249 lines
6.8 KiB
Text
249 lines
6.8 KiB
Text
/-
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Copyright (c) 2018 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import init.lean.level
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import init.lean.kvmap
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namespace Lean
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inductive Literal
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| natVal (val : Nat)
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| strVal (val : String)
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inductive BinderInfo
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| default | implicit | strictImplicit | instImplicit | auxDecl
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namespace BinderInfo
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def isInstImplicit : BinderInfo → Bool
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| instImplicit => true
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| _ => false
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protected def beq : BinderInfo → BinderInfo → Bool
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| default, default => true
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| implicit, implicit => true
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| strictImplicit, strictImplicit => true
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| instImplicit, instImplicit => true
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| auxDecl, auxDecl => true
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| _, _ => false
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instance : HasBeq BinderInfo := ⟨BinderInfo.beq⟩
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end BinderInfo
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abbrev MData := KVMap
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namespace MData
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abbrev empty : MData := {KVMap .}
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instance : HasEmptyc MData := ⟨empty⟩
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end MData
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inductive Expr
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| bvar : Nat → Expr -- bound variables
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| fvar : Name → Expr -- free variables
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| mvar : Name → Expr -- meta variables
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| sort : Level → Expr -- Sort
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| const : Name → List Level → Expr -- constants
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| app : Expr → Expr → Expr -- application
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| lam : Name → BinderInfo → Expr → Expr → Expr -- lambda abstraction
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| pi : Name → BinderInfo → Expr → Expr → Expr -- Pi
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| elet : Name → Expr → Expr → Expr → Expr -- let expressions
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| lit : Literal → Expr -- literals
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| mdata : MData → Expr → Expr -- metadata
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| proj : Name → Nat → Expr → Expr -- projection
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instance exprIsInhabited : Inhabited Expr :=
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⟨Expr.sort Level.zero⟩
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attribute [extern "lean_expr_mk_bvar"] Expr.bvar
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attribute [extern "lean_expr_mk_fvar"] Expr.fvar
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attribute [extern "lean_expr_mk_mvar"] Expr.mvar
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attribute [extern "lean_expr_mk_sort"] Expr.sort
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attribute [extern "lean_expr_mk_const"] Expr.const
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attribute [extern "lean_expr_mk_app"] Expr.app
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attribute [extern "lean_expr_mk_lambda"] Expr.lam
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attribute [extern "lean_expr_mk_pi"] Expr.pi
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attribute [extern "lean_expr_mk_let"] Expr.elet
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attribute [extern "lean_expr_mk_lit"] Expr.lit
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attribute [extern "lean_expr_mk_mdata"] Expr.mdata
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attribute [extern "lean_expr_mk_proj"] Expr.proj
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-- deprecated Constructor
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@[extern "lean_expr_local"]
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constant Expr.local (n : Name) (pp : Name) (ty : Expr) (bi : BinderInfo) : Expr := default _
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def mkApp (fn : Expr) (args : List Expr) : Expr :=
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args.foldl Expr.app fn
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def mkCApp (fn : Name) (args : List Expr) : Expr :=
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mkApp (Expr.const fn []) args
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namespace Expr
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@[extern "lean_expr_hash"]
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constant hash (n : @& Expr) : USize := default USize
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instance : Hashable Expr := ⟨Expr.hash⟩
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-- TODO: implement it in Lean
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@[extern "lean_expr_dbg_to_string"]
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constant dbgToString (e : @& Expr) : String := default String
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@[extern "lean_expr_quick_lt"]
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constant quickLt (a : @& Expr) (b : @& Expr) : Bool := default _
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@[extern "lean_expr_lt"]
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constant lt (a : @& Expr) (b : @& Expr) : Bool := default _
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@[extern "lean_expr_eqv"]
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constant eqv (a : @& Expr) (b : @& Expr) : Bool := default _
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instance : HasBeq Expr := ⟨Expr.eqv⟩
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@[extern "lean_expr_has_mvar"]
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constant hasMVar (a : @& Expr) : Bool := default _
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@[extern "lean_expr_has_fvar"]
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constant hasFVar (a : @& Expr) : Bool := default _
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def isSort : Expr → Bool
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| Expr.sort _ => true
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| _ => false
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def isBVar : Expr → Bool
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| bvar _ => true
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| _ => false
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def isMVar : Expr → Bool
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| mvar _ => true
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| _ => false
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def isFVar : Expr → Bool
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| fvar _ => true
