints
safety : DefinitionSafety
deriving Inhabited
@[export lean_mk_definition_val]
def mkDefinitionValEx (name : Name) (levelParams : List Name) (type : Expr) (val : Expr) (hints : ReducibilityHints) (safety : DefinitionSafety) : DefinitionVal := {
name := name,
levelParams := levelParams,
type := type,
value := val,
hints := hints,
safety := safety
}
@[export lean_definition_val_get_safety] def DefinitionVal.getSafetyEx (v : DefinitionVal) : DefinitionSafety :=
v.safety
structure TheoremVal extends ConstantVal where
value : Expr
deriving Inhabited
/- Value for an opaque constant declaration `constant x : t := e` -/
structure OpaqueVal extends ConstantVal where
value : Expr
isUnsafe : Bool
deriving Inhabited
@[export lean_mk_opaque_val]
def mkOpaqueValEx (name : Name) (levelParams : List Name) (type : Expr) (val : Expr) (isUnsafe : Bool) : OpaqueVal := {
name := name,
levelParams := levelParams,
type := type,
value := val,
isUnsafe := isUnsafe
}
@[export lean_opaque_val_is_unsafe] def OpaqueVal.isUnsafeEx (v : OpaqueVal) : Bool :=
v.isUnsafe
structure Constructor where
name : Name
type : Expr
deriving Inhabited
structure InductiveType where
name : Name
type : Expr
ctors : List Constructor
deriving Inhabited
/-- Declaration object that can be sent to the kernel. -/
inductive Declaration where
| axiomDecl (val : AxiomVal)
| defnDecl (val : DefinitionVal)
| thmDecl (val : TheoremVal)
| opaqueDecl (val : OpaqueVal)
| quotDecl
| mutualDefnDecl (defns : List DefinitionVal) -- All definitions must be marked as `unsafe` or `partial`
| inductDecl (lparams : List Name) (nparams : Nat) (types : List InductiveType) (isUnsafe : Bool)
deriving Inhabited
@[export lean_mk_inductive_decl]
def mkInductiveDeclEs (lparams : List Name) (nparams : Nat) (types : List InductiveType) (isUnsafe : Bool) : Declaration :=
Declaration.inductDecl lparams nparams types isUnsafe
@[export lean_is_unsafe_inductive_decl]
def Declaration.isUnsafeInductiveDeclEx : Declaration → Bool
| Declaration.inductDecl _ _ _ isUnsafe => isUnsafe
| _ => false
@[specialize] def Declaration.foldExprM {α} {m : Type → Type} [Monad m] (d : Declaration) (f : α → Expr → m α) (a : α) : m α :=
match d with
| Declaration.quotDecl => pure a
| Declaration.axiomDecl { type := type, .. } => f a type
| Declaration.defnDecl { type := type, value := value, .. } => do let a ← f a type; f a value
| Declaration.opaqueDecl { type := type, value := value, .. } => do let a ← f a type; f a value
| Declaration.thmDecl { type := type, value := value, .. } => do let a ← f a type; f a value
| Declaration.mutualDefnDecl vals => vals.foldlM (fun a v => do let a ← f a v.type; f a v.value) a
| Declaration.inductDecl _ _ inductTypes _ =>
inductTypes.foldlM
(fun a inductType => do
let a ← f a inductType.type
inductType.ctors.foldlM (fun a ctor => f a ctor.type) a)
a
@[inline] def Declaration.forExprM {m : Type → Type} [Monad m] (d : Declaration) (f : Expr → m Unit) : m Unit :=
d.foldExprM (fun _ a => f a) ()
/-- The kernel compiles (mutual) inductive declarations (see `inductiveDecls`) into a set of
- `Declaration.inductDecl` (for each inductive datatype in the mutual Declaration),
- `Declaration.ctorDecl` (for each Constructor in the mutual Declaration),
- `Declaration.recDecl` (automatically generated recursors).
This data is used to implement iota-reduction efficiently and compile nested inductive
declarations.
