Init.Guard

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.

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def Lean.Parser.Tactic.guardExprConv :

Lean.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.

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def Lean.Parser.Tactic.guardTarget :

Lean.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.

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def Lean.Parser.Tactic.guardTargetConv :

Lean.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.

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def Lean.Parser.Tactic.guardHyp :

Lean.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.

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def Lean.Parser.Tactic.guardHypConv :

Lean.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.

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def Lean.Parser.Command.guardExprCmd :

Lean.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.

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def Lean.Parser.Command.guardCmd :

Lean.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.

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