def Lean.Parser.colonR : ParserDescr

Reducible defeq matching for guard_hyp types

def Lean.Parser.colonD : ParserDescr

Default-reducibility defeq matching for guard_hyp types

def Lean.Parser.colonS : ParserDescr

Syntactic matching for guard_hyp types

def Lean.Parser.colonA : ParserDescr

Alpha-eq matching for guard_hyp types

def Lean.Parser.colon : ParserDescr

The guard_hyp type specifier, one of :, :~, :ₛ, :ₐ

def Lean.Parser.colonEqR : ParserDescr

Reducible defeq matching for guard_hyp values

def Lean.Parser.colonEqD : ParserDescr

Default-reducibility defeq matching for guard_hyp values

def Lean.Parser.colonEqS : ParserDescr

Syntactic matching for guard_hyp values

def Lean.Parser.colonEqA : ParserDescr

Alpha-eq matching for guard_hyp values

def Lean.Parser.colonEq : ParserDescr

The guard_hyp value specifier, one of :=, :=~, :=ₛ, :=ₐ

def Lean.Parser.equalR : ParserDescr

Reducible defeq matching for guard_expr

def Lean.Parser.equalD : ParserDescr

Default-reducibility defeq matching for guard_expr

def Lean.Parser.equalS : ParserDescr

Syntactic matching for guard_expr

def Lean.Parser.equalA : ParserDescr

Alpha-eq matching for guard_expr

def Lean.Parser.equal : ParserDescr

The guard_expr matching specifier, one of =, =~, =ₛ, =ₐ

def Lean.Parser.Tactic.guardExpr : ParserDescr

Tactic to check equality of two expressions.

• guard_expr e = e' checks that e and e' are defeq at reducible transparency.
• guard_expr e =~ e' checks that e and e' are defeq at default transparency.
• guard_expr e =ₛ e' checks that e and e' are syntactically equal.
• guard_expr e =ₐ e' checks that e and e' are alpha-equivalent.

Both e and e' are elaborated then have their metavariables instantiated before the equality check. Their types are unified (using isDefEqGuarded) before synthetic metavariables are processed, which helps with default instance handling.

def Lean.Parser.Tactic.guardExprConv : ParserDescr

Tactic to check equality of two expressions.

• guard_expr e = e' checks that e and e' are defeq at reducible transparency.
• guard_expr e =~ e' checks that e and e' are defeq at default transparency.
• guard_expr e =ₛ e' checks that e and e' are syntactically equal.
• guard_expr e =ₐ e' checks that e and e' are alpha-equivalent.

Both e and e' are elaborated then have their metavariables instantiated before the equality check. Their types are unified (using isDefEqGuarded) before synthetic metavariables are processed, which helps with default instance handling.

def Lean.Parser.Tactic.guardTarget : ParserDescr

Tactic to check that the target agrees with a given expression.

• guard_target = e checks that the target is defeq at reducible transparency to e.
• guard_target =~ e checks that the target is defeq at default transparency to e.
• guard_target =ₛ e checks that the target is syntactically equal to e.
• guard_target =ₐ e checks that the target is alpha-equivalent to e.

The term e is elaborated with the type of the goal as the expected type, which is mostly useful within conv mode.

def Lean.Parser.Tactic.guardTargetConv : ParserDescr

Tactic to check that the target agrees with a given expression.

• guard_target = e checks that the target is defeq at reducible transparency to e.
• guard_target =~ e checks that the target is defeq at default transparency to e.
• guard_target =ₛ e checks that the target is syntactically equal to e.
• guard_target =ₐ e checks that the target is alpha-equivalent to e.

The term e is elaborated with the type of the goal as the expected type, which is mostly useful within conv mode.

def Lean.Parser.Tactic.guardHyp : ParserDescr

Tactic to check that a named hypothesis has a given type and/or value.

• guard_hyp h : t checks the type up to reducible defeq,
• guard_hyp h :~ t checks the type up to default defeq,
• guard_hyp h :ₛ t checks the type up to syntactic equality,
• guard_hyp h :ₐ t checks the type up to alpha equality.
• guard_hyp h := v checks value up to reducible defeq,
• guard_hyp h :=~ v checks value up to default defeq,
• guard_hyp h :=ₛ v checks value up to syntactic equality,
• guard_hyp h :=ₐ v checks the value up to alpha equality.

The value v is elaborated using the type of h as the expected type.

def Lean.Parser.Tactic.guardHypConv : ParserDescr

Tactic to check that a named hypothesis has a given type and/or value.

• guard_hyp h : t checks the type up to reducible defeq,
• guard_hyp h :~ t checks the type up to default defeq,
• guard_hyp h :ₛ t checks the type up to syntactic equality,
• guard_hyp h :ₐ t checks the type up to alpha equality.
• guard_hyp h := v checks value up to reducible defeq,
• guard_hyp h :=~ v checks value up to default defeq,
• guard_hyp h :=ₛ v checks value up to syntactic equality,
• guard_hyp h :=ₐ v checks the value up to alpha equality.

The value v is elaborated using the type of h as the expected type.

def Lean.Parser.Command.guardExprCmd : ParserDescr

Command to check equality of two expressions.

• #guard_expr e = e' checks that e and e' are defeq at reducible transparency.
• #guard_expr e =~ e' checks that e and e' are defeq at default transparency.
• #guard_expr e =ₛ e' checks that e and e' are syntactically equal.
• #guard_expr e =ₐ e' checks that e and e' are alpha-equivalent.

This is a command version of the guard_expr tactic.

def Lean.Parser.Command.guardCmd : ParserDescr

Command to check that an expression evaluates to true.

#guard e elaborates e ensuring its type is Bool then evaluates e and checks that the result is true. The term is elaborated without variables declared using variable, since these cannot be evaluated.

Since this makes use of coercions, so long as a proposition p is decidable, one can write #guard p rather than #guard decide p. A consequence to this is that if there is decidable equality one can write #guard a = b. Note that this is not exactly the same as checking if a and b evaluate to the same thing since it uses the DecidableEq instance to do the evaluation.

Note: this uses the untrusted evaluator, so #guard passing is not a proof that the expression equals true.