A series of checks are performed by the kernel to check whether a `inductiveDecls`
is valid or not. -/
structure InductiveVal extends ConstantVal where
numParams : Nat -- Number of parameters
numIndices : Nat -- Number of indices
all : List Name -- List of all (including this one) inductive datatypes in the mutual declaration containing this one
ctors : List Name -- List of all constructors for this inductive datatype
isRec : Bool -- `true` Iff it is recursive
isUnsafe : Bool
isReflexive : Bool
isNested : Bool
deriving Inhabited
@[export lean_mk_inductive_val]
def mkInductiveValEx (name : Name) (levelParams : List Name) (type : Expr) (numParams numIndices : Nat)
(all ctors : List Name) (isRec isUnsafe isReflexive isNested : Bool) : InductiveVal := {
name := name
levelParams := levelParams
type := type
numParams := numParams
numIndices := numIndices
all := all
ctors := ctors
isRec := isRec
isUnsafe := isUnsafe
isReflexive := isReflexive
isNested := isNested
}
@[export lean_inductive_val_is_rec] def InductiveVal.isRecEx (v : InductiveVal) : Bool := v.isRec
@[export lean_inductive_val_is_unsafe] def InductiveVal.isUnsafeEx (v : InductiveVal) : Bool := v.isUnsafe
@[export lean_inductive_val_is_reflexive] def InductiveVal.isReflexiveEx (v : InductiveVal) : Bool := v.isReflexive
@[export lean_inductive_val_is_nested] def InductiveVal.isNestedEx (v : InductiveVal) : Bool := v.isNested
def InductiveVal.numCtors (v : InductiveVal) : Nat := v.ctors.length
structure ConstructorVal extends ConstantVal where
induct : Name -- Inductive Type this Constructor is a member of
cidx : Nat -- Constructor index (i.e., Position in the inductive declaration)
numParams : Nat -- Number of parameters in inductive datatype `induct`
numFields : Nat -- Number of fields (i.e., arity - nparams)
isUnsafe : Bool
deriving Inhabited
@[export lean_mk_constructor_val]
def mkConstructorValEx (name : Name) (levelParams : List Name) (type : Expr) (induct : Name) (cidx numParams numFields : Nat) (isUnsafe : Bool) : ConstructorVal := {
name := name,
levelParams := levelParams,
type := type,
induct := induct,
cidx := cidx,
numParams := numParams,
numFields := numFields,
isUnsafe := isUnsafe
}
@[export lean_constructor_val_is_unsafe] def ConstructorVal.isUnsafeEx (v : ConstructorVal) : Bool := v.isUnsafe
/-- Information for reducing a recursor -/
structure RecursorRule where
ctor : Name -- Reduction rule for this Constructor
nfields : Nat -- Number of fields (i.e., without counting inductive datatype parameters)
rhs : Expr -- Right hand side of the reduction rule
deriving Inhabited
structure RecursorVal extends ConstantVal where
all : List Name -- List of all inductive datatypes in the mutual declaration that generated this recursor
numParams : Nat -- Number of parameters
numIndices : Nat -- Number of indices
numMotives : Nat -- Number of motives
numMinors : Nat -- Number of minor premises
rules : List RecursorRule -- A reduction for each Constructor
k : Bool -- It supports K-like reduction
isUnsafe : Bool
deriving Inhabited
@[export lean_mk_recursor_val]
def mkRecursorValEx (name : Name) (levelParams : List Name) (type : Expr) (all : List Name) (numParams numIndices numMotives numMinors : Nat)
(rules : List RecursorRule) (k isUnsafe : Bool) : RecursorVal := {
name := name, levelParams := levelParams, type := type, all := all, numParams := numParams, numIndices := numIndices,