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| _ => false
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def isApp : Expr → Bool
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| app _ _ => true
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| _ => false
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def isConst : Expr → Bool
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| const _ _ => true
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| _ => false
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def isForall : Expr → Bool
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| Expr.pi _ _ _ _ => true
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| _ => false
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def isLambda : Expr → Bool
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| Expr.lam _ _ _ _ => true
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| _ => false
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def isBinding : Expr → Bool
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| Expr.lam _ _ _ _ => true
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| Expr.pi _ _ _ _ => true
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| _ => false
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def isLet : Expr → Bool
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| Expr.elet _ _ _ _ => true
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| _ => false
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def getAppFn : Expr → Expr
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| Expr.app f a => getAppFn f
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| e => e
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def getAppNumArgsAux : Expr → Nat → Nat
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| Expr.app f a, n => getAppNumArgsAux f (n+1)
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| e, n => n
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def getAppNumArgs (e : Expr) : Nat :=
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getAppNumArgsAux e 0
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def getAppArgsAux : Expr → List Expr → List Expr
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| Expr.app f a, as => getAppArgsAux f (a::as)
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| e, as => as
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@[inline] def getAppArgs (e : Expr) : List Expr :=
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getAppArgsAux e []
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def isAppOf (e : Expr) (n : Name) : Bool :=
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match e.getAppFn with
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| Expr.const c _ => c == n
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| _ => false
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def isAppOfArity : Expr → Name → Nat → Bool
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| Expr.const c _, n, 0 => c == n
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| Expr.app f _, n, a+1 => isAppOfArity f n a
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| _, _, _ => false
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def constName : Expr → Name
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| const n _ => n
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| _ => panic! "constName called on non-const"
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def constLevels : Expr → List Level
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| const _ ls => ls
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| _ => panic! "constLevels called on non-const"
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def bvarIdx : Expr → Nat
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| bvar idx => idx
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| _ => panic! "bvarIdx called on non-bvar"
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def fvarName : Expr → Name
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| fvar n => n
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| _ => panic! "fvarName called on non-fvar"
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def bindingDomain : Expr → Expr
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| Expr.pi _ _ d _ => d
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| Expr.lam _ _ d _ => d
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| _ => default _
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def bindingBody : Expr → Expr
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| Expr.pi _ _ _ b => b
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| Expr.lam _ _ _ b => b
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| _ => default _
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/-- Instantiate the loose bound variables in `e` using `subst`.
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That is, a loose `Expr.bvar i` is replaced with `subst[i]`. -/
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@[extern "lean_expr_instantiate"]
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constant instantiate (e : Expr) (subst : Array Expr) : Expr := default _
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@[extern "lean_expr_instantiate1"]
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constant instantiate1 (e : Expr) (subst : Expr) : Expr := default _
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/-- Similar to instantiate, but `Expr.bvar i` is replaced with `subst[subst.size - i - 1]` -/
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@[extern "lean_expr_instantiate_rev"]
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constant instantiateRev (e : Expr) (subst : Array Expr) : Expr := default _
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/-- Replace free variables `xs` with loose bound variables. -/
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@[extern "lean_expr_abstract"]
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constant abstract (e : Expr) (xs : Array Expr) : Expr := default _
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/-- Similar to `abstract`, but consider only the first `min n xs.size` entries in `xs`. -/
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@[extern "lean_expr_abstract_range"]
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constant abstractRange (e : Expr) (n : Nat) (xs : Array Expr) : Expr := default _
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instance : HasToString Expr :=
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⟨Expr.dbgToString⟩
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-- TODO: should not use dbgToString, but constructors.
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instance : HasRepr Expr :=
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⟨Expr.dbgToString⟩
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end Expr
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def mkConst (n : Name) (ls : List Level := []) : Expr :=
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Expr.const n ls
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def mkBinApp (f a b : Expr) :=
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Expr.app (Expr.app f a) b
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def mkBinCApp (f : Name) (a b : Expr) :=
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mkBinApp (mkConst f) a b
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def mkDecIsTrue (pred proof : Expr) :=
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mkBinApp (Expr.const `Decidable.isTrue []) pred proof
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def mkDecIsFalse (pred proof : Expr) :=
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mkBinApp (Expr.const `Decidable.isFalse []) pred proof
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end Lean
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