numMotives := numMotives, numMinors := numMinors, rules := rules, k := k, isUnsafe := isUnsafe
}
@[export lean_recursor_k] def RecursorVal.kEx (v : RecursorVal) : Bool := v.k
@[export lean_recursor_is_unsafe] def RecursorVal.isUnsafeEx (v : RecursorVal) : Bool := v.isUnsafe
def RecursorVal.getMajorIdx (v : RecursorVal) : Nat :=
v.numParams + v.numMotives + v.numMinors + v.numIndices
def RecursorVal.getFirstIndexIdx (v : RecursorVal) : Nat :=
v.numParams + v.numMotives + v.numMinors
def RecursorVal.getFirstMinorIdx (v : RecursorVal) : Nat :=
v.numParams + v.numMotives
def RecursorVal.getInduct (v : RecursorVal) : Name :=
v.name.getPrefix
inductive QuotKind where
| type -- `Quot`
| ctor -- `Quot.mk`
| lift -- `Quot.lift`
| ind -- `Quot.ind`
deriving Inhabited
structure QuotVal extends ConstantVal where
kind : QuotKind
deriving Inhabited
@[export lean_mk_quot_val]
def mkQuotValEx (name : Name) (levelParams : List Name) (type : Expr) (kind : QuotKind) : QuotVal := {
name := name, levelParams := levelParams, type := type, kind := kind
}
@[export lean_quot_val_kind] def QuotVal.kindEx (v : QuotVal) : QuotKind := v.kind
/-- Information associated with constant declarations. -/
inductive ConstantInfo where
| axiomInfo (val : AxiomVal)
| defnInfo (val : DefinitionVal)
| thmInfo (val : TheoremVal)
| opaqueInfo (val : OpaqueVal)
| quotInfo (val : QuotVal)
| inductInfo (val : InductiveVal)
| ctorInfo (val : ConstructorVal)
| recInfo (val : RecursorVal)
deriving Inhabited
namespace ConstantInfo
def toConstantVal : ConstantInfo → ConstantVal
| defnInfo {toConstantVal := d, ..} => d
| axiomInfo {toConstantVal := d, ..} => d
| thmInfo {toConstantVal := d, ..} => d
| opaqueInfo {toConstantVal := d, ..} => d
| quotInfo {toConstantVal := d, ..} => d
| inductInfo {toConstantVal := d, ..} => d
| ctorInfo {toConstantVal := d, ..} => d
| recInfo {toConstantVal := d, ..} => d
def isUnsafe : ConstantInfo → Bool
| defnInfo v => v.safety == DefinitionSafety.unsafe
| axiomInfo v => v.isUnsafe
| thmInfo v => false
| opaqueInfo v => v.isUnsafe
| quotInfo v => false
| inductInfo v => v.isUnsafe
| ctorInfo v => v.isUnsafe
| recInfo v => v.isUnsafe
def name (d : ConstantInfo) : Name :=
d.toConstantVal.name
def levelParams (d : ConstantInfo) : List Name :=
d.toConstantVal.levelParams
def numLevelParams (d : ConstantInfo) : Nat :=
d.levelParams.length
def type (d : ConstantInfo) : Expr :=
d.toConstantVal.type
def value? : ConstantInfo → Option Expr
| defnInfo {value := r, ..} => some r
| thmInfo {value := r, ..} => some r
| _ => none
def hasValue : ConstantInfo → Bool
| defnInfo {value := r, ..} => true
| thmInfo {value := r, ..} => true
| _ => false
def value! : ConstantInfo → Expr
| defnInfo {value := r, ..} => r
| thmInfo {value := r, ..} => r
| _ => panic! "declaration with value expected"
def hints : ConstantInfo → ReducibilityHints
| defnInfo {hints := r, ..} => r
| _ => ReducibilityHints.opaque
def isCtor : ConstantInfo → Bool
| ctorInfo _ => true
| _ => false
def isInductive : ConstantInfo → Bool
| inductInfo _ => true
| _ => false
@[extern "lean_instantiate_type_lparams"]
constant instantiateTypeLevelParams (c : @& ConstantInfo) (ls : @& List Level) : Expr
@[extern "lean_instantiate_value_lparams"]
constant instantiateValueLevelParams (c : @& ConstantInfo) (ls : @& List Level) : Expr
end ConstantInfo
def mkRecName (declName : Name) : Name :=
Name.mkStr declName "rec"
end Lean